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+{
+  "A. Weißmann1, 2 , H. Böhringer1 , R. Šuhada3 and S. Ameglio4 ": [],
+  "arXiv:1210.6445v2  [astro-ph.CO]  10 Dec 2012 ": [
+    "Received xxxx; Accepted yyyy "
+  ],
+  "ABSTRACT ": [
+    "X-ray observations of galaxy clusters reveal a large range of morphologies with various degrees of disturbance, showing that the assumptions of hydrostatic equilibrium and spherical shape which are used to determine the cluster mass from X-ray data are not always satisfied. It is therefore important for the understanding of cluster properties as well as for cosmological applications to detect and quantify substructure in X-ray images of galaxy clusters. Two promising methods to do so are power ratios and center shifts. Since these estimators can be heavily affected by Poisson noise and X-ray background, we performed an extensive analysis of their statistical properties using a large sample of simulated X-ray observations of clusters from hydrodynamical simulations. We quantify the measurement bias and error in detail and give ranges where morphological analysis is feasible. A new, computationally fast method to correct for the Poisson bias and the X-ray background contribution in power ratio and center shift measurements is presented and tested for typical XMM-Newton observational data sets. We studied the morphology of 121 simulated cluster images and establish structure boundaries to divide samples into relaxed, mildly disturbed and disturbed clusters. In addition, we present a new morphology estimator -the peak of the 0.3-1 r500 P3/P0 profile to better identify merging clusters. The analysis methods were applied to a sample of 80 galaxy clusters observed with XMM-Newton. We give structure parameters (P3/P0 in r500, w and P3/P0max) for all 80 observed clusters. Using our definition of the P3/P0 (w) substructure boundary, we find 41% (47%) of our observed clusters to be disturbed. ",
+    "Key words. X-rays: galaxies: clusters – Galaxies: clusters: Intracluster medium "
+  ],
+  "1. Introduction ": [
+    "Clusters of galaxies form from positive density fluctuations and grow hierarchically through the extremely energetic process of merging and mass accretion. With due time they are thought to reach dynamical equilibrium and form the largest virialized structures in the Universe. This makes them very interesting tools to study cosmology and the evolution of large scale structure in which they appear as nodes at the intersection of filaments. In the soft X-ray band the hot intracluster medium (ICM) which resides in the intergalactic space and makes up about 15% of the total cluster mass is observed. Already early X-ray observations of galaxy clusters revealed that the ICM distribution is not smooth and azimuthally symmetric for all objects. In the beginning of the 1990s it became more clear from ROSAT observations that galaxy clusters are not relaxed objects but that they contain substructure (e.g. (<>)Briel et al. (<>)1992, (<>)1991). Since then, a lot of effort was put into the identification and characterization of substructure in the ICM in order to determine the dynamical state of the cluster. (<>)Jones & Forman ((<>)1991) showed that around 30% of their ∼200 clusters observed with the EINSTEIN satellite contain substructure. This was an important step in the understanding of structure formation, because it showed that cluster formation and evolution has not finished yet. In previous studies different parameter boundaries for the distinction of substructured and regular clusters have been used. The fraction of clusters with substructure was ",
+    "estimated to be about 40-70% for X-ray observations ((<>)Jones (<>)& Forman (<>)1999; (<>)Kolokotronis et al. (<>)2001; (<>)Mohr et al. (<>)1995; (<>)Schücker et al. (<>)2001). This indicates that the merging and accretion activity, which is reflected by the presence of multiple surface brightness peaks or disturbed morphologies, has not yet ceased in clusters. Substructure as a tracer of merging activity indicates a deviation from the relaxed and virialized state and can make a precise cluster mass determination very difficult. Since hydrostatic equilibrium is one of the main assumptions for cluster mass estimates, large errors can occur, which influence the constraints of cosmological parameters which are derived using cluster masses. Recent studies of simulations (e.g. (<>)Jeltema (<>)et al. (<>)2008; (<>)Lau et al. (<>)2009; (<>)Meneghetti et al. (<>)2010; (<>)Nagai (<>)et al. (<>)2007; (<>)Piffaretti & Valdarnini (<>)2008; (<>)Rasia et al. (<>)2012) and observations (e.g. (<>)Okabe et al. (<>)2010; (<>)Zhang et al. (<>)2008) show that the hydrostatic X-ray mass can be biased low between 10% and 30%. The largest deviations are expected to occur for galaxy clusters with substructure and it is therefore very important to accurately characterize substructure and the dynamical state of a cluster. ",
+    "Over the years many methods to characterize and quantify substructure in galaxy clusters were proposed (see (<>)Buote ((<>)2002) for a review). A simple and descriptive method to reveal substructure in a galaxy cluster is to subtract a smooth elliptical β model from the X-ray cluster image and to examine the residuals (e.g. (<>)Davis (<>)1993; (<>)Neumann & Böhringer (<>)1997). Wavelet ",
+    "analysis and decomposition have been applied to many clusters in X-rays (e.g. (<>)Arnaud et al. (<>)2000; (<>)Maurogordato et al. (<>)2011; (<>)Slezak et al. (<>)1994). This technique enables substructure analysis on different scales and the separation of different components. Another approach is the classification of cluster morphologies by visual inspection for X-ray images (e.g. (<>)Jones & Forman (<>)1991). Several other methods classify the morphology of galaxy clusters. Measuring e.g. a clusters ellipticity is very common (e.g. (<>)McMillan et al. (<>)1989; (<>)Pinkney et al. (<>)1996; (<>)Plionis (<>)2002; (<>)Schücker et al. (<>)2001), but this property is not a good indicator for a clusters dynamical state because both relaxed and disturbed clusters can have significant ellipticities. Better indicators of the dynamical state of a cluster are power ratios ((<>)Buote & Tsai (<>)1995, (<>)1996) and center shifts ((<>)Mohr et al. (<>)1993), which will be both addressed in this paper. ",
+    "Most substructure studies were performed on low-redshift clusters (e.g. (<>)Buote & Tsai (<>)1996; (<>)Jones & Forman (<>)1999; (<>)Mohr et al. (<>)1995). With the recent increase in the detection of high-redshift clusters, also the number of substructure studies of fairly large high-z samples using power ratios and other substructure parameters became important (e.g. (<>)Bauer et al. (<>)2005; (<>)Hashimoto et al. (<>)2007; (<>)Jeltema et al. (<>)2005). However, studies of the uncertainties and bias using these methods especially for low-quality (low net counts and/or high background) observations are sparse (e.g. (<>)Böhringer et al. (<>)2010; (<>)Buote & (<>)Tsai (<>)1996; (<>)Jeltema et al. (<>)2005). ",
+    "This is the main issue we want to address in this paper. We use a large sample of simulated X-ray cluster images to study the influence of shot noise on the power ratio and center shift calculation and present a method based on (<>)Böhringer et al. ((<>)2010) (B10 hereafter) to correct for it. We give parameter ranges in which a cluster can be expected to be relaxed or significantly disturbed. In addition, we give updated substructure parameters for a sample of 80 galaxy clusters based on XMM-observations which are part of several well-known samples. We discuss power ratios, center shifts and a new parameter in detail and present possible applications. ",
+    "The paper is structured as follows. In Sect. (<>)2 we introduce structure parameters used in this study. We briefly present the set of simulated X-ray cluster images in Sect. (<>)3 which were used to calibrate and test our method. The investigation of the influence of Poisson noise and net counts on the reliability of power ratios and center shifts is given in Sect. (<>)4. We also introduce our method to correct for the noise and background contribution and test its accuracy. In Sect. (<>)5 we define different morphological boundaries for power ratios and center shifts. We apply our analysis to a sample of 80 galaxy clusters observed with XMM-Newton, which is characterized in Sect. (<>)6. A short overview of the data reduction is given in Sect. (<>)7. In Sect. (<>)8 we show results of the morphological analysis of the observed cluster sample and introduce an improved morphological estimator. We discuss the results in Sect. (<>)9 and conclude with Sect. (<>)10. Throughout the paper, the standard ΛCDM cosmology was assumed: H0=70 km s−1 Mpc−1 , ΩΛ=0.7, ΩM=0.3. "
+  ],
+  "2. Substructure parameters ": [
+    "Power ratios ",
+    "The power ratio method was introduced by (<>)Buote & Tsai ((<>)1995) with the aim to parametrize the amount of substructure in the intracluster medium and to relate it to the dynamical state of a ",
+    "cluster. Only the distribution of structure on cluster scales which dominates the global dynamical state is of interest. Power ratios are based on a 2D multipole expansion of the clusters gravitational potential using the surface mass density distribution. Power ratios are thus giving an account of the azimuthal structure where moments of increasing order describe finer and finer structures. The powers are calculated within a certain aperture radius (e.g. r500) with the aperture centered on the mass centroid. ",
+    "The 2D multipole expansion of the two-dimensional gravitational potential ψ(R, φ) can be written as ",
+    "where am and bm are ",
+    "(2) ",
+    "(3) ",
+    "where x=(R , φ) are the coordinates, G is the gravitational constant and Σ represents the surface mass density ((<>)Buote & Tsai (<>)1995). The powers are defined by the integral of the magnitude of ψm, the m-th term in the multipole expansion of the potential, and evaluated in a circular aperture with radius R ",
+    "(4) ",
+    "Ignoring factors of 2G, this relates to the following relations which are used to calculate the powers, where am and bm are taken from Eq. (<>)2 and (<>)3 ",
+    "(5) ",
+    "and ",
+    "(6) ",
+    "In X-rays the surface brightness is used instead of the projected surface mass density, assuming that the X-ray surface brightness distribution traces the gravitational potential ((<>)Buote (<>)& Tsai (<>)1995). In order to obtain powers which are independent of the X-ray luminosity, they are normalized by the zeroth-order moment and thus called power ratios. This allows a direct comparison of clusters with different X-ray brightness. P0, the monopole, gives the flux. P1 and P2 represent dipole and quadrupole, P3 and P4 can be associated with hexapole and oc-topole moments. Higher order moments become more sensitive to disturbances on smaller scales which do not significantly contribute to the characterization of the global dynamical state of a cluster. The power ratios P2/P0 and P4/P0 are strongly correlated, however P4 is more sensitive to smaller scales than P2. While relaxed but elliptical clusters rather yield low P2/P0 and merging systems show higher P2/P0, this power ratio is not a clear indicator of the dynamical state because it is sensitive to both ellipticity or bimodality. Odd moments are sensitive to ",
+    "unequal-sized bimodal structures and asymmetries, while they vanish for relaxed, single-component clusters. P3/P0 is thus the smallest moment which unambiguously indicates substructure in the ICM and provides a clear measure for the dynamical state of a cluster (e.g. (<>)Buote & Tsai (<>)1995; (<>)Jeltema et al. (<>)2005, B10). It is therefore the primary substructure measure in our analysis. ",
+    "Center shifts ",
+    "The center shift parameter w measures the centroid variations in different aperture sizes. The centroid is defined as the \"center of mass\" of the X-ray surface brightness and obtained for each aperture size separately. The X-ray peak is determined from an image smoothed with a Gaussian with σ of 8 arcseconds. We calculate the offset of the X-ray peak from the centroid for 10 aperture sizes (0.1-1 r500) and obtain the final parameter w as the standard deviation of the different center shifts in units of r500 (e.g. (<>)Mohr et al. (<>)1993; (<>)O’Hara et al. (<>)2006, B10): ",
+    "(7) ",
+    "where Δi is the offset between the centroid and the X-ray peak in aperture i. "
+  ],
+  "3. Sample of simulated clusters ": [
+    "We use a set of 121 simulated cluster X-ray images to test the power ratio and center shift method, their bias due to shot noise and their uncertainties. This set includes 117 simulations from (<>)Borgani et al. ((<>)2004) and 4 from (<>)Dolag et al. ((<>)2009) to populate the desired mass range. All clusters were simulated using the TreePM/SPH code GADGET-2 ((<>)Springel (<>)2005). The clusters were extracted from the simulation at z=0 and the X-ray images were created by (<>)Ameglio et al. ((<>)2007, (<>)2009). The simulated cluster images do not include any observational artifacts (noise, bad pixels etc.) or background and were already used by B10. Due to the so-called overcooling problem in galaxy cluster simulations (e.g. (<>)Borgani & Kravtsov (<>)2011), the images may contain clumps of cold gas which appear as point-like sources. (<>)Ameglio et al. ((<>)2007) detected and removed these gas clumps. All remaining structures are therefore infalling groups or clusters. Keeping cold gas clumps in the simulated X-ray images may lead to a larger fraction of disturbed clusters and a different distribution of substructure parameters than is observed ((<>)Nagai (<>)et al. (<>)2007; (<>)Piffaretti & Valdarnini (<>)2008, B10 -Sect. 5.2.). The distribution of the parameters, however, is only critical for a direct comparison of simulations and observations, which is not the scope of this paper. ",
+    "Although the clusters are drawn from two sets of simulations they cover the full range of morphologies of clusters in the Universe and include a wide mass range (0.8 × 1014 − 2.2 × 1015h−1 M). This sample is used exclusively to test the bias correction method and to calibrate the structure boundaries, thus to relate the visual impression of the image to a P3/P0 and w range. For these purposes it is not crucial to use a representative sample of the full mass range, especially since the simulated cluster morphology distribution is only weakly mass dependent. We only required the sample to cover the full range of morphological parameters and do not take into account any global cluster properties. ",
+    "A comparison between the substructure parameters w and P3/P0 of the sample of 80 observed clusters and the simulations ",
+    "without noise is given in Fig. (<>)1. This figure also gives a first impression of the parameter range clusters occupy in this diagram -namely 10−10 < P3/P0 < 10−4 and 10−4 < w < 1. Clusters sometimes yield negative P3/P0 values after the bias correction (P3/P0c, see Sect. (<>)4.3) with an uncertainty indicating that the result is consistent with zero. Such clusters are not displayed in the figures. ",
+    "Fig. 1. Comparison of the sample of 80 clusters observed with XMM-Newton (black circles) and 121 simulated X-ray cluster images (red crosses) in the P3/P0-w plane. The solid and dotted lines show the different morphological ranges as discussed below in Sect. (<>)5. "
+  ],
+  "4. Study of the systematics of substructure measures ": [
+    "Observations, in particular those with low photon statistics, suffer from shot noise which will produce artificial structure and lead to inaccurate results in the substructure analysis. It is therefore important to characterize this bias (difference between real and spuriously detected amount of structure). Power ratios are applied to clusters since 1995 and several studies regarding the influence of photon noise on the measured power ratios and center shifts were performed (e.g. (<>)Hart (<>)2008; (<>)Jeltema et al. (<>)2005, B10). In this paper we extend the work of B10 who introduced two methods (azimuthal redistribution and repoissonization) to estimate the bias and the uncertainties. However it was left open which approach yields better results in which signal-to-noise range. Using the repoissonization algorithm of B10, we make a comprehensive investigation of the performance of the bias and uncertainty estimates for a wide range of observational parameters and derive recipes on how to best correct the bias. ",
+    "4.1. Study of shot noise bias and uncertainties ",
+    "Let’s consider an idealized, radially symmetric cluster. Such an object should yield substructure parameters (power ratios and w) equal to zero. Once noise is added, the parameters of the same cluster increase significantly. We therefore denote the difference between the power ratio signal of the ideal image of a cluster (Pideal) and the signal of the same cluster with noise as true bias. For the simulations and if not stated otherwise, we give the bias as the true bias in % of the ideal value: ",
+    "(8) ",
+    "For center shifts, the bias (Bw) is defined analogously. In this and all following sections, we focus our analysis on the power ratio P3/P0, which is more sensitive to shot noise than the center shift parameter w. ",
+    "Shot noise makes very symmetric clusters appear more structured (positive bias). On the other hand, it can smooth out structure and a very structured cluster may actually seem more relaxed (negative bias). How the amount of shot noise and thus the reliability of the identification of substructure depend on the photon statistics of an observation and the measured substructure value is investigated using our set of 121 simulated clusters with different morphologies. In order to perform a realistic study, we create four images with different total count numbers (1 000, 2 000, 30 000 and 170 000 counts within r500) for each simulated cluster. These four different count levels were chosen to sample a range of XMM-Newton cluster observations, e.g. 1000 − 2000 counts are typical for high redshift systems, while the values for the REXCESS sample for example range between 30 000 and 170 000 counts. ",
+    "First, we take the simulated cluster image and normalize the surface brightness in such a way that the counts equal the chosen total count number. At this point, the pixel content is still a real number. In a second step, we poissonize the ideal cluster image (introducing shot noise) using the zhtools1 (<>)task poisson. We call such images poissonized images or realizations, with integers as pixel content. ",
+    "As is apparent from the visual inspection of two simulated clusters in Fig. (<>)2, the effect of photon noise is severe at low counts (middle), but also high counts images (right) are affected. It is therefore important to estimate and correct the bias as accurately as possible. The influence of shot noise and the uncertainties can be explained using Fig. (<>)3, which provides a summary of our study. In the 4 subpanels we show the behavior of P3/P0 for different total count numbers (top left: 1 000, top right: 2 000, bottom left: 30 000 and bottom right: 170 000 counts) and several dynamical states (5 simulated cluster observations). The solid line indicates P3/P0ideal, the power ratio of the ideal image without shot noise. The mean P3/P0 of 1 000 poissonizations of the ideal cluster image is shown by the dotted line. In addition this figure shows the uncertainty (σ) of the mean P3/P0 as the width of the P3/P0 distribution. ",
+    "We find that the bias introduced to the P3/P0 results behaves differently for different morphologies (subpanels in all 4 figure panels). The upper panel shows the case of clus20165 -a cluster with little intrinsic structure. Photon noise boosts the power ratio signal and the whole P3/P0 distribution is shifted to higher substructure values. This is reflected by the obtained mean signal (dotted line), which is significantly larger than the real signal (solid line). This effect is strong, especially below 30 000 counts. In addition, the uncertainty (width of the distribution) is large. Going step by step to more disturbed clusters (from top to bottom panel) shows the dependence of the bias on the degree of disturbance and the total count number. While clus008 still shows a large bias up to 2 000 counts, it is already very small for 30 000 counts. More disturbed clusters therefore are not as affected by photon noise as relaxed objects. This is apparent when looking at the P3/P0 distribution in the bottom panels (clus20674 and clus19007). Even at 1 000 counts the bias is very small and the P3/P0 distribution narrow, which reflects a mean ",
+    "P3/P0 signal with a relatively small bias and uncertainty. The statistical summary of these results is given in Table (<>)1, where we list the ideal and mean structure parameter of poissonized images along with the bias in percent and the uncertainties in real (top) and log space (bottom). For all values in the table we have repeated the poissonization process using just 100 instead of 1 000 realizations and found this lower number to be sufficient to obtain accurate statistical results. We thus work in the following studies with 100 poissonizations per case. In addition, we studied the influence of Poisson noise on the individual powers -P0 and P3. The flux P0 is only marginally sensitive to Poisson noise and does not contribute to the bias of P3/P0. The bias of P3/P0 thus reflects the influence of Poisson noise on P3. ",
+    "The dependence on the counts is due to the increasing effect of photon noise when dealing with low photon statistics. For relaxed clusters this leads to a very large bias and uncertainties, especially for low counts. In the case of very structured clusters with e.g. two components, the bias is negligible and the uncertainties small. For clusters with only a moderate amount of structure, we find a clear dependence on the counts. Therefore, one should be careful when applying this method to low counts observations (significantly less than 30 000 counts). ",
+    "Fig. 2. Example of a relaxed (upper panels) and a disturbed (lower panels) simulated cluster X-ray image including no noise (left) and pois-sonized images with 1 000 (middle) and 30 000 counts (right) within r500 (indicated by circle). ",
+    "For the center shift parameter w the behavior is similar, but less pronounced. Bw is more robust and in general significantly smaller than BP3. In addition, the distributions are narrower, which shows that w is less sensitive to photon noise than P3/P0. This allows an accurate calculation of the center shift parameter down to ∼200 counts. An overview of the absolute value of the bias as a function of counts (different colored lines) and the ideal value is given in Fig. (<>)4, left. We combined the bias of the substructure parameters (BP3 thick black solid and red dotted line, Bw different thin lines) as a function of P3/P0ideal (lower x-axis) and wideal (upper x-axis) for a direct comparison. However, while the simulated clusters occupy the full P3/P0 range, they only have w parameters between 3.1×10−4 and 2.4×10−1 . This and all other fits which will be displayed later are obtained using the orthogonal BCES linear regression ",
+    "Table 1. Statistical results on P3/P0 and w for poissonized simulated cluster images. We give the ideal substructure values and the mean for 100 realizations including their 1-σ uncertainties in real (top) and log space (bottom). The bias (BP3 and Bw) is listed in % of the ideal value, as defined in Eq. (<>)8. The results are given for 4 different total count numbers. This table corresponds to Fig. (<>)3, but with less realizations. ",
+    "The dependence of the bias on photon statistics and the substructure measurement encourages a bias correction as a function of these parameters. However, the bias depends also on the morphology of the cluster itself. We thus performed the following test: if we consider two clusters with the same P3/P0 or center shift value, they have nominally the same amount of structure. If this cluster pair also has the same amount of counts, only the intrinsic shape of the cluster remains variable. We chose six pairs of clusters with the same wideal and P3/P0ideal value and four different counts: 1 000, 2 000, 30 000 and 170 000 counts. For a dependence of the bias on the amount of structure and counts only, one would expect very similar distributions and mean values. However, this is not the case. Especially for the unstructured cluster pair and low counts the offset and the behavior of BP3 is significant. For high counts or structured clusters, this off-set decreases. We thus cannot give a general correction factor as a function of counts and P3/P0 or w but have to treat the estimate of the bias correction for each cluster individually. ",
+    "4.2. Significance threshold ",
+    "As we have shown, shot noise can introduce spurious structure. While our bias correction alleviates this to some extent it is use-",
+    "ful to relate the measured (and corrected) signal to its error. In order to do so, we define a significance S as ",
+    "(9) ",
+    "and call values with S ≥ 3 significant signals. This value however strongly depends on the photon statistics. ",
+    "We studied the significance S as a function of the bias corrected substructure parameters for different total count numbers and show some results in Fig. (<>)5. The bias correction was done using the method described in Sect. (<>)4.3. Different total count numbers are color-coded and displayed using different linestyles (Top: 1 000 red dotted and 30 000 black solid line; bottom: 200 green dot-dashed and 500 blue dashed line) for P3/P0 (top) and w (bottom). The lines represent a BCES fit to all 121 simulated clusters. The significance thresholds (S = 3) for both structure parameters and several total count numbers are given in Table (<>)2 and displayed as horizontal lines in Fig. (<>)5. ",
+    "We will take a closer look at P3/P0 first. For a typical observation of 30 000 counts we are able to detect intrinsic structures corresponding to P3/P0 = 6 × 10−8 at S = 3 confidence level (P3/P0  10−8 at S = 1 level). This shows that the errors are small enough to ensure significant results even for clusters with little intrinsic structure. In the case of a low counts observation with only 1 000 counts, the S = 3 confidence level is located around 3.4 × 10−6 , which means that we can only obtain significant results for very structured clusters. In such cases, we use ",
+    "a less conservative and lower value like S = 1. However, when dealing with such low counts observations special care has to be taken. The well-defined behavior of the center shift parameter is confirmed by the significance of the measurements. We find the S = 3 values to be in the lower center shift range and can thus obtain significant results even for relaxed clusters. This result holds well below 1 000 counts. For 200 and 500 counts we find S = 3 to coincide with the median of the sample. A discussion of the implications of these results for a morphological analysis will be provided in a later section. ",
+    "Fig. 5. Significance S of the P3/P0 (top) and w (bottom) measurements for different counts. Top: 1 000 red dotted line and 30 000 black solid line, bottom: 200 green dot-dashed, 500 blue dashed line. The different thresholds are marked (S = 3: solid line, S = 1 dotted line). ",
+    "4.3. Bias correction method ",
+    "After characterizing the bias and its dependence on the photon statistics, we propose a statistical method to estimate and correct for the true bias BP3 and Bw (for P3/P0 and w). In Sect. 4.1 we defined the true bias as the difference between the true signal P3/P0ideal or wideal and P3/P0raw or wraw, the signal obtained after the first poissonization or the signal of the observation. Simulated images do not contain noise and give the true structure parameters. Observations however are poissonized, where this first poissonization is due to photon shot noise. They allow us to measure only P3/P0raw or wraw but not the true signal P3/P0ideal and wideal. We therefore cannot obtain ",
+    "Table 2. Dependence of the significance of the signal (S =signal/error) on total number counts (net counts within r500) for P3/P0c and wc. We call values with S > 3 significant signals, however for low counts observations a less conservative value like S = 1 has to be used. ",
+    "the true bias directly but need to estimate it. ",
+    "We assume that a second poissonization step returns roughly the same bias and error as the first poissonization. Analogously to the true bias we therefore define the \"estimated bias\" as the difference between the signal after the first (P3/P0raw or wraw) and second poissonization (P3/P0realization or wrealization). For simulated images, we mimiced the effect of the first poissoniza-tion by adding artifical Poisson noise creating observation-like images. The second poissonization is performed on the observation/observation-like image to create a repoissonized image (realization of the observation). Using the mean P3/P0 or w value of 100 realizations of the observation in combination with P3/P0raw or wraw to calculate the estimated bias BP3 ∗ or Bw∗ yields a good approximation for the true bias. Subtracting BP3 ∗ or Bw∗ from the substructure parameters of the cluster image returns the corrected substructure parameters P3/P0c and wc. The remaining bias after this correction approaches zero for high-quality observations and is defined as BP3,c and Bw,c, respectively. ",
+    "Considering this, we present a refined version of the B10 method including the following steps: ",
+    "Obtain the estimated bias BP3 ∗ and Bw∗ as the difference of the mean parameters of these 100 realizations and P3/P0raw and wraw: ",
+    "BP3 ∗ = P3/P0realizations − P3/P0raw and B∗w = wrealizations − wraw ",
+    "In case of a real observation, also the background needs to be considered (see Sect. (<>)4.5). After testing several methods, the ",
+    "generally best performing method for power ratios is to subtract the moments am and bm (where m=1,2,3,4; see Eq. 2 and 3) of the background image from the measured moments of the cluster image and its realizations before calculating the powers ((<>)Jeltema et al. (<>)2005). Since w is not additive as am and bm, we have taken a different approach in the case of the center shift method and subtract the background prior to the calculation of wraw and wrealizations. This rather simple method works very well in a statistical way, as is shown below. ",
+    "In some cases, we do not gain any information about the cluster because the estimated bias is larger than the true bias. We then obtain a negative P3/P0c with a large uncertainty which indicates that the signal is consistent with zero. For a few % of realizations we found that the repoissonization leads to a change of the brightest pixel and thus the zero-point of the center shift calculation. This can change the values significantly, however does not influence the mean w value of all 100 realizations. Also the centroid, which is calculated using the surface brightness distribution, can change for different realizations, especially when dealing with low photon statistics. This shift is included in the error estimation when recalculating the centroid for each realization. In our analysis however we found that the remaining bias of the corrected P3/P0 values (BP3,c) vary only slightly. The mean change in the absolute P3/P0 value for 1 000 counts is a factor of 2, however in 19 cases the increase is larger (max. 17). All clusters with such a considerable change in the centroid are very obvious merging systems with two distinct surface brightness peaks. The error increases especially for large P3/P0 values, but still remains small compared to the P3/P0 value itself. ",
+    "4.4. Testing of the method ",
+    "We tested and refined this method using simulated images as described in Sect. (<>)3. As with the characterization of the bias, we used different counts to simulate different depths of observations. We poissonized each simulated image 100 times and treated each of those 100 images as an \"observation\" which are subject to a second poissonization step. After the bias correction of all 100 \"observations\" using the estimated bias from the second poissonization, we obtain a mean value of the corrected parameter to show the statistical strength of this method. ",
+    "The results of the bias correction method are shown in Fig. (<>)4 for P3/P0 and w. The figure on the left shows the absolute value of the bias before noise correction (discussed in Sect. (<>)4.1), while the right side displays the remaining bias after applying the correction method. In both panels, we simultaneously show the absolute value of the bias as defined in Sect. (<>)4.1 for P3/P0 (thick lines and lower x-axis) and w (thin lines and upper x-axis) for different counts. The decrease of BP3,c is apparent for cases with 1 000 counts, where the correction method is successful down to the detection limit (S = 1 at 3 × 10−7). In the insignificant range (S < 3) BP3,c lies below 10% after noise-correction. The solid black line shows the case for high-counts observations, where a drop below 10% can be seen around the S = 3 cut at 6 × 10−8 . ",
+    "The center shift parameter is more robust, even at 200 counts, where Bw,c ∼ 10% for S = 3. Center shifts are less sensitive to shot noise and their bias is smaller. This is especially interesting when looking at relaxed clusters (w < 0.01), where Bw,c is significantly smaller than BP3,c. Motivated by these results at low counts, we decided to test even lower photon ",
+    "statistics - 500 and 200 counts. With such observations the power ratios are not reliable anymore, but the center shifts show remarkably good results. ",
+    "In some of the 100 realizations of the poissonized images we find that a negative bias correction is needed, where the structure in the poissonized images has a too small value. However, the mean of the bias correction of all poissonizations is always positive, except for a few cases with very high structure parameters. For these clusters the bias correction is only around 1% as is shown in Fig. (<>)6, where we plot the applied bias correction BP3 ∗ (mean of 100 realizations) as a function of P3/P0c. ",
+    "Fig. 6. Illustration of the probability of a negative bias. We show the applied bias correction B∗ P3 (mean of 100 realizations) as a function of P3/P0c. The colors indicate the different counts within r500: 1 000 (red crosses) and 30 000 (black circles). A negative bias correction is only needed for very structured clusters and even then it is only of the order of 1%. The solid and dotted lines show the different morphological ranges as discussed below in Sect. (<>)5. ",
+    "4.5. Effect of the X-ray background ",
+    "The quality of X-ray observations suffers from several components - including photon noise which was discussed in Sect. (<>)4.3 and the X-ray background, which was not taken into account yet. We thus investigated how the background and different cluster-to-background count (S/B) ratios influence the measurements. Motivated by the work of (<>)Jeltema et al. ((<>)2005), in which the authors use an analytic approach to assess and correct for the background contribution for power ratios by subtracting moments due to noise, we inspected the behavior of power ratios and moments when adding or subtracting them. Power ratios are not additive, moments (a0 to b4) however are and thus can be used for background noise subtraction. ",
+    "When correcting for the background two issues have to be addressed: the increase of total counts (normalization) and the noise component of the background image. Depending on S/B, the noise in the background image can influence the power ratio and center shift calculation. In order to account for the noise in both the cluster signal and in the background, we add a poissonized cluster and a poissonized flat background image to obtain an \"observation\". As during the bias study, we create 100 \"observations\" per simulated cluster image and show mean values. The correction of the bias is done using a two-step ",
+    "process. In step one, the background is treated by subtracting the moments (a0 to b4) of the background image from the moments of the observation before calculating the power ratios (in Sect. (<>)4.3, Step 1). For a flat background image without noise, only a0 should be non-zero. However, vignetting and other instrumental artifacts cause also higher moments to be non-zero. The background-subtracted moments should thus (statistically) only contain the cluster emission and the signal noise component. The background moments have to be subtracted also from the 100 realizations of the observation. As a second step, the power ratios and the bias are calculated using the background-subtracted moments. We therefore recommend the following power ratio treatment of the observation: ",
+    "4.3",
+    "5. Correct the bias and obtain the σ as described in Sect. , Step 4-6. ",
+    "In the next step, we studied the influence of the background noise component as a function of net/background counts using typical XMM-Newton values. We first discuss the power ratios and show the results for 30 000 net counts and a S/B (net/background counts within r500) of 2:1 and 1:1. We chose these values to test the method simulating an observation with a large number of net counts but poor S/B ratios. Figure (<>)7 (left) compares the background and bias corrected power ratio P3/P0c with P3/P0ideal for these cases and shows that we can very accurately determine P3/P0 well below 10−8 for an observation with 30 000 net counts and a S/B=2 (black circles). For a higher background (red crosses) the method still works well, however below 10−7 the scatter increases. Our sample of 80 observed low-z clusters includes only 6 clusters with a S/B<2 of which RXCJ0225.1-2928 shows the lowest with S/B=1.2. For observations with more than 30 000 net counts, we find a mean S/B of 6.7 and a median S/B of 5.6. In such cases, the background noise component is not significant. ",
+    "This situation changes when analyzing high-z observations which typically have low-photon statistics (< 1 000 net counts) and where the S/B can become < 1. We therefore show on the right side of Fig. (<>)7 the results of the background and bias correction for 1 000 net counts and a S/B of 0.5 (blue asterisks), 1 (red crosses) and 2 (black circles). Although the relation shows more scatter than for the high-counts case, the method works well down to 10−7 for S/B=1. For observations with higher background the scatter increases, however even under such conditions we can distinguish well between high power ratios values (S > 1) and values below 10−7 , with typically S < 1. ",
+    "In the case of center shifts, the background noise influences mainly the position of the centroid. This effect is more pronounced for smaller center shifts and higher backgrounds. Analogous to the power ratios, we correct the bias using poissoniza-tions of the observation (incl. background). However, we subtract the background counts for each pixel (instead of the moments) from the observation and its 100 poissonizations before calculating the X-ray peak and the centroid. The bias is then obtained as described in Sect. (<>)4.3. We again tested the method for ",
+    "the above mentioned cases and found that the correction works very well down to 10−3 for the 30 000 net counts case, even for S/B=1. This behavior is due to the lower sensitivity to noise and shown in Fig. (<>)8 on the left. In addition, it enables us to probe even lower photon statistics, going down to 200 net counts. Even in such an extreme case, the method works well down to about w = 10−2 . A plateau forms which characterizes the remaining noise level (Fig. (<>)8, right). As expected, the plateau level moves to lower values for larger S/B, representing the decreasing influence of the background with larger S/B. "
+  ],
+  "5. Morphology ": [
+    "After establishing in which parameter range we can obtain significant results, we want to discuss the strength of power ratios and center shifts in distinguishing different cluster morphologies. One aim of this analysis is to find a substructure value below which a cluster can be considered essentially relaxed. An overview of the results is given in Table (<>)3. ",
+    "Fig. 9. Example gallery of clusters visually classified as essentially relaxed (top four panels) and disturbed (bottom four panels). The classification is not unambiguous in all cases, however the overall visual appearance within r500 (green circle) was more important than small-scale disturbances. ",
+    "We first consider P3/P0. As a result of the visual screening of the ideal simulated cluster images (no noise or background contribution), we classified all clusters as essentially relaxed (relaxed hereafter) or disturbed, depending on whether they show some signs of substructure (asymmetries, second compo-",
+    "nent of comparable size, general disturbed appearance) within r500 or not. A few examples are given in Fig. (<>)9, which also illustrates that this division is not always unambiguous, however the overall visual appearance within r500 (green circle) was more important than small-scale disturbances. ",
+    "Taking all this into account, we found P3/P0 ranges for relaxed and disturbed morphologies with a boundary value of about 10−7 , which we call simple P3/P0 boundary. The motivation for this condition is shown in Fig. (<>)10, where we give the substructure parameters for all 121 simulated ideal cluster images including their visual classification as relaxed or disturbed. The horizontal line at P3/P0 = 10−7 divides the sample into the two populations. Out of 121 we find 6/58 (∼10%) relaxed and 13/63 (∼20%) disturbed clusters to be differently classified. For two of these 6 relaxed clusters however a merging subcluster is just entering r500 and thus boosting the P3/P0 signal while the main cluster still seems relaxed. The remaining 4 show a slight elongation but no clear sign of structure or disturbance. For the 13 disturbed clusters we found that they have structure mostly in the inner region of the aperture radius which is not picked up by the power ratio method. ",
+    "Fig. 10. Motivation for the simple and morphological boundaries for P3/P0 and w. We show the P3/P0-w plane for ideal simulated cluster images. The classification into relaxed (red crosses) and disturbed (black circles) was done visually. The boundaries are displayed by horizontal and vertical lines and fit the data well. ",
+    "For high-quality observations a more detailed morphological analysis is possible because power ratios can be obtained more precisely. Taking a closer look again at Fig. (<>)10, three distinct regions present themselves: P3/P0 < 10−8 , 10−8 < P3/P0 < 5 × 10−7 and P3/P0 > 5 × 10−7 . These three regions are occupied by only relaxed, a mix of relaxed and disturbed and only disturbed clusters and are indicated by the dotted lines in the figure. The borders between these regions at P3/P0 = 10−8 and P3/P0 = 5 × 10−7 are named morphological boundaries. At the lower boundary of 10−8 we reach S = 2 for 30 000 counts images. With lower photon statistics such a classification is not possible. Making use of the morphological boundaries, we find 32% of our simulated clusters to be significantly disturbed, while only 17% show no signs of structure (see Table (<>)3). The majority however (51%) ",
+    "Table 3. Overview of the boundaries for P3/P0 and w including statistics when applying them to the simulated cluster sample. ",
+    "is found somewhere in the middle and called mildly disturbed objects. ",
+    "For the center shift parameter we define a boundary at w = 0.01. This value also agrees with our visual classification and analysis (see Fig. (<>)12). Figure (<>)11 shows wideal histograms for relaxed (filled black histogram) and disturbed (filled red histogram) clusters, including the distribution of all clusters (thick black line). This w boundary at log(wideal)= −2 is apparent and the misclassification lies below 10%. The w boundary is significant with S > 2 down to lowest counts (e.g. 200). ",
+    "Fig. 11. Center shift histogram of all simulated clusters (thick black dashed line) defining the w boundary. Relaxed clusters are represented by the filled black (left) and disturbed ones by the red filled histogram (right). The vertical line marks the w boundary at log(wideal)=-2. "
+  ],
+  "6. Cluster sample ": [
+    "Our sample comprises 80 galaxy clusters which are part of differ-ent larger samples observed with XMM-Newton. An overview of the samples from which the clusters were taken and their redshift are given in Table (<>)A.1. For this study we use 31 targets from the Representative X-ray Cluster Substructure Survey (REXCESS, (<>)Böhringer et al. (<>)2007), which was created as a morphologically and dynamically unbiased sample, selected mainly by X-ray luminosity and restricted to redshifts z < 0.2. Except for RXCJ2157.4-0747 (OBSID: 0404910701) and RXCJ2234.5-",
+    "3744 (OBSID: 0404910801), where we were able to obtain longer exposures, we used the observation IDs as described in (<>)Böhringer et al. ((<>)2007, Table 5). ",
+    "From the Local Cluster Substructure Survey (LoCuSS, Smith et al.), we use a small subsample of 30 clusters, which was published by (<>)Zhang et al. ((<>)2008). Except for A2204 (OBSID: 0306490401), we use the same observations as stated in (<>)Zhang (<>)et al. ((<>)2008, Table A.1.). ",
+    "34 targets were taken from the Snowden Catalog ((<>)Snowden et al. (<>)2008), while 10 clusters are part of the REFLEX-DXL sample ((<>)Zhang et al. (<>)2006). In addition, we use 9 clusters discussed in (<>)Buote & Tsai ((<>)1996), from which only A1651 (properties taken from (<>)Arnaud et al. ((<>)2005)) is not part of the Snowden sample. In total, 28 clusters are found in at least two samples. In such cases, the cluster properties are taken from the larger sample -as indicated in Table (<>)A.1. The clusters were chosen to be well-studied, nearby (0.05 < z < 0.45) and publicly available (in 2009) in the XMM-Archive2 (<>). In addition, we required r500 to fit on the detector. Our full sample populates the whole observed substructure range, as is shown in Fig. (<>)1. In addition, except for 13 cases, all clusters are high-quality observations with > 30 000 net counts. Of those 13 observations, only RXCJ2308.3-0211 has less than 9 000 net counts (∼2130 net counts with a S/B∼4.6). This merged sample has no unique selection function, but a wide spread in luminosity, temperature and mass. A large fraction of the clusters comes from representative samples like REXCESS and LoCuSS and we therefore expect the sample to have a very roughly representative character. In addition, the aim to test the presented structure estimators does not necessarily need a representative sample but a large number of clusters with different morphologies which is fulfilled with this sample. "
+  ],
+  "7. Data analysis ": [
+    "7.1. XMM-Newton data reduction ",
+    "The XMM-Newton observations were analyzed with the XMM-Newton SAS3 (<>)v. 9.0.0. The data reduction is described in detail in B10 and (<>)Böhringer et al. ((<>)2007). We followed their recipe except for the point source removal and background subtraction. Our method of detecting point sources is consistent with B10 and (<>)Böhringer et al. ((<>)2007), where the SAS task ewavelet is run on the combined image from all 3 detectors in order to increase the sensitivity of the point source detection. However, we removed the point sources from each detector image in the 0.5-2 keV band individually and refilled the gaps using the CIAO4 (<>)task dmfilth. In the next step we subtracted the background from the point source corrected images and combined them. This method yields point source corrected images without visible artifacts of the cutting regions. ",
+    "7.2. Structure parameters ",
+    "Power ratios and center shifts were calculated according to the repoissonization method described in Sect. (<>)4.3, subtracting the background moments from the full (background included) image to obtain power ratios and correcting the bias due to shot noise. For center shifts we subtract the background pixel values ",
+    "Table 4. Sample statistics. Clusters defined as relaxed, disturbed and mildly disturbed objects using different boundary conditions and three different substructure estimators P3/P0c, P3/P0max and wc. ",
+    "before calculating the positions of the X-ray peak and centroid. Errors were taken as the σ of 100 poissonized realizations. Unless stated otherwise, all displayed P3/P0 and w values are background and bias corrected and calculated in the full r500 aperture. "
+  ],
+  "8. Morphological analysis of 80 observed clusters ": [
+    "In this section, we will apply the substructure estimation method to our sample of 80 observed clusters and show that power ratios can give more than just a global picture of the cluster. We will briefly recapitulate the dependence of the power ratio signal on the aperture size and discuss improved morphology estimators based on these findings. In order to do so, we visually classify and divide the sample into 4 categories: a) DOUBLE -clusters with two distinct maxima, b) COMPLEX -clusters without two distinct maxima but global complex structure, c) INTERMEDIATE -overall regular clusters which show some kind of locally restricted structure or slight asymmetry, d) REGULAR -regular clusters without structure. The classification was done visually using two smoothed images (smoothed with a Gaussian with σ=4 and 8 arcseconds). This classification can then be compared to the boundaries defined in the morphological analysis of simulated cluster images. All 80 clusters are sorted according to their morphology and displayed in Figs. (<>)B.1-(<>)B.4. We give the three different structure parameters (P3/P0c, wc and P3/P0max) and the morphology for each cluster in Table (<>)A.2, while an overview of the dynamical state of the sample using these three morphology estimators is detailed in Table (<>)4. ",
+    "8.1. Improved structure estimator ",
+    "A simple application of P3/P0 and w using the repoissonization method to estimate the bias yields good results. As expected, we find very structured and in particular double clusters at high P3/P0 and w, while regular clusters are found to have low power ratios, but have a large spread in the w range. This was already shown by (<>)Buote & Tsai ((<>)1996) for power ratios and several authors afterwards for both substructure measures. The center shift parameter was already discussed in detail (e.g. (<>)Mohr et al. (<>)1995; (<>)O’Hara et al. (<>)2006; (<>)Poole et al. (<>)2006, B10) and shows a wide spread for disturbed and regular clusters. We therefore focus on the P3/P0 parameter and discuss it in more detail. ",
+    "For a sizeable cluster sample with the P3/P0 parameter calculated in the r500 aperture we are able to distinguish between very structured clusters (P3/P0 > 5 × 10−7 - double in our classification), clusters which show some kind of structure (5 × 10−7 < P3/P0 < 10−8 - complex and intermediate) and ",
+    "Fig. 13. P3/P0 -w plane for all 80 observed clusters including the w boundary at 10−2 and both the simple (10−7 , black solid line) and the morphological P3/P0 boundaries (10−8 , 5 × 10−7 , dotted lines) in an r500 aperture. The substructure parameters are background and bias-corrected. The outlier at w < 10−4 can be considered as w = 0 and is excluded from the analysis. The different morphological types show a rough segregation with double (blue circles) and complex (green diamonds) with high structure parameters, while intermediate (red asterisks) and regular (black crosses) clusters are found to have very low structure values. In addition, we show the mean of the 4 populations and their spread (standard deviation). ",
+    "Fig. 14. P3/P0 profile. P3/P0 calculated in 8 apertures (0.3-1 r500) is shown for 3 different clusters. The horizontal lines show the simple (solid line) and the morphological P3/P0 boundaries (dotted lines). A115 (red asterisks) shows a clear second component, which is located around 0.8 r500. In the r500 aperture it is thus classified as highly disturbed. The Bullet cluster (green circles) also clearly shows a second component, however this component lies at 0.3 r500 and thus P3/P0 becomes less important for larger apertures. A2204 (black crosses) on the other hand is a regular cluster, which does not reach a large P3/P0 value in any aperture. ",
+    "regular clusters (P3/P0 < 10−8 -regular). However, as is shown in Fig. (<>)13, there is an overlap of all three classifications in the P3/P0 = 5 × 10−7 − 10−8 range. This is due to the definition of the powers (see Sect. (<>)2) and the stronger weighting of structures closer to the aperture radius. In a large aperture like r500 structures in the cluster center are less important than e.g. a merging subcluster at r500. In order to illustrate this and motivate the next step, we show a P3/P0-profile (P3/P0 calculated in different aperture sizes) in Fig. (<>)14 for three different clusters. In addition to the profiles we show the simple (solid line) and morphological P3/P0 boundaries (dotted lines). The different behavior of the three clusters is clearly visible. While both the Bullet cluster (green circles, RXCJ0658.5-5556 in Fig. (<>)B.4) and A115 (red asterisks) show prominent substructure in the visual inspection, only A115 is classified as such in the r500 aperture. This is due to the fact that the \"bullet\" in the Bullet cluster lies at 0.3 r500 and is less prominent in the full r500 aperture. However, in the smaller aperture it would be detected as prominent substructure. As a reference cluster, we use the regular object A2204 (black crosses), which shows low substructure values in all apertures. ",
+    "We use this characteristic to introduce an improved substructure estimator, which will be detailed in the next section: the peak of the P3/P0 profile (0.3-1 r500, in 0.1 r500 steps), thereafter called P3/P0max. If the peak is not significant (S < 1 or P3/P0 < 0), we take the next highest significant value. P3/P0max correlates well with P3/P0 in all apertures (Spearman ρ between 0.5 and 0.75, prob < 10−7). The relation between P3/P0max and w is stronger than that of P3/P0 and w, no matter in which aperture. Figure (<>)15 shows the relation between P3/P0max and w, details are given in Table (<>)5. In addition, one can see the separation of double (blue), complex and intermediate (green and red) and regular (black) much clearer than in the P3/P0-w plane in Fig. (<>)13. ",
+    "Fig. 15. Relation between the significant peak (S > 0) of the P3/P0 profile and the center shift parameter for different morphologies. A tighter correlation than in the P3/P0 -w plane (Fig. (<>)13) can be seen. In addition, a clearer separation between the different morphological categories is apparent. The horizontal lines mark the P3/P0 boundaries (solid: simple at 10−7 , dotted: morphological at 5 × 10−7 and 10−8), the vertical line displays the w boundary at 10−2 . The colors are as described in Fig. (<>)13. "
+  ],
+  "9. Discussion ": [
+    "9.1. Substructure estimation and bias correction ",
+    "The reliability of these substructure estimators suffers from shot noise, especially when dealing with observations with low photon statistics. We therefore performed a detailed analysis of power ratios and center shifts using 121 simulated cluster images to study the influence of shot noise for different ",
+    "Table 5. Correlations between structure estimators. For correlations with P3/P0 we only show the strongest and most interesting apertures. ",
+    "observational set-ups (net counts and background). ",
+    "We find that the center shift parameter is only affected by shot noise at very low photon statistics. This is due to the definition of this parameter, which uses the distance between the X-ray peak and the centroid in several apertures. The position of the X-ray peak is determined from a smoothed image and robust to noise (shift of the position of the brightest pixel in < 5% of the realizations of 5% of the most disturbed cluster cores). The centroid is slightly more influenced by low photon statistics than the X-ray peak. However, in units of r500, this shift of the centroid due to shot noise is rather small. This assures a reliable center shift measurement down to low net counts (∼200). ",
+    "The possible effect of noise on power ratios can be severe, because they are calculated in an aperture, where each pixel can be influenced by shot noise. We find a clear dependence of the bias (spuriously detected structure due to noise) on the photon statistics and the amount of intrinsic structure. Very structured clusters can be identified even in shallow observations (e.g. 1 000 net counts in r500). Clusters without prominent substructure (e.g. without a visible second component) might be misclassified in some cases. We therefore present an improved method to estimate the shot noise and correct for background contributions which suffer from additional noise. We use 100 poissonized realizations of the X-ray image (background included) and calculate moments (a0 to b4) for the image, each realization and the background image. We subtract the background moments from the image moments and those of the 100 realizations before calculating power ratios. The mean power ratio of the poissonized versions of the image gives the bias, which is subtracted from the signal of the original image. ",
+    "This method was influenced by several previous studies. (<>)Hart ((<>)2008) estimates the bias in a similar way using a smoothed (Gaussian with 1-pixel width) image and 20 poissonized realizations of the cluster. (<>)Jeltema et al. ((<>)2005) use an analytic approach to correct the noise in the cluster but also in the background image. ",
+    "B10 introduced two methods to estimate the bias. The approach of poissionizing observed cluster images is the basis of our refined method presented above (see Sect. (<>)4.3). The second method they proposed estimates the bias by azimuthally redistributing the counts in all pixels at a certain radial distance with random angles. Thus only the radial information is stored, but all azimuthal structure is now randomly distributed. The final bias is the mean of 100 such randomizations. Ideally, this ",
+    "mean gives the power ratio of a regular cluster with the same amount of shot noise as the real observation. We performed a direct comparison with this method (thereafter called azimuthal redistribution) using all 121 simulated cluster images and found that both methods yield very similar results for 1 000 counts. Our method yields slightly better results at high counts (e.g. 30 000) because it determines the bias more accurately than the azimuthal redistribution. In addition, our method gives better results at low P3/P0 values, partly already above the lower morphological boundary of 10−8 . However, for the high-quality observations like our sample of XMM-Newton observations, the differences are small. ",
+    "Our method to correct the bias for the center shift parameter is analogous to the one for power ratios, however with the subtraction of background pixel values instead of moments before the calculation. (<>)Mohr et al. ((<>)1995) already investigated the influence of photon noise on w, however they define their center shift parameter in a different way and thus a direct comparison is not possible. ",
+    "Having established a method to correct the bias in the power ratio and center shift calculation to obtain meaningful results, we defined parameter ranges for different morphologies. Due to the variety and complexity of the morphologies of the simulated (and observed) cluster sample, a direct link between a certain substructure value and a distinct morphology could not be found. However, we showed that different types of morphologies occupy on average different regions of the substructure parameter space. Our aim to characterize a large sample can be reached using two types of boundaries for P3/P0 (simple boundary at 10−7 or morphological boundaries at 5 × 10−7 and 10−8) and a center shift value of 10−2 to divide the sample into relaxed, mildly disturbed and disturbed objects. In previous studies, similar values for significant substructure were found. B10 used 1.5×10−7 and 2-4×10−8 for significant and insignificant structure, while (<>)Jeltema et al. ((<>)2008) define all clusters with P3/P0 > 4.5 × 10−7 as disturbed and < 10−8 as relaxed. This agrees well with our findings. ",
+    "The definition of the boundaries shows the large range of cluster morphologies. Merging clusters with two clear components or very irregular structure can be identified under almost all conditions because of their strong signal. Clusters which appear relaxed (spherical or elongated) yield very low substructure values, however noise might increase their signal and some relaxed clusters might have P3/P0 > 10−8 . Applying ",
+    "the morphological boundaries to our sample of simulated clusters, we identify 32% as significantly disturbed. On the other hand, only 17% of our simulated sample show no signs of structure. This leaves the majority of clusters (51%) to be mildly disturbed objects. They show a slightly disturbed surface brightness distribution but no clear sign of a second component, the beginning of a merger, where the merging body lies outside of the aperture radius but already influences the ICM or a post-merger. This agrees well with observed values in X-rays which range between 40-70% of disturbed clusters (e.g. (<>)Jones (<>)& Forman (<>)1999; (<>)Kolokotronis et al. (<>)2001; (<>)Mohr et al. (<>)1995; (<>)Schücker et al. (<>)2001). Using the same visual analysis as for the power ratios, a useful boundary for the center shift parameter was found to be w = 0.01. This value agrees well with the values of B10 and (<>)Cassano et al. ((<>)2010) who also give w = 0.01, and of (<>)Maughan et al. ((<>)2008) and (<>)O’Hara et al. ((<>)2006) with w = 0.02. ",
+    "In general, using this method, we can significantly lower the influence of noise, especially for power ratios. For a shallow observation (1 000 counts), we find significant results (S > 1) for P3/P0c > 3 × 10−7 and are able to reduce the mean bias for this subsample of disturbed clusters from 13% to 5%. At 30 000 counts, even relaxed clusters yield significant results (S = 1 at P3/P0 = 4.5 × 10−9) and reach a mean bias of 7% of the ideal value after applying the correction. Using the morphological boundaries at 5×10−7 and 10−8 to divide the sample into relaxed, mildly disturbed and disturbed objects, we see that the high bias is mainly due to truly relaxed objects with P3/P0 < 10−8 . ",
+    "9.2. Morphological analysis of cluster sample ",
+    "We investigated the morphologies of a sample of 80 galaxy clusters observed with XMM-Newton in detail to give a profound and detailed illustration of these two structure estimators. In addition, we want to demonstrate the statistical strength of power ratios and center shifts and test the above defined boundaries. ",
+    "While power ratios are mainly used in a large aperture of r500 and are more sensitive to structures close to the aperture (e.g. merging component just inside r500), center shifts are sensitive to the change of the centroid in different apertures and should thus be more sensitive to central gas properties. The center shift parameter indeed shows a tighter correlation with e.g. the central cooling time than P3/P0 (aperture of r500), but also the power ratios are not insensitive to central gas properties (e.g. (<>)Croston et al. (<>)2008). In agreement with B10, we find the best correlation between w and power ratios for a large aperture of 0.9 r500 of P3/P0 (B10: 0.7 r500). This indicates that while power ratios are most sensitive to substructures close to the aperture radius, they are also sensitive to large central disturbances and strong cool core activity. Merging clusters like the \"Bullet cluster\" however are not identified as very disturbed in large apertures when the second component is well within the aperture. Although we can see clear signs of merging, the disturbance in the outer region of r500 is not severe enough to be identified as such. Simulations show that a powerful event like a merger influences the global cluster properties and boosts the luminosity and temperature of the cluster for a few hundred Myrs ((<>)Poole et al. (<>)2006). In such a case, a misclassification might lead to a false interpretation. ",
+    "The dependence of the power ratios on the aperture size was already discussed in detail by e.g. (<>)Buote ((<>)2001); (<>)Buote & ",
+    "(<>)Tsai ((<>)1996); (<>)Jeltema et al. ((<>)2005). Looking at P3/P0 profiles, peaks due to substructure are visible in dynamically unrelaxed clusters. Not taking only one aperture size but the whole profile into account increases the probability of finding clusters with prominent structure -also in the central parts of the cluster. We thus introduced a new substructure estimator: P3/P0max, the peak of the P3/P0 profile. Comparing the detection of a merging cluster (P3/P0 > 5 × 10−7; morphological type double - as defined in Sect. (<>)8) using P3/P0 in r500 and P3/P0max, we see that the probability of detecting substructure increases from 33% to 100% (compare Figs. (<>)13 and (<>)15). Also complex clusters are more likely to be identified as disturbed using the P3/P0 profile (45% for P3/P0 and 73% for P3/P0max). This is due to a shift towards larger power ratio values when using the maximum of the profile. In the lower power ratio range this increase leads to a jump of all relaxed clusters (regular and some intermediate) to power ratio values higher than 10−8 . This shows that for this new parameter, the upper morphological boundary at 5 × 10−7 yields best results in dividing the sample into relaxed and disturbed clusters. A few intermediate clusters cross this value, however the statistical strength remains. In order to demonstrate this again, we show the mean of each subsample and the width of the distribution in Figs. (<>)13 and (<>)15. It is visible that disturbed clusters (double (circles) and complex (diamonds)) are in a more defined region and better separated from the relaxed clusters (crosses). ",
+    "In addition to the improved classification when using P3/P0max, it is interesting to see in which aperture this peak resides. A histogram of the position of the P3/P0 peak is shown in Fig. (<>)16 for regular and intermediate (top) and complex and double (bottom) clusters. For complex and double clusters the distribution is as expected with no favored position. While regular clusters show a very homogeneous distribution, intermediate clusters mostly peak in small apertures. This is partly due to noise, which is larger in smaller apertures. However, these values are significant (S > 1). This suggests that the distribution reflects the visual classification. While double and complex clusters are characterized as having two maxima in the surface brightness distribution or a complex global appearance, intermediate clusters show no global structure but slight inhomogeneities or asymmetry in the central region. ",
+    "Comparing our morphological classification to other works with clusters used for our analysis, we find a good agreement. (<>)Okabe et al. ((<>)2010) use asymmetry (A) and fluctuations of the X-ray surface brightness distribution in the 0.2-7 keV band (F) to divide their sample of 12 LoCuSS clusters into relaxed (low A and F) and disturbed (high A or F or both) clusters. For 9 overlapping clusters, we both find A115 to be very disturbed and agree on 2 relaxed clusters. The remaining 6 clusters are found in the P3/P0 range of mildly disturbed clusters and with not too high w values. They show a low A but a spread in the F range, which fits to our definition of intermediate, showing only slight asymmetries and/or some kind of locally restricted structure. We find a large overlap of 59 clusters with (<>)Andersson et al. ((<>)2009) who used power ratios to study the evolution of structure with redshift. However, they use a fixed aperture of 500 kpc for all redshifts (0.069 to 0.89), which relates to very different apertures sizes in our analysis. (<>)Bauer et al. ((<>)2005) also use a radius of 500 kpc to obtain power ratios, however their sample is more restricted in redshift (0.15-0.37). In addition they give a visual classification and divide their sample into relaxed, disturbed and double clusters. We have 11 common clusters and ",
+    "Fig. 16. Histogram for all four morphological types showing the position of P3/P0max. Top: Regular (black dashed line) and intermediate (red filled histogram) clusters are shown. There is a clear excess in the 0.3 r500 aperture. Bottom: Complex (black dashed line) and double (red filled histogram) clusters are displayed. The distribution is homogeneous since the position of the peak depends on the location of the second component or structure. ",
+    "our morphology classification agrees well. Other studies having an overlapping sample but using a different aperture radius are e.g. (<>)Jeltema et al. ((<>)2005) or (<>)Cassano et al. ((<>)2010). ",
+    "For their comparison of X-ray and lensing scaling relations, (<>)Zhang et al. ((<>)2008) visually classified a subsample of the LoCuSS clusters according to (<>)Jones & Forman ((<>)1991) as single, primary with small secondary, elliptical, off-center and complex. The last 4 classes characterize disturbed clusters. Comparing the overlapping 30 clusters to our visual classification, we find all 14 \"single\" clusters to be either regular or intermediate, which agrees well with our definition. Three \"primary with a small secondary\" are found to be complex (A1763, A13) or intermediate (RXCJ2234.5-3744). For the elliptical class, we find 4 intermediate, 1 complex and 3 regular clusters, showing that the definition of \"elliptical\" seems not very precise to asses the dynamical state of a cluster. The same holds for the definition of \"off-center\" for which we find 1 complex, 1 double and 2 intermediate clusters. The last morphological type, \"complex\", does not agree with our definition of complex. The only cluster defined as such, A115, is a clear double cluster. Placing these 30 clusters in the P3/P0-w and P3/P0max-w plane, ",
+    "we find the \"single\" clusters at low P3/P0 and w value, agreeing with our definition of regular and intermediate. For 4 cases, we find either P3/P0 slightly > 10−7 (RXCJ2308.3-0211 and RXCJ0547.6-3152) or w slightly > 0.01 (A209, A2218 and RXCJ0547.6-3152). ",
+    "The result of a direct comparison between power ratios and the \"primary\" class depends on the position and size of the second component. The same holds for center shifts. A small second component close to the center will lead to a much smaller shift than one further outside. Clusters of this class can thus be found almost in the whole P3/P0 range and spread around the w = 0.01 boundary. The same is expected for \"elliptical\" clusters. They will not reach a center shift value as high as for merging clusters due to the lack of a strong second component. On the other hand one would not expect extremely high or low power ratio values. The lower limit is set by the fact that the cluster is elliptical and not completely symmetric and will thus show P3/P0 > 10−8 . Due to an asymmetric elliptical structure however the centroid on which the aperture is centered shifts when going to larger radii, therefore setting an upper limit of a few times 10−7 to the expected value. The \"off-center\" class showing no clear sign of substructure has similar characteristics as the elliptical one and is thus found in the same P3/P0 and w range. Therefore only the morphological type \"complex\" remains to be discussed, which characterizes clusters with complex, multiple structures. This fits to our definition of double clusters with two distinct maxima in the surface brightness distribution. Overall one can conclude that clearly relaxed clusters and apparent mergers are very well described using both morphology schemes. The intermediate range, however, is defined ambiguously. We discussed these two classification schemes in detail because we have a large overlap of clusters and therefore can derive statistics from it. ",
+    "It is important to point out again that morphological classifications are very often done using visual impressions and are dependent on the observer. Power ratios and center shifts on the other hand give numbers, which - using the results of our analysis -can be related to different, simple morphologies. Recalling the morphological boundaries defined for P3/P0 at 10−8 and 5 × 10−7 , we find a clear overlap between our mildly disturbed class and the three intermediate classes of (<>)Jones & (<>)Forman ((<>)1991), \"primary with small secondary\", \"elliptical\" and \"off-center\". Using P3/P0max would help to better filter out clusters of the \"primary\" class, due to the sensitivity in all aperture sizes. ",
+    "It is clearly shown that each of the three discussed parameters (P3/P0 in one aperture, P3/P0 profile and w) is sensitive on different scales. We therefore propose to use all three substructure estimators to characterize the dynamical state of large cluster samples. This can be done without a large computational effort for a large number of objects and help in identifying the potentially most interesting clusters for further analysis. "
+  ],
+  "10. Conclusions ": [
+    "In this paper we provide a well tested method to obtain bias and background corrected substructure measures (power ratio P3/P0 and center shift w). We studied the influence of shot noise in detail and are able to correct for it sufficiently. We demonstrate that a simple parametrized bias correction is not possible and thus we propose a non-parametric bias correction method applicable to each cluster individually. We tested the method for different observational set-ups (net counts and background) using typical ",
+    "XMM-Newton values. We conclude that for low counts observations the influence of the background and bias can be severe. In general, the center shift parameter w is less sensitive to noise and more reliable than power ratios, especially for low photon statistics. However, one should be reminded that this method is statistically strong but might not be completely accurate for each individual cluster. We thus looked in more detail into the power ratio method and how certain parameter ranges can be related to different morphologies. ",
+    "Using the proposed methods is especially interesting when dealing with a large sample, where visual classification of each individual cluster is not required but the global dynamical state of the whole sample is of interest. Applying the modified structure estimators like P3/P0max gives additional constraints and helps to single out very structured or very relaxed clusters. Finding cluster mergers to study structure evolution or strong cool core clusters (very relaxed clusters) requires only a small computational effort, but gives a first indication about the dynamical state and properties of the cluster and whether a detailed analysis is desired. ",
+    "Acknowledgements. We would like to thank the anonymous referee for constructive comments and suggestions. AW wants to thank Heike Modest for helpful discussions. This work is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. The XMM-Newton project is supported by the Bundesministerium für Wirtschaft und Technologie/Deutsches Zentrum für ",
+    "Luft-und Raumfahrt (BMWI/DLR, FKZ 50 OX 0001), the Max-Planck Society and the Heidenhain-Stiftung. AW acknowledges the support from and participation in the International Max-Planck Research School on Astrophysics at the Ludwig-Maximilians University. An early part of this work was financed by the Bundesministerium für Wissenschaft und Forschung, Austria, through a \"Förderungsstipendium nach dem Studienförderungsgesetz\" granted by the University of Vienna. ",
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+    "Fig. 3. P3/P0 distribution (reflecting the bias) for different structured clusters and counts. The solid line marks the ideal P3/P0 value, the dotted line indicates the mean of 1 000 realizations with noise. Details are given in Table (<>)1. A comparison between this figure and Table (<>)1 shows that 100 realizations are sufficient to estimate the bias. ",
+    "Fig. 4. Dependence of the bias as a function of P3/P0ideal (lower axis) and wideal (upper axis). Left: Absolute value of the bias before correcting. Right: Absolute value of the remaining bias after applying the bias correction BP3 ∗ and B∗w. The different counts are color-coded: 30 000 black, 1 000 red, 500 blue, 200 green. BP3 is shown using thick lines, Bw is represented by different thin lines. The dependencies are fits to all 121 simulated cluster images using the BCES linear regression method ((<>)Akritas & Bershady (<>)1996). ",
+    "Fig. 7. Background and bias corrected P3/P0 as a function of P3/P0ideal. Left: Testing the bias correcting method simulating an observation with 30 000 net counts but poor S/B ratios (S/B=2 black circles, S/B=1 red crosses). Right: Simulating a high-z observation with 1 000 net counts and S/B=2 (black circles), 1 (red crosses), 0.5 (blue asterisks). The increasing influence of the background for decreasing net counts and S/B is shown. ",
+    "Fig. 8. Background and noise corrected center shifts as a function of wideal for good photon statistics (left, same S/B ratio as in Fig. (<>)7 on the left side) and low counts observations (right). ",
+    "Fig. 12. Example of cluster images classified using the w boundary. Left 4 panels: w < 0.01, right 4 panels: w > 0.01. "
+  ]
+}

jsons_folder/2013AN....334..321N.json

@@ -0,0 +1,71 @@
+{
+  "J. Nevalainen1,2,⋆ ": [
+    "Received , accepted ",
+    "Published online later ",
+    "Key words galaxies: clusters: general • instrumentation: spectrographs • intergalactic medium • techniques: spectroscopic • X-rays: galaxies: clusters ",
+    "The hierarchical formation of clusters of galaxies by accretion of material releases gravitational energy which dissipates into the intracluster gas. The process heats the material and generates gas turbulence and bulk motions and thus kinetic pressure. Mapping the velocity •elds of the moving subunits would enable a new diagnostics tool for cluster formation studies and unbiased X-ray mass estimates. The required spatially resolved high resolution spectroscopy is not currently available. I demonstrate here the feasibility of detecting and mapping the velocities of the bulk motions using the Doppler shift of the Fe XXV K line with the proposed ATHENA satellite. ",
+    "c 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim "
+  ],
+  "1 Introduction ": [
+    "During its life cycle, a cluster of galaxies experiences collisions and mergers with other clusters and subunits. Eventually the relaxation processes take place and the intraclus-ter material approaches hydrostatic and virial equilibrium. Consequently, there will be bulk motions in the cluster material at different distance scales and velocity levels, depending on the magnitude of the event and at which phase we observe the cluster. ",
+    "Mapping the velocity •elds of the bulk motions would open a new tool for studying the dynamics of the clusters. Comparing the velocity maps with those predicted by cosmological simulations would be useful for the study of the formation of the large scale structure and provide constraints on cosmological parameters. Combining with the measured galaxy density •eld, the bulk velocity maps could be used to test whether the fundamental picture of gravitational collapse is correct (Branchini et al. 2001; da Costa et al. 1998; Dor´e et al., 2003). ",
+    "The bulk motions produce kinetic pressure which can reach a level of 10% level of that of the thermal gas even in most relaxed clusters (Lau et al. 2009). If not accounted for, the kinetic pressure may bias the hydrostatic X-ray mass estimates low by ˘10% at r500. Thus, it would be important to measure this component in clusters in order to obtain unbiased mass estimates for the cosmological applications. ",
+    "In case of recent, strong collisions which happen close to the plane of the sky, the merger shocks can be observed by the X-ray morphology, as in the rare cases of A520 (Marke-vitch et al. 2005), A754 (Macario et al. 2011) and A2146 ",
+    "(Russell et al. 2012). However, in most lines of sight the merger features are hidden by the projection. This allows the possibility of measuring the radial bulk motions via the Doppler shift of the emission lines. ",
+    "Currently the constrains on radial bulk motions are rather poor due to the lack of spatially resolved high spectral resolution instruments. The proposed ATHENA mission would have carried such an instrument, an X-ray Mi-crocalorimeter Spectrometer XMS. In this paper I will examine the expected quality of bulk motion measurements with a mission approximating the capabilities of the proposed ATHENA instruments, i.e. an ATHENA-like mission. "
+  ],
+  "2 Bulk motions in clusters ": [],
+  "2.1 Range of velocities ": [
+    "It is widely accepted that clusters of galaxies form by merging of smaller structures of matter accreted along large scale structure •laments. The velocities of the accretion •ows are assumed to reach a level of 1000 km s−1 (e.g. Frenk et al. 1999). A collision of two clusters or protoclusters of similar mass produces a strong merger. The related bulk motion velocities can reach several 1000 km s−1 as in the case of the Bullet cluster (e.g. Markevitch et al. 2002). Simulations of Nagai et al. (2002;2003) indicate that ongoing minor mergers may produce bulk velocities up to ˘1000 km s−1 . The released gravitational energy is dissipated into the in-tracluster material which eventually approaches the hydrostatic equilibrium. However, simulations indicate that even in the most relaxed clusters there are residual bulk motions present throughout the cluster volume at ˘100 km s−1 level (e.g. Lau et al., 2009; Nagai et al. 2003). "
+  ],
+  "2.2 Doppler shift ": [
+    "The radial components of the bulk motions of 100 -1000 km s−1 correspond to 2-20 eV shift of the Fe XXV and XXVI K emission line centroid energies (˘6 keV). It is challenging to use the currently most powerful X-ray instruments at 6 keV (XMM-Newton/EPIC, Chandra/ACIS and SUZAKU/XIS CCDs) for these measurements due to limitations in the energy resolution (˘100 eV). The Gaussian centroid can still be determined with precision better than 100 eV, assuming that the instrument gain is accurately calibrated. This requirement can be relaxed if one considers relatime motions between the main cluster and the moving part. In the following I discuss only the statistical precision of the line centroid determination, and not the calibration issues nor the uncertainties of the cosmic redshift measurements. "
+  ],
+  "2.3 Observational constraints ": [
+    "Suzaku/XIS instruments have been used to place upper limits for the bulk motion velocities at ˘1000 km s−1 level in several clusters: A2319 (Sugawara et al. 2009), Centaurus (Ota et al., 2007), AWM7 (Sato et al. 2008). A •rst signi•cant detection of a bulk motion has been achieved with Suzaku for the merging subclump in A2256 (Tamura et al. 2011). The radial velocity difference between the main cluster and the subclump is 1500±300±300 km s−1 (where the two sets of uncertainties refer to statistical and systematical ones, respectively). "
+  ],
+  "3 ATHENA-like missions ": [
+    "ATHENA (Advanced Telescope for High ENergy Astrophysics) was one of three L-class (large) missions being considered by the European Space Agency in the Cosmic Vision 2015-2025 plan. In May 2012 the Jupiter mission Jupiter Icy Moons Explorer (JUICE) was chosen for launch. However, ESA has committed to continue supporting technology developments for a future large X-ray facility. At the time of writing this paper (Oct 2012) there was an understanding that ESA would shortly appoint a small team from the community to provide input based on the the ATHENA study team activities. ",
+    "In this paper I used the responses and background estimates for the X-ray Microcalorimeter spectrometer (XMS) and a wide •eld imager (WFI) as reported in the ATHENA assessment report used by the ESA Space Science Advisory Committee (the ATHENA Yellow Book, Barcons et al., 2012). "
+  ],
+  "3.1 X-ray Microcalorimeter Spectrometer XMS ": [
+    "The requirement for the energy resolution of XMS is 3 eV at 6 keV. With its 100-1000 times higher effective area at 0.5 keV, compared to those of the current high resolution ",
+    "instruments onboard XMM-Newton and Chandra, and spatial resolution of 10 arcsec, XMS would enable spatially resolved high resolution spectroscopy. This would yield a breakthrough in mapping the spectral properties for extended sources like clusters. Also, the bandpass extends to 12 keV which allows the measurement of the Fe XXV K emission line, prominent in clusters of galaxies. The downside of XMS is the relatively small FOV (2.3x2.3 arcmin2) which renders the velocity mapping of a whole cluster challenging. "
+  ],
+  "3.2 Wide Field Imager WFI ": [
+    "Even though the energy resolution of WFI (150 eV at 6 keV) is not suf•cient to resolve the components of Fe K complex, it can still determine very precisely the centroid of the Gaussian distribution of the total line emission (see Fig. (<>)1) due to high photon statistics. This is due to the very large effective area (˘0.5 m2) of the X-ray telescopes onboard ATHENA. Thus also WFI is a powerful tool for mapping the cluster velocities. ",
+    "Fig. 1 Data from a 100ks WFI simulation of the A2256 main cluster (red crosses) and the subclump (blue crosses) together with the input models (solid curves). The vertical dashed lines highlight the centroids of the Fe XXV K lines. "
+  ],
+  "4 Improvement with ATHENA-like missions ": [
+    "I examine here the capability of the proposed ATHENA instruments for measuring the expected bulk motions in clusters. I used the MEKAL model (Kaastra 1992) in the XSPEC package to model the cluster emission (bremsstrahlung continuum + collisional excitation lines) adopting the metal abundances of Grevesse & Sauval (1998). ",
+    "I used the current estimates of the instrument responses (Barcons et al., 2012) to simulate the cluster spectra, including the instrument background and 90% resolved cosmic X-",
+    "Table 1 Velocity precision for a cluster with z = 0.1 and kT = 5 keV with 100ks observation ",
+    "ray background. Then I •tted the simulated data in the 5.5• 7.5 keV band (excluding the channels where the Fe XXVI K emission is signi•cant) with a model consisting of a power-law component for the continuum and a Gaussian line for the Fe XXV K emission. The 1 ˙ statistical uncertainty of the Gaussian centroid then yielded the estimate for the statistical precision of the velocity measurement, as summarised in Table (<>)1. "
+  ],
+  "4.1 A2256 and the subclump ": [
+    "In order to obtain a real-life example of the performance of XMS and WFI for measuring the velocities of a nearby minor merger, I used the Suzaku results for the A2256 and the subclump (Tamura et al. 2011) to simulate spectra using an exposure time of 100 ks. ",
+    "A •t to the simulated XMS data (see Fig. (<>)2) yielded a statistical uncertainty of the redshift (˙z ˘10−6) corresponding to a velocity precision at a level of ˘ 1 km s−1 , i.e. a 1500˙ detection for the clump motion. Measurement is very precise because many line features are resolved and each centroid gives weight to ˜2 . Dividing the XMS emission of the subclump into boxes with width of 30 arcsec (i.e. 5×5 pixel map for the full XMS FOV) yielded a statistical precision level of ˘10 km s−1 . This level of detail would provide a breakthrough in modelling the dynamics of the merging subclumps. Since the •ux of A2256 subclump is comparable to that of the central region of similar size in A2256 (Tamura et al., 2011), the above calculations yield an approximate estimate of the expected velocity mapping precision level in the bright nearby cluster centres with XMS. ",
+    "A spectral •t to the data from a 100 ks WFI simulation of A2256 main cluster and subclump (see Fig. (<>)1) yielded a statistical precision for Fe XXV K shift corresponding to velocity precision of 60 km s−1 , i.e. a detection at ˘25 ˙ level. "
+  ],
+  "4.2 Mapping the whole cluster ": [
+    "In order to derive general conclusions about the performance of ATHENA-like missions for the velocity mapping in clusters, one should simulate spectra with a grid of representative values for cluster temperatures, metal abundances and redshifts and realistic exposure times. Also, one should ",
+    "consider a range of luminosities for the moving regions and their velocities and directions of motion. ",
+    "In this work I limited the complexity of the above approach by using an exposure time of 100ks for a cluster with kT = 5 keV and z=0.1, assuming that all of the emission in the line of sight of a studied region originates from the moving subunit. I further assumed that the luminosity of the moving subunit at a given distance from the cluster centre can be estimated with a a -model for the surface brightness with = 2/3 and rcore = 0.1 r500. This may be an underestimate of the actual signal since the likely enhancement of the emission due to the subunit is not accounted for. I adopted a bolometric luminosity Lbol(r500) = 7 × 1044 erg s−1 within r500 from L-T relation of Pratt et al. (2009). Using r500 -T relation of Vikhlinin et al. (2006) I adopted r500 = 10 arcmin. ",
+    "Fig. 2 Data from a 100ks XMS simulation of the A2256 subclump (blue crosses) together with the input model, shifted by 100 km s−1 (red line). "
+  ],
+  "4.2.1 XMS ": [
+    "A single XMS pointing covers only a fraction of the full cluster volume: at z = 0.1 the r500 radius for a cluster with kT = 5 keV is ˘1 Mpc (Vikhlinin et al., 2006) and covers an area of ˘300 arcmin2 , i.e. ˘50 higher than the FOV of XMS. Thus it is not feasible to cover the full r = r500 region in nearby clusters with XMS. Limiting the mapping into the central r=0.25 r500 region would require ˘10 point-ings which might be feasible for a few clusters. Single XMS pointings at larger radii might still be useful, and I thus calculate estimates for these observations in the following. ",
+    "I simulated XMS spectra with the above generic cluster (see Section (<>)4.2) within the full FOV i.e. ˘ (0.2 r500)2 . Fitting the simulated spectra yielded a statistical precision of ˘200 km s−1 at r=0.25 r500. At r=0.5 r500 ˘90% of the total signal in the 5.5•7.5 keV band is due to background emission which degrades the statistical precision of velocity to ˘400 km s−1 and at r500 the data are so noisy due to the background that reliable velocity measurements cannot be obtained. ",
+    "If the above cluster was located at z=1.0, a single central XMS pointing would cover the cluster out to ˘0.5 r500. The received •ux would be similar as that of the z=0.1 cluster at 0.5 r500, when using the full XMS FOV. Thus, with a central 100ks XMS pointing it is feasible to obtain a single bulk motion measurement at z = 1.0 assuming the full cluster within 0.5 r500 is moving with a radial velocity component higher than 400 km s−1 . "
+  ],
+  "4.2.2 WFI ": [
+    "Fitting the simulated data using the generic cluster described in Section (<>)4.2 showed that in the centre the bulk velocity can be mapped with angular resolution of ˘0.1 r500 with statistical precision of ˘ 100 km s−1 . At r=0.25 r500 the lower cluster •ux requires a larger extraction region to achieve similar statistical quality as in the centre. Using an extraction box with size of (˘0.2 r500)2 yields a velocity precision of ˘ 200 km s−1 . At a distance of 0.5 r500 from the centre, the background dominates (as in the case of XMS) and the velocity precision degrades to ˘800 km s−1 level when using an extraction box size of ˘0.3 r500). Repeating the exercise with a very hot cluster (kT = 10 keV) improves the continuum signal but the Fe XXV emission decreases and thus the velocity precision does not improve signi•cantly. "
+  ],
+  "5 Conclusions and discussion ": [
+    "The simulations showed that for a nearby (z  0.1) cluster with kT = 5 keV, using a 100 ks exposure using the instruments proposed for ATHENA, one could ",
+    "The above estimates for the level of statistical precision of velocity measurements with XMS and WFI indicate that an ATHENA-like mission would enable for the “rst time the mapping of radial components of the bulk motions due to recent minor and major mergers in nearby (z0.1) clusters ",
+    "of galaxies within the central 0.25 r500. Also the residual motions due to past mergers can be mapped in these central regions. Single velocity measurements at the distance of 0.5 r500 for a cluster at z=0.1 at the level of ˘400 km s−1 can be achieved with 100ks off-axis pointings using XMS. At higher distances the mapping is more limited due to the background but the average motion within the central 0.5 r500 up to z=1.0 can be measured with a central 100ks pointing with XMS, if the radial velocity component is bigger than ˘400 km s−1 . ",
+    "These measurements would open a new tool to study cluster dynamics. This would be complementary to the current analyses of intracluster shocks and sloshing and thus give a better handle on the 3-dimensional dynamics of clusters. This would yield a breakthrough in modelling the cluster physics and its implications to cosmology. ",
+    "The kinetic Sunyaev Zeldovic (kSZ) effect as measured by WMAP (Kashlinsky et al., 2008; Osborne et al., 2012) has been used to constrain bulk motions of clusters. However these results have been controversial due to relatively weak kSZ signal compared to the thermal one. Thus, one must combine a large sample of clusters and assume a similar motion for all the clusters in the sample. Mak et al. (2011) calculate that a sample of 400 clusters would allow Planck to detect a coherent 500 km s−1 bulk motion. Clearly ATHENA would make improvement here, being able to measure the velocities in individual clusters with better precision and spatial resolution. "
+  ]
+}

jsons_folder/2013ASSP...34..411L.json

@@ -0,0 +1,82 @@
+{
+  "Abstract": [
+    "Abstract Recent work has both illuminated and mystified our attempts to understand cosmic rays (CRs) in starburst galaxies. I discuss my new research exploring how CRs interact with the ISM in starbursts. Molecular clouds provide targets for CR protons to produce pionic gamma rays and ionization, but those same losses may shield the cloud interiors. In the densest molecular clouds, gamma rays and 26Al decay can provide ionization, at rates up to those in Milky Way molecular clouds. I then consider the free-free absorption of low frequency radio emission from starbursts, which I argue arises from many small, discrete H II regions rather than from a “uniform slab” of ionized gas, whereas synchrotron emission arises outside them. Finally, noting that the hot superwind gas phase fills most of the volume of starbursts, I suggest that it has turbulent-driven magnetic fields powered by supernovae, and that this phase is where most synchrotron emission arises. I show how such a scenario could explain the far-infrared radio correlation, in context of my previous work. A big issue is that radio and gamma-ray observations imply CRs also must interact with dense gas. Understanding how this happens requires a more advanced understanding of turbulence and CR propagation. "
+  ],
+  "1 Introduction ": [
+    "Starbursts are detected in synchrotron radio, which is generated from cosmic ray (CR) electrons and positrons (e±) interacting with magnetic fields ((<>)Condon (<>)1992), and now in gamma rays, which are generated by CR pro-tons colliding with ambient gas and creating pions ((<>)Acciari et al. (<>)2009; (<>)Acero et al. (<>)2009; (<>)Abdo et al. (<>)2010). While nearby starbursts can be re-",
+    "1 ",
+    "solved in radio emission, this is not true for the gamma rays. Furthermore, because the gamma rays are a recent discovery, our understanding of CRs is at a basic, phenomenological level. Thus, much of the theoretical work about CRs in starbursts uses one-zone steady-state models ((<>)Paglione et al. (<>)1996; (<>)Torres (<>)2004; (<>)Domingo-Santamar´ıa & Torres (<>)2005; (<>)de Cea del Pozo et al. (<>)2009; (<>)Lacki et al. (<>)2010). These assume that the interstellar medium (ISM), magnetic fields, and CR injection of starbursts are completely homogeneous – essentially, that starbursts have no structure, which is obviously not true in detail. These kinds of models can help us understand the energetics of CRs in starbursts (which, even a few years ago, was mysterious), but the propagation is treated as a black box. ",
+    "Some works have expanded from these assumptions, by correlating radio and gamma ray emission and star-formation to constrain CR di usion ((<>)Murphy et al. (<>)2008, (<>)2012), by creating 3D steady-state models of CR populations in the Milky Way ((<>)Strong & Moskalenko (<>)1998) and the nearby starbursts M82 and NGC 253 ((<>)Persic et al. (<>)2008; (<>)Rephaeli et al. (<>)2010), or by considering the time-and position-dependent contributions of individual CR accelerators to starbursts’ integrated CR spectra ((<>)Torres et al. (<>)2012). ",
+    "Yet even these approaches are simplifications of what actually happens in starbursts. On small enough scales, the apparently smooth fluctuations in gas density and star-formation resolve into a highly chaotic froth with many phases of vastly di erent physical conditions (Figure (<>)1). Molecular gas is highly turbulent in starbursts, leading to strong density fluctuations ((<>)Krumholz & McKee (<>)2005). In star-forming regions, the overdensities of the molecular gas collapse still further into molecular cores and ultimately into protostars. Newborn O stars and star clusters carve out H II regions. Supernovae and clusters blast bubbles of 107 − 108 K plasma which can ultimately fill the volume of a starburst and form into a galactic wind ((<>)Chevalier & Clegg (<>)1985; (<>)Strickland & Heckman (<>)2009). Pervading these phases are magnetic fields and the CRs themselves. ",
+    "The interaction between CRs and these di erent phases must be understood if we are to interpret the results of our phenomenological models. Which phase has the magnetic fields responsible for the radio emission? Which phase provides the target atoms responsible for pionic gamma ray emission? Which phase regulates how CRs are transported spatially? And how do the CRs shape these phases, if at all? "
+  ],
+  "2 How Molecular Clouds Can Stop Cosmic Rays and the Role of Gamma Rays and 26Al ": [
+    "CRs are thought to interact with the bulk molecular ISM, containing most of the gas mass of starbursts, and with some good reason. The observations of gamma rays from starburst galaxies provide evidence that CRs spend some ",
+    "Fig. 1 Starbursts appear more inhomogeneous on smaller scales (the given sizes are to order of magnitude). At large scales (> 30 kpc), the galaxy is completely unresolved (as for gamma-ray observations and high-z radio observations). Closer in, we see the resolution of the host galaxy from the starburst (3 kpc) and then the resolved starburst disk with its superwind (300 pc). Then, individual star-forming regions and large molecular cloud complexes become apparent (30 pc). On these scales, how CRs travel from individual accelerators becomes important (dotted circles). Finally, on the smallest scales (<3 pc) it becomes clear that the ISM seethes with turbulence and is extremely complex. The overall energetics of CRs in starbursts can be represented by the large-scale view of simple one-zone models. More advanced models take a finer view, simulating large-scale density gradients or the e ects of individual CR accelerator regions. Yet, the physics of the CR propagation depends on the chaos of the multiphase ISM on small scales, and so is very poorly understood. ",
+    "time in dense (presumably, molecular) gas. Another line of evidence comes from the observed Zeeman splitting of OH lines in Ultraluminous Infrared Galaxies (ULIRGs), which imply that milliGauss magnetic fields are present in OH megamaser regions ((<>)Robishaw et al. (<>)2008). These regions occur in dense molecular gas, where the number density is at least 104 cm−3 and likely 106−7 cm−3 ((<>)Robishaw et al. (<>)2008). However, magnetic fields require free charges to be frozen into, otherwise the magnetic field lines would slip o the gas through ambipolar di usion (e.g., (<>)Mestel & Spitzer (<>)1956). Therefore, we have evidence that something is ionizing the dense molecular gas in ULIRGs. Since UV light is quickly absorbed and AGNs are not always nearby to provide X-rays, the default assumption is that CRs are ionizing this gas. ",
+    "The high energy densities of CRs in starbursts can sustain high ionization rates (ζˇ 10−16 − 10−14 sec−1) and heat the gas to high temperatures (˘ 50−100 K) ((<>)Suchkov et al. (<>)1993; (<>)Papadopoulos (<>)2010). The molecular gas in starbursts may represent a “Cosmic Ray Dominated Region” (CRDR). It is not clear, though, how much of the gas the CRs can reach. The problems that face ionizing radiation can be understood by considering other kinds of radiation. Extreme ultraviolet photons interact very strongly with the gas, surrendering much of their power into ionization. Yet that same interaction prevents the photons from going very far: they instead create small highly-ionized H II regions, leaving the majority of the starburst untouched. On the other hand, we never consider Neutrino Dominated Regions, even though neutrinos can penetrate any reasonable column and fill the entire starburst volume. They interact so weakly that their power just escapes the starburst rather than contributing to ionization. To ionize a parcel of gas evenly, we must pick some kind of radiation such that the gas’ absorption optical depth is ˘ 1, and this applies to CRs. If CRs interact weakly with the gas, they are blown out by the starburst wind before they can ionize or heat it, or they simply escape through di usion. If CRs interact strongly with the gas, they lose energy to pionic and ionization losses (“proton calorimetry”, (<>)Thompson et al. (<>)2007), stopping them and shielding the densest regions. ",
+    "The gamma-ray observations of M82 and NGC 253 indicate that CR protons lose perhaps ˘ 30−40% of their energy to pionic losses before escaping, implying much stronger losses than in the Milky Way ((<>)Lacki et al. (<>)2011; (<>)Abramowski et al. (<>)2012; (<>)Ackermann et al. (<>)2012). Moreover, the hard GeV-TeV gamma-ray spectra indicate advective losses which simply remove CRs from the starburst, rather than a high di usion constant that would let CRs penetrate deep into molecular clouds (e.g., (<>)Abramowski et al. (<>)2012). ",
+    "The advantage – and trouble – of CRs is that they are deflected by magnetic fields. On the one hand, the e ective scattering of CRs lets them build up to large energy densities. On the other, this also means that CRs see a much bigger column than a neutral particle would, stopping them much closer to their sources. The reach of CR ionization thus depends strongly on propagation. But if CRs are not guaranteed to reach all of the molecular gas, we need something else that can. ",
+    "Fig. 2 Di erent kinds of ionizing radiation are able to penetrate through di erent columns in the ISM, creating a hierarchy of ionization regions. Starbursts emit many ultraviolet photons but these are stopped very rapidly, resulting small highly-ionized regions. The injected power from gamma rays and radioactivity is small, but it can sustain a low level of ionization everywhere in the ISM. ",
+    "There is a known source of neutral radiation that can ionize the densest molecular gas in starbursts: gamma rays. Above a few MeV, they are stopped by γZpair production over columns of ˘ 200 g cm−2 ((<>)Berestetskii et al. (<>)1979). The pair e± then ionize the gas. Hence, even if CRs are quickly stopped, the bulk gas of the starburst is then likely to be a Gamma Ray Dominated Region (GRDR; Figure (<>)2). Gamma ray ionization harnesses proton calorimetry: the more strongly the CRs interact with the gas, the higher the energy density of gamma rays is. The gamma-ray ionization rate is ",
+    "(1) ",
+    "where Fis the gamma-ray flux within the starburst, σZ ˇ 10−26 cm2 is the cross section for γZpair production ((<>)Berestetskii et al. (<>)1979), fion is the eÿciency that energy in gamma rays goes into ionizing gas (I assume 0.1, supported by a cascade calculation), and Eion = 30 eV ((<>)Cravens & Dalgarno (<>)1978) is the energy used in each ionization of an atom. Fdepends on the surface density of star-formation and how proton calorimetric the starburst is – gamma-ray ionization is most e ective in very compact ULIRGs like Arp 220. ",
+    "Fig. 3 Comparison of ionization rates from CRs, gamma rays, 26Al, and 40 K for starbursts on the Schmidt Law. The CR and 26 Al ionization rates depend on their propagation. ",
+    "By using the Schmidt Law ((<>)Kennicutt (<>)1998) to relate gas density to star-formation surface density, I calculate the gamma-ray ionization rate in starbursts. These rates are plotted in Figure (<>)3: they range from 10−22 sec−1 at low densities to 10−17 sec−1 . At the highest gas surface densities, the ionization rates from gamma rays alone are comparable to those sustained by CRs in Milky Way molecular clouds ((<>)Lacki (<>)2012a). Unlike CRDRs, though, GRDRs are not substantially heated by the high energy ionizing radiation. The power dumped by gamma rays is never enough to heat the gas more than a few Kelvin from absolute zero; this is overwhelmed by dust heating, which raises the gas temperature to ˘ 50 K. The coldness of the GRDRs provides a potential observational signature. In molecular lines, the cold GRDRs will appear as shadows against the brighter, hotter CRDR material; the GRDRs should also have a narrower thermal line width ((<>)Lacki (<>)2012a). ",
+    "While the gamma-ray ionization rate is high in starbursts like Arp 220, is there anything that can enhance ionization where CRs cannot penetrate in less extreme starbursts? The decay of short-lived radionuclides like 26Al inject MeV particles, ionizing the ISM (long-lived isotopes like 40K sustain only ζˇ 10−22 sec−1) ((<>)Umebayashi & Nakano (<>)2009). The mean abundance Xof a radionuclide in the ISM is proportional to the star-formation rate divided by the gas mass, inversely proportional to the gas consumption time. Quicker gas consumption means that more of the gas is converted into stars and 26Al per decay time: ",
+    "(2) ",
+    "The gas consumption time in starbursts, ˘ 20 Myr in M82 (using the gas mass from (<>)Weiss et al. (<>)2001), is ˘ 100 times shorter than in the Milky Way ((<>)Diehl et al. (<>)2006), implying mean 26Al abundances in starbursts are ˘ 100 times higher ((<>)Lacki (<>)2012b). The 26Al alone sustains ionization rates of 10−18 sec−1 −10−17 sec−1 . This suggests that 26Al decay ionizes the dense gas in weak starbursts, and gamma rays ionize it in strong starbursts (Figure (<>)3). ",
+    "However, if it takes more than a few Myr for the 26Al to mix with the starburst molecular gas, it cannot contribute to ionization ((<>)Meyer & Clayton (<>)2000). Furthermore, the 26Al may be dumped into the superwind and ad-vected away instead of ionizing molecular gas. On the other hand, the distribution of 1.809 MeV gamma rays from the decay of 26Al in our own Galaxy suggests that it is formed by very massive stars ((<>)Kn¨odlseder (<>)1999). These very massive stars will not have time to migrate from their star-formation regions, and will likely be near star-forming molecular gas. Like CRs, then, the ionization rate from 26Al nuclei depends on the unknown details of their propagation, something which does not a ect gamma rays. ",
+    "Thus, CRs do not necessarily reach all of the molecular gas in the starbursts. Depending on the unknown propagation of CRs, it is conceivable at least that they leave most of the molecular gas untouched. Ionization from gamma rays and radioactivity may penetrate deeper columns, creating the required free charges to retain magnetic fields. But if CRs are not thoroughly mixed with the molecular gas, are they merely confined to pockets of that gas, or do they spend most of their time in another ISM phase entirely? "
+  ],
+  "3 H II Regions and Starbursts’ MHz Radio Spectra: Str¨omgren Sphere Pudding ": [
+    "The molecular gas ultimately collapses into stars: among the youngest stars are massive O stars that generate ionizing photons. The ionizing luminosity in Lyman continuum photons is actually much greater than the luminosity in CRs; however, these ultraviolet photons interact so strongly with the gas that they never travel far from their birth stars. Thus, instead of the weak but pervasive ionization of CRs or gamma rays, the ultraviolet photons create fully ionized H II regions surrounding O stars with low filling factor (Figure (<>)2). ",
+    "The H II regions have two e ects on the observed radio spectra: they make the free-free emission observed at high frequencies, and they host free-free absorption at low frequencies ((<>)Condon (<>)1992). Free-free absorption from individual H II regions is actually observed at low frequencies, both towards the Galactic Center (e.g., (<>)Nord et al. (<>)2006) and in the M82 starburst ((<>)Wills et al. ",
+    "Fig. 4 Illustration of the di erence between a uniform density collection of H II regions and a truly uniform ionized gas. In each case, there is free-free absorbing ionized gas which is spread throughout the starburst, so a “uniform slab” model is useful. As the frequency drops to zero, the ionized gas becomes completely opaque. However, not every sightline passes through an H II region on the left, as seen by the white space in the face-on view: the starburst is partially uncovered. Furthermore, even on sightlines intersecting an H II regions, that ionized gas is at some depth within the starburst (as seen in the oblique view). Thus the H II regions block only a constant fraction of radio emission at low frequency, unlike a uniform gas. ",
+    "(<>)1997). The free-free emission does not depend much on the geometry of the H II regions. This has led to the adoption of the “uniform slab” assumption, where a uniform density of ionized gas pervades the starburst. However, the geometry matters for calculating the free-free absorption: in reality we have a uniform density, not of gas, but of H II regions. If the density of H II regions is low enough, on some sightlines there may be no absorption: the H II regions partially cover the starburst (Figure (<>)4). Furthermore, the nearest H II region on any sightline is buried part way into it. Thus, if the synchrotron emitting material is outside the H II regions, some of it remains unobscured at any frequency. In contrast, the radio flux steeply falls towards low frequencies in a truly uniform slab of ionized gas. ",
+    "The e ective absorption coeÿcient from H II regions is their number density times an e ective cross section that depends on their size and opacity. The H II regions can be thought of as Str¨omgren spheres around super star clusters. I assume these clusters emit ionizing photons for a time tion in proportion to their mass Mand then shut o . Using a super star cluster mass function of dN/dM/ M−2 exp(−M/5 × 106 M⊙) for M 1000 M⊙ (e.g., (<>)McCrady & Graham (<>)2007), I find an e ective absorption coeÿcient of ",
+    "Fig. 5 My fit to the 22 MHz -92 GHz radio spectrum of M82, which assumes that free-free absorption comes from discrete H II regions around super star clusters with O stars. The observed flux is the solid line and the unabsorbed flux is the dotted line. I also break the observed flux down into its synchrotron (short-dashed) and thermal (long-dashed) components. Radio data compiled in (<>)Lacki ((<>)2012c) (from (<>)Roger et al. (<>)1986, (<>)Klein et al. (<>)1988, (<>)Israel & Mahoney (<>)1990, (<>)Cohen et al. (<>)2007, (<>)Laing & Peacock (<>)1980, (<>)Hales et al. (<>)1991, (<>)Basu et al. (<>)2012, and (<>)Williams & Bower (<>)2010). ",
+    "(3) ",
+    "at low frequencies. The H II regions around these SSCs become opaque at a frequency ",
+    "(4) ",
+    "the free-free absorption feature appears in the starburst spectrum around this frequency. If I instead assume that the free-free absorption comes from H II regions around individual O stars with ionizing photon luminosities of 1049 sec−1 , then αe is ˘ 4 times higher. This quantity can then be used in the uniform slab solution to model the actual amount of free-free absorption ((<>)Lacki (<>)2012c). I find this e ective absorption coeÿcient is αe ˇ (0.1 − 1 kpc)−1 as ν! 0 in M82. ",
+    "In Figure (<>)5, I model the radio spectrum of M82 by assuming the free-free absorption and emission comes from Str¨omgren sphere H II regions around ",
+    "super star clusters. I fit to the number of H II regions, their temperature, and density, as well as the unabsorbed synchrotron spectrum shape using the (<>)Williams & Bower ((<>)2010) parameterization: ",
+    "(5) ",
+    "and the amount of free-free emission (including both the free-free emission from the H II regions responsible for the absorption, and a fit component of additional free-free emission): ",
+    "(6) ",
+    "The best-fit model has a spectral index B = −0.56 and an intrinsic synchrotron spectral curvature of C = −0.08. Thermal emission is just 5% of the 1 GHz flux, even including free-free emission not associated with the absorption. The covering fraction of the H II regions is only 50%. In this model, the absorbed flux is still 62% of the unabsorbed flux at low frequencies ((<>)Lacki (<>)2012c), unlike previous models, where the synchrotron flux drops precipitously below 1 GHz. ",
+    "I should note, however, that this fit is preliminary, since the beam sizes of the radio data I used in the fit vary widely. Some of the data, particularly the 22.5 and 38 MHz points have extremely large beam sizes (˘ 1◦), and could easily be contaminated, for example, by the host galaxy of M82. However, the 74 MHz Very Large Array (VLA) sky survey resolved the inner arcminute ((<>)Cohen et al. (<>)2007), and the 333 MHz observations by the Giant Metrewave Radio Telescope (GMRT) actually resolved the starburst itself ((<>)Basu et al. (<>)2012). Both data points are approximately in line with the other data, suggesting that the starburst itself actually is seen at low frequencies. When I redo the fit only including data points with beam sizes smaller than 10 arcminutes, the basic conclusion that most of the radio flux is transmitted stands. It would be interesting to measure the spectrum of the starburst with low frequency interferometers like the upgraded Jansky VLA, the GMRT, or the Low Frequency Array (LOFAR). ",
+    "H II regions naively seem like a good candidate for the location of the CRs: their densities are at least the mean density of the starburst ((<>)Rodriguez-Rico et al. (<>)2004), consistent with models; they surround the star-forming regions that may accelerate CRs; and as highly ionized dense plasmas, they have low Alfven velocities, so CRs can self-confine e ectively ((<>)Kulsrud & Pearce (<>)1969). However, the strong radio emission that seems to be coming from M82 at low radio frequencies constrains this hypothesis – CRs spend some time outside the H II regions. "
+  ],
+  "4 Supernova-Driven Magnetic Fields in the Hot Wind Phase: The Secret of the FIR-Radio Correlation? ": [
+    "So where do CRs spend most of their time? The resolved radio emission appears to be mostly di use. If we take that at face value, CRs and the synchrotron emission really do fill most of the starburst. Then the CRs reside in the phase that fills most of the starburst volume, which is thought to be the hot (˘ 107 − 108 K) phase that ultimately forms into the wind ((<>)Heckman et al. (<>)1990). Evidence for this gas comes from the observations of 6.7 keV iron line emission from M82; the softer di use X-ray emission is mostly thought to be low filling factor gas resulting from when the wind crashes into the galactic halo ((<>)Strickland & Heckman (<>)2007). This is sup-ported by the evidence for CR advection in M82 and NGC 253 ((<>)Lacki et al. (<>)2011; (<>)Abramowski et al. (<>)2012). The picture that arises is that CRs in starbursts are similar to CRs in normal galaxies: the CRs spend most of their time in low density gas that occupies more volume but occasionally di use through the high density molecular gas. Pionic gamma rays and secondary e± arise during the brief times when the CRs plunge into the molecular gas, but the synchrotron emission arises during the intervals when CRs traverse the di use hot phase. Radio emission then mostly traces magnetic fields in the hot phase. ",
+    "What are these fields? The magnetic fields of starbursts are thought to be driven by turbulent dynamos. The energy of supersonic turbulence is injected at some outer scale ℓ, but it rapidly dissipates over a timescale ℓ/σ, where σis the typical velocity dispersion of the turbulence ((<>)Stone et al. (<>)1998): ",
+    "(7) ",
+    "where ρis the gas density and ǫis the volumetric energy injection rate. The energy density is then equal to the volumetric energy injection times the dissipation time. I suppose the outer scale of turbulence is the scale height of the starburst, the largest plausible size. Using the central superwind density from (<>)Strickland & Heckman (<>)2009, I then find σˇ 2500 km s−1 , indicating weakly supersonic turbulence (for a sound speed cS ˇ 1500 km s−1). The magnetic fields are likely amplified until they are in equipartition with turbulent energy ((<>)Stone et al. (<>)1998; (<>)Groves et al. (<>)2003). I find for galaxies on the Schmidt law ((<>)Kennicutt (<>)1998), using the energy injection rate from (<>)Strickland & Heckman ((<>)2009), ",
+    "(8) ",
+    "for star-formation and gas surface densities ΣSFR and Σg respectively, and where εis a factor of order unity ((<>)Lacki (<>)2013). ",
+    "The radio emission of star-forming galaxies of star-forming galaxies is tightly correlated with its far-infrared (FIR) emission, strongly constraining the e ective magnetic fields. In (<>)Lacki et al. (<>)2010, we found a phenomenological scaling of BFRC ˇ 400 µG(Σg/g cm−2)0.7 was necessary for this FIR-radio correlation to work. The B/ Σg0.7 scaling is needed because (1) it keeps the radiation and magnetic fields in equipartition, so the ratio of Inverse Compton and synchrotron cooling times remain constant ((<>)V¨olk (<>)1989): ",
+    "(9) ",
+    "using the (<>)Kennicutt ((<>)1998) Schmidt law (ΣSFR / Σg1.4). (2) At constant synchrotron frequency (instead of constant electron energy), it preserves the ratio of bremsstrahlung and synchrotron cooling times. The characteristic synchrotron frequency of an electron with energy Ee and charge eis ",
+    "(10) ",
+    "((<>)Rybicki & Lightman (<>)1979). Plugging that result into formulae for the syn-chrotron ((<>)Rybicki & Lightman (<>)1979) and bremsstrahlung ((<>)Strong & Moskalenko (<>)1998) lifetimes give: ",
+    "(11) ",
+    "(12) ",
+    "(13) ",
+    "(14) ",
+    "For a given gas scale height, this means that Σg −0.05 . The quote satisfies these conditions. This suggests that the FIR radio correlation is ultimately powered by the Schmidt Law, causing the hot phase turbulent magnetic fields to have the necessary scaling with mean gas density ((<>)Lacki (<>)2013). ",
+    "This model has interesting implications for whether CRs and magnetic fields are in equipartition with magnetic fields in starbursts. Both CRs and magnetic fields would ultimately have the same power source, the mechanical energy of supernovae. Furthermore, the fraction of supernova power they receive is likely similar (of order tens of percent), with turbulence perhaps receiving a few times more power than the CRs. When the CRs are removed by advection (as seems to be the case in M82 and NGC 253), the residence time for both the CRs and turbulence are also similar. In each case, the ",
+    "residence time is of order a sound-crossing time, with the CR lifetime perhaps being a few times longer than ℓ/σ, because the wind takes some time to accelerate to cS and beyond. Then equipartition holds between magnetic fields and CRs, even if there is no direct coupling between the two. However, in strongly proton calorimetric galaxies, the residence time of CRs is instead set by pionic loss times that are much shorter than the sound-crossing time: the CR energy density becomes smaller than the magnetic energy density (compare with (<>)Lacki et al. (<>)2010). ",
+    "Equipartition seems to work in M82 and NGC 253, as suggested by one-zone models ((<>)Persic et al. (<>)2008; (<>)Rephaeli et al. (<>)2010) and gamma-ray observations ((<>)Persic & Rephaeli (<>)2012; (<>)Abramowski et al. (<>)2012). However, in Arp 220 and other ULIRGs, equipartition fails if the far-infrared radio correlation is to work ((<>)Condon et al. (<>)1991; (<>)Thompson et al. (<>)2006), and one-zone models of the radio emission indicate stronger magnetic fields, a few milliGauss ((<>)Torres (<>)2004), than expected from equipartition. It will be interesting to see if equipartition actually fails in Arp 220 if it is detected in gamma rays, perhaps with the Cherenkov Telescope Array (CTA; (<>)Actis et al. (<>)2011). ",
+    "While this can explain the magnetic fields, what about the gas density? Previous one-zone models to interpret starbursts’ nonthermal emission assume that CRs experience the mean (volume-averaged) gas density in the starburst. This can only happen if the CRs leave the hot phase and enter the molecular gas (or possibly H II regions). Interaction with dense gas is needed to flatten the radio spectra through bremsstrahlung and ionization losses ((<>)Thompson et al. (<>)2006), though advective escape also flattens spectra. Finally, much of starbursts’ radio emission probably comes from pionic e± ((<>)Rengarajan (<>)2005; (<>)Lacki et al. (<>)2010): these are created in dense gas, but they would have to di use out into the hot phase to emit radio. How does this mixing of CRs with gas work? Observations of the Galactic Center suggest that CRs don’t mix with the dense molecular gas there ((<>)Crocker et al. (<>)2011), but M82 and NGC 253 seem to be much more eÿcient at stopping protons ((<>)Lacki et al. (<>)2011; (<>)Abramowski et al. (<>)2012). And why does the assumption of mean density seem to work? Only knowledge of how CRs traverse the di erent phases can answer these questions. "
+  ],
+  "5 Conclusion ": [
+    "The matter in a starburst ISM spans the range of energies from 10 Kelvin to 10 teraKelvin: cold molecular gas at 10 Kelvin, H II regions at 10 kilo-Kelvin, the hot wind phase at 10 megaKelvin, the MeV ionizing particles from 26Al decay at 10 gigaKelvin, and the cosmic rays and gamma rays at 10 teraKelvin and beyond. The relationship between these phases, and their e ects on observables, is complex. ",
+    "My hypothesis here is that CRs in starbursts spend most of their time in the volume-filling hot phase of the ISM, but they occasionally mix into the molecular gas to eÿciently produce gamma rays and pionic e± . The relatively eÿcient pionic losses within the molecular phase may shield the densest gas. How this works in detail, like how the competition between the advection in the hot phase and the pionic losses in the molecular gas somehow lets us just use the average gas density of starbursts in one-zone models, is not clear. ",
+    "Yet the ideas presented here are still simplistic compared to the reality of gas in starbursts. I have considered each phase as if it had a single density and magnetic field, but turbulence creates fluctuations in both of these quantities. Ultimately, to understand CRs in starbursts, we must learn what turbulence does to CRs, gas, and magnetic fields as they interact with each other. "
+  ],
+  "Acknowledgements ": [
+    "I am supported by a Jansky Fellowship from the National Radio Astronomy Observatory. The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under cooperative agreement with the National Science Foundation. I would like to acknowledge discussions and comments with Todd Thompson, Padelis Papadopolous, Jim Condon, Rainer Beck, and Diego Torres. "
+  ]
+}

jsons_folder/2013ApJ...762..135S.json

@@ -0,0 +1,93 @@
+{
+  "INITIAL SIZE DISTRIBUTION OF THE GALACTIC GLOBULAR CLUSTER SYSTEM ": [],
+  "Jihye Shin1 , Sungsoo S. Kim1,2 , Suk-Jin Yoon3 , and Juhan Kim4 ": [],
+  "Draft version March 5, 2022 ": [],
+  "ABSTRACT ": [
+    "(<http://arxiv.org/abs/1212.6872v1>)arXiv:1212.6872v1  [astro-ph.GA]  31 Dec 2012 ",
+    "Despite the importance of their size evolution in understanding the dynamical evolution of globular clusters (GCs) of the Milky Way, studies are rare that focus specifically on this issue. Based on the advanced, realistic Fokker–Planck (FP) approach, we predict theoretically the initial size distribution (SD) of the Galactic GCs along with their initial mass function and radial distribution. Over one thousand FP calculations in a wide parameter space have pinpointed the best-fit initial conditions for the SD, mass function, and radial distribution. Our best-fit model shows that the initial SD of the Galactic GCs is of larger dispersion than today’s SD, and that typical projected half-light radius of the initial GCs is ∼4.6 pc, which is 1.8 times larger than that of the present-day GCs (∼2.5 pc). Their large size signifies greater susceptibility to the Galactic tides: the total mass of destroyed GCs reaches 3–5×108 M⊙, several times larger than the previous estimates. Our result challenges a recent view that the Milky Way GCs were born compact on the sub-pc scale, and rather implies that (1) the initial GCs are generally larger than the typical size of the present-day GCs, (2) the initially large GCs mostly shrink and/or disrupt as a result of the galactic tides, and (3) the initially small GCs expand by two-body relaxation, and later shrink by the galactic tides. ",
+    "Subject headings: Galaxy: evolution -Galaxy: formation -Galaxy: kinematics and dynamics -globular clusters: general -methods: numerical "
+  ],
+  "1. INTRODUCTION ": [
+    "Whereas the present-day mass functions (MFs) of globular cluster (GC) systems, which are nearly universal among galaxies ((<>)Brodie & Strader (<>)2006; (<>)Jorn´an et al. (<>)2007), are approximately log-normal with a peak mass Mp ≈2×105 M⊙, the MFs of the young massive star cluster (YMC) systems follow a simple power-law distribution ((<>)Whitmore & Schweizer (<>)1995; (<>)Zhang & Fall (<>)1999; (<>)de Grijs et al. (<>)2003, among others). Motivated by such a di erence between GCs and YMCs, numerous studies have examined the dynamical evolution of the GC MFs to determine whether the initial MFs of GC systems resemble those of YMC systems ((<>)Gnedin & Ostriker (<>)1997; (<>)Baumgardt (<>)1998; (<>)Vesperini (<>)1998; (<>)Fall & Zhang (<>)2001; (<>)Parmentier & Gilmore (<>)2007; (<>)Shin, Kim, & Takahashi (<>)2008, among others). In particular, (<>)Shin, Kim, & Takahashi ((<>)2008, Paper I hereafter) surveyed a wide range of parameter space for the initial conditions of the Milky Way GCs, and considered virtually all internal/external processes: two-body relaxation, stellar evolution, binary heating, galactic tidal field, eccentric orbits and disc/bulge shocks. They found that the initial GC MF that best fits the observed GC MF of the Milky Way is a log-normal function with a peak at 4×105 M⊙ and a dispersion of 0.33, which is quite di erent from the typical MFs of YMCs. ",
+    "Using the outcome of N-body calculations, ",
+    "(<>)Gieles & Baumgardt ((<>)2008) found that the aspect of mass loss in GCs varies with the tidal filling ratio ℜ≡rh/rJ , where rh is the half-mass radius and rJ is the Jacobi radius. More specifically, the mass loss of GCs in the ”isolated regime” (ℜ< 0.05) is driven mostly by the two-body relaxation, which induces the formation of binaries in the core and causes GCs to expand. On the other hand, the mass loss of GCs in the ”tidal regime” (ℜ> 0.05) is influenced by the galactic tides as well, which enables stars in the outer envelope to easily escape (evaporation). Thus, the cluster size (rh) is as important as the cluster mass (M) and the galactocentric radius (RG) in determining the dynamical evolution of GCs. ",
+    "Can YMCs tell us something about the typical initial size of the Milky Way GC system? Observations show that the projected half-light radius Rh of YMCs (ages up to 100 Myr) in the local group ranges between ∼2 and ∼30 pc with a mean value of ∼8 pc ((<>)Portegies Zwart, McMillan, & Gieles (<>)2010), which is a few times larger than that of the present-day Milky Way GCs, Rh ∼2.5 pc. However, GCs could have formed in di erent environments and/or by di erent mechanisms from the YMCs. ",
+    "Perhaps the best way to estimate the typical size of the GCs is to trace them back to their initial state by calculating their dynamical evolution. In this paper, we study the dynamical evolution of the Galactic GCs and identify the most probable initial conditions not only for the MF and radial distribution (RD), but also the size distribution (SD). Using the same numerical method and procedure as in Paper I, we perform Fokker-Planck (FP) calculations for 1152 di erent initial conditions (mass, half-mass radius, galactocentric radius and orbit eccentricity), and then search a wide-parameter space for the most probable initial distribution models that evolve into ",
+    "Fig. 1.— Distribution of the Galactic ”native” (see the text for definition) globular clusters in the L–RG space (a), Rh–RG space (b), and Rh–L (c). Data are from the compilation by Harris (1996). the present-day Galactic GC distributions. ",
+    "The paper is organized as follows. Section 2 describes the properties of the observed GCs, again which we compare our model results. Section 3 presents models and initial conditions for FP calculations, and Section 4 analyzes the aspects of the size evolution of GCs. We synthesize our FP results in Section 5 to construct the GC system, and examine common features of the best-fit MF, RD, and SD models in Section 6. We discuss characteristics of the final best-fit SD models of the Galactic GCs in Section 7. Finally, conclusions are presented in Section 8. "
+  ],
+  "2. PRESENT-DAY GC PROPERTIES ": [
+    "When comparing FP calculations to the present-day Galactic GCs, we consider the ”native” GCs only, i.e., ”old” halo and bulge/disc clusters, which are believed to be created when a protogalaxy collapses while ”young” halo clusters are thought to be formed in external satellite galaxies ((<>)Zinn (<>)1993; (<>)Parmentier et al. (<>)2000; (<>)Mackey & van den Bergh (<>)2005). Our native GC candidates do not include six objects that belong to the Sagittarius dwarf, seven objects whose origins remain unknown, two objects that have no size information, and fifteen objects that are thought to be the remnants of dwarf galaxies ((<>)Lee, Gim, & Casetti-Dinescu (<>)2007). The total number of our present-day Galactic native GCs is 93, and their observed properties, such as luminosity L, Rh, and RG, were obtained from the database compiled by (<>)Harris ((<>)1996). ",
+    "Figure (<>)1 shows scatter plots between observed L, Rh, and RG values for the 93 Galactic native GCs. The L, Rh, and RG values range between 3.9×103–5.0×105 L⊙, 0.3–16 pc, and 0.6–38 kpc, where the mean values are located at 7.2×104 L⊙, 2.5 pc, and 4.1 kpc, respectively. The correlation between Rh and RG is tighter than the other two correlations (see Figure (<>)1b). This tight Rh– RG correlation could be just a result of the initially tight ",
+    "Fig. 2.— Comparison of rh evolution between N-body simulations and our FP calculations for GCs with initial conditions of M = 104 M⊙, RG = 8.5 kpc, and rh = 1, 3, and 5 pc on circular orbits. N-body simulations were performed using Nbody4 code ((<>)Aarseth (<>)2003), and mass loss by stellar evolution was not considered in these test calculations (both N-body and FP). rh values of the two models agree well within ∼20% during the entire cluster lifetimes. ",
+    "correlation between Rh and RG, or it could be due to the preferred disruption of large GCs near the Galactic center ((<>)Vesperini & Heggie (<>)1997; (<>)Baumgardt & Makino (<>)2003). Another possible cause is the expansion of initially small GCs up to rJ , which is roughly proportional to RG 2/3 for a given GC mass. One of the goals of this paper is to determine which of these possibilities is more feasible. ",
+    "Previous studies on the evolution of the GC system assumed a certain constant mass-to-light (M/L) ratio, and converted the observed L to M when comparing their numerical values with observations. But the conversion of GC luminosity function (LF) to GC MF using a constant M/L ratio may lead to MFs in error because low-mass stars, which have higher M/L ratios than the high-mass stars, preferentially evaporate from the cluster and this causes the M/L ratio of the cluster to evolve with time ((<>)Kruijssen & Portegies Zwart (<>)2009). For the same reason, there is not a linear relationship between Rh and rh among di erent GCs. Thus, we transform M to L, instead of L to M, using the stellar mass–luminosity relation of the Padova model ((<>)Marigo et al. (<>)2008) with a metallicity of [Fe/H] = −1.16, which is the mean value for the Galactic native GCs. Our FP calculations, which will be described later, show that the present-day GCs can have M/L ratios ranging between 1.2 and 2.5 and rh/Rh ratios ranging between 1.0 and 2.5. ",
+    "We use dynamical properties such as M and rh when constructing the initial distributions of the Galactic GC system and when calculating the dynamical evolution, while observed quantities, L and Rh, are used when comparing our FP results with the observations. "
+  ],
+  "3. MODELS AND INITIAL CONDITIONS ": [
+    "We adopt the anisotropic FP model used in Paper I, which was originally developed by (<>)Takahashi & Lee ((<>)2000, and references therein). The model integrates the orbit-averaged FP equation of two (energy-angular momentum) dimensions and considers multiple stellar mass components, three-body and tidal-capture binary heating, stellar evolution, tidal fields, disk/bulge shocks, dynamical friction, and realistic (eccentric) cluster orbit (see (<>)Kim & Lee ((<>)1999) for the tidal binary heating and Paper I for the detailed implementation of dynamical friction and realistic orbits). The model implements the Alternating Direction Implicit (ADI) method developed by (<>)Shin & Kim ((<>)2007) for integrating the two-dimensional FP equation with better numerical stability. ",
+    "Parameters for our FP survey are the following four initial cluster conditions: M, rh, apocenter distance of the cluster orbit Ra, and cluster orbit eccentricity e. We choose eight M values from 103.5 to 107 M⊙, six rh values from 10−1 to 101.5 pc, and six Ra values from 100 to 101.67 kpc, all equally spaced on the logarithmic scale. For the eccentricity, we choose e = 0, 0.25, 0.5, and 0.75. We perform FP calculations for all possible combinations of these four parameters, thus the total number of cluster models considered in the present study amounts to 1152. ",
+    "For the initial stellar mass function (IMF) within each cluster, we adopt the model developed by Kroupa (2001) with a mass range of 0.08–15 M⊙, which is realized by 15 discrete mass components in our FP model. Each mass component follows the stellar evolution recipe described by (<>)Schaller et al. ((<>)1992). The stellar density and velocity dispersion distributions within each cluster follow the King model ((<>)King (<>)1966) with a concentration parameter W0 = 7 and with neither initial velocity anisotropy nor initial mass segregation. We use only one value for W0, thus the tidal cut-o radius rt of the King profile is proportional to rh, while rJ varies depending on M and RG. Therefore, the Roche lobe filling ratio (rt/rJ ) and ℜof our FP models are functions of rh, M, and RG. ",
+    "The aspects of mass and size evolution from our FP model are in a good agreement with those from N-body methods. A comparison of mass evolution between our FP calculations and the N-body simulations performed by (<>)Baumgardt & Makino ((<>)2003) for clusters on eccentric orbits with initial masses larger than 104 M⊙ shows good agreement of cluster lifetimes within ∼25%. For a comparison of size evolution, we run a set of N-body simulations using Nbody4 code ((<>)Aarseth (<>)2003) with M = 104 M⊙, RG = 8.5 kpc, and rh = 1, 3, and 5 pc (these correspond to ℜ= 0.04, 0.11, and 0.18), and find that the rh evolutions of the two models agree well within ∼20% during the entire cluster lifetimes (see Figure (<>)2). ",
+    "Due to the expulsion of the remnant gas from star formation in the pre-gas-expulsion cluster, some of the low-mass pre-gas expulsion clusters can quickly disrupt, and even the surviving low-mass pre-gas-expulsion clusters will lose a significant fraction of their mass within the first several Myr and rapidly expand ((<>)Baumgardt & Kroupa (<>)2007; (<>)Parmentier & Gilmore (<>)2007). Since our FP model does not consider the e ect of gas expulsion, our initial GC models are to be regarded as models at several Myr after cluster formation. "
+  ],
+  "4. SIZE EVOLUTION OF INDIVIDUAL GLOBULAR CLUSTERS ": [
+    "The three main drivers of GC size evolution are the two-body relaxation, the mass loss by stellar evolution, and the galactic tides. In this section, we discuss the size evolution of individual GCs with a subset of our FP calculations. Figure (<>)3 shows the ratios between rh values at the present time (13 Gyr) and at the beginning from our FP calculations as a function of rh,0 and M0 for two di erent RG,0 values (subscripts 0 denote the initial value, hereafter). ",
+    "Two-body relaxation causes GC core to collapse and the subsequent formation of dynamical binaries in the core makes the whole cluster expand. For GCs that have undergone core collapse in the early phase of evolution, the size of the post-core-collapse expansion follows a scaling relation rh ∝M0−1/3 t2/3 ((<>)Goodman (<>)1984; (<>)Kim, Lee, & Goodman (<>)1998; (<>)Baumgardt, Hut, & Heggie (<>)2002), and thus for a given initial mass and epoch, rh/rh,0 is simply proportional to rh,−10. Figure (<>)3 indeed shows that the size of the GCs with the same M0 tend to converge to a single value (rh/rh,0 ∝rh,−10), if the GCs have small trh,0 (log trh,0/yr . 9). ",
+    "Mass loss by stellar evolution causes GCs to adiabatically expand to maintain virialization, and the GC sizes evolve following rh/rh,0 ∝M0/M when the stellar evolution is the main driver of the GC size evolution ((<>)Hills (<>)1980). The combination of Kroupa IMF and the stellar evolution recipe described by (<>)Schaller et al. ((<>)1992) yields a mass loss of ∼40% within 13 Gyr. Thus, GCs would expand by a factor of ∼1.67 as a result of the stellar evolution, if two-body relaxation or the galactic tides are relatively less important in driving the size evolution. Indeed, clusters with log trh,0/yr & 9 and ℜ< 0.05 have rh,13/rh,0 values between 1 and 2. ",
+    "While stellar evolution and two-body relaxation cause clusters to expand, galactic tides make clusters shrink in general. A cluster extending farther than rJ (overfilling; rt > rJ ) loses stars outside rJ within a few dynamical timescales, and this naturally causes the mean size of the cluster to decrease. Since rJ ∝RG(M/MG)1/3 where MG is an enclosed mass of the Milky Way in a given RG, the size decrease caused by the galactic tides takes place mostly while the cluster approaches Rp. The cluster re-expands somewhat by two-body relaxation while approaching Ra ((<>)Baumgardt & Makino (<>)2003), but its size gradually decreases while repeating orbital motions. We find that clusters with 0.4 < rt/rJ < 1 can also shrink moderately as a result of the galactic tides even if it underfills, and clusters initially with rt/rJ < 0.4 (or ℜ< 0.05; i.e., ”isolated” GCs) can gradually move into the ”tidal” regime as they lose mass or expand by stellar evolution or two-body relaxation. Figure (<>)3 shows that GCs with larger ℜ0 are smaller at 13 Gyr for a given M0 and RG,0, as expected. ",
+    "Among various initial GC parameters, rh,0 is the most important parameter in the size evolution caused by two-body relaxation and that resulting from galactic tides (ℜ0 ∝M0−1/3RG −2/3 rh,0 for a flat rotation curve). For this reason, initially small GCs gen-",
+    "Fig. 3.— Ratios of rh values at 13 Gyr and at the beginning from some of our 1,152 Fokker–Planck calculations as a function of rh at the beginning for two di erent RG,0 values (4.6 kpc for the left panel and 46 kpc for the right panel) and four di erent initial mass (log M0/M⊙= 4, 5, 6, and 7). The approximate initial half-mass relaxation times and the initial tidal filling ratios are marked with di erent colors and symbol sizes, respectively. The blue line indicates the location of rh/rh,0 = 1.67, which is the expected expansion ratio mainly by the stellar evolution, and the red lines represents the relation rh/rh,0 ∝r h,−10, which is the expected result when the evolution is dominated by the two-body relaxation. ",
+    "Fig. 4.— Comparison of mass functions (a), radial distributions (b), and size distributions (c) at 13 Gyr (solid lines) and at the beginning (dashed lines) from the best-fit initial parameter set for each SD model. ",
+    "erally expand (by two-body relaxation), while initially large GCs generally shrink (by the galactic tides) as they evolve. The size evolution of intermediate GCs is determined by more than one dynamical e ect, and some GCs can even maintain their initial size over their whole lifetime. "
+  ],
+  "5. SYNTHESIS OF FOKKER–PLANCK CALCULATIONS ": [
+    "As discussed in Section 3, we performed a total of 1152 FP calculations with di erent initial cluster conditions in four-dimensional parameter space, M, rh, Ra, and e. The goal of the present study is to find the initial distribution of these variables that best describe the observed GCs. ",
+    "For the initial MF model, we adopt a Schechter function, ",
+    "(1) ",
+    "and for the initial RD model, we use a softened power-law function, ",
+    "(2) ",
+    "We assume that the initial MF is independent of initial RG. For the sake of simplicity, we do not parameterize the distribution for e, and adopt the fixed isotropic distributions, i.e., dN(e) ∝e de. Unlike M, the RG of each FP model evolves by oscillating between Rp and Ra, and thus the model RD at 13 Gyr constructed from our population synthesis may su er from significant random ",
+    "Fig. 5.— Comparison of size distributions at 13 Gyr (solid lines) and at the beginning (dashed lines) from SD Model 1. The upper panels are for initially small GCs (trh,0 < 0.5 Gyr or ℜ0 < 0.05), and the lower panels are for initially large GCs (trh,0 > 0.5 Gyr or ℜ0 > 0.05). ",
+    "noise. To reduce this noise, we build a model RD by summing the probability distributions between Rp and Ra that are given by the orbital information at 13 Gyr, and we call this a phase-mixed RD. Hereafter, RDs in this paper refer to the phase-mixed RD. ",
+    "For initial SDs, we use six distribution models (see Table (<>)1). Models 1, 2, and 3 represent a Gaussian distribution of rh, ˆh (mean density within rh), and ℜ, respectively, implying that the initial GCs have the preferred initial rh, ˆh, and ℜ, with dispersions. The initial rh of Model 1 does not correlate with the initial M or RG, while Models 2 and 3 have initial correlations of and rh ∝M1/3RG 2/3ℜ. In Models 4, 5, and 6, the initial rh is determined by powers of initial M and/or RG. Note that the power of Model 6 (rh ∝M0.615) corresponds to that of the mass– size relation derived from the Faber–Jackson relation for early-type galaxies ((<>)Faber et al. (<>)1989; (<>)Ha¸segan et. (<>)2005; (<>)Gieles et al. (<>)2010). ",
+    "Once the calculations of the 1152 FP models are done, the aforementioned sets of initial MF, RD, and SD models are used to search for the best-fit parameters in five to seven dimensional space, depending on the SD models (Models 1–6). For this, we synthesize our 1152 FP calculations with appropriate weights to produce a given initial MF, RD, and SD, and find a set of parameters that best fit the present-day MF, RD, and SD for each of the six SD models. When finding the best set of parameters for each SD model, we minimize the sum of ˜2 values from all of the L, RG, and Rh histograms, which are constructed by using eight bins between 104 and 105.8 L⊙ for L, nine bins between 100 and 101.6 kpc for RG, and nine bins between 10−0.6 and 101.2 pc for Rh, all equally spaced on a logarithmic scale. Recall that we use dynamical (theoretical) properties M and rh for set-",
+    "ting the initial distributions, while observable quantities such as L and Rh are used for comparing the models and observations. "
+  ],
+  "6. BEST-FIT INITIAL DISTRIBUTION OF THE GALACTIC GLOBULAR CLUSTER SYSTEM ": [
+    "The best-fit parameter sets that minimize the ˜2 values between observations and our calculations are presented in Table (<>)2 for the six SD models. We examine the characteristics of our best initial MFs, RDs and SDs in turn. "
+  ],
+  "6.1. Initial Mass Function ": [
+    "The best-fit values for all six SD models are quite low, ranging between 0.01 and 0.07. The best-fit log Ms/M⊙ values for all six SD models are similar to each other, having values between 5.8 and 5.9. Note that Schechter functions with such small values are similar to log-normal functions, while those of & 2 are closer to power-law functions. Thus, our small values suggest that log-normal functions better describe the initial MF of the Galactic GC system than power-law functions (see Figure (<>)4a), and this result is consistent with the result of Paper I. One way to explain the log-normal-like initial MF is expulsion of the remnant gas due to star formation in the pre-gas-expulsion cluster, which can quickly alter a power-law MF into a log-normal-like MF ((<>)Parmentier & Gilmore (<>)2007). Another possible mechanism resulting in a rapid change in the initial MF is the collisions of clusters with dense clouds or other clusters during the early phase of the galaxy ((<>)Elmegreen (<>)2010). "
+  ],
+  "6.2. Initial Radial Distribution ": [
+    "Initial RDs from the best-fit parameter sets for all six SD models have similar values (4.0–4.5) but a rather wide range of Rs values (0.3–3.6 kpc), and this is consistent with the result of Paper I ( = 4.2 and Rs = 2.9 kpc). ",
+    "Figure (<>)4b shows that most of the GCs that disrupt before 13 Gyr are located in the bulge regime (RG,0 < 3 kpc), and most of the GCs formed in the bulge do not survive until now. We find that only 0.1–8.4 % of the total GC mass initially inside 3 kpc remains in GCs at 13 Gyr, and the total stellar mass that escaped from the GCs inside 3 kpc during the last 13 Gyr amounts to 5 ×107–3 ×108 M⊙, depending on the SD model. "
+  ],
+  "6.3. Initial Size Distribution ": [
+    "The initial SDs from our best-fit parameter sets are of larger dispersion than the present-day SDs for all six SD models (see Figure (<>)4c). The initial SDs evolve into the narrower present-day SDs by two main e ects: (1) expansion of GCs with small rh,0, which normally have small trh,0 and/or small ℜ0, due to two-body relaxation, and (2) shrinkage (evaporation) of large rh,0 GCs, which normally have large trh,0 and/or large ℜ0, due to the Galactic tides. Figure (<>)5 shows that the SDs of initially small GCs (upper panels) indeed shift to the larger rh region and those of initially large GCs (lower panels) shift to the smaller rh region after 13 Gyr. ",
+    "Three p-values (significance levels) for ˜2 tests of LFs, RDs, and SDs are acceptably high, except for Model 3, which has relatively small ˜2 p-values for RDs and SDs (see Table (<>)2). However, the high p-values from the ˜2 ",
+    "Fig. 6.— L (top left), R (top middle), and Rh (top right) histograms at 13 Gyr (thick solid lines) for SD Model 1 with the best-fit parameter set. Also shown together in the upper panels are the corresponding initial distributions (dashed lines) and the observed distributions (thin solid lines). The lower panels show the correlations between Rh and RG (bottom left), Rh and L (bottom middle), and L and RG (bottom right) relationships for the corresponding best-fit models in the upper panels (asterisks) and from the observations (open circles). ",
+    "Fig. 7.— Same as Figure 5, but for SD Model 2. ",
+    "Fig. 8.— Initial SDs of the GCs that survive until 13 Gyr in our best-fit SD models, Models 1 (thick solid line) and 2 (dashed line). Also shown is the currently observed SD (thin solid line with a shaded area). The overall size of the GCs were larger at birth than now even when only the surviving GCs are considered. ",
+    "tests do not necessarily guarantee that the models with the best-fit parameters restore the observed correlation between L, RG, and Rh as well. Thus, we implement Student’s t-tests to see if our models with the best-fit parameters agree with the observed RG dependence of SDs (the Rh–RG correlation), the L dependence of SDs (the Rh–L correlation), and RG dependence of LFs (the L–RG correlation). For the Rh–RG correlation, we calculate ˜2 for the di erence of log Rh and ˙log Rh between the model and the observation as follows: ",
+    "(3) ",
+    "where subscripts o and m stand for the observation and the model, respectively, subscript j represents the equal number RG bins, and . . . denotes the averaged values. The same calculation is applied to Rh–L and L–RG correlation as well. We find that Models 3–6 have t-test p-values that are too small (. 1%) for at least one of the Rh–RG, Rh–L, and L–RG correlation. For this reason, we reject Models 3–6 as being a plausible initial SD candidate. Hereafter, we call SD models 1 and 2 “the final best-fit SD models”. ",
+    "Figures (<>)6 and (<>)7 show our two remaining best-fit SD models, a Gaussian distribution of rh (model 1; rh,c = 6.4 pc, ˙rh = 2.7 pc) and a Gaussian distribution of ˆh (model 2; ˆh,c = 690 M⊙pc−3 , ˙ˆh = 4.6 M⊙pc−3). Note that rh,0 values are not correlated with the RG,0 in either model. This implies that the rh,0 of GCs probably does not depend on the strength of the galactic tides. Therefore, we interpret the observed, present-day Rh–RG correlation (see Figure (<>)1b) as an outcome of a preferential ",
+    "disruption of the larger GCs at smaller RG due to the Galactic tides. "
+  ],
+  "7. DISCUSSION ": [
+    "The typical Rh,0 value from our final best-fit SD models (Models 1 and 2) is ∼4.6 pc (rh,0 ∼7 pc), and this is 1.8 times larger than that of the present-day GCs (∼2.5 pc). This result is rather di erent from a recent argument by (<>)Baumgardt et al. ((<>)2010) that most GCs were born compact with rh,0 < 1 pc. Our result implies that GCs initially have a rather wide SD, the typical value of which is similar to that of YMCs in parsec scale, and have evolved to have a narrower SD with a smaller mean value. ",
+    "We also find that GCs formation favors a ”tidal” environment over an ”isolated” environment. The number of tidal GCs (ℜ0 > 0.05) at 0 Gyr from our final best-fit SD models is approximately five times larger than that of isolated GCs (ℜ0 < 0.05). The ratio of tidal to isolated GCs, however, drastically decreases as GCs evolve because tidal GCs are more easily disrupted, and this ratio becomes ∼0.2 at 13 Gyr. ",
+    "Figure (<>)8 shows the initial SDs of the GCs that survive until 13 Gyr in Models 1 and 2. We find that these initial SDs are broader (˙(Rh) = 2.1 and 2.5 pc, respectively) and centered at higher values (Rh = 4.1 and 4.0 pc) than the currently observed SD (˙(Rh) = 1.2 pc, Rh = 2.5 pc). Thus, the overall size of the GCs were larger at birth than now by a factor of ∼2 even when only the surviving GCs are considered. ",
+    "The initial total masses in GCs (Mt,0) of the final best-fit SD models are 2.8×108 M⊙ (Model 1) and 5.3×108 M⊙ (Model 2), and the masses that have left the GCs during the lifetime of the Galaxy (Mt) are 2.5×108 M⊙ (Model 1) and 5.0×108 M⊙ (Model 2). These give Mt/Mt,0 values of 0.89 and 0.94 for Models 1 and 2, respectively. Our Mt values are several times larger than previous estimates made by (<>)Baumgardt ((<>)1998, 4.0–9.5×107 M⊙), (<>)Vesperini ((<>)1998, 5.5×107 M⊙), and Paper I (1.5–1.8×108 M⊙). Our larger Mt values are due to the facts that (1) we consider virtually all disruption mechanisms in the calculations for the dynamical evolution of individual GCs, and (2) we use more a flexible initial rh distribution, which can have a relatively larger fraction of GCs with a large rh (larger GCs are more vulnerable to the galactic tide). Note that Mt will be larger if one considers the clusters that have been disrupted in the process of remnant gas expulsion. ",
+    "We note that contrary to the finding in the present paper, detailed dynamical modeling of individual clusters shows that at least some of the clusters must have started with a very small size. For example, Monte Carlo calculations by (<>)Heggie & Giersz ((<>)2008) and (<>)Giersz & Heggie ((<>)2009, 2011) find 0.58 pc, 0.40 pc, and 1.9 pc as best-fit initial rh values for the observed current states of M4, NGC 6397, and 47 Tuc, respectively. These values are several times smaller than the typical initial rh found for the Galactic GC system from our calculations, ∼7 pc. However, we also note that the Monte Carlo models used for these three clusters all assume circular cluster orbits while M4 and NGC 6397 have moderate to high orbit eccentricities (0.82 and 0.34, respectively). We have performed several FP calculations for these two clusters and ",
+    "find that consideration of appropriate eccentric orbits can increase the best-fit initial rh by a factor of 3–5. "
+  ],
+  "8. SUMMARY ": [
+    "We have calculated the dynamical evolution of Galactic GCs using the most advanced and realistic FP model, and searched a wide parameter space for the best-fitting initial SD, MF, and RD models that evolve into the present-day distribution. We found the initial MF of the Galactic GC system is similar to the log-normal function rather than the power-law function, and the RD of the GC system undergoes significant evolution inside RG = 3 kpc through the strong Galactic tides. We also found that the initial SD of the GC system evolves to narrower present-day SDs through two e ects: shrinkage of large GCs by the galactic tides and expansion of small GCs by two-body relaxation. The typical initial projected half-mass radius from the final best-fit model, ∼4.6 pc, is 1.8 times larger than that of the present-day value, ∼2.5 pc. The ratio of ”tidal” GCs to ”isolated” GCs is ∼5 at 0 Gyr and decreases down to ∼0.2 at 13 Gyr. ",
+    "Since tidal GCs are found to be dominant in the beginning, one might expect the initial size of the GCs to be correlated with the Jacobi radius, i.e., to be a function of the galactocentric radius. However, our final best-fit SD ",
+    "models (Models 1 and 2) do not seem connected to the galactocentric radius. This implies that the GC formation process favors a certain size and density, regardless of the tidal environment. Such a RG-independent initial SD evolves into a present-day SD, which shows a tight rh–RG correlation through evaporation and two-body relaxation. ",
+    "We thank Holger Baumgardt and Mark Gieles for helpful discussion. This work was supported by Basic Science Research Program (No. 2011-0027247) through the National Research Foundation (NRF) grant funded by the Ministry of Education, Science and Technology (MEST) of Korea. This work was partially supported by WCU program through NRF funded by MEST of Korea (No. R31-10016). J.S. deeply appreciates Koji Takahashi for the help with his FP models. S.J.Y. acknowledges support by the NRF of Korea to the Center for Galaxy Evolution Research and by the Korea Astronomy and Space Science Institute Research Fund 2011 and 2012. S.J.Y. thanks Daniel Fabricant, Charles Alcock, Jay Strader, Nelson Caldwell, Dong-Woo Kim, and Jae-Sub Hong for their hospitality during his stay at Harvard-Smithsonian Center for Astrophysics as a Visiting Professor in 2011– 2012. "
+  ]
+}

jsons_folder/2013ApJ...764...29B.json

@@ -0,0 +1,119 @@
+{
+  "DID THE INFANT R136 AND NGC 3603 CLUSTERS UNDERGO RESIDUAL GAS EXPULSION? ": [
+    "Sambaran Banerjee and Pavel Kroupa ",
+    "(<http://arxiv.org/abs/1301.3491v1>)arXiv:1301.3491v1  [astro-ph.GA]  15 Jan 2013 ",
+    "Argelander-Institut f¨ur Astronomie, Auf dem H¨ugel 71, D-53121, Bonn, Germany; ",
+    "sambaran@astro.uni-bonn.de, pavel@astro.uni-bonn.de ",
+    "In press with The Astrophysical Journal "
+  ],
+  "ABSTRACT ": [
+    "Based on kinematic data observed for very young, massive clusters that appear to be in dynamical equilibrium, it has recently been argued that such young systems set examples where the early residual gas-expulsion did not happen or had no dynamical e ect. The intriguing scenario of a star cluster forming through a single starburst has thereby been challenged. Choosing the case of the R136 cluster of the Large Magellanic Cloud, the most cited one in this context, we perform direct N-body computations that mimic the early evolution of this cluster including the gas-removal phase (on a thermal timescale). Our calculations show that under plausible initial conditions as consistent from observational data, a large fraction (>60%) of a gas-expelled, expanding R136-like cluster is bound to regain dynamical equilibrium by its current age. Therefore, the recent measurements of velocity dispersion in the inner regions of R136, that indicate that the cluster is in dynamical equilibrium, are consistent with an earlier substantial gas expulsion of R136 followed by a rapid re-virialization (in ˇ 1 Myr). Additionally, we find that the less massive Galactic NGC 3603 Young Cluster (NYC), with a substantially longer re-virialization time, is likely to be found deviated from dynamical equilibrium at its present age (ˇ 1 Myr). The recently obtained stellar proper motions in the central part of the NYC indeed suggest this and are consistent with the computed models. This work significantly extends previous models of the Orion Nebula Cluster which already demonstrated that the re-virialization time of young post-gas-expulsion clusters decreases with increasing pre-expulsion density. "
+  ],
+  "keywords": [
+    "Keywords: stars: kinematics and dynamics—open clusters and associations: individual(R136,NGC3603) —galaxies: star clusters: general—galaxies: individual(LMC) "
+  ],
+  "1. INTRODUCTION ": [
+    "The question of how a young star cluster is formed has been debated for decades. According to the classical scenario, a cluster forms essentially through a single star-burst event. The individual proto-stellar cores within the parent or proto-cluster gas cloud approach their hydrogen-burning main-sequences (MS) to form an infant star cluster which still remains embedded within the residual gas that did not collapse to stars. This residual gas receives kinetic energy and radiation-pressure from the radiation of the massive MS and pre-main-sequence (PMS) stars until it gets unbound from the system and then escapes. This gas-removal process can be expected to be very rapid — typically faster than or similar to the dynamical crossing time of the embedded cluster (Lada & Lada 2003). The remaining gas-free cluster must expand due to the corresponding dilution of gravitational potential well. For the hypothetical case of instantaneous gas removal, the resultant cluster should get unbound if the total mass lost as gas is equal to or more than the mass remaining in the stars (i.e., star formation eÿciency (SFE) ǫ 50%), as is true for any gravitationally self-bound system. For slower gas removal, the survivability of the gas-deprived cluster as a bound system, for ǫ 50%, increases (Kroupa 2008). Two-body relaxation, which evolves the cluster towards a higher central concentration until the beginning of gas-expulsion, also enhances survival. ",
+    "The above scenario, applicable to the formation of Galactic and extra-galactic young star clusters, has been first depicted by, e.g., Hills (1980), Elmegreen (1983) and Mathieu (1983) either analytically or by small N",
+    "direct N-body studies (Lada et al. 1984). These milestone works have later been elaborated by Kroupa et al. (2001), Geyer & Burkert (2001) and Baumgardt & Kroupa (2007) by extensive direct N-body calculations of gas-expelling model infant clusters. Such theoretical studies, along with observations of young embedded systems (Lada 1999; Elmegreen et al. 2000), suggest a minimal star-formation eÿciency of ǫˇ 1/3 for forming a bound, gas-free cluster, applicable to embedded systems initially in dynamical (or virial) equilibrium. An observational evidence of the residual gas expulsion process can be the <2.5 Myr old Orion Nebula Cluster (ONC) whose measured velocity dispersion implies that it must be expanding (Jones & Walker 1988). While the ONC was widely considered to end-up in an unbound OB association (e.g., Zinnecker et al. 1993), the detailed modelling by Kroupa et al. (2001) implies that it is rather destined to become a bound cluster very similar to the Pleiades by 100 Myr. Recent proper motion measurements of the Galactic ˇ 1 Myr old NGC 3603 Young Cluster (NYC) by Rochau et al. (2010) also suggests that its stars might be away from energy-equipartition. Notably, a demonstration of the expansion of clusters younger than a few Myr as they age is collated by Brandner (2008). ",
+    "The key properties of the stellar initial mass function (IMF; Kroupa et al. 2013), in particular, its observed universality is also supported by a monolithic cluster formation scenario that involves competitive gas accretion by the most massive proto-stellar cores. For example, detailed three-dimensional, adaptive-mesh FLASH calculations including radiation feedback by Peters et al. (2010, 2011) well reproduce not only the general form of the uni-",
+    "versal IMF but also the relation between the total mass (in stars) of an embedded cluster and the mass of its most massive stellar member (Weidner & Kroupa 2004). Recently, Liu et al. (2012) find observational signatures of competitive accretion in the proto-cluster G10.6-0.4. ",
+    "Very recently however, questions have been raised against the clustered mode of star formation, preferring instead a hierarchical or continuous star formation (e.g., Bressert et al. 2010; Gutermuth et al. 2011). The latter is inferred from the stellar density distribution in young, star forming regions over a “global” scale. Notably, Pfalzner et al. (2012) showed that unless the density contrast among the individual clusters is very high any such conclusions based on surface density profiles can be highly ambiguous and is useful only when suÿ-ciently deep and complete data are available. Furthermore, from the kinematics of several very young clusters indicating their dynamical equilibrium, in particular that of the R136 cluster in the Large Magellanic Cloud (LMC), it has been argued that they must have avoided any substantial residual gas-expulsion phase (i.e., e ec-tively have had 100% star-formation eÿciency, also see Goodwin 2009 in this context); otherwise they would have been found expanding at such a young age. This has been particularly emphasized very recently by H´enault-Brunet et al. (2012). A key ingredient that might be missing in such arguments is the consideration of the re-virialization of the expanding gas-expelled cluster, i.e., quick formation of a bound system after a fraction of the expanding cluster reverses back on a free-fall timescale. ",
+    "The possible fate of the expanding ONC being a Pleiades-like bound system has been shown by Kroupa et al. (2001) whose models already demonstrate that the re-virialization time decreases with increasing initial cluster density (Fig. 1 of Kroupa et al. 2001). The survivability as a bound cluster after gas-removal has been studied later in detail by, e.g., Baumgardt & Kroupa (2007). In this work, we find it crucial to study this issue again with particular focus on the case of R136. This becomes essential because of the current interpretations of the kinematic data of young, massive clusters such as R136, that seem to contradict the classical picture of monolithic cluster formation and the associated event of residual gas expulsion. We show that under plausible conditions, the re-virialization of an R136-like massive cluster, after the gas-removal, is prompt enough to make it be found in virial equilibrium despite of its young age. The recently obtained low (line-of-sight) velocity dispersion of single O-stars in R136 (H´enault-Brunet et al. 2012) is also found to be consistent with a re-virialized system. We also find that the much lighter NYC, on the other hand, is unlikely to be virialized at its current age of ˇ 1 Myr (Stolte et al. 2004, 2006), as indicated by Rochau et al. (2010). "
+  ],
+  "2. MODEL COMPUTATIONS ": [],
+  "2.1. Gas removal ": [
+    "A thorough modelling of gas-removal from embedded clusters is complicated by the radiation hydrodynamical processes which is extremely complex and involves uncertain physical mechanisms. For simplicity, we therefore mimic the essential dynamical e ects of the gas-expulsion process by applying a diluting, spherically-symmetric ex-",
+    "ternal gravitational potential to a model cluster as in Kroupa et al. (2001). Specifically, we use the potential of the spherically-symmetric, time(t)-varying mass distribution ",
+    "(1) ",
+    "Here, Mg(t) is the total mass in gas which is spatially distributed with the same initial Plummer density distribution (Kroupa 2008; see below) as the stars and starts depleting with timescale τg after a delay of τd. The Plummer radius of the gas distribution is kept time-invariant (Kroupa et al. 2001). Such an analytic approach is partially justified by Geyer & Burkert (2001) who perform comparison computations treating the gas with the SPH method. ",
+    "The exact values of the essential parameters quantifying the gas-expulsion timescale, viz., τg and τd depend on gas-physics. For simplicity, we use an average gas velocity of vg ˇ 10 km s−1 which is the typical sound-speed in an H II (ionized hydrogen) region. This gives ",
+    "where rh(0) is the initial half-mass radius of the stellar cluster/gas. The coupling of stellar radiation with the ionized residual proto-cluster gas over-pressures the latter substantially and can even make it radiation-pressure-dominated (RPD), for massive clusters in the initial phase of the expansion of the gas. During the RPD phase, the gas is driven out at speeds considerably exceeding the sound-speed of the ionized medium (Krumholz & Matzner 2009). Once the expanding gas becomes gas-pressure-dominated (GPD), it then continues to flow out with the sound-speed of an H II region (Hills 1980). Hence, the above τg, from vg ˇ 10 km s−1 , represents its upper limit; it can be shorter depending on the duration of the RPD state (also see Sec. 4). Notably, the initial RPD phase is crucial to launch the gas from very massive systems whose escape speed exceeds the sound-speed in H II gas (Krumholz & Matzner 2009). ",
+    "As for the delay-time, we take the representative value of τd ˇ 0.6 Myr (Kroupa et al. 2001). The correct value of τd is again complicated by radiative gas-physics. An idea of τd can be obtained from the lifetimes of the ultra-compact H II (UCHII) regions which can be upto ˇ 105 yr (0.1 Myr; Churchwell 2002). The very compact pre-gas-expulsion clusters (Sec. 2.2) have sizes (rh(0)) only a factor of ˇ 3 − 4 larger than the typical size of a UCHII region (ˇ 0.1 pc). If one applies a similar Str¨omgren sphere expansion scenario (Churchwell 2002 and references therein) to the compact embedded cluster, the estimated delay-time, τd, before a sphere of radius rh(0) becomes ionized, would also be larger by a similar factor and hence close to the above representative value. Once the gas is ionized, it couples strongly with the radiation from the O/B stars and launched immediately (see above). High-velocity jet outflows from proto-stars (Patel et al. 2005) additionally facilitate the gas removal. "
+  ],
+  "Table 1 ": [
+    "Computed model parameters. The ONC-A/B computations are from Kroupa et al. (2001) and included for comparison. The quoted ˝virs correspond to the re-virialization times of 30% of the initial cluster mass (in stars) after the delay time ˝d. The “BSE” column indicates the presence of stellar evolution. ",
+    "ciently eÿcient to possibly form second-generation stars (W¨unsch et al. 2011). Also, as discussed above, the gas-outflow can initially be supersonic which generates shock-fronts. Although shocked, it is unlikely that star-formation will occur in such an RPD gas. Later, during the GPD outflow, the flow can still be supersonic in the rarer/colder outer parts of the embedded cluster where the average sound-speed might be lower than that typical for H II gas. However, it is not clear whether the cooling in the shocked outer regions would be eÿcient enough to form stars. ",
+    "Admittedly, the above arguments do not include complications such as unusual morphologies of UCHIIs and possibly non-spherical ionization front, among others, and only provide basic estimates of the gas-removal timescales. Observationally, Galactic ˇ 1 Myr old gas-free young clusters such as the ONC and the NYC imply that the embedded phase is τd <1 Myr. The above widely-used gas-expulsion model does realize the essential dynamical e ects on the star cluster. In particular, such simplification has practically no e ect on the remaining cluster after the gas is expelled, e.g., on it’s re-virialization, which is the focus of this work. "
+  ],
+  "2.2. Initial configuration, stellar dynamics and evolution ": [
+    "The initial model embedded stellar clusters are Plummer spheres (Kroupa 2008) which the gas follows as well. This is a reasonable approximation since dense interstellar medium (ISM) filaments appear to have Plummer-like sections (Malinen et al. 2012; also see below). The rh(0) of embedded clusters are substantially smaller than the typical sizes of exposed young clusters as found in the semi-analytic calculations by Marks & Kroupa (2012). These calculations constrain the birth-density of a large number of observed clusters by their observed population of binary stars leading to a remarkable overlap with the densities of star-forming molecular clumps (Fig. 6 in Marks & Kroupa 2012). Our initial clusters thus follow the empirical relation between rh(0) and the embedded cluster mass (only the stars) Mecl(0) by Marks & Kroupa (2012), viz., ",
+    "(2) ",
+    "which is a rather weak dependence. This independently obtained result is in excellent agreement with the observed results from Herschel (Andr´e et al. 2011; Fig. 6.3). The star formation eÿciency is taken to be ǫ= 1/3, i.e., Mg(0) = 2Mecl(0) (see Sec. 4 for a discussion). ",
+    "Notably, Andr´e et al. (2011) and Malinen et al. (2012) ",
+    "refer to the shape and the compactness of ISM filament sections. The star forming spherical/spheroidal proto-clusters form within the ISM filaments and at their intersections (Schneider et al. 2012); a part of the filament that collapses under self-gravity to form an embedded cluster would become spherical/spheroidal. Recent Herschel observations of ridges in molecular clouds and of the associated filaments support this (Hennemann et al. 2012; Schneider et al. 2010; Hill et al. 2011). The compact sizes (ˇ 0.1 pc) of these ISM filaments (Andr´e et al. 2011) then dictate the high compactness of the initial embedded systems. There is, of course, the competing viewpoints whether all the stars form within one cloud (the standard scenario) or the final cluster can be formed hierarchically (see Sec. 1). Currently, the possibility of forming massive stars within the filaments but outside any cluster has also been suggested (e.g., Bressert et al. 2012). So far our computations in this paper are concerned, we adopt the standard scenario and investigate whether the observed kinematics of the young clusters like R136 and NYC (to start with) can be reasonably explained within such a context. In that case, our chosen initial conditions well reflect the sizes and the shapes of the observed filaments. ",
+    "The IMFs of the clusters are chosen to be canonical (Kroupa 2001) with the most massive star following the mmax −Mecl(0) relation of Weidner & Kroupa (2004). To that end an “optimized sampling” algorithm (Kroupa et al. 2013) is used instead of randomly sampling the IMF. All the computed models are fully mass-segregated using the method of Baumgardt et al. (2008), as observed in young clusters (Littlefair et al. 2003; Chen et al. 2007; Portegies Zwart et al. 2010). For computational ease, we take all the members of the initial cluster to be single stars. Since the O-stars in young clusters are typically found in binaries (Sana & Evans 2011; Sana et al. 2012), our initial stellar population, admittedly, does not completely represent that of a young cluster. However, binarity is unlikely to substantially influence the expansion of a cluster during gas-expulsion and re-collapse and virialization thereafter, which is the focus of this work. Although the initial segregated state is detected for several Galactic young clusters, it is yet to be confirmed for young clusters in general (see Portegies Zwart et al. 2010 for a discussion). Therefore, for comparison purposes, we compute identical models without any initial mass-segregation. We find that mass-segregation does not influence the conclusions (Sec. 3.1). ",
+    "The dynamical evolution of the model clusters are computed using the state-of-the-art NBODY6 code (Aarseth 2003). In addition to integrating the particle orbits using the highly accurate fourth-order Hermite scheme and ",
+    "dealing with the diverging gravitational forces in close encounters through regularizations, NBODY6 also employs the well-tested analytical stellar and binary evolution recipes of Hurley et al. (2000, 2002), viz., the SSE and the BSE schemes. NBODY6 also includes the time-variable Plummer gas potential as described above. ",
+    "The initial masses of the computed model embedded clusters are chosen to be Mecl(0) ˇ 105M⊙ which is an upper mass limit of R136 (Crowther et al. 2010). Their Plummer radii are chosen from Eqn. (2). We also consider an embedded cluster of Mecl(0) = 1.3 × 104M⊙ to mimic the gas-removal from a Galactic NYC-like cluster (Stolte et al. 2004, 2006; Rochau et al. 2010). The metal-licities of the former models are taken to be Z= 0.5Z⊙, as appropriate for the LMC, and that for the NYC model it is Z= Z⊙. Our computed models are summarized in Table 1, where those in Kroupa et al. (2001) are also added for comparison. For both of our computed models, the τgs are similar to the initial crossing times τcr(0); τg ˇ 2 and 1 time(s) τcr(0) for the R136 and the NYC model respectively. Since τg <τcr(0) for the Kroupa et al. (2001) models, our gas-expulsions are less “prompt” owing to higher initial concentrations. The MCLUSTER program (K¨upper et al. 2011) is used to set the initial configurations. As it is diÿcult to model the weak tidal field of the LMC, the clusters are evolved in absence of any galactic potential. "
+  ],
+  "3. RESULTS ": [],
+  "3.1. Gas-expulsion from an R136-like cluster ": [
+    "Fig. 1 shows the evolution of the Lagrange radii, Rf , in our computed R136 model clusters (Table 1) with τd = 0.6 (top panel) and 0 (bottom) Myr. The τd = 0 case is computed as a test case only to compare with that of the more realistic delay τd = 0.6 Myr. From the beginning of the gas-expulsion, the cluster expands rapidly with timescale τg. At least 60% of the cluster, by mass, then collapses back to a steady size, i.e., regains virial-ization in τvir ˇ 1 Myr (beyond τd). The inner regions virialize even earlier. Given that the bulk of the R136 cluster is ˇ 3 Myr old (Andersen et al. 2009), it ought to be currently in dynamical equilibrium as a whole even if it has undergone a substantial gas-expulsion phase in the past. We discuss this further in Sec. 4. The gas-free cluster is expanded by a factor of ˇ 3 in terms of its half-mass radius, rh, after reverting to dynamical equilibrium. Notably, the re-virialization happened in spite of the wind mass-loss from the massive stars that was operative during these computations. Comparison of the two panels in Fig. 1 makes it apparent that a finite τd (with τg unchanged) keeps the form of the cluster’s expansion and re-virialization identical — it merely applies a time-translation to the overall evolution. ",
+    "Fig. 2 shows the Rf -evolution for identical R136 models but without initial mass-segregation. It demonstrates that the cluster evolutions are throughout identical to the previous cases with primordial mass segregation, in particular during the expanding phase and the re-collapse to virialization. In other words, primordial mass-segregation has no e ect on the re-virialization of a cluster. ",
+    "Very recently, H´enault-Brunet et al. (2012) measured radial/line-of-sight velocities (RV) of single O-stars ",
+    "Figure 1. The evolution of the Lagrange radii, Rf , for stellar cluster mass fractions f (escaping stars inclusive) for the computed R136 models with ˝d = 0.6 Myr (top) and ˝d = 0 (bottom). In each panel, the curves, from bottom to top, correspond to f = 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.625, 0.7 and 0.9 respectively. The thick solid line is therefore the half mass radius of the cluster. ",
+    "within 1 pc . R. 5 pc projected distance from R136’s center 1 with data obtained from the “VLT-FLAMES Tarantula Survey” (VFTS; Evans et al. 2011). They conclude that the RV dispersion, Vr, of the single O-stars within this region is 4 km s−1 . Vr . 5 km s−1 , conforming with R136 being in virial equilibrium. ",
+    "Fig. 3 shows the evolution of Vr corresponding to the R136 computations in Fig. 1 for 1 pc <R<5 pc projection from the density center and stellar masses M>16M⊙, i.e., those of the O-stars. It demonstrates that, after re-virialization, the O-stars indeed have Vr remarkably similar to that measured by H´enault-Brunet et al. (2012). The initial large fluctuations in Vr in the upper panel of Fig. 3 (τd = 0.6 Myr) is due to the initial mass-segregated condition which results in only a few O-stars within 1 pc <R<5 pc initially. The measured RV data is therefore consistent with R136 being through a gas-expulsion phase and then in a re-virialized state now, ",
+    "Figure 2. The evolution of Lagrange radii, Rf , for computed models without any initial mass-segregation but otherwise identical to the R136 models in Fig. 1. The legends are the same as in Fig. 1. ",
+    "unlike claimed by H´enault-Brunet et al. (2012). "
+  ],
+  "3.2. The case of the NGC 3603 Young Cluster ": [
+    "Fig. 4 (top) shows the Lagrangian radii of our computed NYC cluster (Table 1). The mass of NYC (Stolte et al. 2004, 2006; Rochau et al. 2010) is substantially smaller than that of R136, implying a longer free-fall and hence re-virialization time. The model is computed with τd = 0, which is rather unrealistic, to see the e ect of the earliest possible gas removal. Even then the cluster is still expanding in its outer parts and just beginning to fall back in the inner regions (. R0.3) at its very young age of ˇ 1 Myr (Stolte et al. 2004), as can be seen in Fig. 4. In other words, it is practically impossible for NYC to be in dynamical equilibrium at its present age had it undergone a substantial gas-expulsion phase earlier. The computed cluster re-virializes in τvir >2 Myr (<40% of it; c.f. Fig. 4) as opposed to our R136 models (Sec. 3.1) which take ˇ 1 Myr for the same (>60% of them; c.f. Fig. 1, Table 1). ",
+    "From proper motion measurements within the central ˇ 1 pc projection of NYC, Rochau et al. (2010) found no notable di erences among the 1-dimensional velocity dispersions (V1d) of 4 mass (magnitude) bins over 1.7−9M⊙. This indicates that NYC is far from energy equipartition ",
+    "Figure 3. The evolution of the radial velocity (RV) dispersion, Vr , of the O-stars (M > 16M⊙), within the projected distances 1 pc < R < 5 pc from the cluster center, for the computed R136 models. The top and the bottom panels correspond to the computations with ˝d = 0.6 and 0 Myr respectively. ",
+    "as it should be if the system is out of dynamical equilibrium (the converse conclusion that non-equipartition implies non-equilibrium, as used by Rochau et al. 2010, is however not necessarily true). This is explicitly demonstrated in Fig. 4 (bottom), where the initial separation in V1d is practically vanished at t= 1 Myr due to violent relaxation driven by the gas-expulsion. ",
+    "The computed V1d at t= 1 Myr is somewhat less than the measured 2 V1d ˇ 4.5 ± 0.8 km s −1 and the observed system must currently be super-virial, unlike the computed sub-virial state at t= 1 Myr, as the inferred dynamical mass 3 exceeds the photometric mass (Rochau et al. 2010). These can be easily accounted for by a plausible 0.6 <τd <0.8 Myr delay in the gas removal (c.f. Fig. 4) which would then result in agreement with the observed V1d and the super-virial state of NYC. Furthermore, NYC’s mass is uncertain by a factor �� 2 (Rochau et al. 2010). ",
+    "Figure 4. Top: The evolution of the Lagrange radii for the computed NGC 3603 Young Cluster model with ˝d = 0. The legends are the same as in Fig. 1. Bottom: The variation of the 1-dimensional (transverse) velocity dispersion, V1d, within R < 1 pc projection, for 4 mass-bins chosen within the same mass range as in Rochau et al. (2010), for the above model. Note that initially V1d di ers between the mass bins consistent with energy equipartition. This separation of V1d values vanishes as a result of violent relaxation driven by gas-expulsion. Note that the t-axis of the bottom panel is plotted in the logarithmic scale to highlight this. ",
+    "Fig. 5 replots Fig. 4 with a τd ˇ 0.6 Myr delay which, in turn, corresponds to the results of a computation with this delay in gas-expulsion (see Sec. 3.1). This makes the cluster super-virial at its ˇ 1 Myr current age. The corresponding V1d is still somewhat smaller than the observed value but is within 3σlimits. Notably, NYC might, in fact, be somewhat younger (c.f. Fig. 4 of Stolte et al. 2004) and V1d also depends on the exact initial mass and size which are subject to uncertainties. Moreover, NYC’s V1d and age are susceptible to its distance uncertainties. Notably, Cottaar et al. (2012) also find the Westerlund I cluster sub-virial. "
+  ],
+  "4. CONCLUSIONS AND OUTLOOK ": [
+    "The key message from our above computations and analyses is a reminder that an observed dynamical equilibrium state of a very young stellar cluster does not necessarily dictate that the cluster has not undergone a gas-expulsion phase. The non-occurrence of gas-removal ",
+    "Figure 5. Evolutions of the Lagrange radii (top) and 1-dimensional velocity dispersion (bottom) of the same computed NYC models as in Fig. 4 where an initial gas expulsion time-delay of ˝d = 0.6 Myr is applied while plotting. Hence, the plots are essentially the same as in Fig. 4 except that they begin at t = 0.6 Myr and correspond to those from a computation with ˝d = 0.6 Myr (see Sec. 3.1). They show that NYC would be super-virial at its current ˇ 1 Myr age, as observed. ",
+    "has been highlighted, particularly by putting forward the case of R136, by recent authors, e.g., H´enault-Brunet et al. (2012). This is why we focus on R136 in this study. We also demonstrate, choosing the example of NGC 3606, that lower-mass clusters take much longer to re-virialize (c.f. Table 1) so that it is as well appropriate to find non-equilibrium signatures in them. This has been shown to be true also for the ONC by Kroupa et al. (2001) (c.f. Table 1). The above must be remembered while interpreting the kinematics of any young cluster. ",
+    "Notably, R136 exhibits an age-spread; its massive stellar population can be younger, viz., . 2 Myr old (Massey & Hunter 1998). If the gas-expulsion is assumed to commence only after the formation of the most massive stars, a currently equilibrium state is still plausible given the τvir ˇ 1 Myr re-virialization time. It should, however, be remembered that age-estimates of massive stars are highly uncertain. There isn’t any concrete evidence that invalidates the scenario involving the formation of R136’s entire stellar population at once ˇ 3 Myr (Andersen et al. 2009) ago and the most massive single stars forming ",
+    "later via dynamically induced binary mergers (Banerjee et al. 2012b) or appearing younger due to mass transfer in close O-star binaries. ",
+    "Although the present study does not cover a general range of the parameters τd, τg, rh(0) and ǫ, these computations can still provide a fair idea of the e ects of the variation of these parameters over their plausible ranges. By applying time-shifts to the point of expansion of the clusters in Figs. 1 & 2, it can be concluded that τd . 2 Myr required to find R136 virialized at t= 3 Myr, since τvir ˇ 1 Myr. Although an unambiguous τd requires radiation hydrodynamic calculations, this upper limit is perhaps too large a value for τd in the light of the discussions in Sec. 2.1. The currently chosen values of τgs are upper limits based on the typical H II-gas sound-speed of ˇ 10 km s−1 (Sec. 2.1). As discussed in Sec. 2.1, the outflow speed can initially be significantly higher than the sound-speed, driven mainly by radiation pressure, resulting in smaller τgs than those assumed. This would make the gas-expulsion more prompt, keeping τvir practically unchanged. ",
+    "As for the SFE, the chosen ǫˇ 1/3 is in the range of the observationally estimated SFEs by Lada & Lada (2003) (see their Table 2). Recent theoretical modelling of star formation with high-resolution resistive magnetohydrodynamics (Machida & Matsumoto 2012) also suggest ǫˇ 33%. In any case, a larger ǫwould also result in a bound system and shorter τvir as the re-virializing mass would be larger. As for rh(0)s, their increasing values would increase τvirs, so our conclusions depend on our adopted initial high compactness. However, this condition is plausible since such compact star-forming environments (a factor of ˇ 10 smaller than typical young clusters, i.e., rh(0) ˇ 0.3 − 0.4 pc) are inferred observationally by Andr´e et al. (2011) and as well from the semi-analytic study by Marks & Kroupa (2012) independently (the re-virialization time depends on the above typical compactness but, of course, not on the specific Eqn. (2)). In other words, plausible variations of the model parameters are unlikely to alter our above primary conclusions since none imply a substantial lengthening of τd, τg or τvir. ",
+    "An immediate improvement over the present study would be to introduce an appropriate binary population as in Banerjee et al. (2012a,b). In the light of the present and upcoming observations of Galactic and extragalactic young clusters, an important pending task is to systematically and quantitatively study the e ect of gas-expulsion over their entire mass-range with varying parameters such as τd, τg, rh(0) and ǫincluding realistic stellar populations. Such a model-bank would be extremely valuable to interpret the ever-enriching kinematic data of young stellar clusters. ",
+    "We thank the anonymous referee for useful and guiding comments which helped in improving the manuscript. We are thankful to Jan Pflamm-Altenburg of the Argelander-Institut f¨ur Astronomie, Bonn, Germany and Carsten Weidner of the Instituto de Astrof´ısica de Ca-narias, La Laguna, Spain for motivating discussions. ",
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+}

jsons_folder/2013ApJ...764...35M.json

@@ -0,0 +1,77 @@
+{
+  "HALO-TO-HALO SIMILARITY AND SCATTER IN THE VELOCITY DISTRIBUTION OF DARK MATTER ": [
+    "Yao-Yuan Mao, Louis E. Strigari, Risa H. Wechsler, Hao-Yi Wu 1 , Oliver Hahn ",
+    "(<http://arxiv.org/abs/1210.2721v2>)arXiv:1210.2721v2  [astro-ph.CO]  12 Dec 2012 ",
+    "Kavli Institute for Particle Astrophysics and Cosmology & Physics Department, Stanford University, Stanford, CA 94305 and SLAC National Accelerator Laboratory, Menlo Park, CA, 94025 ",
+    "Draft version October 21, 2018 "
+  ],
+  "ABSTRACT ": [
+    "We examine the velocity distribution function (VDF) in dark matter halos from Milky Way to cluster mass scales. We identify an empirical model for the VDF with a wider peak and a steeper tail than a Maxwell–Boltzmann distribution, and discuss physical explanations. We quantify sources of scatter in the VDF of cosmological halos and their implication for direct detection of dark matter. Given modern simulations and observations, we find that the most significant uncertainty in the VDF of the Milky Way arises from the unknown radial position of the solar system relative to the dark matter halo scale radius. ",
+    "Subject headings: dark matter — galaxy: halo ",
+    "1. INTRODUCTION ",
+    "Dark matter is the dominant component of matter in the Universe, and the key to the formation of large-scale and galactic structures. Modern cosmological observations suggest that dark matter is composed of a yet-unidentified elementary particle (e.g. (<>)Feng (<>)2010). However, direct evidence for dark matter particles has proved elusive. Experiments that search for Weakly Interacting Massive Particles (WIMPs), one of the most plausible particle dark matter candidates, seek to identify the scattering of a WIMP with a nucleus in an underground detector ((<>)Bernabei et al. (<>)2008; (<>)CDMS II Collaboration et al. (<>)2010; (<>)Aalseth et al. (<>)2011; (<>)Angloher et al. (<>)2012; (<>)Aprile et al. (<>)2011). Constraining, and eventually measuring, the WIMP mass and cross section requires a precise understanding of the dark matter spatial and velocity distribution at the Earth’s location in the Milky Way ((<>)Strigari & Trotta (<>)2009; (<>)McCabe (<>)2010; (<>)Reed et al. (<>)2011; (<>)Green (<>)2012). ",
+    "Dark matter is distributed in halos extending beyond the visible components of galaxies; many statistical properties including the formation and structure of these halos have been well characterized by simulations. Despite the diversity in the merger and accretion histories of dark matter halos of di erent masses, cosmological simulations have long suggested near universality in the density profiles of halos ((<>)Navarro et al. (<>)1996, (<>)1997). There have been several attempts to connect this universality in the density profile to the dark matter Velocity Distribution Function (VDF) ((<>)Hansen et al. (<>)2006; (<>)Kuhlen et al. (<>)2010; (<>)Navarro et al. (<>)2010). However, there is no well-established model or description for the VDF that has been rigorously tested with cosmological simulations. ",
+    "Both the implications for direct detection and the quest for a theoretical understanding of the phase-space distribution in dark matter halos motivate a study of the VDF. Under specific, and perhaps too stringent, assumptions, including isolation, equilibrium, spherical symmetry, and isotropy, the VDF may be determined uniquely from the density profile. For example, with all assump-",
+    "tions named above and a known density profile, the ergodic distribution function can be calculated using Eddington’s formula ((<>)Eddington (<>)1916). Although useful as an analytic framework, these assumptions are unlikely to strictly hold for halos formed via hierarchical merging. ",
+    "In absence of an understanding from first principles, a practical approach to study the VDF involves appealing directly to dark matter halos with a wide range of physical properties in cosmological simulations. Quantifying the VDF directly from cosmological simulations would provide a better empirically-motivated framework to predict signals in direct detection experiments. Furthermore, with a parametrized VDF, it becomes more tractable to study the relations between the VDF and other physical quantities of the halos, such as mass, density profile, shape, and formation history. ",
+    "In this study, we use a suite of dark matter halos from cosmological simulations to study the VDFs at di er-ent radii of these halos. We identify a similarity in VDFs among a wide range of halos with di erent masses, concentrations, and other physical quantities, that depends primarily on r/rs, the radius at which it is measured divided by the scale radius of the density profile. We further notice that neither standard Maxwell– Boltzmann models ((<>)Lewin & Smith (<>)1996) nor models that have been previously proposed to describe collision-less structures ((<>)Hansen et al. (<>)2006; (<>)Kuhlen et al. (<>)2010; (<>)Navarro et al. (<>)2010) are able to provide an adequate description of cosmological VDFs. Instead, we describe the distribution of the norm of velocity (in the Galactic rest frame) more accurately with an empirical model: "
+  ],
+  "(1) ": [
+    "where the normalization constant A is chosen such that the integral 4ˇ R 0vesc v2f(v)dv equals the number of particles in the region of interest. Note that in this parameterization the VDF approaches an exponential distribution instead of a Gaussian distribution at the low-velocity end. With this model, we quantify the scatter in the VDF from a variety of sources, including halo-to-halo scatter, scatter from finite particle sampling, and ",
+    "scatter from the uncertain position of the Earth within a given halo. We further identify the largest uncertainties that currently exist in our understanding of the VDF at the location of the Earth in our Galaxy, and quantify their relevance for inferences from direct detection experiments. "
+  ],
+  "2. UNIVERSAL VELOCITY DISTRIBUTION IN SIMULATIONS ": [
+    "To identify the relevant physical quantities which affect the VDF and to quantify scatter in the distributions among di erent halos in cosmological simulations, we must examine a large number of halos across a wide range of mass. We also need high resolution to reduce sampling error and distinguish di erences in VDFs for di erent parameters. ",
+    "In this study, we use halos from the Rhapsody and Bolshoi simulations; state-of-the-art dark-matter-only simulations with high mass resolution. Rhapsody consists of re-simulations of 96 massive cluster-size halos with Mvir = 1014.8±0.05M⊙h−1 . The particle mass is 1.3 × 108M⊙h−1 , resulting in ˘ 5 × 106 particles in each halo. This simulation set currently comprises the largest number of halos simulated with this many particles in a narrow mass bin (Fig. 1 of (<>)Wu et al. (<>)2012). Bolshoi is a full cosmological simulation, with similar mass resolution, 1.3 × 108M⊙h−1 . For detailed descriptions of the Rhapsody and Bolshoi simulations, refer to (<>)Wu et al. ((<>)2012) and (<>)Klypin et al. ((<>)2011) respectively. ",
+    "We use the phase-space halo finder Rock-star ((<>)Behroozi et al. (<>)2011) to identify host halos at z = 0. The masses and radii of the halos are defined by the spherical overdensity of virialization, M(< rvir) virvirˆc,= 43ˇ r3 where vir = 94 and ˆc is the critical density. We examine the VDFs at a range of radii. A VDF at radius r uses all particles within a spherical shell centered at the halo center with the inner and outer radii of 10±0.05r, so that the ratio of the shell width to the radius is fixed. In each shell, we assign the escape velocity (vesc) as the spherically-averaged vesc of all particles in the shell. We have verified that vesc determined from this method is consistent with the same quantity deduced from the best-fitting spherically-averaged smooth density profile. ",
+    "We fit each halo with an NFW density profile, ",
+    "(2) ",
+    "where rs is the scale radius at which the log–log slope is −2. The fit uses maximum-likelihood estimation based on particles within rvir. The halo concentration is defined as c = rvir/rs. ",
+    "Fig. (<>)1 shows the VDF at di erent values of r/rs. The value of r/rs a ects the shape of VDF dramatically. The peak of the distribution is a strong function of r/rs. If instead the velocity is normalized by the circular velocity at each radius rather than the escape velocity, this trend will be slightly weakened but still significant. This trend in r/rs is not surprising because the VDF heavily depends on the gravitational potential. If the density profiles of simulated halos can be described by the NFW profile, which is a function of r/rs only (up to a normalization constant), the VDF should mostly depend on ",
+    "Figure 1. Solid colored lines show the stacked velocity distribution for 96 halos in Rhapsody, at di erent values of r/rs: (from left to right) 0.15 (blue), 0.3 (red), 0.6 (green), 1.2 (magenta). Bands show the 68% halo-to-halo scatter in those VDFs. Dashed and dotted colored lines indicate the same values of r/rs in Bolshoi with halos of Mvir ˘ 1012 and 1013 M⊙h−1 respectively. The VDFs of low-mass halos are cut at the head and tail due to limited particle number, and their scatter is not shown. The SHM (v0 = 220 km/s and vesc = 544 km/s) is shown for comparison (black). ",
+    "r/rs until the isolated NFW potential breaks down at large radius. ",
+    "The above trend is robust for halo masses down to ˘ 1012 M⊙, as shown by the Bolshoi simulation in Fig. (<>)1. The scatter of the VDFs in the low-mass halos considered is somewhat larger due to resolution. However, when the high-mass halos are downsampled to have the same particle number, the spreads in the stacked VDF are comparable to the low-mass halos. We further investigated the impact of a variety of parameters characterizing the halo on the shape of the VDF, and found that for a fixed value of r/rs, the halo-to-halo scatter in the VDFs is not significantly reduced when binning on concentration, shape, or formation history. A detailed discussion on this halo-to-halo scatter is in Section (<>)4. "
+  ],
+  "3. MODELS OF THE VELOCITY DISTRIBUTION FUNCTION ": [
+    "The dark matter velocity distribution in halos is set by a sequence of mergers and accretion. The process of violent relaxation ((<>)Lynden-Bell (<>)1967) may be responsible for the resulting near-equilibrium distributions observed in dark matter halos and in galaxies. These near-equilibrium distributions explain why existing VDF models (see e.g. (<>)Frandsen et al. (<>)2012), including the Standard Halo Model (SHM), King model, the double power-law model, and the Tsallis model, are all variants of the Maxwell–Boltzmann distribution. Recent studies have shown that the widely-used SHM, which is a Maxwell–Boltzmann distribution with a cut-o put in by hand, is inconsistent with the VDF found in a handful of individual simulations ((<>)Sti & Widrow (<>)2003; (<>)Vogelsberger et al. (<>)2009; (<>)Kuhlen et al. (<>)2010; (<>)Purcell et al. (<>)2012) and in the study of rotation curve data ((<>)Bhattacharjee et al. (<>)2012). The double power-law model was proposed to suppress the tail of the distribution, by raising the SHM to the power of a parameter k ((<>)Lisanti et al. (<>)2011). The Tsallis model replaces the Gaussian in Maxwell–Boltzmann distribution with a q-Gaussian, which approaches to a Gaussian ",
+    "Figure 2. The VDF for one representative dark matter halo in Rhapsody (histogram), along with the best fits using Eq. ((<>)1) with (v0/vesc, p) = (0.13, 0.78) (black, ˜2 = 0.59), SHM (blue, 9.67), the double power-law model (cyan, 9.47), the Tsallis model (green, 1.99), and the analytic VDFs from Eddington’s formula with isotropic assumption (red dash, 8.48), Osipkov–Merritt (magenta dash, 6.41), and constant = 1/2 (yellow dash, 11.8). The y-axis is in log scale in the main figure and linear in the inset. ",
+    "as q ! 1 ((<>)Vergados et al. (<>)2008). It was argued that the Tsallis model provides better fit to simulations with baryons ((<>)Ling et al. (<>)2010), although this conclusion may be a ected by the relatively low resolution of the simulations. ",
+    "In contrast, our empirical model, Eq. ((<>)1), is not based on a Gaussian distribution but rather on an exponential distribution. It also has a power-law cut-o in (binding) energy. Fig. (<>)2 shows the VDF in a simulated halo, along with the best fit from Eq. ((<>)1) and the best fits from other conventional models. All the best-fit parameters are obtained from the maximum-likelihood estimation in the range of (0, vesc). The fits using Eq. ((<>)1) are statistically better than other models or the analytic VDFs, especially around the peak and the tail. We performed the likelihood-ratio test and found that our model fits significantly better for all Rhapsody halos than the SHM or the double power-law model at all four radii shown in Fig. (<>)1. ",
+    "In Fig. (<>)2 we also compare three analytic VDFs. For the isotropic model shown, the analytic VDF is given by Eddington’s formula, which gives a one-to-one correspondence between the density profile and the VDF. For anisotropic systems, one must also model the anisotropy parameter, defined as ), where ˙2 is the variance in each velocity component. There simple and representative anisotropic models: constant 2)/(2˙ r numerically ((<>)Binney & Tremaine (<>)2008). For all three 2˙+° 21 − (˙=  is currently no analytic VDF whose anisotropy profile matches that measured in simulations, so we choose three anisotropy (with = 0 and 1/2) and the Osipkov– Merritt model ((<>)Osipkov (<>)1979; (<>)Merritt (<>)1985). The phase-space distributions of these models can be determined cases, we adopt the NFW profile as in Eq. ((<>)2), with the best-fit scale radius. For the Osipkov–Merritt model, we use the best-fit anisotropy radius. It is shown in Fig. (<>)2 and also suggested by the chi-square test for the models considered that the analytic VDFs do not describe the simulated VDF well. ",
+    "Our VDF model, Eq. ((<>)1), consists of two terms: the exponential term and the cut-o term. The origin of the ",
+    "the exponential term can be explained by the anisotropy in velocity space. Fig. (<>)3 shows the distributions, the dispersion, and the kurtosis of the velocity vectors along the three axes of the spherical coordinate. Kurtosis is a measure of the peakedness of a distribution, defined as (with zero kurtosis), there will be a larger di erence be-o term, v2 exp(−v/v0). (For a formal discussion on this to 0.6, the norms of those random vectors will follow a distribution which resembles our model without the cut-topic, see e.g. (<>)Bjornson et al. (<>)2009.) This suggests that if one can find a coordinate system where the distributions of the velocity components are all distributed normally tween the dispersion along the three axes in this new coordinate system than in the spherical coordinate. ",
+    "The (vesc 2 − v2)p term in our VDF model introduces a cut-o at the escape velocity. It further suppresses the VDF tail more than the exponential term alone does. Despite that this cut-o term has the form of a power-law in (binding) energy, the best-fit values of the parameter p does not necessarily reflect the “asymptotic” power-law index k, defined as k = limE→0(d ln f/d ln E), where f(E) is the (binding) energy distribution function. The relation between k and the outer density slope has been studied in the literature ((<>)Evans & An (<>)2006; (<>)Lisanti et al. (<>)2011). However, because d ln f/d ln E deviates from its asymptotic value k rapidly as E deviates from zero, the asymptotic power-law index k could be very di er-ent from the best-fit power-law index for the VDF tail (e.g. v > 0.9vesc). Furthermore, the shape of the VDF power-law tail could be set by recently-accreted subha-los that have not been fully phase-mixed ((<>)Kuhlen et al. (<>)2012), and hence has no simple relation with the density profile. In high-resolution simulated dark matter halos, particles stripped o of a still-surviving subhalo are seen to significantly impact the tail of the VDF. A larger sample of simulations at higher resolution than we consider in the current analysis will be needed to further test this hypothesis. "
+  ],
+  "4. HALO-TO-HALO SCATTER IN VELOCITY DISTRIBUTIONS ": [
+    " =0 ",
+    "Figure 3. Left: The histograms of vr and v° of the same halo shown in Fig. (<>)2, with the best-fit normal distributions (red lines). Right: The velocity dispersion ˙v/vesc and the kurtosis, along the three axes: vr (red), v (green), and v° (blue). Both the dispersion and the kurtosis are measured in spherical shells at di erent r/rs and averaged over all halos in Rhapsody, with the error bars showing the 68% halo-to-halo scatter. The dashed lines are only to guide the eyes. ",
+    "We demonstrated above that there exists a similarity in VDFs for a wide range of simulated dark matter halos; Eq. ((<>)1) provides a good description of this similarity. We now quantify explicitly how the VDF depends on r/rs and the associated halo-to-halo scatter. Fig. (<>)4 shows a scatter plot of the velocity distributions for di erent halos, characterized by the two parameters of Eq. ((<>)1), for di erent r/rs. The regions of (v0, p) parameter space for di erent r/rs are distinct, which implies that r/rs is the most relevant quantity in determining the shape of the velocity distribution. We also found that the parameter v0/vesc has a linear relationship in log(r/rs), as shown in the inset of Fig. (<>)4. ",
+    "We note that there is significant degeneracy between the two parameters (v0, p). This degeneracy comes from the fact that a larger value of p is needed to steepen the tail of the VDFs which have larger values of v0. In our fitting process we left both parameters free because there is no simple relation between v0 and p for all radii. Because of this degeneracy, there also exists a linear relation between p and log(r/rs). However, since the best-fit p is not well-constrained due to the low number of particles in the tail of the VDF, the relation between p and log(r/rs) is not well determined either. ",
+    "In Fig. (<>)4 we see there exists halo-to-halo scatter even for a fixed r/rs. This intrinsic scatter could arise from the statistics of the samples or some other physical quantities. Fig. (<>)5 shows the best-fit v0/vesc at di erent radii as a function of concentration, halo shape (c/a), formation time (z1/2), and local density slope (−d ln ˆ/d ln r) respectively, as defined in (<>)Wu et al. ((<>)2012). We found that at a given r/rs (a fixed color), v0/vesc does not have a ",
+    "Figure 4. Distribution of the best-fit parameters, v0 and p of Eq. ((<>)1), which describes the simulated VDFs. Each dot represents one halo from the Rhapsody simulation at a certain r/rs: (from left to right) 0.15 (blue), 0.3 (red), 0.6 (green), 1.2 (magenta). The cross symbols show the best-fit parameters to isotropic analytic VDFs obtained from Eddington’s formula at corresponding radii. The typical uncertainty of the fit is shown in the lower left corner. The lower right inset shows the linear relation between v0/vesc and log(r/rs). ",
+    "Figure 5. Scatter plots of the best-fit parameter v0/vesc with concentration, halo shape (c/a), formation time (z1/2), and local density slope on the x-axes respectively. Each dot represents one halo from the Rhapsody simulation at a certain r/rs: (from bottom to top in each panel) 0.15 (blue), 0.3 (red), 0.6 (green), 1.2 (magenta). For any fixed r/rs, there is no significant correlation between v0/vesc and the aforementioned quantities on the x-axes. See text for details. ",
+    "significant correlation with the physical quantities on the x-axis (except for z1/2 in the two smallest radial bins). This reinforces the main result of this study: the VDF is mostly determined by r/rs (i.e. the gravitational potential). We note that the lower left panel of Fig. (<>)5 shows a weak correlation between z1/2 and v0/vesc; however if the halos with z1/2 < 0.25 are removed, this correlation is no longer statistically significant. Halos with recent accretion tend to have larger deviations from the NFW ",
+    "profile, and this results in a slight overestimate of the best-fit scale radius (fit to an NFW profile). We do not expect the Milky Way has had a recent major merger with z1/2 < 0.25. This indicates that for possible Milky Way host halos, one can exclude these systems with recent major mergers, and there will be no remaining correlation between formation time and v0. ",
+    "For Milky Way size halos, it has been suggested that the VDF has a universal shape depending only on the velocity dispersion and the local density slope ((<>)Hansen et al. (<>)2006). This is related to our finding in a way that the magnitude of the velocity dispersion is roughly proportional to vesc and the local density slope for an NFW profile is given by a monotonic function of r/rs, ",
+    "(3) ",
+    "However, our study suggests that r/rs is a more fundamental quantity than the local density slope in determining the shape of the VDF. Fig. (<>)5 illustrates that v0/vesc does not grow with the local density slope when one only looks at a fixed r/rs (points with the same color), but it does grow with r/rs when the local density slope is fixed. "
+  ],
+  "5. IMPLICATIONS FOR DIRECT DETECTION RATES ": [
+    "Given the known dependence on r/rs, we can now examine the impact on direct dark matter detection experiments. The di erential event rate per unit detector mass of dark matter interactions in direct detection experiments is ",
+    "(4) ",
+    "where Q is the recoil energy, ˆ0 is the local dark matter density, ˙0 is the WIMP-nucleus cross section at zero momentum transfer, mdm is the WIMP mass, µ is the WIMP-nucleus reduced mass, A is the atomic number of the nucleus, |F(Q)|2 is the nuclear form factor, vmin = (QmN /2µ2)1/2 for an elastic collision, f is the VDF in the Galactic rest frame, and ve is the velocity of Earth in the Galactic rest frame ((<>)Lewin & Smith (<>)1996). ",
+    "With Eq. ((<>)4) one can calculate the event rate given VDF and vmin. We calculated this rate for each halo using the best-fit exponential model of the VDF, for different vmin and di erent r/rs. The results are shown in Fig. (<>)6, where we divided the rate by the rate calculated from the SHM with conventional parameters v0 = 220 km/s and vesc = 544 km/s for comparison. ",
+    "The rate as a function of vmin behaves very di erently for di erent r/rs as shown in Fig. (<>)6. For low values of r/rs, the change in detection rates between experiments can be much larger than the predictions of the SHM, e.g., the ratio between the rates of CoGeNT ((<>)Aalseth et al. (<>)2011) to DAMA-I ((<>)Bernabei et al. (<>)2008) is three times larger in our model than in the SHM. This clearly motivates e orts to better constrain the scale radius of the Milky Way: comparing the scatter coming from measurements of VDF with the intrinsic physical di erences among halos, the uncertainty on r/rs appears to be the dominant contribution to the uncertainty in event rates, ",
+    "Figure 6. Ratio of detection rate predicted by Eq. ((<>)1) with parameters obtained from Rhapsody, for di erent r/rs: (from bottom to top) 0.15 (blue), 0.3 (red), 0.6 (green), to that of the SHM with conventional parameters. Vertical dotted lines show vmin for di erent detectors: (from left to right) CoGeNT, DAMA-Na, XENON, CDMS, DAMA-I, expressed in (nucleus, threshold energy) ((<>)Aalseth et al. (<>)2011; (<>)Bernabei et al. (<>)2008; (<>)Aprile et al. (<>)2011; (<>)CDMS II Collaboration et al. (<>)2010), assuming a WIMP mass of 10 GeV. The error bars show the 68% halo-to-halo scatter, and those with wider caps include the scatter in di erent directions. The x-axis is slightly o set for clarity. The lines which connect the data points are only to guide the eyes. ",
+    "especially for smaller vmin. "
+  ],
+  "6. DISCUSSION AND CONCLUSION ": [
+    "When deducing the direct detection event rate from cosmological simulations, the primary sources of uncertainty arise from: (i) finite particle sampling of the VDF, (ii) intrinsic scatter from physical processes that a ect the VDF during the halo formation process (i.e. the halo-to-halo scatter), (iii) the quality of the fit and the validity of a smooth model, (iv) the observational constraint on r/rs for the Milky Way, (v) the variation of the VDFs in various directions at a fixed radius, and (vi) the impact of baryons. ",
+    "An important outcome of our analysis is that at present the scatter from (iv) is significantly larger than the corresponding scatter due to each of (i), (ii), and (iii), combined, by more than two orders of magnitude. This is particularly important given that the observational constraint on the scale radius suggests the concentration c = rvir/rs is 10−20 ((<>)Klypin et al. (<>)2002; (<>)Deason et al. (<>)2012), which corresponds to r⊙/rs ˘ 0.15 − 0.6 ((<>)Xue et al. (<>)2008; (<>)Gnedin et al. (<>)2010; (<>)Brown et al. (<>)2010; (<>)Busha et al. (<>)2011). Thus, although the distance from the Earth to the Galactic center is well known ((<>)Ghez et al. (<>)2008; (<>)Gillessen et al. (<>)2009), we find that the largest current theoretical uncertainty on the VDF is the uncertainty in r/rs. ",
+    "Our determination of the VDF represents an average over a spherical shell. In reality, spherical asymmetry and substructures will a ect the VDF and result in additional scatter along di erent directions. In the Rhapsody simulations, if we divide the spherical shell into several regions while maintaining enough particles (of the order 1000) in each analysis region, we find that this directional scatter is comparable to the halo-to-halo scatter, and that the combined scatter will be 10 − 40% larger than only the halo-to-halo scatter, as illustrated in Fig. (<>)6. Similar scatter is also seen in the Aquar-",
+    "ius Milky Way simulations ((<>)Vogelsberger et al. (<>)2009). This directional scatter will grow at larger radii because it is a consequence of substructures, tidal e ects, and streams ((<>)Helmi et al. (<>)2003; (<>)Vogelsberger & White (<>)2011; (<>)Maciejewski et al. (<>)2011; (<>)Purcell et al. (<>)2012). At present, we have no robust way to relate this scatter to direct observables, and in practice this directional scatter may be the most important uncertainty in determining the direct detection rates once other sources have been minimized. ",
+    "We have not yet investigated the impact of baryons; we expect that adiabatic contraction of dark matter halos would raise the velocity but preserve the shape of the VDF, so that our model will serve as a useful tool for these studies in the future. Baryonic e ects in isolated halos have been studied in the context of dark matter detection ((<>)Bruch et al. (<>)2009; (<>)Ling et al. (<>)2010); however, simulating a statistical sample of halos similar to what we consider here, with both suÿcient resolution and realistic baryonic physics is not yet tractable. ",
+    "The results presented here highlight the need to significantly improve the determination of the Milky Way scale radius. Although the concentration is now only weakly constrained with present data ((<>)Busha et al. (<>)2011; (<>)Deason et al. (<>)2012), improvements will be forthcoming with spectroscopy and astrometry from large scale surveys ((<>)An et al. (<>)2012). Analysis along these lines will usher in a new era of complementarity between astronomical surveys and particle dark matter constraints deduced from terrestrial experiments. ",
+    "This work was supported by the U.S. Department of Energy under contract number DE-AC02-76SF00515 and by a KIPAC Enterprise Grant. Mao is supported by a Weiland Family Stanford Graduate Fellowship. We thank the Aspen Center for Physics and NSF Grant 1066293 for hospitality during the workshop “A Theoretical and Experimental Vision for Direct and Indirect Dark Matter Detection”. We thank Anatoly Klypin and Joel Primack for providing access to the Bolshoi simulations, and Peter Behroozi for the halo catalogs for both simulations. We thank Tom Abel, Peter Behroozi, Michael Busha, Eduardo Rozo, and Li-Cheng Tsai for useful discussion. The Rhapsody simulations were run using computational resources at SLAC; we gratefully acknowledge the support of Stuart Marshall, Amedeo Per-azzo, and the SLAC computational team. "
+  ]
+}

jsons_folder/2013ApJ...767...46C.json

@@ -0,0 +1,159 @@
+{
+  "PROTOTYPING NON-EQUILIBRIUM VISCOUS-TIMESCALE ACCRETION THEORY USING LMC X-3 ": [
+    "Hal J. Cambier ",
+    "arXiv:1303.6218v1  [astro-ph.HE]  25 Mar 2013 ",
+    "Physics Department, University of California, Santa Cruz, CA 95064 ",
+    "and ",
+    "David M. Smith ",
+    "Physics Department, University of California, Santa Cruz, CA 95064, USA and ",
+    "Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064, USA ",
+    "Draft version April 21, 2022 "
+  ],
+  "ABSTRACT ": [
+    "Explaining variability observed in the accretion flows of black hole X-ray binary systems remains challenging, especially concerning timescales less than, or comparable to, the viscous timescale but much larger than the inner orbital period despite decades of research identifying numerous relevant physical mechanisms. We take a simplified but broad approach to study several mechanisms likely relevant to patterns of variability observed in the persistently high-soft Roche-lobe overflow system LMC X-3. Based on simple estimates and upper bounds, we find that physics beyond varying disk/corona bifurcation at the disk edge, Compton-heated winds, modulation of total supply rate via irradiation of the companion, and the likely extent of the partial hydrogen ionization instability is needed to explain the degree, and especially the pattern, of variability in LMC X-3 largely due to viscous dampening. We then show how evaporation–condensation may resolve or compound the problem given the uncertainties associated with this complex mechanism and our current implementation. We briefly mention our plans to resolve the question, refine and extend our model, and alternatives we have not yet explored. "
+  ],
+  "1. INTRODUCTION ": [
+    "The X-ray spectrum of black hole X-ray binaries (BHXRBs) often shows variability in intensity and hardness on timescales of order the viscous timescale, but much larger than the innermost orbital period, including the well-known “q”-diagram hysteresis patterns traced by transient BHXRBs ((<>)Fender et al. (<>)1999; (<>)Homan & (<>)Belloni (<>)2005; (<>)Done et al. (<>)2007, and see fig.(<>)1). The properties of such variability may also evolve over multiple viscous-timescale cycles. The high-soft (but sub-Eddington) and quiescent intensity-hardness limits are understood as manifestations of the thin-disk ((<>)Shakura (<>)& Sunyaev (<>)1973) and radiatively-inefficient advection-dominated accretion flow (ADAF; (<>)Narayan & Yi (<>)1995a) accretion limits while states between are typically understood as some evolving combination of disk and ADAF flows ((<>)Chakrabarti & Titarchuk (<>)1995; (<>)Esin et al. (<>)1997; (<>)Nandi et al. (<>)2012). Theoretical work has begun in this regime, but still cannot fully explain observations, especially regarding viscous timescales where detailed simulations require prohibitively many time steps and steady-state assumptions lose validity. This motivates us to develop theory in more detail starting with a system like LMC X-3, whose behavior is more constrained than that of the transients, but still exhibits substantial variability that is quantitatively challenging to explain. ",
+    "In the current paradigm, transient BHXRBs are those systems where the outer disk reaches temperatures low enough to trigger the partial hydrogen ionization instability (PHII) in which accretion proceeds via cycles as viscosity alternately concentrates mass into rings and diffuses it inward (see (<>)Cannizzo (<>)1998, and (<>)Lasota (<>)2001 for a review). The part of the cycle where viscosity concentrates mass leads to the quiescent phase where any emis-",
+    "sion is presumably powered by some fraction of the flow that escapes the viscosity trap. Eventually, density increases enough to raise disk temperature above the transition point in viscosity, and the sudden jump in accretion rate leads to a rise in luminosity (often several orders of magnitude) while still in the hard state, followed by a softening of the spectrum at this same, peak luminosity (the vertical and horizontal shifts by the dashed line in fig.(<>)1). Jet emission is seen to shut off as the system enters the extreme high-soft state ((<>)Fender et al. (<>)1999). Afterward, the system typically makes partial transitions in hardness (with small, erratic shifts in luminosity) on sub-viscous timescales and associated with intermittent jet emission on top of a secular decline in luminosity. Eventually the system transitions completely back to the hard state and then finishes fading back into quiescence. ",
+    "There are a handful of persistent BHXRBs and black-hole-candidate X-ray binaries that do not execute such extreme quiescence-flaring cycles, and consistent with the transient paradigm they appear to avoid the PHII through an appropriate combination of disk size, luminosity (for disk irradiation), and mass supply rate ((<>)Co-(<>)riat et al. (<>)2012). Despite the label, these systems may still show significant variability and a variety of behaviors. Cygnus X-1 appears to slide between canonical high-soft and low-hard states with some scatter but no clear hysteresis ((<>)Smith et al. (<>)2002, hereafter SHS02). The black hole candidates GRS 1758–258 and 1E 1740.7–2942 exhibit transient-like hysteresis but seldom reach the soft or quiescent limits (SHS02). LMC X-3 is typically bright in soft X-rays, but shows some hysteresis that circulates in the opposite direction to transients (see fig.(<>)1), and does occasionally transition completely to the hard state ((<>)Wilms et al. (<>)2001; (<>)Smale & Boyd (<>)2012). ",
+    "Accounting for irradiation of the outer disk, LMC X-3 ",
+    "Fig. 1.— Shaded points show a typical spectral evolution cycle of LMC X-3 (first episode in fig.(<>)5) with darker points corresponding to earlier observations, showing that it winds around in the opposite sense of typical transients’ cycles shown schematically in the gray, dashed “q” or “turtle-head”. ",
+    "accretes at rates high enough to usually avoid the ionization instability completely ((<>)Coriat et al. (<>)2012), though the outer disk likely becomes susceptible for the deeper drops in disk luminosity, and almost certainly for rare, complete state transitions. Such high accretion rates are explained via Roche-lobe overflow (RLO); optical measurements of the companion’s spectral type that take disk irradiation into account indicate B5IV ((<>)Soria et al. (<>)2001) or B5V ((<>)Val-Baker et al. (<>)2007) spectral type. Such a star will fill the Roche lobe for a 1.7 day orbit around a black hole with mass equal to the recent 9.5M lower bound ((<>)Val-Baker et al. (<>)2007). Furthermore, (<>)Soria et al. ((<>)2001) have argued that feeding the observed X-ray luminosities via winds would lead to column densities far higher than measured. Although its distance precludes direct measurement or exclusion of radio jets, the jet quenching observed in transient BHXRBs as they approach the high-soft state also suggests that LMC X-3 does not usually possess strong jets ((<>)Fender et al. (<>)1998). Thus, if LMC X-3 shares similar variability mechanisms with transients, while being far less prone to the ionization instability and jet outflows, then LMC X-3 provides a more controlled setting to study such mechanisms. Below we list the major mechanisms we have considered so far in modeling LMC X-3, also summarized in fig.(<>)2. ",
+    "For RLO systems like LMC X-3, hard X-rays from the inner accretion disk can lead to supply-rate modulation (SRM) from the companion by inflating the companion’s atmosphere to increase the density of gas at the L1 Lagrange point, as well as the area and pressure behind the nozzle ((<>)Lubow & Shu (<>)1975; (<>)Meyer & Meyer-Hofmeister (<>)1983). We elaborate in §(<>)3.1. ",
+    "As the stream of gas from the companion dissipates energy and spirals onto the circularization radius, it may encounter the edge of the viscously spreading disk and ",
+    "from this point the flow can undergo disk corona bifurcation (DCB) as some fraction can efficiently shock, cool, and join the disk while some fraction may stream past the thin disk edge and maintain its virial temperature ((<>)Hessman (<>)1999; (<>)Armitage & Livio (<>)1998). ",
+    "Warping of the outer disk, whether driven by irradiation ((<>)Pringle (<>)1992; (<>)Ogilvie & Dubus (<>)2001; (<>)Foulkes et al. (<>)2010) or a lift force ((<>)Montgomery & Martin (<>)2010) can affect the accretion flow by changing the density profile that the disk presents to the RLO stream (§(<>)3.2), and by varying how the companion is exposed to or shadowed from inner disk X-rays. For LMC X-3 specifically, (<>)Ogilvie (<>)& Dubus ((<>)2001) and (<>)Foulkes et al. ((<>)2010) predict that the system is potentially unstable to irradiation-driven warping. Because the dominant long-term effects of warping are through bifurcation, and because we will lump them together as a boundary condition in our simulations, we combine discussion of them into §(<>)3.2. ",
+    "X-rays from the inner disk can Compton heat gas in the disk atmosphere and any corona at large radii above the local virial temperature thus driving a Compton-heated wind (CHW), discussed in §(<>)3.3, which is not only important for removing gas, but for removing hot corona that might otherwise help evaporate the disk or condense further inward (item (EC) below). As noted, for large enough disks and insufficient irradiation, a finite strip in the outer disk becomes susceptible to the PHII. For now, we do not treat it in any detail, but discuss the likely extent and manner of its effects in LMC X-3 in §(<>)3.4. ",
+    "If the disk and corona are coupled thermally, then the disk and corona may exchange mass through evapora-tion and condensation (EC). (<>)Mayer & Pringle (((<>)2007), hereafter MP07) provide a thorough introduction and numerical treatment, and (<>)Liu et al. ((<>)Liu et al., hereafter LTMHM07) and (<>)Meyer-Hofmeister et al. ((<>)2009) discuss more applications and provide the steady-state prescription for our modified method. Through EC, extant disks will tend to preserve the soft state down to lower luminosities via Compton-cooling-driven condensation, providing a natural explanation of why BHXRBs return to the hard state at lower luminosity and thus show hysteresis ((<>)Meyer-Hofmeister et al. (<>)2009 focus on this aspect). We discuss other interesting effects possible in §(<>)3.5. ",
+    "We will restrict our focus to an alpha-viscosity prescription for the disk. For the present work describing long-timescale variability over accretion rates typical to LMC X-3 where uncertainties regarding conventional mechanisms still loom large, we consider this perfectly adequate, but acknowledge the possibility of more intrinsic variability mechanisms (§(<>)5). ",
+    "In §(<>)2 we review key features of LMC X-3’s accretion behavior, summarize how we infer the innermost disk and corona/ADAF accretion rates from the X-ray data (additional details are provided in the Appendix), and critically examine the qualitatively simple bifurcation-only model in (<>)Smith et al. (?, hereafter SDS07). The latter motivates §(<>)3, in which we furnish additional detail on the mechanisms as listed above, including estimated constraints on their effects and their current level of implementation in our modeling. In §(<>)4.1 we argue that a model including mechanisms besides EC cannot explain the data, but does best when given an unreasonably small disk radius and very large variations in corona-disk ratio at this boundary. We then show in §(<>)4.2 how EC may ef-",
+    "Fig. 2.— A cartoon of the primary mechanisms considered for driving long timescale changes observed in inner disk and corona accretion rates. These are: supply-rate modulation (SRM, §(<>)3.1) from the companion, disk-corona bifurcation (DCB, §(<>)3.2) at the disk’s edge, where disk warping may affect SRM and DCB, the partial hydrogen ionization instability (PHII, §(<>)3.4), Compton-heated winds (CHW, §(<>)3.3) at large radii, and evaporation and condensation (EC, §(<>)3.5) exchanging mass between disk and corona. ",
+    "fectively recreate such seemingly ad-hoc conditions, but how it may also imply behavior inconsistent with observations, including an extremely easily triggered “sympathetic” mode where the innermost disk and corona accretion rates rise and fall simultaneously. We briefly review the results and caveats of the current model, and state our current plans to resolve the question in §(<>)5. "
+  ],
+  "2. LMC X-3 AS PROTOTYPE ": [
+    "Besides simplifying initial modeling as discussed above, LMC X-3 offers additional practical advantages. The Rossi X-ray Timing Explorer (RXTE) monitored LMC X-3 for over 16 years, and at least five of those include observations each about a kilosecond long taken roughly twice a week, thus providing a long, uninterrupted history of accretion with sufficient resolution at the timescales we seek to study. Also, the X-ray blackbody component, when present, tracks the Stefan– Boltzmann law fairly well (see fig.(<>)3) indicating that inner disk geometry (i.e. truncation, warping) changes fairly little, and that the corona optical depth, τc, is small, simplifying estimates of the inner corona accretion rate, M˙ c. Unless specified otherwise, we will use symbols M˙ d (M˙ c) as shorthand for disk (corona) accretion rates at the inner disk radius, Rid, and reserve the italic-face for general, local accretion rates M˙ d = M˙ d(R, t), M˙ c = M˙ c(R, t). Also, unless otherwise indicated, we will use the following system parameters: black hole mass, Mbh=10M, companion mass M∗=5M, orbital period Psys=1.705d, inclination i=67o and system distance, dsys=48 kpc ((<>)van (<>)der Klis et al. (<>)1985; (<>)Val-Baker et al. (<>)2007), which also imply a circularization radius of Rcirc = 2.7 × 1011cm. ",
+    "We first fit individual RXTE spectra with a disk blackbody and a power law of fixed photon index, Γpli = 2.34 (as in SDS07) with total absorption of fixed column density nH = 3.8 × 1020cm−2 ((<>)Page et al. (<>)2003), using the wabs*simpl*diskbb models in XSPEC ((<>)Arnaud (<>)1996). To systematically identify transitions to the low-hard state we looked for cases where the first fitting gave reduced χ2 > 1.1, and refit these with a wabs*(plaw) model where the power-law index is not frozen. Reassuringly, spectra identified this way were fit better with fewer parameters, and are also typically preceded by obvious declines in the blackbody component (fig.(<>)4). ",
+    "For low τc one can describe the flows qualitatively by taking M˙ d(t) ∼ Tbb 4 and M˙ c(t) proportional to the ratio of power-law to blackbody count fluxes (as in SDS07, though there the disk central temperature was confused ",
+    "Fig. 3.— Fitted blackbody-component fluxes plotted against fit-ted temperature with a pure T 4 curve in faint gray for comparison. ",
+    "with the effective temperature giving M˙ d(t) ∼ Tbb 20/6). We obtain absolute normalization for M˙ d by fixing Rid and comparing observed and predicted fluxes in the high state where agreement should be best, while for M˙ c, we obtain an estimate based on the simple τc and a typical ADAF solution, and check this against a more detailed calculation. We relegate the details to the Appendix to focus on a general description of accretion behavior (fig.(<>)5). ",
+    "From fig.(<>)5, one can see that the M˙ c “turns on” in pulses (referring to the secular month-long features and not the jagged week-long sub-pulses) roughly a viscous timescale apart and slightly shorter in duration, and that these pulses tend to anticipate drops in M˙ d. This trend was already noted in ((<>)Smith et al. (<>)2007) based on inferred qualitative accretion rates, and led the authors to posit a “bifurcation-only” model where a fairly-constant total supply rate (M˙ s) is split far from ",
+    "Fig. 4.— Fitted power-law (top panel) and blackbody (bottom panel) components of LMC X-3’s X-ray flux since 53436.1 MJD. Diamond points in the top panel mark observations categorized as the pure hard state by the criteria in §(<>)2. ",
+    "Fig. 5.— Inferred accretion history since 53436.1 MJD, barring times LMC X-3 was observed in the low-hard state (gray vertical lines) where inferring accretion rates is more ambiguous. Note the vertical labels refer to inner accretion rates here. In the top panel, solid trace shows simple, direct estimate of M˙ c as well as results (points) of a more detailed method and arrowheads indicate points where the detailed method required abnormally high M˙ c (see §(<>)A). Overall, one can see trend for M˙ c to pulse “on” quasi-periodically and anticipate episodic drops in M˙ d ",
+    "the black hole between non-interacting quickly-draining-corona and slowly-draining-disk components. Our normalization estimates for M˙ c(t) suggest that for any given episode there is generally insufficient total mass in a M˙ c(t) pulse to explain the associated M˙ d drop. Even if our overall normalization is off, we still found that scaling M˙c to conserve mass for one episode does not work very well for other episodes. This mass-conservation problem motivated considering mechanisms that can adjust the total supply rate, remove mass, and/or exchange it between disk and corona flows. ",
+    "The secular evolution of the episodes on super-viscous timescales also lends itself to interpretation as multiple mechanisms acting on similar timescales effectively ",
+    "generating “beat-frequency” behaviors. The simple alternative of some mechanism(s) acting on super-viscous timescales coupled to viscous-timescale variability mechanisms lacks good candidates for the former. Nuclear evolution is too slow, we do not expect significant magnetic cycles from a companion with a radiative outer envelope (but keep the possibility in mind regarding other systems), and the inferred mass ratio in LMC X-3 is too high for slowly-growing tidal resonances to be significant ((<>)Frank et al. (<>)2002). Furthermore, based on the observed inclination, the warps would have to reach heights of 30o relative to the orbital plane, and survive the severe drops in M˙ d, to exhibit precession effects if irradiation-driven, which poses difficulties if LMC X-3 is only marginally unstable to irradiation-driven warping as (<>)Ogilvie & Dubus ",
+    "((<>)2001) suggest. ",
+    "The disk component in LMC X-3 tends to fall and recover more rapidly for larger drops than for shallow drops, a trend quantified in SDS07 and recently over an expanded data set in (<>)Smale & Boyd ((<>)2012). This aspect is qualitatively consistent with a bifurcation-only model given sufficient variation in the amplitude and duration of a drop at the outer edge - sensitivity to duration for a single input amplitude can be seen in figures 7&8 of ?. However, using their analytical machinery, with and without crude representation of SRM and outflow effects, we will later show that rough quantitative agreement with observations of LMC X-3 requires inputs that are extremely unlikely without additional physics (§(<>)4.1). An interesting exception to the usual of M˙ c pulses heralding steep M˙ d drops is the small drop in M˙ d at 1100d into fig.(<>)5 not associated with any M˙ c pulse above the typical noise level. ",
+    "Inferring accretion rates in the absence of the disk component introduces additional parameters and uncertainties, but we wish to make a few relevant observations while we work on a more definitive analysis of the hard state. The disk component drops and recovers on timescales of days in transitions into and out of the hard state, and tends to return more quickly than it decays when LMC X-3 is at its “hardest” in our data, circa the 1500d mark in bottom of fig.(<>)5, consistent with the notion of an extant inner disk preserving itself through condensation. Also, the power-law component tends to increase before failed and successful disk restarts, which may physically correspond to the inner edge of a truncated disk moving inward to provide more and hotter seed photons, and/or rapid condensation. "
+  ],
+  "3. VARIABILITY MECHANISMS CONSIDERED ": [
+    "Though the basic physics of companion irradiation and streaming are simple, the dynamics are potentially complicated to initialize and implement in detail, especially if the outer disk warps. However, we can estimate bounds on both mechanisms individually, and because they sit at the edge of the accretion flows, we can lump them into a manual boundary condition for now and still derive meaningful results. Compton-heated winds can be launched a bit further inward, but can be described fairly well by simple analytical functions of radius and X-ray luminosity assuming that the corona is easily replenished, and thus we can quickly obtain upper bounds on CHW losses. ",
+    "Evaporation–condensation can depend sensitively on disk and corona conditions at all radii making it the least amenable to simple estimates, and as noted earlier this same strong dependence on the system’s state can naturally engender hysteresis. EC also allows the disk component to vary more substantially and more rapidly by evaporating disk material interior to the circularization radius, but this evaporated disk material can also condense further inward much faster than inner disk conditions change, potentially to the point that M˙ d rises and falls simultaneously with M˙ c. This “sympathetic” accretion mode can be seen in the more detailed simulations of Mayer and Pringle (their fig.8) and in many cases we simulated (e.g. figures (<>)8,(<>)11,(<>)12), but is effectively absent (or negligible) in our observations of LMC X-3, and thus ",
+    "primarily poses a challenge to our basic EC model. "
+  ],
+  "3.1. SRM Estimates and Remarks ": [
+    "The total supply rate of mass through the L1 nozzle M˙s, will scale with the product of local gas density ρL1, speed at which gas streams through the nozzle (roughly the local sound speed cs), and area of the nozzle An where the latter has width and height roughly equal to the isothermal scale height in the local tidal field, HL1 2 ≈ cs2/Ωorb 2 ((<>)Lubow & Shu (<>)1975). Under X-ray irradiation, each layer of the atmosphere will tend to heat up until it emits the intrinsic stellar flux plus the incident X-ray flux at that altitude. Due to the very steep transition in density at the photosphere, we find most of the X-ray energy is deposited in a thin layer there, which we will take to be infinitesimally thin for now. Thus, the modulation with respect to a given reference state as a function of stellar temperature T, effective incident X-ray luminosity Lx,eff, gravity-darkened stellar luminosity L,eff, and distance between L1 and the photosphere dL1 − dph is given by (e.g. (<>)Meyer & Meyer-Hofmeister (<>)1983): ",
+    "(1) ",
+    "where ",
+    "(2) ",
+    "Short of solving the structure of the stellar envelope in the Roche-lobe potential under time-varying irradiation, we can estimate the extent of SRM by computing the ratio of effective incident-to-intrinsic luminosity. One can make a simple estimate by computing the effective gravity at a point sitting about halfway between the nozzle and the pole of the companion giving L∗,eff/L∗ ≈ 0.68, and also use the inclination of this point relative to the inner disk to get the fraction of X-rays emitted into this latitude, cos βx = 0.28, yielding ",
+    "(3) ",
+    "The companion’s effective stellar luminosity falls within ∼500 –1000L based on the reported bolometric stellar luminosity 800 –1600L ((<>)Soria et al. (<>)2001). More carefully integrating the incident-to-intrinsic ratio over the irradiated face (again, with gravity darkening) agrees closely with this simple estimate as the projected area and fraction of disk flux fall concurrently with (and faster than) the effective gravity toward L1. ",
+    "For irradiation operating alone, choosing the maximum observed luminosity as the reference point in eqn.(<>)1 would permit drops to ≈50% of the observed maximum and only if the X-ray source were turned off completely, but this estimate is still fairly sensitive to companion temperature. Harder and more isotropic X-ray flux from a hot corona may enhance modulation, but for LMC X-3 the maximum observed power-law flux is barely a fifth that ",
+    "of the disk, roughly equal to the projection factor reducing inner-disk flux onto the companion. However, even if much deeper drops are possible, and irradiation-driven warping or some other mechanism were included to prevent the system from settling into a permanent steady high-soft state, the fact that SRM affects the flow at the very boundary means that any changes it introduces will suffer severe viscous dampening (§(<>)4.1). Altogether, this suggests that SRM is significant, but certainly cannot explain the steep M˙ d declines by itself. ",
+    "Furthermore, we consider this simple model’s predictions of the SRM magnitude an upper bound in light of as detailed two-dimensional hydrodynamic simulations of the envelope by (<>)Viallet & Hameury ((<>)2007). They find that irradiation will still drive gas toward the nozzle, but the gas will also have ample time to cool down as it crosses the disk’s shadow. They note that because they do not solve for perpendicular velocity it may exceed their estimates near the nozzle, and we remark that warping of the outer disk might reveal more of the companion’s equator and nozzle and negate the effects of cooling. For our disk/corona simulations, we ignored the delay between irradiation and changes in M˙ s since we estimated the sound-crossing time of the envelope near L1 to be ≈16 hr, far less than the viscous timescale. However, in the case (<>)Viallet & Hameury ((<>)2007) studied they found that some of the gas may take longer, up to several system orbital periods, to reach the nozzle. "
+  ],
+  "3.2. Bifurcation (DCB) and warping estimates ": [
+    "Matter streaming from the L1 point typically collides with the edge of the disk, which usually sits outside the circularization radius due to viscous spreading. Because the disk is relatively cold at this radius, the collision is highly ballistic ((<>)Armitage & Livio (<>)1998). The fraction of matter streaming around the disk instead of immediately joining it can then be estimated simply by finding the altitudes at which the vertical disk and stream (both roughly Gaussian) density profiles match, and supposing ((<>)Hessman (<>)1999) that all the stream within this range immediately joins the disk while matter outside may stream further in. This yields a streaming fraction, ",
+    "(4) ",
+    "where ρd0 and ρs0 are disk and stream densities at z = 0 and the stream scale height Hs will not differ much from HL1—we also refer to Hessman ((<>)1999) for fits to the results of (<>)Lubow & Shu ((<>)1975). ",
+    "Irradiation-driven warping of the outer disk may also affect the streaming fraction. Again, (<>)Ogilvie & Dubus ((<>)2001) and (<>)Foulkes et al. ((<>)2010) suggest warping is possible in LMC X-3, and the latter work specifically finds a disk tilt of 10o likely for LMC X-3. However, both use an isotropic central luminosity, and the latter use an Eddington ratio in luminosity for LMC X-3 comparable to our derived maximum Eddington ratio in M˙ d, so we consider their results an upper bound on warping. ",
+    "We generalize the fs(t) estimate to a stream that scans the edge of a disk tilted by an angle ϑd(t) above the orbital plane. Here, the vertical density centroid follows z0 = Rd sin(ϑd(t) cos(Ωsynt)) where Rd is the radius of ",
+    "the disk edge, and Ωsyn = ΩK (Rd) − Ωsys is the beat frequency between the Keplerian frequency at the disk edge and the system orbital frequency. The finite travel time of the stream should add a roughly constant delay of order the local free-fall time, and for now we ignore this effect. Assuming dϑd/dt  Ωsyn, the altitudes of equal density are ",
+    "(5) ",
+    "We will see that EC can depend very non-linearly on fs(t) at the boundary, but for now we use the orbit-averaged fs(t) as a gauge of plausible DCB strength: ",
+    "(6) ",
+    "We plot fs at the outer boundary for relevant ranges of total supply rate, M˙ tot, and Rd, and for ϑd of 0o and 10o in fig.(<>)6. For an untilted disk, the contours are explained by the drop in disk scale height with radius and much slower drop with accretion rate, while for a tilted disk, the scanning greatly washes out the Rd dependence leaving accretion rate as the dominant factor. Our simple estimate also does not resolve the fate of the surviving stream beyond the edge ((<>)Foulkes et al. (<>)2010 do, but unfortunately not for LMC X-3 in particular), but should bound the fraction of mass diverted. ",
+    "Fig. 6.— Solid and dashed contours show fs for a disk edge tilted by 0o and 10o respectively, for a gas temperature of 16500K, and range of relevant M˙ tot and outer disk radius. Tilting the disk edge generally increases fs, but can also substantially change its dependence on the parameters, with the greatest effects at large Rd and M˙ tot. "
+  ],
+  "3.3. CHW Prescription and Estimates ": [
+    "In Begelman et al. ((<>)1983), the authors considered an optically thin corona subject to Compton heat-ing/cooling (ignoring bremsstrahlung and other heat-ing/cooling mechanisms) and pointed out that accretion X-rays can heat the corona at all radii up to a temperature, TiC, at which inverse-Compton heating and cooling equilibrate. Whether a wind is launched at a given radius then depends mostly on whether this TiC is greater or smaller than the local virial temperature, Tvir, and the authors define a radius RiC by where the temperatures are equal, as well as a critical luminosity, L ≈ L cr Edd/33 at which the gas can be Compton-heated to the virial temperature within the sound-crossing time of the local corona’s scale height. Because the tidal gravitational field falls off faster than the source luminosity, gas flows out most easily at large radii. Though primarily a function of source X-ray luminosity and radius, the shape of the source spectrum can affect the mass-loss rate slightly but we ignore this effect. (<>)Begelman et al. ((<>)1983) computed mass-loss rates for total M˙ w  M˙ tot, while later work addresses dynamics and wind limit cycles ((<>)Shields (<>)et al. (<>)1986). ",
+    "(<>)Woods et al. ((<>)1996) performed simulations to test the previous analytical prescription and amend it slightly— mostly by noting a shift in the location of RiC and providing corrections for low luminosities that do not immediately concern us. We take their fitting formula for wind losses per unit area ",
+    "where the normalization m˙ ch is the ratio of corona pressure to sound speed at RiC, ξ = R/RiC ≈ 2R/Rcirc, and their η = L/Lcr. We then also introduce a factor fxh in η ≡ fxhL/Lcr for how well X-ray luminosity from an inner disk Compton heats the outer corona compared to the point source considered in the references. Although the outflow geometry may permit parts of the outflow to eventually reach low inclinations relative to the inner disk, the chief hurdle is heating the gas when it is sitting deepest in the tidal gravity field. Integrating cos i over the solid angle subtended by the outer corona versus half the disk’s sky gives fxh ≈ 0.025. This factor suppresses CHW considerably, while fxh ≈ 1 implies CHW will have significant effects at the maximum observed luminosities (fig.(<>)7). Furthermore, the fxh for depleting disk flow is likely different and smaller than the corona as the X-rays will have to reach higher inclination, and heat conduction from a transition layer will be competing with advection by the wind. ",
+    "Winds may also be driven by other means, i.e., magneto-centrifugal and line driving, but extensive simulations by (<>)Proga ((<>)2003) with parameters relevant to LMC X-3 indicate that these losses in LMC X-3 will be at most a few percent of the total accretion rate. ",
+    "To gauge CHW self-screening, or screening the companion, consider a wind carrying away 1019g s−1 (total, half this per disk face) at the local sound speed at RiC. If the density did not fall off with radius, the Thomson ",
+    "Fig. 7.— Prescription M˙ w losses per decade in R/RiC with left (right) vertical axis showing Eddington ratio when irradiation ef-ficiency fxh is 0.01 (1). The dashed (dotted) lines show a radial extent of 2R circ and luminosity range for LMC X-3 with (without) reduced fxh. ",
+    "optical depth would be: ",
+    "where a is orbital separation. That this extremely generous upper bound gives marginal absorption indicates the Compton wind will not screen the companion. Instead, CHW and SRM will likely dampen each other’s contribution to M˙ tot-variability seen at inner radii as additional X-ray luminosity simultaneously increases M˙ s supplied by the companion and M˙ w lost to space. However, their interaction could enhance the scaling of M˙ d/M˙ c with Lx at large radii. "
+  ],
+  "3.4. PHII limits and discussion ": [
+    "The PHII is fundamental to the picture of transient BHXRBs and thus to future extension of our work, but the physics itself is not trivial to implement let alone fully understood as the (60 page) review by Lasota ((<>)2001) attests. However, for LMC X-3, the strong, persistent disk emission should generally stabilize the disk within at least 1Rcirc, and we will later show (§(<>)4.1) that even drastic disk variability outside Rcirc/25 is still too viscously dampened to explain observations, though the PHII may still contribute to the magnitude of disk variability, and likely plays an important role during complete state transitions. ",
+    "Taking either the mean or median of M˙ d(t) over our data set as a suitable proxy for supply rate gives M˙ s ≈ 0.1M˙ and while the disk beyond ∼ REdd, circ/3 will be cool enough to experience the PHII absent irradiation at 0.1M˙ Edd (e.g. fig.1 of (<>)Janiuk & Czerny (<>)2011), irradiation can stabilize more and possibly all of the outer disk ((<>)Coriat et al. (<>)2012). Work by (<>)Dubus et al. ((<>)1999) indicates that LMC X-3’s disk would become susceptible to instability just beyond Rcirc at 1018g s−1 for typical values of α (0.1) and an overall accretion to irradiation ",
+    "efficiency factor C, originally fit to light curves of the BHXRB A0620-00 and roughly consistent with simple calculations based on an annulus-to-annulus irradiation geometry (see discussion in (<>)Kim et al. (<>)1999 and comparison at the end of (<>)Dubus et al. (<>)1999 to (<>)King et al. (<>)1997). ",
+    "Because we do not see M˙ d(t) decay on Rcirc-viscous timescales in LMC X-3, it appears that the PHII would also lack a large span of starved inner disk for a heating front to propagate through. After the long, complete state transition of fig.(<>)5 however, the disk recovery is flare-like, consistent with the notion that the PHII can play a significant role in LMC X-3 at low enough disk blackbody flux. "
+  ],
+  "3.5. EC Background and Implementation ": [
+    "As stated in §(<>)1, EC may occur if the disk and corona are thermally coupled—if the disk cannot efficiently radiate away corona heat conducted onto it, nor sufficiently cool the corona via inverse-Compton cooling, then it will experience net heating and evaporate, but otherwise it cools the corona which then condenses onto it. Thus the mass-exchange, or “EC” rate M˙ z, is sensitively dependent on the balance of heating and cooling, and the very different scalings of heating and cooling mechanisms involved make possible a wide variety of behaviors. At present, several EC models incorporate viscous and compressive heating, bremsstrahlung, and inverse-Compton cooling in the accretion flow including LTMHM07 and MP07. ",
+    "Besides separating the thresholds for disk for-mation/destruction normally degenerate under a bremsstrahlung-only density criterion via inverse-Compton cooling, and thus engender hysteresis ((<>)Meyer-(<>)Hofmeister et al. (<>)2009), it is also possible to evaporate the outer disk but condense it back onto the inner disk rapidly enough to drive correlated rises (and falls) of M˙ d with M˙ c (again, fig.8 of MP07 and prominently in the left panel of our fig.(<>)11). It is also possible to preferentially evaporate the middle of a disk to the point of destroying it as visible in (<>)Meyer et al. ((<>)2007), MP07, and several of our simulations. ",
+    "For our initial EC implementation, we do the following. We assume azimuthal symmetry for the accretion flow and divide it into 45 logarithmically-spaced radial zones with a single virtual corona zone associated with each disk zone (i.e. the code is 1.5D). We evolve the disk by solving mass fluxes with the standard viscous-disk equations ((<>)Frank et al. (<>)2002) and a simple donor-cell scheme. Meanwhile we assume that the local corona properties and EC rates match those of the steady-state corona and M˙ z solutions from LTMHM07 for the same local accretion rate and evolve the corona working inward from the outer boundary condition. ",
+    "More specifically, for each disk zone we compute zone-boundary (j ± 1/2) velocities ",
+    "(9) ",
+    "with a viscosity based on a standard thermal equilibrium thin disk solution assuming Kramer’s opacity as in (<>)Frank ",
+    "(<>)et al. ((<>)2002) : ",
+    "The overall disk and corona evolution is then governed by: ",
+    "and ",
+    "(12) ",
+    "where ΔAj is the zone area. The fluxes are also limited so as not to draw mass from a disk zone or the corona flow than is physically available, and the “Rx” emphasizes that we are plugging in the EC rates of LTMHM07 as a function of radius, and local M˙ c and effective disk temperature. If M˙ c and M˙ z are anywhere comparable (of the same order of magnitude) to the viscous disk fluxes, then the computations are performed only once. Otherwise, the latter two steps are relaxed further, and allowed to change Σd but not M˙ d, until their iterations converge within a given tolerance (or exceed an iteration limit). ",
+    "We note that large |M˙ z| can lead to oscillatory behavior with this simple scheme, which can be subdued but not fundamentally fixed with smaller time steps and tolerances. This can be seen in the results of our simulations (fig. (<>)11-(<>)13) as small sudden jumps in M˙ c (and somewhat in M˙ d when EC is strong at small radii), but by changing time step and tolerance we have found that this does not impact the general, longer timescale features that immediately concern us. We also explored small changes in the number of radial zones, obtaining similar results with 40 or more grid points, but our results diverged very quickly for coarser grids. ",
+    "For steady input conditions, we confirm that our method does well reproducing cases considered by LTMHM07 (treating the disk fully lets it spread viscously to larger sizes mildly enhancing condensation). To test our method’s treatment of dynamic behavior, we looked at the same case MP07 studied: a disk spanning 3000 Schwarzschild radii around a 10M black hole with fixed boundary corona fraction fs of 0.1 and mass supply rate of 10−3 times Eddington M˙ Edd. Their time-dependent method evolves the corona self-consistently on its dynamical timescale making it more physically realistic, but this also requires many more time steps. We found that with default parameters and physics our code never evaporates any part of the disk, while MP07 predict the formation of a gap that eats its way inward. However, we also found that if we scaled up the heat-conduction fluxes predicted by LTMHM07 for zones where inverse Compton cooling does and does not set the electron temperature by a factor of three and five respectively (adjusting the formula identifying the zones accordingly) then we do obtain good agreement with MP07 (see fig.(<>)8, and their fig.8). By preferentially scaling up heat fluxes in the zones where inverse-Compton cooling limits electron temperature we obtained more rapid evaporation starting further inward while doing the same for heat fluxes in non-Compton zones led to increased stability. In this particular case, we saw little change when lowering the ",
+    "magnetic-to-gas pressure ratio, βc, a global constant in LTMHM07, from 0.8 to 0.1. ",
+    "Time @ksD ",
+    "Fig. 8.— The larger, darker empty squares and filled diamonds show M˙ d and M˙ c respectively at the inner boundary for a run with modified heat conduction fluxes (see text §(<>)3.5), and the smaller, lighter symbols show the corresponding M˙ d and M˙ c for default parameters -here we plot time logarithmically for more direct comparison with figure 8 of MP07. ",
+    "Both the models of LTMHM07 and MP07 necessarily neglect, or precede, some additional physical effects which may be relevant to our early results so we discuss them here (and summarize in fig.(<>)9) to motivate our more exploratory simulations (§(<>)4.2 and fig.(<>)13). In both models, condensation is a smooth, unresolved flow, but applying the results of (<>)Wang et al. ((<>)2012) shows that the corona is liable to clump at radii greater than roughly 100Rid under typical conditions for LMC X-3. Such clumping potentially increases cooling (thus condensation) efficiency. Both LTMHM07 and MP07 use Spitzer electron conduction throughout the problem domain, and both suspect that the effective thermal conduction coefficient κ may be significantly smaller. Although the degree of tangling in the magnetic fields of the transition zone is far harder to constrain, it is amenable to parameterization. Meanwhile, (<>)Cao ((<>)2011) provides a recent calculation for how much the ordered component of field shifts from predominantly poloidal outside ∼ 10Rid to predominantly toroidal inside. Lastly, neither model includes mechanisms to spontaneously produce corona, a point MP07 especially emphasize. Indeed, since (<>)Galeev et al. ((<>)1979) derived that within a certain radius, the buoyancy of magnetic loops formed within the disk can outpace their reconnection leading to a carpet of buoyant loops, this solar-like corona has often been invoked as a partial or complete source of corona. For LMC X-3, the condition on radius in (<>)Galeev et al. ((<>)1979) gives R  300(M˙ M . It is hard to imagine thisEdd/ ˙ d)RS mechanism alone generating M˙ c pulses that anticipate M˙ d drops lasting substantially longer than the viscous timescale at ∼ 100RS , but it may play an important role by reheating and replenishing the corona, and affecting the local magnetic field geometry. ",
+    "An important caveat in applying the LTMHM07 model came to our attention after running our simulations. For M˙ c  0.1 Eddington near R ∼100RS, the conduction ",
+    "or Compton-cooling (at high M˙ d) limiting temperatures may cross the coupling temperature (e.g. (<>)Bradley & (<>)Frank (<>)2009). Under these conditions, the model will tend to overpredict condensation and thus exaggerate the amplitude and duration of the sympathetic mode, but triggering the effect requires strong, correlated M˙ c, M˙ d to already be underway. "
+  ],
+  "4. SIMULATION RESULTS ": [],
+  "4.1. Models without EC ": [
+    "To illustrate how a combination of non-EC mechanisms has difficulty explaining the magnitude of M˙ d drops and especially the pattern of rapid decline versus slow recovery, we employ a very simple model where disk accretion is computed using the analytical machinery of ?. The latter is derived assuming a time-independent viscosity with power-law dependence on radius, and we referred to the thin-disk solutions on pg.93 of (<>)Frank et al. ((<>)2002) for all relevant viscosity parameters. This method prevents incorporating radial dependence of M˙ w, but because wind losses fall rapidly with decreasing radius, and since we predict they are fairly weak anyway, assuming that they take place near the boundary does not invalidate the main results of this toy model. This method also precludes incorporating he PHII, but as discussed in §(<>)3.4 the main effects of the PHII should typically be limited to radii beyond ∼ Rcirc in LMC X-3. ",
+    "The left panel in fig.(<>)10 shows a calculation with this reduced model geared toward reproducing the first disk drop in fig.(<>)5. We set fs manually, and SRM and wind losses were also computed beforehand as functions of the observed M˙ d. To reproduce the depth of the first drop, we first allowed sustained fs of 100% and when this proved insufficient we moved the outer disk radius inward to a mere 0.04Rcirc for the runs shown, still employing fs of 100%, and leading to massive M˙ c pulses compared to our estimates. This can be corrected somewhat by invoking a wind stronger than our estimates. ",
+    "Besides requiring unrealistic values with respect to our estimates, and an extreme ad-hoc disk truncation, the toy model resists efforts to simultaneously improve agreement with other major features of the data. To improve model-data agreement for the second disk drop in the left panel of fig.(<>)10 without increasing disk radius (which would obviously undo agreement with the first M˙ d drop) requires either increased SRM or increasing the height and duration of the second coronal pulse. The latter will generate obvious disagreement with the second M˙ c pulse by attaching a tail that is very clearly not observed; the former significantly reduces the amplitude of the first coronal pulse relative to the second so that one must invoke a stronger and more complicated wind mechanism. ",
+    "Again, the chief problem is that a disk flow will be viscously smeared too much to match observations unless variability is driven at a relatively small radius where even maximally efficient CHW should be insubstantial, and the PHII should not operate nor regularly drive heating fronts. In the next section, we will show how EC may introduce a evaporation-to-condensation transition or gap at radii comparable to the outer edge of the arbitrarily truncated disk of the toy model, but that it also tends to overpredict condensation at inner radii, gener-",
+    "Fig. 9.— A cartoon summarizing possible complications to the model especially concerning EC (§(<>)3.5,§(<>)5). At small radii, the magnetic field (dotted lines) in the corona and at the disk-corona interface may be significantly non-poloidal thus suppressing condensation (A), and further outward buoyant magnetic loops may still alter the magnetic field geometry besides introducing additional reconnection heating to the corona to continue supressing condensation (B). MHD winds might also be stronger than predicted and carry away more of the corona (C), while clumping of the corona at large radii may instead enhance condensation over evaporation there (D). The potential for the corona to viscously outflow radially wherever it achieves large density gradients (E) may also significantly affect our results. ",
+    "Fig. 10.— The solid curves in the bottom (top) panels show M˙ d (M˙ c) simulated with the simplified model discussed in §(<>)4.1 and empty circles show the observed M˙ d (M˙ c), where the simulation units first are chosen to match the observed and simulated initial M˙ d, as the simple model’s disk machinery has no direct dependence on absolute accretion rate. The data points in the top panels are then scaled so that the maximum observed M˙ c equals the initial M˙ d which is a much larger absolute scale than our estimates suggest. The right panels are for a run with greater variability in the total mass supply which is shown as a dotted curve in all panels. The dashed curves show the effective corona/disk inputs at the outer boundary so that the remaining difference between solid and dashed curves in top panels indicates the wind loss. ",
+    "ating correlated M˙ d -M˙ c rises and falls inconsistent with observations. "
+  ],
+  "4.2. Models including EC ": [
+    "Except where specifically noted otherwise, for these simulations we again use but a corona the standard Spitzer coefficient for electron thermal conduction, for the LTMHM07 EC prescription, SRM results from §(<>)3.1 specifically correspond to a value for and to 6.5 scaleheights between the nozzle and the stellar surface for ",
+    "For the EC-inclusive model, we first simulated a disk with standard density profile extending to the circular-ization radius reacting to a mild Gaussian fs(t) pulse, and show the results in the left panel of fig.(<>)11. Two immediately remarkable features include the sympathetic rise and fall of M˙ d with M˙ c, and the general saturation of M˙ c response when the outer disk is most intensely siphoning onto the inner disk. This saturation physically arises from the steep transition between evaporation and condensation. In the mass exchange model of LTMHM07 that we employ, the local evaporation/condensation rate M˙z, varies with the local corona accretion rate in terms ",
+    "of Eddington ratio, m˙ c, like ",
+    "(13) ",
+    "where a and b are functions of many other parameters, local variables, and radius itself. If these other variables vary weakly with radius, then a very dense corona at some radius will lead to efficient condensation slightly further inward, and subsequent changes in M˙ z about zero will be driven by the weaker variations in the critical value of m˙ c. ",
+    "The issue of sympathetic accretion prompted us to consider a scenario in which the outer disk mass most vulnerable to being siphoned has already been evaporated away, such that there is a gap in the outer disk. We first studied the effects of simply truncating the disk, and show an example with radius 3×1010cm and default LTMHM07 EC parameters in the right panel of fig.(<>)11. Truncating the disk to this radius prevents triggering sympathetic accretion while generating appreciable M˙ d variability and diminishing, but not eliminating, EC’s role in amplifying variability over the simulation domain. ",
+    "We next attempted to generate this gap self-consistently, while preserving the interior aspect of the accretion flow that works fairly well. To this end, we first subjected a full disk to a constant fs at the boundary. The run confirmed that a small seed corona can rapidly evaporate the outer disk, that this corona is immediately ",
+    "condensed only slight inward, but also that the process of forming a complete gap would take on the order of years in our standard EC implementation. To pursue this idea further, we ran simulations with a gap already inserted of which fig.(<>)12 is representative. Besides the initial relaxation of M˙ d due to viscous spreading of the inner disk exceeding and resupply via condensation, one can see that sympathetic accretion is still an issue, and M˙c variability inward of the gap is severely suppressed again, as the high corona fraction of the gap triggers the saturation effect described above. ",
+    "Since our standard model and implementation of EC faces fundamental problems in reproducing major features of the data, we studied the effects of introducing physically motivated, if not yet rigorously justified mod-ifications. Thus far, it appears that the most successful modifications follow a fairly strict pattern of effectively raising the coronal heating and critical evaporation-to-condensation m˙ c over the innermost two decades in R/Rid. The latter is nearly inversely proportional to b in eqn.(<>)13 which in the model of LTMHM07 scales with the corona viscosity parameter αc, radius, electron thermal conduction coefficient κ, and gas-to-total pressure ratio βc as ",
+    "(14) ",
+    "though we should point out that βc enters their model strictly via a prescription for compressive heating. In the simulations producing fig.(<>)13, we raised αc linearly from 0.2 to 0.4 inwards over 100Rid, and independently adjusted b over radial zones spanning 100–102.7 , 102.7– 103.4 , and 103.4–104.6 in R/Rid. For run A in fig.(<>)13, we scaled b in these zones by 0.1, 0.2, and 0.4 respectively, and for run B by 0.4, 0.6, and 0.8. Although the simulated M˙ c pulses are far more massive than observations indicate, these modifications very clearly control the degree of hysteresis versus sympathetic accretion. If the overall magnitude of EC is smaller, then for higher fs, and/or SRM moderately larger than expected, this mod-ified model could reproduce the observed hysteresis. ",
+    "The most conceivably adjustable parameters in eqn.(<>)14 are αc, especially if understood to include other heating mechanisms, and κ. Since the current contrast between simulation and observation still favors weaker EC, the requirement on additional heating would not likely be as extreme as implied by our modifications, but this then requires even greater deviation in κ which affects b rather weakly, and these parameters are not necessarily independent in reality. "
+  ],
+  "5. DISCUSSION AND CONCLUSIONS ": [
+    "Thus far, we still cannot offer a very definitive solution for LMC X-3’s behavior, but we have more rigorously examined several physical mechanisms popularly invoked to explain variability in LMC X-3 and additionally considered evaporation and condensation. We have found that if condensation is suppressed at inner radii (or over-predicted in the current model), then EC may naturally reconcile the observational evidence for RLO accretion and associated circularization radius, as well as the large amplitude, long duration, and rapid declines in hysteresis episodes with our estimates of other major ",
+    "viscous timescale variability mechanisms and the viscous dampening that they would undergo. ",
+    "However, we wish to emphasize that our current EC implementation and the steady-state theory informing it by default led to excessive condensation when compared as accurately as possible to observations, and it led to significantly different predictions for the particular low-M˙s case studied by MP07. As discussed in §(<>)3.5, both the LTMHM07 and MP07 models necessarily neglected some physics, some of which might enhance heating and/or suppress conduction closer to the black hole, and thus help explain the discrepancy between observations and the predictions of our code with the default EC prescription. ",
+    "To this end, we have reproduced and are testing a code that follows MP07 and evolves the disk and corona mass and energy equations self-consistently. An additional advantage is that we can naturally include physics behind the PHII by incorporating detailed results for disk cooling as a function of density and central temperature from previous work - crucial to studying transient systems. However, this explicit method suffers from advancing by a very small time step. We have started building a parallelized implicit method which we hope to develop further during simulations with the explicit method, but we also hope to find ways to save on excessive computation through better physical understanding of the problem. ",
+    "Our estimates for the reduced efficiency of CHW, and cursory examination of theory results for MHD winds in similar systems. (<>)Proga ((<>)2003) suggest that winds in general will have little affect on accretion dynamics in LMC X-3. However, we will continue to consider how efficiency of CHW might be increased, or that MHD winds may be stronger than anticipated (e.g. (<>)King et al. (<>)2012). ",
+    "Other assumptions in our current modeling that bear repeated mention include the alpha-prescription disk, and how we infer and interpret the disk and coronal accretion rates. Regarding the former, it is at least expected that under conditions associated with jet flow, angular momentum transport via the magnetically driven outflow may become substantial or dominant compared to viscous transport (i.e. the magneto-rotational instability) at least within the inner flow (e.g. (<>)Zanni et al. (<>)2007; (<>)Casse & Ferreira (<>)2000). Evolution of the magnetic fields in the disk may also lead to intrinsic variability out to ∼100Rid, as in (<>)de Guiran & Ferreira ((<>)2011). The potential for corona flow to stall centrifugally as a function of external flow conditions and local viscosity (e.g., (<>)Chakrabarti & Titarchuk (<>)1995; (<>)Garain et al. (<>)2012) might be realized in LMC X-3, but is also usually expected to occur well within the innermost 100Rid of the flow and to destroy the disk interior to the centrifugal shock, so it may be most relevant to state transitions. If more frequently prevalent though, the latter could alter our picture of spectral production, enhance M˙ c variability especially on shorter timescales, and change the dynamics of EC. Based on the pattern of the power-law component to anticipate declines in blackbody flux and the viscous recovery timescale of the blackbody component, we are still naturally inclined to favor a picture where variability is driven outside-in so that mechanisms like these and EC would predominantly accelerate and enhance M˙ d declines driven by known mechanisms operat-",
+    "Fig. 11.— Results with rough EC-implementation showing black tot (dotted line), fs ×1018g s−1 (dashed line) while M˙ d without EC turned on (gray empty squares) is included for the right panel. The run on the left uses the full circularization radius and shows strong condensation while the right panel shows a run with a disk size of 3 × 1010cm. (§(<>)4.2). ",
+    "Fig. 12.— Accretion history (left, see fig.(<>)11 caption for symbol meanings) and evolution of the disk surface density profile (right) with snapshots at 80, 100, and 120 days shown in long-dashed, thick-dashed, and dot-dashed lines while the thin solid curves show the gap initial conditions relative to the standard thin disk. ",
+    "Fig. 13.— The left panel shows accretion histories for M˙ d (empty squares) and M˙ c (diamonds) in cases A (thin, black), and B (thick, light gray) as described in §(<>)4.2 where fs × 1018g s−1 is also shown again, but M˙ s and M˙ w are omitted. The right panel shows evolution of disk surface density profile for case A at 60, 90, and 120 days with the same convention as in fig.(<>)12. ",
+    "ing in the outer flow. ",
+    "Our immediate focus will be resolving the outstanding questions regarding the current mechanisms considered, especially evaporation and condensation. After un-",
+    "derstanding and constraining these better, we hope to extend our investigations to additional physics, systems, and phenomena, especially the transients and jet launching. "
+  ],
+  "6. ACKNOWLEDGEMENTS ": [
+    "The authors acknowledge support through the NASA ADP program grant NNX09AC86G. The authors would ",
+    "also like to thank the referee for suggestions that improved the content and clarity of the paper. "
+  ]
+}

jsons_folder/2013ApJ...769...81C.json

@@ -0,0 +1,157 @@
+{
+  "MISSING LENSED IMAGES AND THE GALAXY DISK MASS IN CXOCY J220132.8-320144 ": [
+    "arXiv:1211.6449v2  [astro-ph.CO]  13 Apr 2013 ",
+    "Jacqueline Chen 1 , Samuel K. Lee1,2 , Francisco-Javier Castander 3 , Jos´e Maza 4 , and Paul L. Schechter 1 Draft version August 31, 2021 "
+  ],
+  "ABSTRACT ": [
+    "The CXOCY J220132.8-320144 system consists of an edge-on spiral galaxy lensing a background quasar into two bright images. Previous efforts to constrain the mass distribution in the galaxy have suggested that at least one additional image must be present ((<>)Castander et al. (<>)2006). These extra images may be hidden behind the disk which features a prominent dust lane. We present and analyze Hubble Space Telescope (HST) observations of the system. We do not detect any extra images, but the observations further narrow the observable parameters of the lens system. We explore a range of models to describe the mass distribution in the system and find that a variety of acceptable model fits exist. All plausible models require 2 magnitudes of dust extinction in order to obscure extra images from detection, and some models may require an offset between the center of the galaxy and the center of the dark matter halo of 1 kiloparsec. Currently unobserved images will be detectable by future James Webb Space Telescope (JWST) observations and will provide strict constraints on the fraction of mass in the disk. "
+  ],
+  "keywords": [
+    "Keywords: gravitational lensing: strong – dark matter – galaxies: structure – galaxies: halos – galaxies: spiral "
+  ],
+  "1. INTRODUCTION ": [
+    "Gravitational lensing is a potent probe of the matter distribution in the central regions of lensing galaxies. A particularly promising application of gravitational lensing is to the study of the mass distribution in edge-on disk galaxies. As the geometry of the luminous disk galaxy differs significantly from the dark matter halo in which the galaxy is embedded, disentangling the relative contributions to the total mass of the luminous and the dark components is, at least in principle, feasible. ",
+    "The decomposition of the disk galaxy from the dark matter halo has customarily employed a maximum disk model ((<>)van Albada et al. (<>)1985). In systems where the mass-to-light ratio of the disk is unknown, the contribution of the disk mass to the rotation curve is taken to be as large as permitted by the observed rotation curve, and the galaxy dominates the mass near the center of the galaxy. The accuracy of the maximum disk model is unsettled, although (<>)Debattista & Sellwood ((<>)1998) suggest that disk galaxies with bars are likely to be maximal. The characteristic radius at which one typically characterizes the fraction of matter in disk galaxy is 2.2 disk scale lengths (2.2Rd), as this is the radius at which the circular speed peaks for a thin exponential disk. In what follows, we parameterize the size of the galaxy disk by the fraction of mass in the disk galaxy inside a sphere of radius 2.2Rd, referred to hereafter as fdisk(2.2Rd). ",
+    "Progress on this front has until now been impeded by the small number of edge-on spiral galaxy lenses. Four lens systems with quasar sources are known: ",
+    "Q2237+0305 ((<>)Huchra et al. (<>)1985), B1600+434 ((<>)Jackson (<>)et al. (<>)1995; (<>)Jaunsen & Hjorth (<>)1997), PMN J2004-1349 ((<>)Winn et al. (<>)2003), and CXOCY J220132.8-320144 ((<>)Cas-(<>)tander et al. (<>)2006). In addition the Sloan WFC Edge-on Late-type Lens Survey (SWELLS, (<>)Treu et al. (<>)2011) has assembled 20 galaxy-galaxy lenses. ",
+    "As the lens galaxy in Q2237+0305 has a low redshift, zlens = 0.04, the lensing is mostly sensitive to the bulge mass ((<>)van de Ven et al. (<>)2010). Still, combining with stellar kinematic information, (<>)Trott & Webster ((<>)2002) and (<>)Trott et al. ((<>)2010) find that the lens galaxy has a submaximal disk – i.e., the disk does not dominate the mass in the inner regions of the galaxy. (<>)Koopmans et al. ((<>)1998) and (<>)Maller et al. ((<>)2000) put constraints on a lower-limit for the halo axis ratio in B1600+434, finding that is greater than q ∼ 0.5, and (<>)Maller et al. ((<>)2000) rules out a maximal disk. For PMN J2004-1349, only the bulge-to-disk mass is constrained ((<>)Winn et al. (<>)2003). ",
+    "The SWELLS survey team has analyzed one galaxy-galaxy lens, SDSS J2141-0001, combining gas and stellar kinematics data with the constraints from the lensed arc of the source galaxy ((<>)Dutton et al. (<>)2011; (<>)Barnab`e (<>)et al. (<>)2012). In one analysis, performed before stellar kinematic data became available, the disk of the lensing galaxy was found to be submaximal, and fdisk(2.2Rd) is 0.45. In the analysis including stellar kinematic data, the disk of the lensing galaxy is maximal and fdisk(2.2Rd) is 0.72. ",
+    "CXOCY J220132.8-320144 (hereafter CX 2201) was discovered as part of the Cal´an-Yale Deep Extragalac-tic Research (CYDER) survey of Chandra fields ((<>)Cas-(<>)tander et al. (<>)2003; (<>)Treister et al. (<>)2005). Ground-based optical imaging and spectroscopy were carried out, con-firming the lensed nature of the system and measuring z = 0.323 and z = 3.903 for the galaxy and the quasar respectively ((<>)Castander et al. (<>)2006). At first examination, CX 2201 may not appear to be a prime candidate for studying edge-on spiral galaxy lenses, since it has only two observed images of the background quasar. It ",
+    "Figure 1. Combined 160W, 475W, and 814W HST image of CX 2201. Image A is located above the disk of the galaxy and image B is located below. They are separated by ∼0. 8. The size of the displayed image area is 9 × 2. 7. ",
+    "displays some intriguing features, however, that make it worthy of inquiry. The lensing galaxy has no visible bulge, further eliminating one possible impediment to a clean estimate of the dark matter to disk mass fraction. In addition, both lensed images lie close to the plane of the disk and have similar fluxes. If the galaxy disk were maximal, the matter distribution should be highly elongated and it might be expected that CX 2201 would be a four-image system. Previous efforts to constrain the mass distribution in the galaxy have suggested that at least one additional image must be present ((<>)Castander (<>)et al. (<>)2006). These extra images may be hidden behind the disk which features a prominent dust lane. ",
+    "In this paper, we present Hubble Space Telescope (HST) observations of the system. These were carried out at longer wavelengths than the original detection observations in an effort to observe extra images that may have been extincted by dust in the disk at shorter wavelengths. In addition, we improve upon the astrometry and photometry of the observed images and use the improved constraints to narrow a range of lensing models to describe the mass distribution in the system. "
+  ],
+  "2. HST OBSERVATIONS ": [
+    "Observations using the HST Advanced Camera for Surveys (ACS) and the Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) were carried out on 2006 May 11 and 2006 April 13, respectively (GO:10518). ACS observations were taken in the F814W and F475W filters; NICMOS observations were taken in the F160W filter. ",
+    "ACS imaging consisted of 4 dithered exposures taken in ACCUM mode in each filter; total exposure times were 2228 seconds and 2252 seconds in the F814W and F475W filters, respectively. The exposures were reduced and calibrated using the CALACS calibration pipeline (including the PyDrizzle algorithm). NICMOS imaging consisted of 4 dithered exposures taken in MULTIACCUM mode; total exposure time was 2688 seconds. The exposures were reduced and calibrated using the CALNICA/CALNICB calibration pipeline. Quadrant bias was corrected using the pedsub routine in the STSDAS IRAF package. ",
+    "In each image, the two quasar images straddle the galaxy, with the line connecting the two images intersecting the galaxy disk at a point offset from the galaxy center. There appears to be no pronounced bulge component in the galaxy. The disk is highly-inclined, but has a non-zero projected axis ratio and is thus not perfectly edge-on. A dust lane is visible in the ACS images. Figure (<>)1 shows a combined 160W, 475W, and 814W HST image of CX 2201. ",
+    "The images were fit using the GALFIT program ((<>)Peng ",
+    "(<>)et al. (<>)2002) to extract positions and fluxes of the images and the galaxy and other parameters necessary to completely characterize the galaxy. The galaxy was modeled as an exponential disk, while the quasar images were modeled as Gaussians (quasi-delta functions). The positions, fluxes, and scale radii of the quasar images and the galaxy were allowed to vary, as were the galaxy position angle and axis ratio. The combined model was convolved with the point spread functions (PSFs) of each instrument, which were calculated using the tinytim program. In constructing the PSFs, a frequency power-law of −0.5 was assumed for the source quasar spectrum. ",
+    "The dust lane is quite prominent in the ACS images, and is visible even in the NICMOS image. Despite the difficulty of fitting with the dust lane obscuring much of the galaxy center, the positions of the quasar images and the galaxy are consistent in the different filters. The results of the best fit are shown in Table (<>)1, where the error-weighted average values are given and positions are rotated such that the galaxy plane is horizontally aligned. The position angle of the galaxy East of North is 140.5◦ , 139.3◦ , and 140.1◦ in the F160W, F814W, and F475 fil-ters, respectively. In every filter observed, the quasar images do not straddle the center of the galaxy; instead, they are offset from the center of the galaxy and lie left of the galaxy center in the rotated frame. This offset is a key factor in the mass models used to describe the lens system and is discussed further in Section (<>)3. We measure an offset along the disk plane from the galaxy center to the line connecting the two images of ∼0. 2, which is smaller than the value of ∼0. 3 previously measured by (<>)Castander et al. ((<>)2006) using ground-based data. ",
+    "Although GALFIT gives the same galaxy center position in all the filters, the fit is quite uncertain. Indeed, measuring the center through other means (such as using elliptical galaxy isophotes or masking out the dust lane in the fit) gives offsets which vary from ∼0. 15 to ∼0. 5. In addition, the disk scale length, Rd, varied over the differ-ent filters, increasing with decreasing wavelength. This is consistent with a spiral galaxy with redder old stars in the core and bluer star-forming regions in the outer arms. However, this variation introduces additional uncertainty in defining Rd for models and is discussed further in later sections. ",
+    "The results of the photometry for each filter are shown in Table (<>)2. The flux ratio A/B is higher in the F160W filter than in the F814W and F475W filters; that is, im-",
+    "Table 2 ",
+    "CX 2201 Photometry ",
+    "age A appears slightly redder than image B. In addition, (<>)Castander et al. ((<>)2006) previously measured a flux ratio A/B of ∼1.1 in the Sloan r-band with the Magellan Clay telescope. Since image A is closer to the disk than image B, this suggests differential extinction by a galaxy dust profile which decreases with distance from the plane of the galaxy. However, other possible explanations for the apparent reddening include microlensing and intrinsic variability on timescales greater than the time delay between the images. Without an explicit accounting for those effects, we cannot determine an unreddened flux ratio. In the lens modeling, we use the F160W flux ratio which would be the least affected by reddening, and mi-crolensing and intrinsic variability effects are indirectly accounted for by increasing the error in the flux ratio measurement. Thus, reddening effects are unlikely to bias our modeling results. "
+  ],
+  "3. GRAVITATIONAL LENS MODELING ": [
+    "We now fit several mass models to the observations using the observational constraints summarized in Table (<>)1. The two observed quasar images provide 4 position constraints and 1 flux ratio constraint, a total of 5. For models that have additional unobserved lensed images, the non-detection of such images gives us additional constraints. ",
+    "For every lens model considered, all have common inputs. Flux errors are artificially increased to 20% to allow for microlensing or intrinsic variability; likewise, position errors are increased to 5 milliarcseconds (mas) to account for substructure effects. For every model we test, 2 of the free parameters must be used to fit the position of the source, xs and ys. A Gaussian prior on the position of the center of the lensing galaxy is included with the standard deviation given by the measured error in Table (<>)1. ",
+    "Sampling the lens model parameter space is performed using emcee, the Python ensemble sampling toolkit for affine-invariant MCMC ((<>)Foreman-Mackey et al. (<>)2012), in order to sample the parameter space of the mass models. "
+  ],
+  "3.1. Two-Image Lens Models ": [
+    "Under the assumption that the two observed lensed images are the only images created by the lens, the small number of observable constraints can overconstrain only simple lens models with 4 or fewer free parameters. We choose for a simple lens model a singular isothermal ellipsoid (SIE). A SIE is a logical model to test, as many strong lens systems with early-type lensing galaxies have been successfully modeled by mass profiles with the same slope as the SIE ((<>)Koopmans et al. (<>)2006). ",
+    "A SIE has a dimensionless projected surface density ",
+    "(1) ",
+    "Table 3 Lens Models ",
+    "where ξ2 = x2 +y2/q2 and where q is the axis ratio of the mass distribution. In the case where the halo is spherical and q = 1, b is the Einstein radius and related to the 1-d velocity dispersion, σ, by b = 4π(σ/c)2Dls/Dos, where Dls and Dos are the angular diameter distances from the lens to the source and from the observer to the source, respectively. Solutions for the deflection and magnification from this model are given by ((<>)Kassiola & Kovner (<>)1993; (<>)Kormann et al. (<>)1994). The model and free parameters are summarized in Table (<>)3. ",
+    "Models of the two-image system with a SIE have a best-fit χ2 ∼ 1000. A summary of the results of our modeling runs is presented in Table (<>)4. The poor outcomes are due to the asymmetry of the observed images. Both images are located to the left of the galaxy center (in the rotated frame). In addition, they have similar fluxes. The SIE model creates solutions where one image is located to the left of the galaxy center and the counterimage (on the opposite side of the disk) is found to the right of the galaxy center and with a much smaller relative flux. ",
+    "A simple solution to this problem would be to shift the galaxy center to be collinear with the observed images. Such a shift might be justified. The lensing galaxy in CX 2201 could be analogous to NGC 4631, a nearby edge-on spiral galaxy. NGC 4631 is lopsided, the disk of the galaxy extending further from one side of the galaxy center than from other other side. In CX2201, the dust lane in the galaxy obscures the center of the galaxy. It is possible that the true center of CX 2201 lies offset from the midpoint of the galaxy disk. However, NGC 4631 is interacting with another edge-on spiral neighbor, NGC 4656 ((<>)Roberts (<>)1968; (<>)Weliachew (<>)1969; (<>)Weliachew et al. (<>)1978), and CX 2201 has no such interacting neighbor. In addition, the amount of dust obscuration should differ by wavelength, such that we might expect to measure differ-ent offsets along the disk plane from the galaxy center to the line connecting the two images, and we do not. Every single filter in our data of CX 2201 shows that the images are ∼ 0.2” away from the galaxy center, and Magellan observations reported in (<>)Castander et al. ((<>)2006) show the images as ∼ 0.3” away from the galaxy center. On the whole, it is unlikely that dust lane obscuration is suf-ficient to motivate a galaxy center located between the images. Adopting such a model for the sake of argument, however, achieves good model fits, χ2 = 1.5. "
+  ],
+  "3.2. Models with 3 & 5 Images ": [
+    "A more realistic mass model would include both a component for the dark matter halo and a component to de-",
+    "Table 4 ",
+    "Summary of Lens Modeling Results ",
+    "scribe the disk galaxy. We describe the dark matter by a non-singular isothermal ellipsoid (NIE), which is a SIE modified by the inclusion of a core radius, such that the dimensionless projected surface density is ",
+    "(2) ",
+    "where s is the core radius. The dark matter halo, then, has 3 free parameters associated with it: bh, qh, and sh. A hard prior is included in the modeling such that bh > 0, qh = [0, 1] and sh > 0. ",
+    "Simulations of dark matter halos find an inner mass profile of halos that is shallower than an isothermal pro-file (e.g., (<>)Navarro et al. (<>)1997; (<>)Moore et al. (<>)1999). On the other hand, in a halo with a galaxy in the center of it, lensing studies show that isothermal is a good fit for the total mass profile (dark matter + galaxy). A NIE pro-file provides sufficient flexibility to capture the change in the density profile in the central regions and a range of possible dark matter profile behavior (c.f., (<>)Dutton et al. (<>)2011). ",
+    "The galaxy disk is described by an exponential profile. We approximate the exponential profile by the difference of two NIEs, as described by (<>)Maller et al. ((<>)2000), where the core radii of the NIEs are given by sg,1 = (1/3)Rd and sg,2 = (7/3)Rd. This is referred to as a ‘Chameleon’ profile. Since the axis ratio and the scale length of the disk is measured observationally, only 1 free parameter is associated with the galaxy: bg. A hard prior is included such that b > 0. g ",
+    "With the addition of xs and ys to describe the source position, and our disk+halo model requires a total of 6 free parameters. The model and free parameters are summarized in Table (<>)3. With 6 free parameters, more than 2 images are needed to constrain the model. It might be thought that every additional image should ",
+    "Figure 2. The top panels show the galaxy with images subtracted, while the bottom panels show the resulting brightness in a slice along the plane of the disk. Left: The two bright modeled images are subtracted from 160W observation. Center: An image modeled with flux 1/20 the brightness of image A is subtracted from the left-hand image. Right: An image modeled with flux 1/10th the brightness of image A is subtracted from the left-hand image. ",
+    "provide an additional 3 observable constraints. This is incorrect for the constraints on non-detections of images. There are no real constraints on the location of such images. However, there are constraints on the brightness of extra images. ",
+    "In order to determine how bright an extra image needs to be to be detected, we model an extra image by smoothing the flux in the image over the measured point spread function (PSF) and locate it between the two observed images, where extra images are expected. Model images with fluxes greater than 1/10th the brightness of image A are clearly detectable in the observations. Figure (<>)2 shows that subtracting a model image of that brightness is observable as a ”divot” in the galaxy disk. We set the flux ratio of image A to an extra image of 10 (A/[extra image] = 10) as the threshold of detectability and consider this a 2.5σ detection. Images of this brightness add an additional χextra 2 = 6.25 to the χ2 of the model. Images that are N times brighter than the cutoff add χextra 2 = N × 6.25 to the model. ",
+    "Table 5 ",
+    "Best-Fit Parameter Values for Model with One Extra Image and 2 Magnitudes of Dust Extinction ",
+    "A model image could be significantly brighter than this cut-off and still be unobservable due to extinction by the dust lane in the galaxy. By way of illustration, consider the dust extinction towards the center of the Milky Way. We observe CX 2201 at a redshift of z = 0.323 at 1.6µm. This corresponds to J band (1.2µm) observations in the rest frame. The dust extinction toward the center of the Milky Way is AV = 31 ((<>)Scoville et al. (<>)2003) and AJ = 8 ((<>)Rieke & Lebofsky (<>)1985). So significant amounts of dust extinction might be expected near the centers of edge-on spiral galaxies with dust lanes such as CX 2201. As discussed in the following sections, all extra images lie in the plane of the disk. For this reason, we test models which add a set amount of extinction to the modeled extra image or images. In a model with 1 magnitude of extinction, extra images with a flux ratio of 4 are at the limit of detectability. At 2 magnitudes of extinction, the limit is a flux ratio of 1.6, and at 3 magnitudes the limit is a flux ratio of 0.63. "
+  ],
+  "3.3. Models with One Extra Image ": [
+    "Using our NIE + Chameleon model, two different lens system configurations could give rise to 3 image solutions: a mass model without a naked cusp (e.g., (<>)Ibata et al. (<>)1999; (<>)Egami et al. (<>)2000) and a naked cusp mass model. In a model without a naked cusp, any non-singular mass distribution should produce an odd number of lensed images. Given this, observed lens system 2-image systems are truly 3 image systems, where the central image has been demagnified sufficiently to be unobservable. The predominance of lens systems with even numbers of images has been used to limit the core radius in lensing systems, as small cores result in the demagnification of the central image ((<>)Keeton (<>)2003). In this configuration, the source lies between the inner diamond-shaped tangential caustic and the outer elliptical radial caustic, and the two outer images have different image parities. ",
+    "Naked cusps occur in systems with highly elongated mass distributions, when the tangential caustic extends outside the radial caustic. Generically, a source inside this extension produces three roughly collinear images (e.g., (<>)Keeton & Kochanek (<>)1998). It is commonly reported that the central image is of similar brightness to the outer images. The only current detection of a naked cusp in a system with a galaxy lens is APM 08279+5255 ((<>)Lewis et al. (<>)2002), where the central image is observed to be 0.2 times the brightness of the brightest outer image, although lens models put the brightness flux ratio at ∼ 0.75. In the case of a naked cusp, the two outer images have the same image parity. ",
+    "A summary of the modeling results using no dust ex-",
+    "Figure 3. Top: The critical curve (thick line) and caustic (thin line) of the best-fit model, along with the positions of the source (plus marker) and the images (observed: circles, modeled: crosses). Bottom: The marginalized probability for the flux ratio of image A to the extra image. The left-hand panels show the results using no dust extinction; the right-hand panels the results using 2 magnitudes of dust extinction. ",
+    "tinction and 1 and 2 magnitudes of dust extinction is found in Table (<>)4. Here we see that the no extinction case results in a poorly-fit model and ∼ 2 magnitudes of dust extinction is necessary for the modeled image to be faint enough to escape detection. The best-fit model with one extra image with no dust extinction and the best-fit model with one extra image and 2 magnitudes of dust extinction are described in Figure (<>)3, which shows the locations of the source, the images, the critical curve (in the image plane), and the caustic (in the source plane). While the caustics in the two best-fit models are differ-ent, both are naked cusp solutions. In fact, in every case tested, the only acceptable models of the 2 observed images in CX 2201 consist of naked cusp solutions or require a lopsided galaxy. ",
+    "We might expect that the model would adapt to the different constraints on the extra image and that the flux of the modeled extra image would be dimmer in the case of no dust extinction than in the case with 2 magnitudes of dust extinction. This is not the case; the model does not have the flexibility to make the extra image very dim while also matching the observed images. Thus, extinction does not play a strong role in the modeling, aside from hiding images that have not been observed. The probability distribution the flux of the extra image, as shown in Figure (<>)3, remains the same regardless of the amount of extinction; the extra image has a flux ratio A/[extra image] ∼ 1.9 − 2.4; and models with more dust extinction have better fits. We describe the best-fit parameters below using the 2 magnitudes of dust extinction results as our fiducial result. ",
+    "The best-fit model and 68% unmarginalized errors for the model with 2 magnitudes of dust extinction are shown in Table (<>)5. We display unmarginalized errors ",
+    "Figure 4. The 80%, 68%, and 50% contours for the the two-dimensional marginalized probability for a model with 2 magnitudes of dust extinction and one extra image. The top panel shows that the amplitude of the halo and the disk, bh and bg , are negatively correlated to each other. The bottom panel shows that bh is correlated with the size of the core radius in the halo, sh. The disk mass fractions are shown in labeled dashed contours; the contours shown are fdisk(2.2Rd) = [0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]. The location of the best-fit parameter value is marked by a plus marker. ",
+    "as they better represent the range of acceptable values when we consider the full set of parameters (and not any subsets of parameters). The error intervals for the parameters are large and the modeling does not robustly constrain the parameter values. For example, the entire permitted range of values for q, the halo axis ratio, falls within the unmarginalized 68% error interval, and the probability distribution of q when marginalizing over all the other parameters is flat. The poor constraints on parameter values are due in part to degeneracies between parameters in the model. These degeneracies are illustrated in Figure (<>)4. Parameter degeneracies are best represented by a probability distribution for two selected parameters and marginalizing over the remaining parameters. Marginalized distributions are narrower than the unmarginalized probability distribution cited in Table (<>)5. In addition, given the degeneracies, the complicated parameter space, and the wide unmarginalized errors, the peak of the marginalized distribution will not necessarily match the best-fit value of the parameter. The two-dimensional marginalized probability show that the am-",
+    "Figure 5. The marginalized probability for the flux ratio A/[extra image] for a model with one extra image, 2 magnitudes of dust extinction, and a smaller disk scale length, Rd = 1. 01. ",
+    "Figure 6. The probability distribution of the fraction of mass in the disk at 2.2Rd for the fiducial model with one extra image and 2 magnitudes of dust extinction. ",
+    "plitude of the halo and the disk, bh and bg, are anti-correlated with each other. In addition, bh is correlated with the size of the core radius in the halo, sh, such that larger bh is associated with larger sh. ",
+    "In our models we use the mean measured scale length, Rd = 1. 60, but the measured values vary with wavelength between Rd() = [1.01−2.37]. We have also tested a smaller value of Rd = 1. 01. In general, employing a different Rd doesn’t appreciably change the best-fit parameters (not surprising given the size of the unmarginal-ized errors), but it does have a significant effect on the brightness of the extra image found. As shown in Figure (<>)5, smaller disk scale lengths are associated with dimmer extra images. ",
+    "We measure the fraction of mass in the galaxy disk enclosed within a sphere of radius of 2.2 times the disk scale length (fdisk(2.2Rd)). The model degeneracies make it difficult to constrain parameters, but the probability distribution of the galaxy disk mass fraction is not flat. Figure (<>)4 shows that the disk mass fraction is strongly correlated with the parameter that measures the mass in the galaxy disk, bg, and weakly correlated with the ",
+    "Figure 7. The marginalized probability distribution for fdisk(2.2Rd) as a function of the distance of the extra image from the galaxy center. The contours show where the 85%, 68%, and 50% of the probability lie and the location of the best-fit parameter value is marked by a plus marker. The set of the contours on the left employ the fiducial disk scale length, Rd = 1. 60, while the contours on the right use a smaller disk scale length. Rd = 1. 01. ",
+    "Einstein radius of the halo, bh, because the mass in the dark matter halo within 2.2Rd is dependent upon both bh and the core radius size, sh. The value of fdisk for the best-fit χ2 parameter values is fdisk(2.2Rd) = 0.23, indicating a sub-maximal disk mass. As we see from Table (<>)5, the errors on the best-fit parameters are large, so the constraints on fdisk will be poor. In Figure (<>)6, we show the probability distribution of fdisk(2.2Rd). The distribution is very wide and only very small fractions (< 10%) are ruled out. As discussed previously, the best-fit value of fdisk is not required to and does not match the peak of the marginalized distribution. Without additional observational information to break the parameter degeneracies, a definitive statement about the size of the galaxy disk – whether it is maximal or sub-maximal – cannot be made. ",
+    "Figure (<>)7 shows the extent to which information about the third image can be used to discriminate between the model fits. Extra images which are located further from the galaxy center are associated with larger fdisk(2.2Rd). The location of the extra image, however, is also highly dependent upon the disk scale length, such that smaller disk scale lengths are associated with images located further from galaxy center. Constraining the model with information about the extra image will require breaking the ambiguity surrounding the disk scale length. Now let us consider the case of a smaller disk scale length, Rd = 1. 01. If the extra image is located at dextra = 0. 33 away from the galaxy center, then the disk mass fraction is fdisk(2.2Rd) = [0.6−0.7] within 50% confidence intervals. If the extra image is located just 20 miliarcseconds (mas) further, dextra = 0. 35, then 50% confidence interval expands all the way to fdisk(2.2Rd) = [0.6−1.0] . So milliarcsecond constraints on the position of the extra image could provide significant constraints on the disk mass fraction. ",
+    "The probability distribution of fdisk(2.2Rd) for the smaller disk scale length is tilted to larger values than for the fiducial disk scale length. Fractions smaller than fdisk(2.2Rd) = 20% are ruled out, and, for the best-fit ",
+    "The parameter space for five-image lens systems also consists of naked cusp systems, although the image con-figuration is no different from 5-image lenses with buried cusps. In this case, the tangential caustic extends outside of the radial caustic, and the source is located within both caustics. In general, the five image solution has unobserved extra images which lie along the plane of the disk. Figure (<>)8 illustrates this image configuration. In all cases tested, at least one of the extra images is as bright as the extra image in the 3 image configurations. Thus, 2 magnitudes of dust extinction are necessary in order to obscure all the extra images. Regardless the amount of dust extinction the modeled positions of the observed images (not the flux from the three extra images) is the leading factor in the size of the χ2 , and χ2im = 7, a sig-nificantly poorer fit than the best-fit 3-image solution. ",
+    "Good 5-image solutions are difficult to produce because no mass configurations exist where two bright images line up perpendicular to the plane of the disk and offset from the galaxy center. The x position of the observed images are x = −0.225 and x = −0.210. The best-fit model positions are x = −0.232 and x = −0.200; the model tilts the image positions, bringing one closer to the galaxy center and one further away. Despite the poorer fit to the model, a five-image solution might be preferable because very flattened dark matter halos are ruled out. ",
+    "One option to find a better fit is to, once again, offset the position of dark matter halo. In our two-component lens model, we can move the center of the dark matter halo while leaving the disk galaxy center at its observed values. This may be more plausible than shifting both halo and disk to lie collinearly with the lensed images, especially as the size of the offset required is small, ∼ 1 kpc. ",
+    "Offsets between the halo center and the brightest cluster galaxy have been observed in galaxy clusters ((<>)Allen (<>)1998; (<>)Shan et al. (<>)2010) and in galaxy groups ((<>)van den (<>)Bosch et al. (<>)2005; (<>)Skibba et al. (<>)2011). In a sample of galaxies from the H I Nearby Galaxy Survey (THINGS), the offset between galaxy and halo center was less than one radio beam (∼ 10 or 150 − 700 pc) for 13 of 15 galaxies, with the two remaining galaxies exhibiting larger offsets ((<>)Trachternach et al. (<>)2008). ",
+    "Evidence for a small offset is also present in our Galaxy. (<>)Su & Finkbeiner ((<>)2012) examine gamma-ray emission which may be indicative of dark matter and suggest that there is a 1.5◦ (0.2 kpc) offset between the center of the galaxy and the center of the dark matter halo in the Milky Way. (<>)Kuhlen et al. ((<>)2012) use a dark matter plus hydrodynamics simulation of the Milky Way (”Eris”) to show that the dark matter halo may be offset from the galaxy center by 300 − 400 pc, and this offset lies preferentially near the plane of the disk. The predicted offset is smaller than necessary in the CX 2201 system, but it is oriented similarly. In addition, the (<>)Kuhlen et al. ((<>)2012) produced the offset without requiring an external perturber like a passing satellite galaxy or an incomplete accretion event which might be visible in observations of CX 2201. They suggest that the offset is produced via a density-wave-like excitation by the stellar bar. ",
+    "If we offset the center of the dark matter halo to xoff = ",
+    "Table 6 ",
+    "Best-Fit Parameter Values for Model with Three Extra Images, Dark Matter Halo Offset, and 2 Magnitudes of Dust Extinction ",
+    "Figure 8. Left: the critical curve (thick line) and caustic (thin line) of the best-fit model with three extra images, a dark matter halo offset, and 2 magnitudes of dust extinction, along with the positions of the source (plus marker) and the images (observed: circles, modeled: crosses). Right: the corresponding probability distribution of the fraction of mass in the dark matter at 2.2Rd. ",
+    "−0.210 and yoff = 0.000 (leaving the galaxy center at the observed location) and with 2 magnitudes of dust extinction, we find a best-fit χ2 = 0.3. The χ2 from the observed images is as good as that found for the 3-image best-fit solution. The left-hand panel of Figure (<>)8 shows the positions of the images, the critical lines and caustics of this best-fit 5-image solution. We show the best-fit parameter values and the 68% unmarginalized errors in Table (<>)6. The probability distribution of fdisk(2.2Rd), shown in the right panel of Figure (<>)8, rules out very large fractions (> 80%) and disfavors a maximal disk solution. The best-fit parameter value gives fdisk(2.2Rd) = 0.41. While the shapes of the distribution is different than in Figure (<>)6, the constraints on the disk fraction is consistent with the constraints from the 3-image result. ",
+    "Another option for improving the model fits for 5 image lens systems is to include substructure in the lensing galaxy. For simplicity, we model the substructure with a pseudo-Jaffe profile (see (<>)Mu˜noz et al. (<>)2001), a profile where the projected surface density is constant inside a core radius, falls as R−1 between the core radius and a break radius, and falls as R−3 outside the break radius. If we introduce a substructure clump that is located in the galaxy disk, on the other side of the images from the galaxy center, we can reduce the χ2 to 0.5. However, despite several attempts, only massive substructure clumps of ∼ 109M were sufficient to improve the model fit. In addition, the mass of the substructure must be well concentrated. We set the break radius to 0.1 (0.47 kpc) to ensure the mass well contained within the 0.8 separating image A from image B. A substructure of this mass would be ∼ 10% of the disk galaxy mass. This size substructure is too large to be plausible if the substructure were to be ",
+    "located near the physical center of the galaxy as it would cause a visible disruption to the galaxy disk. The substructure could be located far from the galaxy center, as a faint dwarf galaxy hidden behind the disk. However, the substructure has to be located exactly behind the disk galaxy and further away from galaxy center than images A and B in projection. Several studies have shown that finding substructure of mass greater than 10−5 the mass of the lens projected anywhere in the vicinity of the lens center has a probability of only 10−3 to 10−2 (e.g., (<>)Chen (<>)2009; (<>)Xu et al. (<>)2009; (<>)Chen et al. (<>)2011). The likelihood of a substructure of 109M being serendipitously located near the image positions is small. "
+  ],
+  "4. DISCUSSION AND CONCLUSIONS ": [
+    "Edge-on disk galaxies have the potential to disentangle the relative contributions to the mass from the disk galaxy and the dark matter halo, as the geometry of the luminous disk galaxy differs significantly from the dark matter halo in which the galaxy is embedded. However, to date, only a small number of edge-on spiral galaxy lenses have been available and have been studied. ",
+    "CX 2201 represents a particularly interesting case. Consisting of a background quasar lensed by an edge-on spiral galaxy into two bright images, the lensed images are of similar brightness and lie to one side of the galaxy center. Previous efforts to constrain the mass distribution in the galaxy have suggested that at least one additional image must be present ((<>)Castander et al. (<>)2006). These extra images may be hidden behind the disk which features a prominent dust lane. The image configuration is also suggestive of a naked cusp configuration, of which only one galaxy-scale lens system has been observed to date. "
+  ],
+  "4.1. Summary of Results ": [
+    "We present Hubble Space Telescope (HST) observations of the system, better constraining the observable parameters of the lens system but without detecting any extra images. We have explored a range of models to describe the mass distribution in the system, discovering that a variety of acceptable model fits exist. Our conclusions are summarized as follows: ",
+    "on the unobserved extra image would break many of the parameter degeneracies and put strict limits on the dark matter halo fraction. "
+  ],
+  "4.2. Future Observations with JWST ": [
+    "In order to put robust constraints on the mass distribution of the lensing galaxy, better constraints on the disk scale length and imaging of the extra image or images in CX 2201 are needed. In both cases, observations at longer wavelengths are the key to reducing the impact of dust extinction. The James Webb Space Telescope (JWST) is expected to observe the near and mid-infrared (0.6−30µm) with unprecedented resolution and sensitivity. In addition to longer wavelengths, JWST observations will provide further improvements as it will feature a smaller PSF than current HST observations. ",
+    "We estimate the amount of dust extinction that may be observed in CX 2201 at JWST wavelengths using the fit-ting formula given by (<>)Calzetti ((<>)1997) and (<>)Calzetti et al. ((<>)2000). The longest HST wavelength observation we use is at 1.6µm H band (1.2µm in the rest frame). At this wavelength our extra images fall below the threshold of detection and at least 2 magnitudes of dust extinction are required. Let us consider the case where there are exactly 2 magnitudes of dust extinction in the H-band. If we observe CX 2201 in K-band (2.2µm), there are 1.1 magnitudes of extinction and extra images with flux ratios (A/[extra image]) smaller than 3.6 are detectable. If there are 3 magnitudes of dust extinction in the H-band, then at K-band there are 1.6 magnitudes of extinction and extra images with flux ratios smaller than 2.3 are detectable. In both these cases, the extra images in our fiducial models would be observable (c.f., Figure (<>)3). The Calzetti relations for dust extinction encompass the far-UV to near-IR spectral range and the longest wavelength probed is 2.2µm. If we extend the relation to observations in the L band (3.5µm observed, 2.6µm rest frame), just outside of the Calzetti spectral range, we find that there are 0.25 and 0.37 magnitudes of dust extinction for 2 and 3 magnitudes in the H band, respectively, and flux ratios (A/[extra image]) smaller than ∼ 7.5 are detectable. In fact, if there were 12 magnitudes of extinction in our H band observations (more than the 8 magnitudes estimated for the Milky Way), we could still detect the extra images predicted by our models in the L-band. ",
+    "At longer wavelengths, we would expect the amount of dust extinction to be even lower than these limits. However, at those wavelengths attempts to observe extra images will be hampered by dust emission, and observations of CX 2201 between near-infrared and mid-infrared wavelengths may be where both effects are minimized (see, for example, (<>)da Cunha et al. (<>)2008). Thus, future observations with the James Webb Space Telescope (JWST) represent the most promising avenue to observing central ",
+    "images and measuring the mass of the disk in CX 2201. ",
+    "ACKNOWLEDGEMENTS ",
+    "The authors would like to thank Jeffrey Blackburne for his invaluable assistance with the data reduction. JC acknowledges support through grant HST: GO:10518. JM gratefully acknowledges support from CONICYT project BASAL PFB-06. ",
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+}

jsons_folder/2013ApJ...769..150C.json

@@ -0,0 +1,148 @@
+{
+  "CLOSE STELLAR ENCOUNTERS IN YOUNG, SUBSTRUCTURED, DISSOLVING STAR CLUSTERS: STATISTICS AND EFFECTS ON PLANETARY SYSTEMS ": [
+    "Jonathan Craig & Mark R. Krumholz ",
+    "(<http://arxiv.org/abs/1304.7683v1>)arXiv:1304.7683v1  [astro-ph.EP]  29 Apr 2013 ",
+    "Department of Astronomy & Astrophysics, University of California, Santa Cruz, CA 95064 USA ",
+    "Draft version April 18, 2021 "
+  ],
+  "ABSTRACT ": [
+    "Both simulations and observations indicate that stars form in filamentary, hierarchically clustered associations, most of which disperse into their galactic field once feedback destroys their parent clouds. However, during their early evolution in these substructured environments, stars can undergo close encounters with one another that might have significant impacts on their protoplanetary disks or young planetary systems. We perform N-body simulations of the early evolution of dissolving, substructured clusters with a wide range of properties, with the aim of quantifying the expected number and orbital element distributions of encounters as a function of cluster properties. We show that the presence of substructure both boosts the encounter rate and modifies the distribution of encounter velocities compared to what would be expected for a dynamically relaxed cluster. However, the boost only lasts for a dynamical time, and as a result the overall number of encounters expected remains low enough that gravitational stripping is unlikely to be a significant e ect for the vast majority of star-forming environments in the Galaxy. We briefly discuss the implications of this result for models of the origin of the Solar System, and of free-floating planets. We also provide tabulated encounter rates and orbital element distributions suitable for inclusion in population synthesis models of planet formation in a clustered environment. ",
+    "Subject headings: open clusters and associations: general — planets and satellites: formation — stars: kinematics and dynamics "
+  ],
+  "1. INTRODUCTION ": [
+    "Stars form in giant molecular clouds (GMCs) that possess a high degree of substructure. They tend to be clumpy and filamentary ((<>)Williams et al. (<>)1994, (<>)2000), almost certainly as a result of pervasive supersonic turbulence ((<>)Larson (<>)1981; (<>)Mac Low & Klessen (<>)2004). Stars that form out of these clouds inherit the substructures of their parents, leading to a hierarchy of clustering ((<>)Lada & Lada (<>)2003; (<>)Bressert et al. (<>)2010; (<>)Gutermuth et al. (<>)2011), and to self-similar (fractal) structures within star clusters ((<>)Larson (<>)1995; (<>)Elmegreen (<>)2000; (<>)Elmegreen & Elmegreen (<>)2001; (<>)Cartwright & Whitworth (<>)2004; (<>)Chen et al. (<>)2005). Numerical simulations of star formation produce similar results ((<>)Klessen & Burkert (<>)2000; (<>)Bonnell et al. (<>)2003; (<>)O ner et al. (<>)2009; (<>)Krumholz et al. (<>)2012). ",
+    "(<>)Aarseth & Hills ((<>)1972) were the first to study the evolution of star clusters with initial substructure. They found that any substructure initially present was typically destroyed within one free-fall time, and observations generally support this picture ((<>)Cartwright & Whitworth (<>)2004; (<>)Schmeja et al. (<>)2008). However, simulations indicate that substructure can be destroyed quickly only in initially subvirial clusters, a case characterized by an initial collapse of the star cluster towards the center of mass followed by a chaotic evolutionary phase ((<>)Goodwin & Whitworth (<>)2004; (<>)Allison et al. (<>)2010). For supervirial clusters, on the other hand, substructure can survive for up to several crossing times ((<>)Goodwin & Whitworth (<>)2004). ",
+    "Both observations and theory suggest that clusters typically form subvirially with respect to the gas, though not ",
+    "(<mailto:krumholz@ucolick.org>)krumholz@ucolick.org ",
+    "necessarily with respect to the stars alone ((<>)F˝ur´esz et al. (<>)2008; (<>)Tobin et al. (<>)2009; (<>)O ner et al. (<>)2009). However, the star formation process is ineÿcient, with relatively small amounts of the mass in a given molecular cloud being converted into stars, which then expel the remainder of the cloud into back into the di use interstellar medium through their radiation, winds, and supernovae ((<>)Hills (<>)1980; (<>)Lada (<>)1999; (<>)Lada & Lada (<>)2003; (<>)Matzner (<>)2002; (<>)Krumholz et al. (<>)2006; (<>)Fall et al. (<>)2010; (<>)Goldbaum et al. (<>)2011; (<>)Kruijssen (<>)2012). Once the gas is expelled, stars disperse into the field, with only a minority remaining in bound clusters for many dynamical times after gas dispersal. As a result, even if stars are born subvirial with respect to the gas, they may be rendered supervirial by its rapid dispersal. Real star clusters may therefore experience periods of both subvirial and supervirial evolution.1 (<>)",
+    "Whether subvirial or supervirial, this early evolutionary stage is of considerable interest for the problem of planet formation. In denser environments and massive clusters containing massive stars, where a signifi-cant fraction of stars appear to form ((<>)Lada & Lada (<>)2003; (<>)Chandar et al. (<>)2010), close passages between Solar-type stars and massive stars may lead to the photoevaporation of protoplanetary disks and modification of the planet formation process ((<>)Adams et al. (<>)2004; (<>)Throop & Bally (<>)2005; (<>)Adams (<>)2010, and references therein). Close encounters with passing stars can also gravitationally dis-",
+    "rupt both disks and planetary systems, potentially truncating disks, exciting planetary orbits, or ejecting planets completely. Such encounters have been suggested as a potential explanation for such diverse observations as the existence of free-floating planets (e.g. (<>)Sumi et al. (<>)2011; (<>)Veras & Raymond (<>)2012) and the structure of the Kuiper Belt (e.g. (<>)Lestrade et al. (<>)2011; (<>)Jim´enez-Torres et al. (<>)2011). The need to avoid disruptive encounters has also been used as a constraint on the potential birth environment of the Sun ((<>)Adams & Laughlin (<>)2001; (<>)Adams et al. (<>)2006). Our Solar System is remarkably well ordered compared to many extrasolar planetary systems, with all of the planets on nearly circular orbits (every planet except Mercury has e < 0.09), while the Kuiper belt is also relatively undisturbed. (<>)Adams & Laughlin ((<>)2001) and (<>)Adams ((<>)2010) have argued that this implies that the Sun could have been formed in a cluster no larger than ∼103 stars, though this conclusion has recently been questioned by (<>)Dukes & Krumholz ((<>)2012). ",
+    "A crucial input to all these questions is the rate and distribution of orbital elements of the encounters that a star in a cluster will experience. These are a necessary ingredient for population synthesis models for planet formation in clustered environments (e.g. (<>)Adams (<>)2010; (<>)Dukes & Krumholz (<>)2012; (<>)Ovelar et al. (<>)2012). While a number of authors have measured these distributions numerically (e.g. (<>)Bonnell et al. (<>)2001; (<>)Adams et al. (<>)2006; (<>)Spurzem et al. (<>)2009; (<>)Olczak et al. (<>)2006, (<>)2010), none thus far have done so in the context of a dispersing, initially highly-substructured cluster, which modern observations suggest is the typical condition for the formation of most stars. ",
+    "Several authors have recently studied properties of initially substructured (fractal) clusters in slightly di erent contexts. (<>)Parker et al. ((<>)2011) find that reproducing the observed present-day binary properties of the ONC require that it have formed with a high degree of substructure and a high initial binary fraction. (<>)Parker & Meyer ((<>)2012) find that the surface density of fractal star clusters decreases rapidly in time, which implies that a large fraction of star-star encounters will occur very early on in the cluster life. (<>)Smith et al. ((<>)2013) found that gas removal after multiple crossing times typically results in relaxed clusters, with no remaining substructure, whereas quick gas expulsion before one crossing time leads to a stochastic, unpredictable outcome. ",
+    "The two papers closest to our work are (<>)Adams et al. ((<>)2006), who calculate encounter rates in both dispersing and cold clusters, but do not include any initial substructure, and (<>)Parker & Quanz ((<>)2012) who do include substructure and study how star clusters a ects orbital elements of planetary systems. We add to these studies by conducting a series of N-body simulations of dispersing, fractal star clusters across a much broader parameter space than has been considered before. We consider a wide range of dynamical environments, from unbound, supervirial stellar associations to subvirial stars in a gas-dominated clump that are subsequently unbound by gas expulsion. For each simulation we track every event in which two or three stars pass within 1000 AU of one another, giving a nearly complete dynamic profile of possible interactions. Our work expands on that of (<>)Adams et al. ((<>)2006) and (<>)Parker & Quanz ((<>)2012) by surveying a significantly broader parameter space, with ",
+    "cluster masses from 30 −30, 000 M⊙and surface densities from 0.1 −3.0 g cm−2 . This broad survey allows us to measure how the results depend on cluster mass and surface density, and thereby to extrapolate into the regime of high mass and surface density clusters that are too computationally expensive to simulate directly. ",
+    "The remainder of this paper is as follows. Section (<>)2 discusses the model parameters, the initial conditions for the clusters, and the simulations and data reduction methods, and defines the statistical distributions of interest. Section (<>)3 details our results, and Section (<>)4 discusses their implications. Our conclusions are presented in section (<>)5. "
+  ],
+  "2. METHODS ": [
+    "To study stellar encounters in dissolving clusters, we perform an ensemble of N-body simulations using a modified version of the numerical integrator NBODY6 ((<>)Aarseth (<>)1999). Below we describe the parameters in our simulations, the initial conditions, and how we process the resulting data. "
+  ],
+  "2.1. Simulation Parameters and Initial Conditions ": [
+    "We characterize clusters by four parameters: the virial ratio, Q, defined as the ratio of kinetic to potential energy (so that a cluster in equilibrium has Q = 0.5), the fractal dimension D, the stellar mass Mc, and the cluster surface density, c. We describe below how we use these parameters to set up the initial conditions in our simulations. We consider four combinations of Q and D, and for each combination we then simulate clusters with a broad range of masses Mc and surface densities c. ",
+    "We use the surface density c rather than the radius Rc or the volume density ˆc as a parameter for two reasons. First, while the volume density determines encounter rates, the quantity of interest for the standpoint of studying how clusters a ect planetary systems is the total number of encounters a star can expect to experience over the cluster lifetime, not the encounter rate. The natural time scale for a disrupting cluster is the crossing time, and the total number of encounters per crossing time depends on the surface density rather than the volume density ((<>)Dukes & Krumholz (<>)2012). Second, observations of cluster-forming gas clumps appear to indicate that, while clusters span a very wide range of volume densities and radii, they form a sequence of relatively constant surface density ((<>)Fall et al. (<>)2010, and references therein). Thus in discussing embedded clusters that have until recently been dominated by the potential of the gas, it is also natural to work in terms of surface rather than volume density. ",
+    "Our base case is a cluster with Q = 0.75 and D = 2.2; this value of virial ratio corresponds approximately to a cluster that has just expelled its residual gas but has not been completely unbound by the process, and the fractal dimension describes a cluster with a moderate degree of substructure. This is consistent with observations which have typically found that D goes from 1.9 to 2.5 ((<>)Falgarone et al. (<>)1991; (<>)Vogelaar & Wakker (<>)1994; (<>)Elmegreen & Falgarone (<>)1996; (<>)de La Fuente Marcos & de La Fuente Marcos (<>)2006; (<>)S´anchez et al. (<>)2010). These runs generally result in majority of the stars escaping promptly, but some remaining as a bound structure for long times. Our ",
+    "second case is Q = 1.25 and D = 2.2, corresponding to a cluster that has been completely unbound by gas expulsion, or that was never bound in the first place. In these runs essentially all the stars disperse. Our third case is a model with D = 1.6 with Q = 0.75, corresponding to a case like the base model but with more substructure. In our fourth model, we explicitly include a phase in which the stars are confined by an external potential, which we rapidly remove after four crossing times, where the crossing time is ",
+    "(1) ",
+    "Our motivation for this choice is that observations indicate that the lifetime of the embedded phase of star cluster formation is roughly four crossing times ((<>)Tan et al. (<>)2006), or possibly even less ((<>)Elmegreen (<>)2000). We should note here that substructure is typically erased after several crossing times in a confined potential ((<>)Smith et al. (<>)2013). The first three cases assume that the gas is expelled very early while the substructure still remains. While it is present, we describe the gas potential by a Plummer model, ",
+    "(2) ",
+    "and we choose Mgas = (0.7/0.3)Mc, so that the gas mass is 70% of the total gas plus stellar mass. This cluster has Q = 0.3 and D = 2.2 initially. We should note that this value of the virial ratio is computed using only the potential energy due to the interactions between stars, not the coupling of the stars to the gas. The total potential energy is ",
+    "where N is the number of stars, rij is the distance between the ith and jth stars, and ri is the radial position of the ith star. This means that the real virial ratio is then T/Utot. The gas mass term dominates, which leaves us with Q < 0.1, an extremely subvirial case. This e ec-tively gives us a bound on how important the e ect of gas might be on the evolution of the cluster. ",
+    "We summarize the model parameters in Table (<>)1, and the number of independent realizations we perform at each (Mc, c) combination in Tables (<>)3 – (<>)6. The numbers of runs for each (Mc, c) value are chosen so that the number of interactions, and thus the statistical error on our results, is roughly constant. This implies a large number of runs for small, low surface density cases, and a smaller number of runs for more massive, higher surface density cases. As we will see below when we discuss our error budget, this does limit our accuracy to some extent in the high mass and surface density regime. Unfortunately this regime is too computationally-costly to allow a significantly larger number of simulations. The relatively small number of simulations limits our accuracy, but even with this limitation we show below that the errors on our measured encounter rates are typically no more than ∼10%. "
+  ],
+  "TABLE 1 ": [
+    "Model parameters "
+  ],
+  "TABLE 2 ": [
+    "Cluster mass and number of stars. ",
+    "TABLE 3 ",
+    "Number of realizations for model Q0.75D2.2 "
+  ],
+  "TABLE 4 ": [
+    "Number of realizations for model Q1.25D2.2 "
+  ],
+  "TABLE 5 ": [
+    "Number of realizations for model Q0.75D1.6 ",
+    "TABLE 6 ",
+    "Number of realizations for model Gas "
+  ],
+  "2.2. Initial Conditions ": [
+    "We initialize our clusters using the fractal initial conditions model with slight modifications ((<>)Scally & Clarke (<>)2002; (<>)Goodwin & Whitworth (<>)2004). We refer the reader to the second paper for full details of the method, which we briefly summarize below. To generate the cluster we start by defining a cube with sides of length 2 (in arbitrary units, which will be scaled later to give the correct physical units), centered at the origin. This cube is subdivided into the 8 Cartesian sectors, and a first generation particle is placed at the center of each subcube. Each of these first generation cubes is then subdivided again, with second generation particles placed at the center of each second generation subcube. We repeat this subdivision procedure, with one additional constraint for the second and subsequent generations: each parent particle only has a probability 2D−3 of producing o spring. When D = 3 this ensures that all positions are equally populated and there is no substructure, but for D < 3 parts of the cube will be empty, yielding substructure. At each generation g, we also add a random displacement of position of magnitude 2−g−1 to prevent the development of an overly gridded structure. ",
+    "We repeat this procedure until the number of particles generated greatly exceeds the number we will actually use in the simulation. We then randomly select a subset of the points with radius less than 1 (in our arbitrary units) to be the initial locations of our stars. The radial positions of the stars are then multiplied by a factor ",
+    "(4) ",
+    "so that the average surface density of the cluster is c. ",
+    "The number of stars is simply Mc/m¯ , where m¯ is the mean stellar mass for our chosen IMF (see below). Table (<>)2 gives the correspondence between the cluster mass and the number of stars N. Note that this means that for a given Mc the actual cluster mass may be slightly larger or smaller, depending on drawing from the IMF. We therefore interpret Mc as the expectation value of the cluster mass, though deviations from this value are small as long as Mc ≫m¯ . ",
+    "We assign initial velocities to the stars using a recursive procedure to ensure that positions and velocities are correlated, as suggested by observations and simulations. At each generation we assign a random scalar velocity drawn from a Maxwellian distribution to each particle ",
+    "(5) ",
+    "The direction of the velocity vector is chosen randomly. A particle’s velocity is the value produced by this drawing added to the velocity of its parent. Since the magnitude of the velocity perturbation decays with generation, the positions of the stars are then highly dependent on the velocities of the first few parents. Note that the choice of ˙v, 2 0 is arbitrary, since we scale the final speeds so that the cluster has a specified virial ratio (see below). Figure (<>)1 shows an example of a cluster generated via this procedure. ",
+    "Finally, we assign stellar masses by randomly drawing ",
+    "Fig. 1.— Asterisks indicate the positions of stars in an example cluster projected onto the xy-plane; colors indicate stars’ z velocities. Notice that velocities and positions are correlated. ",
+    "from an extended version of the (<>)Kroupa ((<>)2002) IMF, ",
+    "(6) ",
+    "This IMF yields a mean stellar mass m¯ ≈0.59 M⊙. Once we have drawn all the stellar masses, positions, and velocities, we scale the velocities by a constant factor so that the initial virial ratio is the desired value. "
+  ],
+  "2.3. Simulations and Analysis ": [
+    "We simulate the evolution of each cluster for 5 crossing times, except for the Gas runs, which we compute for 9 crossing times (i.e. 5 crossing times after the gas potential is removed). Since we are interested in close encounters for Solar-like stars, we track every instance in which a star of mass 0.8 −1.2 M⊙passes within 1000 AU of another star and the pair has a non-negative center of mass energy; the latter condition excludes cases where the two stars form a binary. In addition, once we have found a pair of stars that meet this criterion, we also check for any other star passing within 1000 AU of either body. ",
+    "The raw data we obtain from NBODY6 is a list of 2-body and 3-body interactions with positions, masses, velocities, indices and the time. Almost all interactions are recorded as a time series, since the stars involved are within 1000 AU of one another for more than a single simulation time step. Our end goal is to use these time series to calculate the distribution of impact parameters b and relative velocities at infinity v∞for encounters in clusters. For a given pair of particle positions and velocities, it is straightforward to compute what values of b and v∞would be required to produce that particular separation and relative velocity. However, in practice interactions are often complex, particularly in the high surface density cases where stars are tightly packed, and the values of b and v∞that one computes in this manner are not constant over the time series of positions and velocities that describes a particular interaction. For this reason, we must first classify interactions in order to decide how to analyze them. Our classification scheme is as follows. ",
+    "1+1 interactions — These are true single star-by-single star scattering events. Two bodies are said to be well-described as a 1+1 interaction if, for that pair of parti-",
+    "cles, the set of impact parameters bk and relative velocities v∞,k we compute from our time series satisfy the condition that ",
+    "(7) ",
+    "where ˙b and ¯b are the standard deviation and mean of the time series bk and similarly for ˙v1 and v¯∞, and T1+1 = 0.1 is the tolerance ratio we adopt for 1+1 interactions. This value is somewhat arbitrary, but provides a reasonable separation between cases where two interacting stars have their orbits perturbed slightly by the potential of other stars during the interaction, and cases where another nearby star provides a large perturbation to the orbits. For 1+1 interactions, we record ¯b and v¯∞as the impact parameter and relative velocity of the encounter. ",
+    "1+2 interactions — These are events in which a single star scatters o a binary. We label an encounter involving three stars within 1000 AU of one another as a 1+2 interaction if two conditions are met. First, exactly one pair of the three stars must be gravitationally bound, while the other pairs are unbound. Second, if we replace this gravitationally bound pair by a single star at the center of mass position and velocity of the pair, and with a mass equal to the sum of the pair’s masses, and we compute a set of impact parameters bk and relative velocities v∞,k between this binary and the remaining star, we find that ",
+    "(8) ",
+    "where T1+2 = 0.3. We set the tolerance somewhat higher than in the 1+1 case because, even in the absence of perturbations from external stars, tidal forces exerted by the binary on the single star may lead to some exchange of energy and angular momentum between the binary’s internal energy and angular momentum and that of the orbit of the binary and the single star about one another. For 1+2 interactions, we record ¯b and v¯∞as the impact parameter and relative velocity of the encounter. ",
+    "1+1+1 interactions — These are events in which three unbound stars encounter one another. We classify an event as 1+1+1 if no pair composed of two of the three stars involved is mutually gravitationally bound. We decompose encounters of this type into three 1+1 events; since these 1+1 events clearly will not satisfy the tolerance criteria for 1+1 events, we simply calculate b and v∞in these cases using the positions and velocities the stellar pairs have at their point of closest approach. ",
+    "Complex interactions — These are events which do not fall into one of the above categories. They may, for example, be cases where a metastable hierarchical multiple star systems forms and then dissolves some time later. These interactions do not have well-defined orbital elements. We do not attempt to define an impact parameter or relative velocity in these cases, and we do not include them in our statistical distributions of b and v∞. We do, however, record such interactions and include them in our total counts of events. "
+  ],
+  "2.4. Statistical Distributions ": [
+    "For each set of simulations, we are interested in three quantities. The first is simply the expected number of encounters Nenc within 1000 AU. The other two are the distributions of impact parameters p(b) and relative velocities p(v∞) that describe these encounters. For a fully relaxed cluster, we expect these to follow ",
+    "and ",
+    "(9) ",
+    "(10) ",
+    "but they need not for fractal, dispersing clusters that have not had time to relax. To evaluate the distributions from our simulations, we bin all our encounters into Nbin = 20 equally-spaced bins of impact parameter from 0−1000 AU, and into Nbin equally-spaced bins of relative velocity from 0 −20 km s−1 . "
+  ],
+  "3. RESULTS ": [],
+  "3.1. Base Case (Q0.75D2.2) ": [
+    "We first describe the results of our base case, model Q0.75D2.2, and then in subsequent sections describe how the results change for the other models. We report the quantitative results for all models in Tables (<>)7 – (<>)10. "
+  ],
+  "3.1.1. Distributions of Encounter Velocities and Impact Parameters ": [
+    "Figure (<>)2 shows the distributions of impact parameter for two example runs, one at low and one at high surface density. We find that the distribution of impact parameters follows equation ((<>)9), p(b) ∝b, very closely for many of our cases, and in all cases the distribution of 1 + 1 events follows a linear trend. We find a deviation from linearity with the 1 + 1 + 1 events. This is not terribly surprising since we have made a rather large assumption that we can reliably describe a 3-body event as three 2-body events. As 3-body interactions become more prevalent with higher mass (for reasons to be discussed later) the deviation of the overall distribution from linearity tends to increase (blue in the figures). However, even for the highest surface density cases we consider, the overall distribution of impact parameters summed over all 1+1, 1 + 2, and 1 + 1 + 1 events remains reasonably linear. ",
+    "While the distribution of impact parameters is close to what one would expect for a relaxed cluster, we find that the distribution of relative velocities is strongly non-Maxwellian in all our simulations. We show some examples of the distributions p(v∞) from our simulations in Figure (<>)3. The deviation from Maxwellian is not surprising, given the correlated position-velocity distribution with which we begin, and that is observed in young clusters. "
+  ],
+  "3.1.2. Number of Encounters ": [
+    "We now turn to the question of the number of encounters and their typical velocities as a function of Mc and c. First note that nearly all of the events for these clusters occur in the first crossing time. Figure (<>)4 shows an example of the temporal distribution of encounters in one of our cases; other combinations of mass and surface density are similar or even more heavily weighted toward encounters occurring during the first crossing time. These ",
+    "TABLE 7 ",
+    "Encounter Statistics for model Q0.75D2.2 "
+  ],
+  "TABLE 8 ": [
+    "Encounter Statistics for model Q1.25D2.2 ",
+    "TABLE 9 ",
+    "Encounter Statistics for model Q0.75D1.6 ",
+    "TABLE 10 ",
+    "Fig. 2.— Distribution of impact parameters for run Q0.75D2.2, with Mc = 101.5 M⊙, c = 0.1 g cm−2 (top), and for Mc = 104.5 M⊙, c = 1.0 g cm−2 (bottom). Black plus signs show the 1 + 1 encounters, orange triangles the 1 + 1 + 1 encounters, purple stars 1 + 2 encounters, and blue squares are the sum of all interactions with a well-defined impact parameter. In all cases data points show the results of the simulation, with error bars indicating the 1˙ Poisson error, and lines show linear best fits to the data. ",
+    "results are similar to those of (<>)Parker & Quanz ((<>)2012), who note that the stripping rate of planets from parent stars decreases with time, and (<>)Parker & Meyer ((<>)2012), who find that the surface density decreases rapidly after one crossing time. ",
+    "For a relaxed, bound cluster, the mean number of encounters per star per crossing time (and thus over the cluster’s entire life for a dispersing cluster) is a function of the cluster surface density alone, and does not depend on the mass ((<>)Dukes & Krumholz (<>)2012). We find that this is not the case for unrelaxed fractal clusters. Figure (<>)5 shows the number of encounters per solar mass star as a function of the cluster mass and surface density; clearly the number increases with both mass and surface density. ",
+    "We can understand this result by realizing that the manner in which our fractal clusters are generated leads to an implicit dependence of the surface density on the mass of the cluster. This dependence arises because, although the mean surface density of the cluster averaged over its entire face is mass-independent, as the cluster mass increases at constant c and D the stars become packed into smaller and smaller substructures. In the Appendix we derive an expression for the e ective surface density c,e as a function of Mc and D. Figure (<>)6 shows the same data as Figure (<>)5, but plotted using this e ective surface density rather than the nominal one. As shown in the Figure, the number of encounters is in fact nearly independent of Mc and fixed c,e . ",
+    "One should regard this result with caution, since it is not clear that it remains valid for real clusters, which may ",
+    "Fig. 3.— Distributions of encounter relative velocities in model Q0.75D2.2, for the cases (Mc, c) = (101.5 , 0.1) (top), (103.5 , 3.0) (middle), and (4.5, 1.0) (bottom), where masses are in M⊙and c in g cm−2 . Plus signs show data measured from the simulations, and lines show the best-fitting Maxwellian distribution. Typical reduced ˜2 values are of order 100, reflecting the poor fits. Notice the deviation is largest where the relative frequency of complex interactions is higher. ",
+    "or may not be truly fractal in their stellar distributions. Any attempt to define either c or the volume density ˆc for a fractal cluster necessarily requires specifying an averaging scale over which the quantity is to be measured. c,e is best considered as the surface density obtained by a process which averages over the initial clumps of the substructure, as opposed to the entire cluster. Alternately, one could envision c,e as being closer to a mass-weighted surface density, as opposed to c, which is an area-weighted surface density. Our result simply shows that, if clusters are fractal, then more massive ones will produce more encounters than one might guess from their surface densities averaged over large scales. This is because in a fractal cluster the surface density increases as one averages over smaller and smaller scales in the vicinity of individual stars. ",
+    "It is also interesting to compare our measurements to ",
+    "Fig. 13.— The distribution of impact parameters for the GAS case with Mc = 103.0M⊙and c = 0.5 g cm−2 . Here we include only events which occur between one and four crossing times (the relaxed phase of our model). Black crosses are 1+1 events and purple stars are 2+1 events. ",
+    "bution of encounters for this model, which is consistent with this expectation. For the first crossing time, there is a highly elevated encounter rate as stars fall toward the center of the potential well and interact. After this they revirialize and the encounter rate drops and becomes roughly constant. Once gas is removed after four crossing times, the cluster disperses and the encounter rate drops to very small values. ",
+    "The results of (<>)Parker & Goodwin ((<>)2012) suggest that the distribution function of impact parameters (equation ((<>)9)) could be significantly altered even in relaxed clusters due to the presence of intermediate separation binaries. To investigate this possibility, in Figure (<>)13 we shows the ensemble distribution of impact parameters for our Gas model, considering only encounters that occur at times from 1−4tc. During this phase the cluster is well-relaxed, since it is old enough to have lost most of its initial substructure, but we have not yet removed the confining gas potential. As the Figure shows, the distribution function still follows P(b) ∝b for 1+1 interactions, although some evidence of stochastic behavior is observed for the 2+1 encounters. We have typically seen such deviations for 2+1 encounters (such as figure (<>)2), and this is probably more due to the diÿculty of assigning orbital elements when a binary interacts with the single star, as opposed to the conditions within the cluster more broadly. ",
+    "The number of encounters is shown in Figure (<>)15, and is larger than the number of encounters in the base case (shown in Figure (<>)5), but only slightly – certainly by less than the factor of 4 di erence in times for which the cluster survives before dispersing. Contours of encounter number in the (c, Mc)-plane are somewhat flatter for the Gas case than the base case, and are much flatter in the plane of (c,e , Mc). Comparing Figures (<>)16 and (<>)7, we see that median encounter velocities are larger in the Gas case than in the base case. Figure (<>)17 shows the results of taking a horizontal slice to see how the median encounter velocity behaves as a function of Mc at fixed c. We find that the median encounter velocity is increasing more quickly with mass in the Gas case than the base case, but not quite as quickly as for a fully relaxed cluster. ",
+    "We can summarize all of these results by saying that the Gas case represents a compromise between the case ",
+    "Fig. 14.— The temporal distribution of encounters for a typical gas case. This particular model has Mc = 102.5m⊙, c = 0.5 g cm−2 , so the crossing time is tcr = 0.078 Myr. Gas removal occurs at 4tcr = 0.31 Myr. ",
+    "Fig. 15.— Same as figure (<>)5 but for the gas case. ",
+    "of a fully relaxed cluster and the substructured clusters we have considered thus far; the first crossing time, which produces a significant fraction of the encounters due to the elevated encounter rate during the relaxation phase, looks much like the substructured clusters. After a crossing time the stars revirialize, and the evolution from that point until gas expulsion looks like that in a dynamically relaxed cluster. Because a significant fraction of the encounters occur during the early, subvirial relaxation phase, the overall number of encounters and encounter velocity distribution ends up being intermediate between the substructured and fully-relaxed cases. A lifetime of four crossing times before gas expulsion is not long enough for the overall statistics to be dominated by the relaxed phase rather than the unrelaxed one. "
+  ],
+  "4. DISCUSSION AND IMPLICATIONS ": [
+    "the fact that there is slight deviation from the distribution P(b) ∝b, especially at high c, is a source of error. At low surface density, however, this error should be minimal. To obtain an entirely correct result for i one should repeat the calculations of (<>)Dukes & Krumholz ((<>)2012) using the same IMF and distribution of impact parameters as found in these simulations. "
+  ],
+  "4.3. Free-Floating Planets ": [
+    "Ever since their discovery by (<>)Sumi et al. ((<>)2011), there has been considerable debate about the origin of planetary mass objects that are either completely unbound or very distant from their parent stars. Models for the origin of these objects include planet-planet scattering leading to ejection in a young planetary system (e.g. (<>)Nagasawa & Ida (<>)2011; (<>)Boley et al. (<>)2012), escape caused by mass loss during late stages of stellar evolution (e.g. (<>)Veras et al. (<>)2011), direct formation from the interstellar medium ((<>)Strigari et al. (<>)2012), and dynamical stripping of planets from stars in clusters (e.g. (<>)Boley et al. (<>)2012; (<>)Veras & Raymond (<>)2012; (<>)Ovelar et al. (<>)2012). While a full discussion of this topic is beyond the scope of this paper, we do note that our simulations provide new insight into the latter mechanism. ",
+    "Our results from the previous section show that significant orbital disturbance for a planet at 30 AU, the distance of Neptune, is likely to be a relatively rare event. Only for clusters whose masses exceed ∼104 M⊙and are very highly substructured (D = 1.6) do orbital excitations become common. Complete ejection will be even rarer. This suggests that, unless the planet formation process is capable of producing large numbers of planetary mass objects at radii significantly beyond 30 AU by internal mechanisms (e.g. planet-planet scattering), cluster stripping cannot be a significant source of free-floating planets. A more precise and quantitative version of this statement may be obtained by combining the orbital element distributions we have obtained here with population synthesis models for star clusters and planets. ",
+    "Finally, it is interesting to compare the results of our simulations with those of (<>)Parker & Quanz ((<>)2012). They find large orbital excitations only in their Q = 0.3 case, which includes no gas potential term. This will lead to a tightly bound final cluster. This fact together with their long simulation times (10 Myr, or ∼30 crossing times) means that it is not surprising that there are a large fraction of planets becoming unbound. In addition, they consider orbital excitations of planets from stars of any mass, and by number the majority of stars are smaller than the 0.8 −1.2M⊙mass range that we consider. The binding energy of planets in such systems will be smaller than is typical of the planetary systems we consider. ",
+    "The closest match in parameters between our simulations and those of (<>)Parker & Quanz is between our Q = 0.75, D = 2.2 and their Q = 0.7, D = 2.0 runs. Their figure 8 corresponds roughly to clusters with Mc = 102−103M⊙and c = 0.1 g cm−2 . They find that ∼10% of planets at 30 AU are stripped from their parent star in this case, whereas we find typically that ∼2 −3% of orbits are excited in such a case. These di erences are most likely due to the issue of binding energies mentioned above. For the IMF used by (<>)Parker & Quanz, and their assumption that planets are equally likely to occur around stars of any mass, only ∼20% of planets or-",
+    "bit stars of mass > 1 M⊙, while ∼40% are born around stars with mass < 0.5 M⊙. Thus, it is not surprising that they find a higher rate of orbital perturbation and stripping. Which model will more accurately predict numbers of free-floating planets is unclear, due to the lack of reliable estimates of planet fractions around stars with mass ≪1M⊙. "
+  ],
+  "5. SUMMARY AND CONCLUSIONS ": [
+    "We have conducted a series of simulations of the evolution of dispersing young star clusters that possess a high degree of substructure. These simulations cover a wide range of masses (30−30, 000 M⊙), surface densities (c = 0.1 −3.0 g cm−2), dynamical states (supervirial but bound, unbound, and subvirial but then unbound by gas expulsion), and degrees of substructure (fractal dimension D = 1.6 and 2.2). These parameters are chosen to reproduce the range of properties for young star clusters suggested by both observations and star formation simulations. We provide tabulated distributions of number of encounters, impact parameters, and relative velocities as a function of these properties. These may be used as inputs in population synthesis models of planet formation. ",
+    "Our calculations produce a number of interesting conclusions. First, during the ∼1 crossing time it takes for the initial substructure to be erased by dynamical interactions, the number of encounters is significantly elevated compared to what one would expect for a relaxed system. The amount of elevation depends the amount of substructure and other cluster properties. Regardless of its strength, though, the enhancement is transient. Either the substructure dissolves (if the cluster is not confined or mildly bound), or the cluster disperses (if it is strongly unbound). Thus for moderate degrees of substructure the overall enhancement in the number of encounters is only a factor of a few for clusters that do remain bound for some period before gas dispersal. Only if the gas has extremely strong substructure (fractal dimension D = 1.6) is the enhancement larger. ",
+    "Second, early in the evolution of a substructured cluster, before the cluster has dispersed or the substructure has been erased, the distribution of encounter impact parameters is not far o from the expectation for a relaxed cluster, but the distribution of velocities is significantly non-Maxwellian. Because this early phase contributes an appreciable fraction of all encounters even in clusters that remain bound for four crossing times, the overall distribution of encounter velocities is non-Maxwellian even in such clusters. Compared to a Maxwellian, our clusters show both a sharper peak at moderate encounter velocities, and a longer tail extending to higher velocities. The overall median velocity increases with cluster mass more slowly than one would expect in a relaxed cluster, and scales with the virial velocity ratio. Clusters with larger virial ratios, and thus larger velocity dispersions, actually tend to produce lower median encounter velocities because they are less e ective at dissolving the velocity substructure and randomizing stellar relative velocities. ",
+    "Third, even with the enhanced encounter rates that we find, we conclude that planetary systems or protoplane-tary disks around stars in dissolving clusters are unlikely to experience significant dynamical perturbations from other stars in the cluster, at least for planets that are "
+  ],
+  "TABLE 11 ": [
+    "Number of Generations Versus Cluster Mass ",
+    "within tens of AU of their parent star. Such planets are simply too tightly bound and have cross sections that are too small for many of them to be disturbed. This remains true even in our most highly substructured cases, which produce the largest number of encounters, up to cluster masses of 103.5 M⊙. This means that there is no dynamical constraint on the size of the Sun’s parent cluster, and that cluster stripping is unlikely to be an important contributor to the population of free-floating planets in the Milky Way. ",
+    "We thank D. Dukes for help running simulations and analyzing the data, and S. Aarseth for assistance with NBODY6. MRK acknowledges support from the Alfred P. Sloan Foundation, the NSF through grant CAREER-0955300, and NASA through Astrophysics Theory and Fundamental Physics Grant NNX09AK31G, and a Chandra Space Telescope Grant. "
+  ]
+}

jsons_folder/2013ApJ...772..132C.json

@@ -0,0 +1,137 @@
+{
+  "INTERMEDIATE-AGE STELLAR POPULATIONS IN CLASSICAL QSO HOST GALAXIES ": [],
+  "Gabriela Canalizo ": [
+    "(<http://arxiv.org/abs/1306.0268v1>)arXiv:1306.0268v1  [astro-ph.CO]  3 Jun 2013 ",
+    "Department of Physics and Astronomy, University of California, Riverside, CA 92521: gabriela.canalizo@ucr.edu and "
+  ],
+  "Alan Stockton ": [
+    "Institute for Astronomy, University of Hawaii, 2680 Woodlawn Dr., Honolulu, HI 96822: stockton@ifa.hawaii.edu Draft version September 19, 2018 "
+  ],
+  "ABSTRACT ": [
+    "Although mergers and starbursts are often invoked in the discussion of QSO activity in the context of galaxy evolution, several studies have questioned their importance or even their presence in QSO host galaxies. Accordingly, we are conducting a study of z ˘ 0.2 QSO host galaxies previously classified as passively evolving elliptical galaxies. We present deep Keck LRIS spectroscopy of a sample of 15 hosts and model their stellar absorption spectra using stellar synthesis models. The high S/N of our spectra allow us to break various degeneracies that arise from di erent combinations of models, varying metallicities, and contamination from QSO light. We find that none of the host spectra can be modeled by purely old stellar populations and that the majority of the hosts (14/15) have a substantial contribution from intermediate-age populations with ages ranging from 0.7 to 2.4 Gyr. An average host spectrum is strikingly well fit by a combination of an old population and a 2.1 (+0.5, −0.7) Gyr population. The morphologies of the host galaxies suggest that these aging starbursts were induced during the early stages of the mergers that resulted in the elliptical-shaped galaxies that we observe. The current AGN activity likely corresponds to the late episodes of accretion predicted by numerical simulations, which occur near the end of the mergers, whereas earlier episodes may be more diÿcult to observe due to obscuration. Our o -axis observations prevent us from detecting any current star formation or young stellar populations that may be present in the central few kiloparsecs. ",
+    "Subject headings: galaxies: interactions — galaxies: evolution — galaxies: stellar content — quasars: general "
+  ],
+  "1. INTRODUCTION ": [
+    "A paradigm is beginning to emerge that links galaxy mergers, starbursts, QSOs, and the formation of spheroids in galaxies into a single coherent picture that promises to explain a range of disparate phenomena connected to galaxy formation and evolution (e.g., (<>)Hopkins et al. (<>)2006a). In outline, galaxy mergers involving gas-rich galaxies drive gas into the center of the resulting merger remnant, fueling both a starburst and the black hole that results from the merger of the central black holes of the merging galaxies. Initially, both the resulting QSO activity and much of the starburst are hidden at optical wavelengths by enshrouding dust, but eventually the strong outflow from the QSO clears a path along at least some sightlines ((<>)Canalizo and Stockton (<>)2001; (<>)Di Matteo et al. (<>)2005). This same outflow, however, also clears out much of the gas that is feeding both the starburst and the QSO activity, quenching both within a relatively short time and providing a self-limiting mechanism for the growth of both the black hole and the stellar mass of the galaxy. This removal of the gas feeding the black hole also means that the optically luminous phase of the QSO is necessarily brief, ˘ 107–108 years. The coupling between black-hole growth and star formation provides a plausible explanation for the correlation between black-hole mass and spheroidal velocity dispersion ((<>)Gebhardt et al. (<>)2000; (<>)Ferrarese and Merritt (<>)2000), and relations between the QSO luminosity and the strength of the outflow may also explain the shape of the QSO luminosity function ",
+    "((<>)Hopkins et al. (<>)2005). Furthermore, there may be a link between the QSO and merging galaxy luminosity functions ((<>)Hopkins et al. (<>)2006b). ",
+    "This close relationship between gas-rich mergers and nuclear activity is supported by evidence for recent starbursts in galaxies with high-luminosity AGN ((<>)Canalizo and Stockton (<>)2001; (<>)S´anchez et al. (<>)2004; (<>)Letawe et al. (<>)2007; (<>)Jahnke et al. (<>)2007; (<>)Wold et al. (<>)2010). However, it is seemingly diÿcult to reconcile such star formation with claims that most QSOs in the low-redshift universe are found in normal ellipticals with stellar populations overwhelmingly dominated by old stars ((<>)McLure et al. (<>)1999; (<>)Nolan et al. (<>)2001; (<>)Dunlop et al. (<>)2003). Indeed, much skepticism remains concerning the relevance of major mergers (and their ensuing starbursts) in the triggering of AGN activity (e.g., (<>)Cisternas et al. (<>)2011; (<>)Kocevski et al. (<>)2012), although many agree that mergers do play an important role for higher luminosity AGN, such as QSOs (e.g., (<>)Treister et al. (<>)2012). ",
+    "Given that determining the relationship between mergers and the QSO population has important consequences in our understanding of galaxy evolution, it is pertinent to revisit the question whether or not QSO hosts have populations indicative of merger-induced starbursts. (<>)Bennert et al. ((<>)2008) studied the morphologies of five low-redshift QSO host galaxies that had been previously classified as undisturbed elliptical galaxies using deep (5 orbit) Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) images. They found that, while the hosts are reasonably fit by a de Vaucouleurs ",
+    "profile, they also show significant tidal debris indicative of a merger event within the last ˘ 2 Gyr. ",
+    "Following (<>)Bennert et al. ((<>)2008), we now turn to the stellar populations in these and other similar bulge-dominated QSO host galaxies. Using high signal-to-noise ratio (S/N), deep Keck spectroscopy, we model the stellar populations to search for traces of significant starburst episodes in the recent past. In Section (<>)2 we describe the sample, spectroscopic observations, and data reduction. In Section (<>)3 we describe our modeling strategy and consider possible caveats, while in Section (<>)4 we compare our results to those of similar studies. In Section (<>)5 we discuss the interpretation of our results in the framework of galaxy evolution. Throughout the paper, we assume a cosmological model with H0 = 71 km s−1Mpc−1 , m = 0.27 and  = 0.73 ((<>)Spergel et al. (<>)2003). "
+  ],
+  "2. OBSERVATIONS AND DATA REDUCTION ": [],
+  "2.1. Sample Selection ": [
+    "Our sample is drawn from the sample of 23 (10 radio-loud and 13 radio-quiet) QSOs of (<>)Dunlop et al. ((<>)2003). This sample contains radio-loud and radio-quiet QSOs in the redshift range of 0.1 < z < 0.26 that are matched in optical luminosity. For details of the original sample selection, see (<>)Dunlop et al. ((<>)1993). ",
+    "(<>)Dunlop et al. ((<>)2003) and (<>)McLure et al. ((<>)1999) performed a morphological study of this sample based on HST images and concluded that all of the host galaxies having nuclei in the QSO luminosity range are bulges that have properties “indistinguishable from those of quiescent, evolved, low-redshift ellipticals of comparable mass” ((<>)Dunlop et al. (<>)2003). Similarly, by studying the stellar populations using spectroscopy obtained with 4-m class telescopes ((<>)Hughes et al. (<>)2000), (<>)Nolan et al. ((<>)2001) conclude that these galaxies are dominated by truly old stellar populations with no significant episodes of star formation in the more recent past. ",
+    "For this paper, we obtained spectra of as many of the 23 QSOs as we were able to observe during our runs, giving priority to those objects classified as ellipticals by (<>)Dunlop et al. ((<>)2003). The 17 targets that we observed are listed in Table (<>)1, along with their host galaxy redshifts as measured from absorption lines in our spectra. We use the IAU designation listed in this table to refer to any given object throughout the paper. "
+  ],
+  "2.2. Spectroscopic Observations ": [
+    "Spectroscopic observations were carried out with the Low-Resolution Imaging Spectrometer (LRIS; (<>)Oke et al. (<>)1995) on the Keck I telescope on the nights of UT 2002 March 4 and 8, and 2002 October 3 and 12. For the blue side (LRIS-B), we used either the 400 groove mm−1 grism blazed at or the 600 groove mm−1 grism blazed at 4000A ° yielding dispersions of 1.09 A ° pixel−1 and 0.63A ° pixel−1 , respectively. For the red side (LRISR), we used either the 300 groove mm−1 grating blazed at 5000 ° A or the 400 groove mm−1 grating blazed at 8500 ° A, yielding dispersions of 2.55 A ° pixel−1 and 1.86 A ° respectively. The slit was 1 ′′wide, projecting to ˘7 pixels on UV-and blue-optimized CCD on LRIS-B and ˘5 pixels on the Tektronix 2048×2048 CCD on LRIS-R. A few of the objects were observed with a set up that resulted in a gap of a few hundred angstroms between the blue and ",
+    "red sides. We obtained between two and six exposures for each host galaxy, typically 1800 s each, dithering along the slit between exposures. A spectrum of the QSO nucleus for each object was obtained separately, with total integration times between 600 and 1200 s, depending on the magnitude of each QSO, so as to obtain a S/N  100. The typical seeing for all observations was 0′′.7 in B. Four or five spectrophotometric standards from (<>)Massey et al. ((<>)1988) were observed each night for flux calibration. ",
+    "Objects 0157+001 and 1012+008 were observed with the old LRIS (single camera) on the Keck II telescope on UT 1997 September 13 and 1998 April 6, respectively. We used a 300 groove mm−1 grating blazed at 5000A ° with a dispersion of 2.44 A ° pixel−1 . The slit was also 1 ′′wide, projecting to ˘5 pixels on the Tektronix 2048×2048 CCD. ",
+    "In Table (<>)1 we show a complete journal of observations, including slit positions, total exposure times, and wavelength resolutions for the blue and red sides, respectively. ",
+    "The slit was placed o set from the nucleus for each object, with a separation that depended on the brightness of the QSO and the seeing conditions, so as to minimize the contamination from QSO light. Thus, the spectra that we obtained correspond to regions of the host galaxy at a given distance from the center, as listed in Table (<>)1. For two objects, 1012+008 and 1635+119, we placed the slit through the nucleus. However, the spectra that we recovered corresponded to regions at a distance >5 kpc from the nucleus. ",
+    "The majority of objects were observed near transit to minimize the e ects of di erential atmospheric refraction. In a few cases when the objects were observed at somewhat higher airmasses (1.1 to 1.4), shorter exposures at parallactic angle were obtained to correct the continuum of the QSO and the host galaxy. Only one object, 0204+292, was observed at high airmass (˘2). ",
+    "Spectra were reduced using standard procedures and corrected for galactic reddening using the values given by NED, which are calculated following (<>)Schlegel et al. ((<>)1998). For each object, a scaled version of the QSO spectrum was subtracted from that of the host galaxy. In order to model the contribution of the QSO to the host galaxy spectrum at each wavelength, we obtained spectra of bright standard stars by placing the slit at several distances from the star and at di erent angles to simulate our o -nuclear observations of the host galaxies. We then multiplied the spectrum of each QSO by the corresponding model. Finally, we scaled the model of the QSO contribution for each object by measuring the flux in broad lines in the spectrum of the host and subtracted it from the latter. The precise determination of the scaling of the QSO spectrum was an iterative process where we tested a range of factors until we obtained clearly over-and under-subtracted host spectra. We used these extreme cases to determine the e ects of the uncertainty introduced by the subtraction of the QSO light from the hosts on the modeling of the stellar populations, as described below. The QSO contribution to the observed host spectrum that was subtracted, as measured at rest wavelength 4500 ° A, is listed as a percentage value in Table (<>)2. ",
+    "The red-side spectrum of 0244+194 was corrupted, so we only used the blue-side spectrum when modeling stel-",
+    "TABLE 1 ",
+    "Journal of Spectroscopic Observations ",
+    "lar populations. As mentioned above, 0204+292 was observed at high airmass and the host galaxy spectrum suffered from strong contamination from the QSO that we were not able to model appropriately. Therefore, we were unable to recover a clean spectrum of the host galaxy. For this reason, this object was not included in the analysis. The spectrum of the host galaxy of 1549+023 was also too noisy to be modeled and it is also excluded from the analysis. Our final sample thus consists of 15 objects. "
+  ],
+  "3. MODELING OF STELLAR POPULATIONS ": [],
+  "3.1. Fitting method ": [
+    "Several di erent strategies for modeling stellar populations in QSO and other AGN host galaxies have been developed over the last two decades. Some authors (e.g., (<>)S´anchez et al. (<>)2004; (<>)Jahnke et al. (<>)2004) use the SEDs and colors of hosts obtained from images, while others (e.g., (<>)Kau mann et al. (<>)2003) use diagnostic diagrams such as the Dn(4000)/HA plane. Although these techniques are powerful to analyze large samples of galaxies, they could potentially be vulnerable to degeneracies, such as the age-metallicity degeneracy, and contamination by scattered QSO light (e.g., (<>)Young et al. (<>)2009). ",
+    "There are relatively few studies in the literature that include modeling of absorption-line spectroscopy of QSO hosts. Even in those few studies, the techniques employed are vastly di erent. For example, (<>)Nolan et al. ((<>)2001) model o -nuclear spectra of QSO hosts in the (<>)Dunlop et al. ((<>)2003) sample using stellar synthesis models. They use the nuclear spectrum of one of the QSOs in the sample to account for QSO light contamination, and they fix a 0.1 Gyr population to account for any recent star formation that may have occurred. They then vary the age of the old underlying population and determine the relative contribution between the older and the younger populations. One problem with this method is that the spectra of younger populations change much more rapidly with age than those of older populations. Whereas the SEDs and stellar features change vastly from 0 to 1 Gyr, they remain almost unchanged for ages greater than 6 Gyr, and the only parameter that changes ",
+    "significantly is the contribution by mass to the spectrum. Thus, this method is prone to result in more degeneracies, and it is unable to determine the actual age and contribution of the younger population. Not surprisingly, they find that the host galaxies are dominated by old stellar populations with a very small contribution of the 0.1 Gyr population ",
+    "(<>)Wold et al. ((<>)2010) do a more detailed modeling of the o -nuclear spectra of ten QSOs. Their fitting method is based on that of (<>)Cid Fernandes et al. ((<>)2005): They fit simultaneously instantaneous burst models of 15 di er-ent ages ranging from 0.001 to 13 Gyr. In addition, they account for scattered QSO light and reddening. In contrast to the results by (<>)Nolan et al. ((<>)2001), they find an average light-weighted age of 2 Gyr for the host galaxies in their sample. ",
+    "Our approach is a simplified version of the technique used by (<>)Wold et al. ((<>)2010). The main question we want to answer is whether the host galaxies were formed at high redshift, with their populations only passively evolving, or whether there have been any significant episodes of star formation in the more recent past. Therefore, we have chosen to employ a method that we have used in the past ((<>)Canalizo et al. (<>)2007; (<>)Canalizo and Stockton (<>)2001, (<>)2000a,(<>)b) which has proved to be very robust. We assume an old stellar population (with a fixed age) corresponding to the populations existing in the host galaxy or galaxies. To this, we add a younger stellar population representing a star forming event in the more recent past. We then vary the relative contribution of the two stellar populations and the age of the younger population, and we perform a least square fit to the observed data, masking out regions of obvious emission lines and any regions showing excessive noise, and giving a lower relative weight to regions that contained pure stellar continuum, i.e., no absorption features. A clear advantage of this method is that there are only two free parameters and thus we encounter fewer degeneracies. ",
+    "We typically assume the old population to be a 10 Gyr-old population, although we have found that the precise choice of the older population has no significant e ect on ",
+    "the age of the younger population determined from the best fit. However, the choice of the old population does have an e ect on the determination of the relative contribution between the older and younger populations, in the sense that over-estimating the age of the older population will result into an over-estimation of the contribution of the younger population and vice versa. This systematic uncertainty is of the order of a few percent, even when the age of the old population is varied by as much as five Gyr. ",
+    "We use the stellar population synthesis models by (<>)Bruzual and Charlot ((<>)2003, heareafter BC03) because they provide a good match to the spectral resolution of our data and allow us to test the e ects of varying a wide range of metallicities. They are also widely used in the literature and allow for us to readily compare our results to those of previous studies. While a recent study by (<>)Zibetti et al. ((<>)2013) indicates that the BC03 models are still the most successful at reproducing the observed SEDs and features of post-starburst galaxies, we have chosen to also use two other sets of models that include di erent AGB star prescriptions: those by (<>)Maraston ((<>)2005, hereafter M05) and S. Charlot & G. Bruzual (2007, private communication; hereafter CB07). As we discuss below, we find remarkable consistency in the results obtained with the three sets of models. The description of the fitting and analysis below refers to the BC03 models, unless otherwise specified. ",
+    "In carrying out the fitting procedure, we smoothed the models to match the velocity dispersion of the host galaxies and the various resolutions of the spectra. Velocity dispersions were determined by using the penalized pixel-fitting procedure (pPXF) of (<>)Cappellari and Emsellem ((<>)2004). We followed their prescription for adjusting the bias parameter, although, for our spectra, the results were not particularly sensitive to this choice. ",
+    "Although the uncertainties in the determination of the QSO contribution to the host spectrum (listed in Table (<>)2) are only of the order of a few percent, they could have an e ect in the determination of the age of the stellar populations. In order to estimate the magnitude of this e ect, we created versions of host spectra in which the QSO contribution was clearly under- and over-subtracted, and we modeled these extreme spectra. The best-fit stellar population ages determined for the under-and over-subtracted spectra were somewhat different from those determined for the spectra with the best QSO subtractions, but the di erence was typically smaller than the 68% confidence intervals in the fits given in Table (<>)2. Moreover, the ˜2 of the best fits in the extreme spectra was significantly greater. ",
+    "Many of the spectra of the individual objects show narrow emission lines. In most cases, the emission lines come from gas ionized by the QSO in the extended narrow line region (NLR). However, in a few cases (discussed in more detail in the Appendix), we see [O II] 3727 even when [O III] is weak or absent. This may be indicative of a small amount of current star formation or low velocity shocks in these hosts. ",
+    "The presence of narrow emission lines in the host galaxy spectra a ects the strength of the observed Balmer absorption features. In fact, Balmer absorption features cannot be relied on because of (1) uncertainty in the ratio of narrow to broad emission in the scaled QSO ",
+    "spectrum relative to that in the scattered light (i.e., the QSO spectrum may miss some of the NLR, which will still be present in the scattered component), and (2) the frequent direct contamination from extended narrow-line emission. For this reason, we do not use their equivalent widths or their corresponding Lick indices directly in our analysis. The Balmer absorption lines, when available, do still enter as one component in our spectral fits. In some cases, the emission is clearly narrower than the absorption and can be masked out during the fitting procedure. ",
+    "For any objects for which there were concerns about the accuracy of the spectrophotometric calibration, we normalized the continuum of both the host galaxy spectrum and the models to unity to eliminate any depen-dance on the shape of the continuum. In all cases, these fits gave essentially the same starburst ages as the original fits that included the continuum shape. ",
+    "As an additional check, we have attempted to analyze the stellar populations, again using the pPXF routine of (<>)Cappellari and Emsellem ((<>)2004). In the mode we used, pPXF finds the best linear combination of spectral synthesis models to fit the observed spectrum over the rest-frame 3500–4500 ° A. A 4th-order multiplicative polynomial is included in the fit to remove the low-order dependence on flux calibration and reddening. Because this procedure introduces many more free parameters, it will work best for the spectra for which we have the highest S/N. This indeed seems to be the case: for the roughly half of the sample with the highest S/N and the least impact from extended emission, we find significant contributions from populations with ages within the range given in Table 2. For all but one of the remaining QSO hosts, we find contributions from intermediate-age populations with ages slightly outside this range. For 2135−147, this procedure finds only an old stellar population; but this host galaxy is the one most strongly impacted by an extended emission region, so Balmer absorption lines have no influence on the solution. ",
+    "We used models with metallicities ranging from 0.004 to 2.5 Z⊙to fit the host galaxy spectra. Invariably, models with Z < 0.4 Z⊙led to poor fits or did not converge. For most objects, the fits with the lowest ˜2 values corresponded to those of models with solar metallicity. Even in cases where models with metallicities somewhat lower or higher than solar gave reasonable fits, the ages of the best fitting populations changed only by ˘ 30%. For consistency, we report results using solar metallicity models for all objects, except for 1217+023, where a 2.5 Z⊙resulted in a significantly better fit. See Section (<>)3.3.1 for further discussion on metallicities. "
+  ],
+  "3.2. Results: Starburst Ages ": [
+    "Our results are summarized in Figure (<>)1 and Table (<>)2. Figure (<>)1 shows each of the QSO host spectra in the sample along with the best-fit model. As mentioned above, each model consists of a 10 Gyr old population plus a younger (typically of intermediate-age) starburst. The models have been matched in resolution to the host-galaxy spectra, taking into account both the instrumental profile and the velocity dispersion of the host galaxy. In Table (<>)2, we list the relative contribution at 4500 ° A (rest wavelength) of the QSO component that was sub-",
+    "tracted from the observed host spectrum as described above, and the o -nuclear stellar velocity dispersion, ˙v. We also list the starburst ages and the percentage by mass that they contribute to the best-fit models. The age range given corresponds to the 68% confidence intervals in the fits for starburst ages, with their respective contributions listed as a contribution range. The first striking result is that the majority of the hosts have a substantial contribution from an intermediate-age starburst population. ",
+    "In Table (<>)3 we compare the results obtained using the BC03 models with the CB07 and M05 models. In spite of the di erences in these sets of models, the best fit starburst ages obtained from these three sets of models are in remarkable agreement. There is considerably more variation among the models in the values of the relative contribution of the starbursts. This is not surprising considering the large ranges of values that are given as confidence levels in Table (<>)2. The large uncertainties in the relative contributions are explained as follows: While the total flux emitted per solar mass changes rapidly (by more than a factor of two) between a population of 1 and 2 Gyr, the spectral features (including the shape of the continuum) change much more slowly and, therefore, ˜2 changes relatively slowly. In other words, a small increase in age for the starburst requires a larger increase in its relative contribution toward the total spectrum. This results in a broad range of values for the contribution that give similar values of ˜2 (see insets in Fig. (<>)1). Thus, the precise values of the relative contribution should not be taken at face value, but rather as a general guide for the relative importance of the starburst population. Even taking into account the large uncertainties, our results show that the contribution from the intermediate-age populations is rather substantial. ",
+    "Six of the objects (0054+144, 0137+012, 0244+194, 1020−103, 2135−147, 2247+140) have a second minimum in ˜2 (see insets in Fig. (<>)1). The second minimum corresponds to a model with a very small contribution from a very young (tens of Myr or younger) population. This combination of populations reproduces the general shape of the continuum of the host galaxies quite well, and hence the lower value of ˜2 . However, close examination of the stellar absorption features reveals that the model corresponding to the primary minimum is, indeed, a much better fit to the data than the values of ˜2 would seem to indicate. Figure (<>)2 illustrates this point. While the continuum of the 0137+012 host is well fit by a model composed of a 40 Myr plus a 10 Gyr old population, the stellar absorption features are best fit by a model including a 1.7 Gyr population. ",
+    "In our analysis, we did not account for the e ects of potential dust in the host galaxies. Any dust extinction will redden the continua and will therefore lead to overestimating the age and/or metallicity when fit with unreddened models. Therefore, the ages that we determine for the intermediate-age populations should be regarded as upper limits. However, the fact that we get similar ages for the intermediate-age populations from techniques that include the overall continuum SED and those that depend primarily on the absorption lines indicates that these populations cannot be substantially ",
+    "younger than these limits. ",
+    "There was only one object, 2247+140, for which we found a significant age-metallicity degeneracy. For this object, increasingly older populations with increasingly lower metallicities result in equally good fits. At the lowest extreme, the spectrum is well fit by a single BC03 model of a 10 Gyr population with a metallicity of 0.4 Z⊙. The M05 models show a similar trend, but in that case the extreme is a fit by a single 1 Gyr population of 0.5 Z⊙. ",
+    "As noted in the Appendix, 1012+008 presents special challenges, in that the host galaxy spectrum is slightly contaminated by the interacting spiral galaxy, and no observations of a star to calibrate the wavelength variation in scattering of the QSO light were available. Nevertheless, the qualitative presence of an intermediate-age population is quite secure because of the strength of the Balmer absorption lines. ",
+    "We created an average QSO host galaxy spectrum (Figure (<>)3) by combining the spectra of all the host galaxies (except for 1012+008, for the reasons given above). The spectra were normalized to their median flux in the region between 4020 and 4080 ° A and weighted by their S/N. The resulting average spectrum is best fit by the combination of a 10 Gyr population with a 2.1 (+0.5, −0.7) Gyr population contributing 64% (+36, −36) to the total model by mass. A similar, but inferior, fit may be achieved for the 0.4 Z⊙models with a 10 Gyr plus a 2.0 Gyr population contributing 18% of the total mass. ",
+    "Thus, our results indicate that, far from being passively evolving elliptical galaxies, almost all of the QSO host galaxies have su ered a major event of star formation within the past ˘ 2 Gyr. "
+  ],
+  "3.3. Alternatives ": [
+    "We have found that the majority (14/15) of the host galaxies in our sample are composed of large fractions of intermediate-age stellar populations. Here we consider alternative scenarios that may be physically plausible. "
+  ],
+  "3.3.1. Purely old populations ": [
+    "Our results clearly rule out the possibility that these hosts are “red and dead” elliptical galaxies. The ˜2 values that we obtain by fitting a single population older than ˘8 Gyr are at least four times higher than those obtained from fits including an intermediate-age population. Figure (<>)4 shows the average host galaxy spectrum described in Section (<>)3.2 above. For comparison, we over-plot the Keck LRIS spectrum of a z=0.1930 elliptical galaxy from a control sample (G. Canalizo et al., in preparation), normalized to the flux at 4000 ° A. We also over-plot single 10 Gyr bursts of 0.4 and 1 Z⊙. Neither the elliptical galaxy, nor the di erent models match the host galaxy spectrum. The right panel of Figure (<>)4 shows that the stellar population would have to have a metal-licity lower than 0.4 Z⊙in order to match the continuum of the host galaxy spectrum and, even then, the stellar features would not be a good fit to the data, as we discuss below. In any case, it is highly unlikely that galaxies in this mass range (˘ 1011 − 1012 M⊙; (<>)Dunlop et al. (<>)2003; (<>)Decarli et al. (<>)2010) would have such low metallicities. ",
+    "One might argue that the di erence between the host galaxy spectra and a purely old population may be explained if the continuum of the host galaxy is a ected by ",
+    "Fig. 1.— Rest-frame Keck LRIS spectra of the QSO host galaxies. The black trace in the upper panel of each object is the host galaxy corrected for QSO light contamination and for Galactic reddening. In some cases (0054+144, 0137+012, 0157+001, 1012+008, 2135−147, 2247+140), the spectra have been smoothed with a gaussian of sigma <1 ° A for displaying purposes. The red trace is the best-fit BC03 model to the data, consisting of the combination of a 10 Gyr-old population and a younger population. The age and relative contribution of this younger population are given in Table (<>)2. The bottom panel for each object shows the residuals obtained by subtracting the model from the observed spectrum. The insets are two-dimensional plots of ˜2 as a function of the age and relative contribution by mass of the younger population to the total spectrum. ",
+    "Fig. 1.— Continued. ",
+    "Fig. 1.— Continued. ",
+    "TABLE 2 ",
+    "Stellar Populations ",
+    "TABLE 3 ",
+    "Comparison of BC03, CB07, and M05 Models ",
+    "Fig. 2.— Comparison between two models that fit well the continuum shape of a host galaxy. The black trace is the rest-frame spectrum of the 0137+012 host. The green trace is the sum of a Gyr population and a 40 Myr population, contributing 0.3% of total mass. The red trace is the sum of a 10 Gyr population and a 1.7 Gyr population contributing 50% by mass. Although both models result in a good fit to the continuum, the model including the younger population does not match stellar features such as H&K. ",
+    "QSO light, whether scattered by free electrons and dust, as (<>)Young et al. ((<>)2009) suggest, or simply resulting from poor corrections of the QSO light contamination on the host. It is clear from the shape of the residuals in Figure (<>)4 that the di erence in the continuum between old population and our QSO hosts cannot be accounted for by QSO light. ",
+    "To further show that the QSO host spectra di er from old population spectra by more than just the continuum, we subtracted di erent amounts of QSO continuum from the average host to attempt to match the SED of the purely old populations discussed above. We subtracted a fit to an average QSO spectrum without including the emission lines, since the latter would otherwise be obviously over-subtracted from the average host. We found ",
+    "Fig. 3.— Average of the 14 QSO host galaxies with intermediate-age populations. The red trace is the sum of a 10 Gyr population and a 2.1 Gyr population contributing 64% by mass along the line of sight. The inset is a two-dimensional plot of ˜2 as a function of the age and relative contribution by mass of the younger population to the total spectrum. ",
+    "that there is no way to reproduce the SED of either the elliptical galaxy or the single 10 Gyr-old model of solar metalicity, regardless of the amount of QSO continuum subtracted. We were able to reproduce roughly the SED from 4000 to 6000 ° A of the 0.4 Z⊙10 Gyr-old model by subtracting an additional 18% (at 4500 ° A) of QSO continuum (with no emission lines). It is clear from Figure (<>)5 that even if the artificially modified average spectrum can match a portion of the SED of a low-metallicity purely old population, the stellar features are better fit by a population that includes an intermediate-age population. Thus, we conclude that the QSO host galaxy spectra cannot be fit by purely old stellar populations, regardless of metallicity or whether the spectra are contaminated by QSO light. ",
+    "3.3.2. A very small contribution from a very recent starburst ",
+    "Fig. 4.— Comparison between QSO host galaxies and purely old stellar populations. The black trace is the rest-frame average of 14 QSO host spectra. The elliptical galaxy spectrum (red trace in the left panel) and the 10 Gyr models (red and purple traces in the right panel) are normalized to the flux of the host galaxy spectrum at 4000 ° A. ",
+    "Fig. 5.— Comparison between the average QSO host spectrum and a purely old, low-metalicity model. Top two panels: The black trace is the rest-frame average of 14 QSO host spectra. The blue trace is the best fit 1 Z⊙model for the average host spectrum, composed of a 10 Gyr-old population and a 2.1 Gyr starburst contributing 64% of the total mass along the line of sight. Bottom two panels: The black trace is a modified version of the average host spectrum, created by artificially subtracting a large amount of QSO continuum (with no emission lines) in order to match the SED of the low-metalicity model. The purple trace is a 10 Gyr-old model with metallicity of 0.4 Z⊙. Refer to Figure (<>)4 to see the actual di erence in SEDs between the average spectrum and the 0.4 Z⊙model. ",
+    "Fig. 6.— Comparison of a 10-Gyr-old stellar population with a blue horizontal branch (BHB; blue trace) with a 1.5-Gyr-old stellar population (black trace). A 10-Gyr-old stellar population with a red horizontal branch is shown in red for comparison. All models are from M05 and have solar metallicity. ",
+    "As we mentioned in Section (<>)3.2, the combination of an old population with a very small fraction of a very young (a few Myr-to a few tens of Myr-old) population can mimic the SED of some (6/15) of the hosts in the spectral range that we cover in our observations. This is essentially the result that (<>)Nolan et al. ((<>)2001) obtained. However, we have already shown that this particular combination of models is not a good fit to the absorption features in the spectrum. ",
+    "Adding any other population to a mostly old (10 Gyr) population results in much worse fits. We experimented with di erent possibilities, such as adding a very small amount of sustained star formation rate, or an old population with an exponentially decaying star formation rate with a long e-folding time. None of these options resulted in acceptable fits. "
+  ],
+  "3.3.3. Contamination by Blue Horizontal Branch Stars ": [
+    "Can a moderately young (1–2 Gyr) population be impersonated by blue horizontal branch (BHB) stars in an old population? Figure (<>)6 shows that such a scenario is at least roughly possible, in that a 10-Gyr-old model with a blue horizontal branch can mimic a 1.5 Gyr population fairly closely. One now has to ask whether it is astrophys-ically reasonable that luminous elliptical galaxies should have a suÿcient population of BHB stars to produce the spectral variations that we have inferred to be signs of a 1–2-Gyr-old starburst. ",
+    "The color of a star on the horizontal branch is determined to a large degree by its metallicity: the lower the metallicity, the bluer the star. By carefully modeling and subtracting o a maximum old, metal-poor component for a number of local ellipticals, (<>)Trager et al. ((<>)2005) show that, if a significant intermediate age population is actually present, correcting for the metal-poor population does not alter the age obtained for the intermediate-age population by very much. More importantly, the presence of the metal-poor population does not do away with the need for the intermediate-age population to explain ",
+    "the observed line strengths. ",
+    "In our spectra, we do not have as good a calibration of line strengths as in studies of local ellipticals. On the other hand, for many of our host galaxies, the Balmer lines are considerably stronger than in the local sample and the inferred intermediate-age population is much more significant than in the galaxies discussed by (<>)Trager et al. ((<>)2005). Plausible levels of BHB contamination are quite insignificant in comparison. For our few marginal cases, we cannot completely exclude the possibility that BHB stars might reduce or eliminate the need for a younger component. However, given the clear presence of intermediate-age populations in much of our sample, it seems more likely that even these are examples of the same trend. "
+  ],
+  "4. COMPARISON TO OTHER STUDIES ": [
+    "(<>)Nolan et al. ((<>)2001) use stellar synthesis models by (<>)Jimenez et al. ((<>)2004) to model o -nuclear spectra of the hosts of 14 of the 15 objects in our sample. Their spectra were obtained with the Mayall 4-m telescope at Kitt Peak and the 4.2-m William Herschel Telescope on La Palma. In stark contrast to our results, they find that the hosts are dominated by populations of ages 8–14 Gyr, with at most a 1% contribution from younger stars. As we mentioned in Section (<>)3.1, they fix a 0.1 Gyr population to account for any recent star formation that may have occurred, and find the best fit by varying the age of the old underlying population. Given their fitting method and the apparent degeneracy that we found at least for some objects in fitting the shape of the continuum, it is not hard to see how (<>)Nolan et al. ((<>)2001) arrived at this conclusion, especially since their spectra are best constrained redward of the 4000 ° A break. Our spectra have much higher S/N that allow us to discriminate between the two combinations of populations that result into a good fit to the shape of the continuum. ",
+    "(<>)Letawe et al. ((<>)2007) use Very Large Telescope FORS1 on-axis spectroscopy of the host galaxies of 20 luminous (MB < −23) QSOs at z < 0.35 to study the stellar populations in these objects. The QSOs are of comparable to slightly higher optical luminosity than the objects in the (<>)Dunlop et al. ((<>)2003) sample (see Figure 1 in (<>)Letawe et al. (<>)2007 for a direct comparison of the samples). The morphologies of the hosts are not exclusively bulge dominated, as in the (<>)Dunlop et al. ((<>)2003) sample, but they also include disks and evidently disturbed hosts. Using the multi-object mode, they simultaneously observe several PSFs that they then use to deconvolve the 2-D spectra. They measure Lick indices in the 15 objects for which they are able to recover absorption-line stellar spectra. By comparing them with the Lick indices of different types of galaxies, they find that only two of their hosts are consistent with being elliptical galaxies, while the rest of them have indices closer to those of late-type galaxies. They also find that the majority of the hosts harbor large amounts of gas. ",
+    "(<>)Jahnke et al. ((<>)2007) conducted a study similar to that of (<>)Letawe et al. ((<>)2007), but they used a fundamentally di erent approach to the deconvolution of the host spectra from the PSF. They perform a semi-analytic two-component spatial PSF fitting of the 2-dimensional spectra of 18 z < 0.3 quasars observed on-axis with EFOSC at the ESO 3.6-m telescope and FORS1 at the ESO VLT. ",
+    "They then determine stellar population ages of eight of the host galaxies by using two single stellar population BC03 models, including continuous star formation. They find that the light-weighted age for the hosts is 1-2 Gyr, regardless of whether they are disk or bulge dominated. ",
+    "The results of (<>)Letawe et al. ((<>)2007) and (<>)Jahnke et al. ((<>)2007) agree with those of other studies of AGN hosts based on multi-band imaging studies ((<>)Kau mann et al. (<>)2003; (<>)Jahnke et al. (<>)2004; (<>)S´anchez et al. (<>)2004). While these studies focus on AGN that are, on average, ˘1 magnitude fainter than those of the (<>)Dunlop et al. ((<>)2003) sample, they find that the galaxies hosting the most luminous AGN are most often bulge-dominated. However, in agreement with our results and those of (<>)Letawe et al. ((<>)2007), they find that the host colors are significantly bluer than those of inactive elliptical galaxies, indicating the presence of intermediate-age populations. In particular, based on their position on the Dn(4000)/HA plane, (<>)Kau mann et al. ((<>)2003) suggest that AGN hosts have had significant bursts of star formation in the past 1-2 Gyr. ",
+    "(<>)Vanden Berk et al. ((<>)2006) use an eigenspectrum decomposition technique to isolate the host galaxy spectra from those of the broad-lined AGN they host in a sample of 4666 objects from the Sloan Digital Sky Survey. The median redshift of the objects with detected hosts is z = 0.236. The majority of the AGN in this sample have lower luminosities than those of the QSOs in the (<>)Dunlop et al. ((<>)2003) sample, but a significant fraction of them have comparable luminosities (see their Figure 13). (<>)Vanden Berk et al. find that the hosts have much higher luminosities than expected for early-type galaxies, and that their colors become increasingly bluer with higher luminosities, when compared with the colors of ellipticals and bulge dominated galaxies. They define two classification angles formed from the first three galaxy eigenco-eÿcients (equations 2 and 3 in (<>)Vanden Berk et al. (<>)2006), which are correlated to spectral type and post-starburst activity, respectively ((<>)Connolly et al. (<>)1995). Based on the distribution of the second classification angle in the hosts, they determine that host galaxies have significantly more post-starburst activity than their inactive counterparts. Although their analysis does not supply specific ages for the stellar populations, their results are at least in qualitative agreement with ours. ",
+    "(<>)Wold et al. ((<>)2010) obtain o -nuclear Keck LRIS and WIYN SparsePak spectra of 10 QSO hosts at z < 0.3. Their sample includes four of the objects in our sample, and six other QSOs with similar optical luminosities. Seven of the host galaxies are classified as elliptical. Their observations are similar to ours and those of (<>)Nolan et al. ((<>)2001): short exposures of the QSO followed by longer o -axis integrations of the host, with o sets from the nuclei between 2 ′′and 4′′.5. We described their modeling strategy in Section (<>)3.1. They also find that the elliptical hosts have rest frame B−V colors that are bluer than those of inactive ellipticals. Moreover, they detect substantial intermediate-age populations in each of the hosts, with an average light-weighted age for the sample of ˘ 2 Gyr. We are unable to compare directly the precise starburst ages and contributions that we obtain with the results of (<>)Wold et al. ((<>)2010) because of the way they present their results. Although they obtain relative contributions of populations with 15 di erent ages, they bin ",
+    "their results into three groups: young (age <100 Myr), intermediate (age between 100 Myr and 1 Gyr), and old (age >1 Gyr). Since the majority of our objects have starbursts with ages somewhat greater than 1 Gyr, they would be classified as old if we were to use a similar classification. With this in mind, we find general agreement for the four objects that we have in common with their sample (see Appendix for details). ",
+    "(<>)Cales et al. ((<>)2013) model the starburst component in the host galaxies of 38 z ˘0.3 “post-starburst quasars” observed with Keck LRIS and with the KPNO 4-m May-all telescope and the R-C spectrograph. These objects show, simultaneously, broad lines from an AGN and absorption lines from a luminous post-starburst stellar population. The sample includes objects with a large range of AGN luminosities, with the high end having significant overlap with our sample. (<>)Cales et al. use the CB07 models along with models to simulate the AGN contribution. They do not include a stellar component for a possible old underlying population, as they argue that doing so does not significantly a ect the age they determine for the starburst component. Their results are remarkably similar to ours: The age of the starburst component in 36/38 of their hosts ranges from 0.5 to 2.6 Gyr, with only two objects having ages of <0.3 Gyr. It is interesting to note that these objects were selected to have intermediate-age populations by design, whereas our objects were selected based on QSO luminosity, yet the two samples of objects have dominant starbursts with the same distribution of ages. "
+  ],
+  "5. DISCUSSION ": [
+    "The studies discussed in the previous section use vastly di erent techniques to (1) observe the objects, (2) recover the host galaxy spectra, and (3) model the stellar pop-ulations. Yet, with the exception of (<>)Nolan et al. ((<>)2001), all of these studies point to the presence of a major starburst episode in the host galaxies of low-z QSOs within the last ˘2 Gyr. ",
+    "What caused these massive starbursts and how are they related to the AGN activity? We have previously reported on the presence of striking tidal features and/or close interacting galaxies for six of the objects in our sample: 0157+001 ((<>)Canalizo and Stockton (<>)2000b), 1635+119 ((<>)Canalizo et al. (<>)2007), 0054+144, et al. (<>)2008). The timescales implied by these various features are, in very rough terms, consistent with a picture where mergers were responsible for the starbursts that we observe. Assuming a projected velocity of 300 km s−1 on the plane of the sky for the stars that make up the tail, (<>)Canalizo and Stockton ((<>)2000b) estimate a dynamical age for the prominent tidal tail in 0157+001 of 330 Myr, compared to the stellar population of 0.8 (+0.2, −0.6) Gyr that we find (and already reported in (<>)Canalizo and Stockton (<>)2000b). The dynamical age could be underestimated if the projected velocity is lower than 300 km s−1 . (<>)Canalizo and Stockton speculate that the intermediate-age population may be the relic of a starburst ignited at an initial passage of the two interacting galaxies. ",
+    "(<>)Bennert et al. ((<>)2008) estimate a dynamical age between 250 Myr and 1 Gyr for the tidal tails seen in deep HST/ACS images of 2141+175 and 0054+144 . While ",
+    "this age estimate is of the same order as the starburst that we observe in 2141+175 (0.8 [+0.2, −0.2] Gyr), it is younger than the starburst in 0054+144 (2.1[+0.6,−0.8] Gyr). Thus, the starburst in the latter may have been triggered in a previous passage of the interacting galax-ies, as in the case of 0157+001. Similarly, (<>)Bennert et al. estimate a dynamical age of ˘1 Gyr for the tidal structure (including ripples, tidal arms, and a faint long tidal tail) surrounding the host of 0736+201, which is of the order of, but younger, than the starburst age of ˘2.2 (+0.2,−0.6) Gyr that we find in the host. ",
+    "(<>)Canalizo et al. ((<>)2007) find striking shell structure in the host of 1635+119, along with ripples or tails and other debris extending out to a distance of ˘65 kpc. Their N-body simulations allow the structure to be as old as 1.7 Gyr, which is similar to the 1.6 (+0.4,−0.2) Gyr starburst age we determine for the host. ",
+    "While the host of 0923+201 does not show any obvious tidal features, it lies in a galaxy group of at least six members at similar redshifts ((<>)Bennert et al. (<>)2008, and references therein), with several of the galaxies showing clear signs of interaction. There is one pair of interacting large elliptical galaxies at a projected distance of ˘37 kpc from the QSO host, and a smaller galaxy with tail-like structures ˘56 kpc away. It is likely that these galaxies have interacted with the host galaxy within the past 1.4 Gyrs, triggering the star formation in the host. ",
+    "We will present deep HST/WFPC2 images of the remaining objects in the sample, together with similar images of a matched control sample, in a forthcoming paper. In summary, we find clear traces of merger and interaction events in almost two thirds of the QSO hosts and hardly any such traces in the control sample. ",
+    "A few of the spectroscopic surveys discussed in Section (<>)4 also examine the morphologies of the hosts. (<>)Jahnke et al. ((<>)2007) and (<>)Letawe et al. ((<>)2007) find that ˘50% of the hosts in their samples show morphological signs of interactions and disturbed radial velocity curves. Of the 29 post-starbursts quasars that have HST images (presented by (<>)Cales et al. (<>)2011), 17 (˘59%) show signs of interactions or mergers. The early-type galaxies in the sample, which host the most luminous AGN, have a similar fraction of objects with signs of interaction. ",
+    "Although at first it would seem that the fractions of interacting objects in these samples are lower than in ours, we must keep in mind that our results are derived from high-resolution, very deep (five orbits) HST images that allow us to detect the aging tell-tale signs of mergers as they are fading away. If we were to analyze shallow and/or ground-based images of the six objects in our sample discussed above, we would find that only two (0157+001 and 2141+175) have obvious signs of tidal interactions and one (0923+201) has close interacting galaxies. Thus, based on this subsample, we would conclude that only 50% of the hosts are connected to mergers. It is then possible that most, if not all, of the QSO host galaxies that appear to be bulge dominated may indeed be more evolved merger remnants hosting intermediate age populations. ",
+    "Thus, we find compelling evidence that the aging starbursts we observe in early-type QSO hosts were triggered during the early stages of a merger event. Typical QSO lifetimes are expected to be, at most, ˘ 108 years, so the currently observed QSO activity cannot have been ",
+    "triggered at the same time as these ˘ 109-year-old starbursts. How, then, can we explain this correlation between QSO activity and intermediate-age starbursts? ",
+    "Numerical simulations of merging galaxies show that the amplitude and duration of enhanced star forming activity, as well as the stage at which it occurs during a merger, depend on the specific parameters of the encounter (orbits, mass ratios, etc.) as well as the morphological type of the progenitors (e.g., (<>)Di Matteo et al. (<>)2007). It is clear, however, that many mergers result in two major epochs of star formation: one soon after first passage, and one during final coalescence (e.g., (<>)Mihos and Hernquist (<>)1996; (<>)Cox et al. (<>)2008; (<>)Torrey et al. (<>)2012; (<>)Van Wassenhove et al. (<>)2012). Similarly, numerical simulations show that accretion onto the central black hole(s) is episodic, and there can be two (or more) major epochs of AGN activity roughly corresponding to (but somewhat delayed with respect to; see (<>)Hopkins (<>)2012) the times at which star formation is dramatically enhanced (e.g., (<>)Hopkins et al. (<>)2008; (<>)Van Wassenhove et al. (<>)2012, N.R. Stickley and G. Canalizo, in preparation). The time delay between the first and second epochs of enhanced star formation/AGN activity naturally depends on the details of the merger; typical values are of the order of 1 Gyr, i.e., of the same order as the ages of the starbursts that we observe in the QSO hosts. ",
+    "Thus, our observations appear to be consistent with the predictions made by numerical simulations. In this picture, the QSO hosts in our sample are products of galaxy mergers. Strong bursts of star formation are induced in the early stages of a galaxy interaction. As the galaxies continue to merge for the next billion or so years, the new stars mix with the older populations, and they age as the morphology of the newly formed galaxy begins to relax. When gas continues to concentrate in the central regions of the galaxy, a new central starburst is triggered, followed by a final epoch of AGN activity. It is precisely at this moment that we seem to be observing the QSOs in our sample. ",
+    "A glaring di erence between this picture and our results is the absence of young stellar populations, expected to be the result of the major starburst triggered during the final coalescence of the galaxies, and a short time (of the order of ˘100 Myr; (<>)Hopkins (<>)2012) before the triggering of the QSO. However, these starbursts are expected to occur very close to the nucleus (P. Hopkins, S. Van Wassenhove, private communication), whereas our spectroscopic observations cover regions of the host galaxies that are typically ˘8 kpc away from the center (see Table 1). Stars formed during earlier stages of mergers are more easily mixed with the rest of the population by the end of the merger because of the multiple passes that the interacting galaxies experience. However, once the galaxies merge, there is no further violent event to help mix the new stars. This is supported by numerical simulations that show that the velocity dispersions of stars formed in the late stages of mergers remain low compared to those of stars formed earlier on (N.R. Stickley and G. Canalizo, in preparation). ",
+    "At least for the one object for which we have spatially resolved spectra, 0157+001 ((<>)Canalizo and Stockton (<>)2000b), we do find significantly younger populations (˘200 Myr old) near the QSO nucleus. There are a few other QSO hosts for which spatially resolved informa-",
+    "tion on stellar populations exists. (<>)Canalizo and Stockton ((<>)2000a) show that the most luminous and youngest (<10 Myr) stellar populations in the host galaxy of 3C 48 are concentrated in the central regions of the host (in the central ˘5 kpc), while the outer regions are dominated by an older population. Unfortunately, the S/N of the spectra in the outer regions is not suÿcient to discriminate between a purely old population and a population including intermediate-age stars. Similarly, the youngest starbursts (<50 Myr) in the host of Mrk 231 are found in a region ˘3 kpc from the QSO nucleus ((<>)Canalizo and Stockton (<>)2000b), whereas the outer regions are dominated by older populations. As in the case of 3C 48, the S/N is insuÿcient to determine the precise composition of the older populations. Finally, (<>)Brotherton et al. ((<>)2002) report on the presence of a .40 Myr starburst in the central 600 pc of the host galaxy of the prototype post-starburst quasar, UN J1025−0040, which is significantly younger than the dominant population of the host of 400 Myr. ",
+    "However, there is evidence that the picture may be more complicated. (<>)Shi et al. ((<>)2007) found strong evidence that QSOs selected by di erent criteria showed different levels of star formation. In particular, their sample of PG QSOs (generally radio quiet; (<>)Schmidt and Green (<>)1983) showed significantly more star formation than did their sample of 3CR (i.e., radio-loud) QSOs. This result is amplified by (<>)Fu and Stockton ((<>)2009), who found that, of a sample of 13 radio-loud QSOs, only the compact-steep-spectrum quasar 3C 48 showed any evidence of star formation. For the remaining 12 QSOs, all with FR II radio morphologies, a stack of deep Spitzer IRS spectra indicated a conservative average star-formation rate upper limit of ˘12 M⊙yr−1 . These di erences in typical star-formation rates between radio-quiet QSOs and FR II quasars most likely reflect di erences in environments ((<>)Fu and Stockton (<>)2009, and references therein), but it is tempting to speculate that there may also be a dependance on merger stage. In any case, when (<>)Shi et al. ((<>)2009) say, “We propose that type-1 quasars reside in a distinct galaxy population that shows elliptical morphology but that harbors a significant fraction of intermediate-age stars and is experiencing intense cir-cumnuclear star formation,” the last part of this statement appears not to hold generally for FR II quasar hosts. ",
+    "We have concentrated on the QSO sample of (<>)Dunlop et al. ((<>)2003) precisely because of their contention that the host galaxies of this sample have properties indistinguishable from those of local quiescent ellipti-",
+    "cals. We find instead that virtually all of them have intermediate-age populations comprising a significant fraction of the total mass of the host galaxies. These populations can be interpreted in a natural way in terms of models of galaxy mergers, where the star formation is triggered by a previous passage of the galaxies, while the current QSO activity results from the final merger. While there certainly are some cases of QSOs seen in conjunction with contemporaneous starbursts, or at least with much younger populations ((<>)Canalizo and Stockton (<>)2001), these seem to be relatively rare, and they probably depend on having serendipitous sightlines to the QSO through otherwise dusty host galaxies. In most objects at similar stages, the QSO nucleus is likely obscured, and the galaxies would be classified as ULIRGs or HyLIRGS. By the time the starburst has subsided and the dust has cleared, the QSO activity likely will have stopped, only to be re-triggered during the final merger. ",
+    "We are grateful to the anonymous referee for useful comments and suggestions that helped improve both the contents and the presentation of this paper. This work was supported in part by the National Science Foundation, under grants number AST 0507450 and AST 0807900. Additional support was provided by NASA (programs GO-10421, GO-11101, and AR-10941) through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. G.C. is grateful for the hospitality of the Institute for Astronomy, University of Hawaii, where part of this work was conducted. The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors recognize the very significant cultural role that the summit of Mauna Kea has within the indigenous Hawaiian community and are grateful to have had the opportunity to conduct observations from it. This research made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. ",
+    "Facilities: Keck:I (LRIS) "
+  ]
+}

jsons_folder/2013ApJ...773...17S.json

@@ -0,0 +1,125 @@
+{
+  "CONFRONTING MODELS OF DWARF GALAXY QUENCHING ": [],
+  "WITH OBSERVATIONS OF THE LOCAL GROUP ": [
+    "Colin T. Slater and Eric F. Bell ",
+    "arXiv:1306.1829v1  [astro-ph.CO]  7 Jun 2013 ",
+    "Department of Astronomy, University of Michigan, 500 Church St., Ann Arbor, MI 48109; (<mailto:ctslater@umich.edu>)ctslater@umich.edu "
+  ],
+  "ABSTRACT ": [
+    "A number of mechanisms have been proposed to connect star-forming dwarf irregular galaxies with the formation of non-star-forming dwarf spheroidal galaxies, but distinguishing between these mechanisms has been difficult. We use the Via Lactea dark matter only cosmological simulations to test two well-motivated simple hypotheses—transformation of irregulars into dwarf spheroidal galaxies by tidal stirring and ram pressure stripping following a close passage to the host galaxy, and transformation via mergers between dwarfs—and predict the radial distribution and inferred formation times of the resulting dwarf spheroidal galaxies. We compare this to the observed distribution in the Local Group and show that 1) the observed dSph distribution far from the Galaxy or M31 can be matched by the VL halos that have passed near the host galaxy at least once, though significant halo-to-halo scatter exists, 2) models that require two or more pericenter passages for dSph-formation cannot account for the dSphs beyond 500 kpc such as Cetus and Tucana, and 3) mergers predict a flat radial distribution of dSphs and cannot account for the high dSph fraction near the Galaxy, but are not ruled out at large distances. The models also suggest that for dSphs found today beyond 500 kpc, mergers tend to occur significantly earlier than dwarf–host encounters, thus leading to a potentially observable differ-ence in stellar populations. We argue that tidal interactions are sufficient to reproduce the observed distribution of dSphs if and only if a single pericenter passage is sufficient to form a dSph. ",
+    "Subject headings: galaxies: dwarf — Local Group — galaxies: evolution "
+  ],
+  "1. INTRODUCTION ": [
+    "The origin of the approximate dichotomy between the star-forming dwarf irregular galaxies (dIrrs) and the non-star-forming, pressure supported dwarf spheroidal galax-ies (dSphs) has long been an open question ((<>)Hodge & (<>)Michie (<>)1969; (<>)Faber & Lin (<>)1983; (<>)Kormendy (<>)1985; (<>)Gal-(<>)lagher & Wyse (<>)1994). Several mechanisms have been proposed to create dSphs, such as tidal stirring and stripping ((<>)Mayer et al. (<>)2001; (<>)Klimentowski et al. (<>)2009; (<>)Kazantzidis et al. (<>)2011a; (<>)Kravtsov et al. (<>)2004), resonant stripping ((<>)D’Onghia et al. (<>)2009), or ram pressure stripping ((<>)Mayer et al. (<>)2006). This broad grouping of models all involve the influence of a large host galaxy, which is motivated by the observed trend in the Local Group for most dSphs to be found within 200-300 kpc of either the Milky Way or M31 ((<>)van den Bergh (<>)1994; (<>)Grebel et al. (<>)2003). Other theories for dSph formation do not require the influence of a larger galaxy and transform dIrrs into dSphs via either heating of the dwarfs’ cold gas by the UV background ((<>)Gnedin (<>)2000), strong feedback ((<>)Dekel (<>)& Silk (<>)1986; (<>)Mac Low & Ferrara (<>)1999; (<>)Gnedin & Zhao (<>)2002; (<>)Sawala et al. (<>)2010), or mergers between dwarfs at early times ((<>)Kazantzidis et al. (<>)2011b). ",
+    "Since many of these mechanisms can all be shown to plausibly produce dSphs given the right initial conditions, it can become difficult to distinguish between these theories as many leave only weak signatures on the individual galaxies. Because of this limitation, one might alternatively study the signatures these processes leave on the population of Local Group dwarfs as a whole. The orbital and assembly histories of the dwarfs in the Local Group vary significantly, and the link between these histories and the resulting morphologies of the dwarfs may be a telling indication of which processes are at work. ",
+    "This perspective aims for differentiating between mechanisms for dSph formation where they are most different— where and when they act—rather than where they are all generally similar in the injection of energy into the orbits of stars in the dwarf. ",
+    "In this work we use cosmological simulations (Via Lactea I & II, (<>)Diemand et al. (<>)2007, (<>)2008, herein VL1 and VL2) to trace the histories of the dwarfs that survive to today, and use these histories to infer which dwarfs (in aggregate) may have been affected either by tidal stirring or by mergers between dwarfs. The large difference in when and where these mechanisms act on dwarfs creates significant differentiation in the resulting distribution of dSphs. These two cases are also particularly suitable for study with high resolution dark-matter-only simulations, since the behavior of the luminous components can be inferred from the behavior of the dark matter. That is, we can infer the effects of tidal forces or mergers experienced by a galaxy by tracking the dark matter halo and applying relatively simple criteria based only on the halo properties. These criteria are physically motivated based on controlled simulations of the individual processes (e.g., (<>)Kazantzidis et al. (<>)2011b, (<>)2013). Clearly these simulations will predict some detailed properties of the dwarfs that will not be captured by our binary dSph-or-not criteria, but our focus on the bulk properties of the dwarf population as a whole will minimize the impact of these differences on our conclusions. These simplifications enable us to understand the formation of dSph galaxies in a broader cosmological context rather than only in controlled experiments. ",
+    "Much of this work focuses on the dwarfs currently outside the virial radius of the Galaxy (or M31). The distribution of distant satellites that were once found inside the virial radius of a host has been investigated before in ",
+    "simulations of cluster or group environments ((<>)Balogh et (<>)al. (<>)2000; (<>)Moore et al. (<>)2004; (<>)Gill et al. (<>)2005; (<>)Wetzel et al. (<>)2013) and Milky Way-like environments ((<>)Diemand et al. (<>)2007; (<>)Teyssier et al. (<>)2012). The existence of such galaxies is well established. Similarly, the rate and timing of mergers between dwarfs in a Milky Way-like environment has been studied with simulations ((<>)Klimentowski (<>)et al. (<>)2010), but comparisons to observations have remained limited. Our work focuses on bringing both of these mechanisms for the formation of dSphs to a spe-cific comparison with the observed distribution of Local Group dwarfs. ",
+    "Towards that goal, we discuss the simulations and our criteria for both interactions and major mergers in Section (<>)2, and present the results and a comparison to the observed dSph distribution in the Local Group in Section (<>)3. The distribution of times at which galaxies either merge or experience close passages is described in Section (<>)4, and we discuss the implications of these results in Section (<>)5. "
+  ],
+  "2. ANALYSIS OF SIMULATIONS ": [
+    "We use both the Via Lactea simulation ((<>)Diemand et al. (<>)2007) and Via Lactea II1 (<>)((<>)Diemand et al. (<>)2008) for our analysis of tidal interactions, and only the VL2 simulation for our analysis of mergers. Both are cosmological, dark matter only simulations centered on a Milky Way-sized halo with a virial mass of 1.93 × 1012M in VL2 (1.77 × 1012M in VL1), corresponding to a virial radius (r200) of 402 kpc (389 kpc in VL1). VL1 used 234 × 106 particles of mass 2 × 104 M, while VL2 had 1.1 × 109 particles each of mass 4.1×103 M. Both simulations are entirely sufficient to resolve all of the luminous observable satellites, and we will generally restrict our results to halos with a maximum circular velocity (Vmax) greater than 5 km/s at z = 0. At this limit halos have an average of 350 particles in VL1 and 800 particles in VL2. Dark matter halos were identified in the simulation using a phase-space friends-of-friends (6DFOF) algorithm, as described in detail in (<>)Diemand et al. ((<>)2006). These halos were then linked across snapshots by identifying halos which share significant numbers of particles; in identifying the most massive progenitor at least 50% of the particles in the descendant are required to be present in the progenitor, and conversely 50% of the progenitor particles to be present in the descendent. This constraint is later relaxed when computing merger trees, but the process is similar. Note that 6DFOF only links the central, low energy particles together; that is, the fraction of common particles between the progenitor and the descendant is usually significantly larger among the 6DFOF particles than among all particles within the virial radius. ",
+    "In addition to the Milky Way-analog halo (referred to as the “main” halo for convenience), in VL2 there is also a second large galaxy present in the simulations that happens to have properties similar to Andromeda. This was identified in (<>)Teyssier et al. ((<>)2012), who refer to it as “Halo 2” and showed that it has a total gravitationally-bound mass of 6.5 × 1011 M, and lies 830 kpc from the main halo. Both of these properties are conveniently similar to Andromeda, and as a result, when we discuss ",
+    "the interaction between dwarf galaxy-sized halos and a massive host, we consider either the main halo or Halo 2 to be sufficient for this purpose. Ignoring Halo 2 would significantly bias our results, since dwarf galaxy halos that become bound to it may experience substantial tidal interactions while their distance from the main halo is still large. Treating both large halos on an equal footing also reflects our treatment of the observed Local Group dwarfs, where we consider the dwarfs’ distance to either the Milky Way or Andromeda, whichever is less. VL1 has no such analogous component, so we do not apply the same conditions. "
+  ],
+  "2.1. Tidal Interactions ": [
+    "With the evolutionary tracks of halos in place, we can identify halos that are strong candidates to have undergone some form of interaction with a larger galaxy. This process is similar to that of (<>)Teyssier et al. ((<>)2012) but not identical. Of the several thousand most massive halos identified at z = 0, we select only those with Vmax values between 5 and 35 km/s. This cut conservatively ensures that the halos we track are well resolved, and broadly spans the Vmax values of classical dwarf galaxies. The position of the halo’s most massive progenitor is then tracked back through each snapshot, and both it and the position of the two host halos are linearly interpolated between snapshots. The pericenter distance and the number of pericenter passages between the halo and either host is then recorded. While interpolation between timesteps is not ideal, it does provide some assurance that we are not substantially overestimating the minimum radius of each pericenter passage by only taking the distance at individual snapshots. We have veri-fied that this interpolation produces accurate results for VL2 (where the larger timesteps make it more important) by using the more densely sampled Via Lactea 1 simulation, downsampling the timesteps to the VL2 resolution and testing the interpolation. The results show the interpolation works particularly well for the distant halos we focus on here as most of them are on strongly radial, fly-by trajectories. ",
+    "The distance between the halo and either of the hosts is then compared to the virial radius (r200,mean, defined to enclose a density 200 times the cosmic mean density) of the main galaxy as a function of redshift, and the minimum of this ratio is found. This establishes the depth to which the halo has reached in a large galaxy. We assume the virial radius of Halo 2 is the same as that of the main halo, and we later show that our results are not particularly sensitive to the exact radius criterion. We also track the number of pericentric passages the halos have undergone inside of Rvir/2 of the host halo by finding minima in the halo-host distance. The resulting halo statistics are in good agreement with those obtained by (<>)Teyssier (<>)et al. ((<>)2012); out of all selected halos, a very large majority (96%) have at some point been inside of half the host virial radius, and approximately 11% of those that have been inside this radius are later found at z = 0 outside of virial radius. ",
+    "We note that our model relies on the assumption that the halos in the simulations are populated with observable dwarf galaxies in an unbiased way. This assumption is potentially called into question by the “missing satellites problem”, which may suggest that the number of ",
+    "subhalos in simulations is substantially larger than the number of dwarf galaxies in the Local Group ((<>)Moore et (<>)al. (<>)1999; (<>)Klypin et al. (<>)1999). For example, in VL1 and VL2 we include 9992 and 2224 halos, respectively, in our analysis, but only 101 observed dwarfs (from the catalog of (<>)McConnachie (<>)2012). This discrepancy can be plausibly resolved within the cold dark matter framework by a combination of observational incompleteness and su-pression of star formation in small halos, thus decreasing their luminosity below detectability in current surveys ((<>)Somerville (<>)2002; (<>)Koposov et al. (<>)2009), or by (additionally) destroying or diminishing the mass of halos through tidal stripping ((<>)Kravtsov et al. (<>)2004; (<>)Brooks et al. (<>)2013). Our use of ratios of number counts of halos limits our sensitivity to models that alter the mapping between halos and dwarfs based only on their mass, since the motion of the halos through the group environment remains unchanged. The selective destruction of halos by tidal stripping has the potential to decrease the fraction of dSphs at large radii, but as we argue below the dominant uncertainty at large radii is variation between halo realizations, and thus we do not impose a more complex tidal destruction criteria. We discuss tidal destruction further in the conclusions. "
+  ],
+  "2.2. Merger Trees ": [
+    "The fraction of galaxies that have experienced major mergers is calculated from the same z = 0 sample and uses the same method of linking halos at each snapshot to their possible progenitors. However, in the merger trees the selection requirement for the number of dark matter particles shared between halos is relaxed, since we are interested in all progenitor halos and not only the most massive progenitor. Starting at z = 0, we traverse the merger tree following the most massive progenitor at each step, until locating a halo that has two progenitors in a 3 : 1 dark matter mass ratio or greater. The timestep where the two halos are identified as a single 6DFOF halo is noted as the merger time. ",
+    "Visual inspection of the merger trees suggests that this simple criteria is effective in identifying whether a halo has merged or not, even though the merger process may be more complex in detail. Halos can often undergo close passages, which can cause particles to be lost from the halos by tidal stripping and thus alter the mass ratio we measure at the final coalescence of the 6DFOF halos. Other halos undergo passages that temporarily appear as one 6DFOF group in a snapshot, even though they will later separate and re-coalesce in subsequent snapshots. Because we track the time of the most recent merger snapshot, in these cases our merger times will tend to reflect this final coalescence rather than initial passes. We are also limited by only tracing the dark matter; we cannot say when the baryonic components of these galaxies will merge. In general we expect that when the dark matter halos merge, the baryons must follow, but this should be delayed by the time required for dynamical friction to bring the baryonic components together. We present a simple calculation of the dynamical friction timescale in Section (<>)5 and find that it is of order 200 Myr or less, which is much smaller than the offset in formation times between the merger model and the tidal processing model. ",
+    "Our ability to resolve mergers at very high redshifts is ",
+    "also limited. Beyond z > 2.5 (11.3 Gyr ago), halos are poorly linked in time and mergers may not be properly resolved while they undergo an initial phase of rapid assembly. We consequently do not track mergers before z = 2.5. Since there is significant merger activity near these redshifts, we note that total fraction of dwarfs that have undergone mergers could be sensitive to the exact cut-off we select, and consequently we focus primarily on the distribution of merged dwarfs rather than their absolute fraction. As we will show, the shape of the radial distribution is unaffected by varying this high redshift cut-off. "
+  ],
+  "3. COMPARISON TO OBSERVATIONS ": [
+    "We compare these simple models to the observed set of Local Group dwarf galaxies, using the catalog assembled by (<>)McConnachie ((<>)2012), which includes all of the known galaxies within 3 Mpc of the Sun. The catalog labels galaxies with MV > −18 as dwarfs by convention, and though this cutoff is somewhat arbitrary, we use the same criterion here. This excludes, for example, M32 and the Large Magellanic Cloud, but includes the Small Magellanic Cloud. The catalog provides both galactocentric and M31-centric distances, and also classifies galaxies as either dSphs, dIrrs, or an intermediate “dSph/dIrr” class. Most of these classifications are uncontroversial. The dSph/dIrr class contains most of the galaxies for which either observational uncertainty or peculiar combinations of properties makes it difficult to definitively call them either a dSph or a dIrr. Since it is beyond the scope of this work to reconsider the classification of each of these galaxies, we treat the classification of (<>)McConnachie ((<>)2012) as authoritative. We account for the uncertainity in the dSph/dIrr class by evaluating two scenarios: one where all of these galaxies are treated as dSphs, and one where they are all treated as dIrrs. The range of values produced by these two cases yields some estimate of the uncertainty from classification. We make only two updates to the classifications of (<>)McConnachie ((<>)2012) based on more recent works: the galaxy Andromeda XXVIII has been confirmed to be a dSph (Slater et al., in prep), as has the galaxy KKR 25 ((<>)Makarov et al. (<>)2012). It is important to note that the set of known dwarfs is not complete, and there may be underlying observational biases in the catalog. In this work we do not attempt to correct for biases in the selection function. We make the assumption that dSphs and dIrrs are equally likely to be detected, and thus the relative fraction of these two types is independent of the selection function. Inside of roughly 800 kpc this condition in general is met, since both dSphs and dIrrs can be detected by their red giant branch stars in the available large surveys (e.g., (<>)Irwin et (<>)al. (<>)2007; (<>)Slater et al. (<>)2011). Outside of this range dIrrs may be preferentially detected, since their young stars can be brighter than the tip of the red giant branch in dSphs. We remain mindful of this potential bias when interpreting the observations, but do not believe it affects our results. Our conclusions are necessarily more cautious at very large radii. ",
+    "For each dwarf we compute the minimum of either its Galactocentric or its M31-centric distance, since we are not concerned with which galaxy the dwarfs may have interacted with. The dwarfs are then binned into groups of ten, and the fraction of dSphs in each bin is plotted ",
+    "Figure 1. Fraction of dSph galaxies as function of galactic radius (minimum of either Galactocentric or M31-centric), grouped into bins of ten dwarfs and plotted with black symbols. Upper and lower black triangles differ by including or excluding intermediate type dwarfs as non-star forming. The span of radius covered by each bin is shown by the horizontal black lines, and the black points are plotted at the mean radius of that bin. The green lines show the fraction of halos that have passed inside Rvir/3 in VL2, either once (solid green) or through more than one pericentric passage (dashed green). The blue lines show the same values but for VL1. The red line shows the distribution of dwarfs that have undergone major mergers. The horizontal series of ticks along the bottom indicate the positions of the dwarfs in the sample. The Magellanic Clouds are included in the bin at 50 kpc. ",
+    "as the black symbols in Figure (<>)1 at the mean radius of its constituent dwarfs. This fixed-number rather than fixed-width binning scheme is used to compensate for the large dynamic range in the number of dwarf galaxies as a function of radius. For each bin, we evaluate the non-star forming fraction with the intermediate dSph/dIrr type galaxies included as dSphs (upper triangles) and as dIrrs (lower triangles), and the two points are connected by the vertical black lines. Bins with no transition galaxies appear as diamonds. The range of radius values spanned by each grouping of ten dwarfs is shown by the black horizontal lines on each point. ",
+    "In Figure (<>)1, the red line shows the radial distribution of Via Lactea II halos that have had a major merger since z = 2.5. This distribution is clearly flat, and does not exhibit the rise in non-star forming dwarfs inside of 1 Mpc as is seen in the Local Group. This radial dependence alone suggests that mergers cannot be the only channel for dSph formation. ",
+    "Also in Figure (<>)1, the fraction of satellite halos from the simulations that have passed inside of Rvir/3 is shown by the solid blue line for VL1 and the green line for VL2. (For VL2 this also uses the minimum distance between a halo at z = 0 and either the main host halo or Halo 2.) This is a simple proxy for the dwarfs that could have undergone transformation by a tidal interaction. ",
+    "The radial profile in VL2 agrees quite well with the distribution of observed dSphs, with a gradual decline in non-star-forming fraction from 400 to 1500 kpc. This illustrates that tidal processes can plausibly reproduce the observed set of dSphs. However, the VL1 profile falls off much more rapidly, with very few tidally processed halos found beyond 800 kpc. The difference between the VL1 and VL2 results suggests that the predicted radial profile of dSphs in this model is clearly not a smooth, universal function. There is a large stochastic component that is evident even with only two realizations of a Local Group-like environment, which produces variations in the dSph profile beyond what would be expected from just Poisson noise. This variation comes from the accretion of subgroups of halos, which follow similar trajectories and introduce correlations in the fraction of processed halos. The accretion of discrete subgroups has been seen in other simulations, such as (<>)Li & Helmi ((<>)2008) and (<>)Kli-(<>)mentowski et al. ((<>)2010), and we include a more detailed illustration of this effect in Section (<>)3.1. With only two realizations we are unable to quantify this effect beyond showing the two simulations as illustrating the possible magnitude of variations. ",
+    "The confirmed dSph KKR 25 at 1.9 Mpc is the most significant outlier from the agreement between the observations and the simulations. Though this discrepancy ",
+    "could result from our two simulations failing to span the entire range of possible outcomes, it is also possible that our simple criteria for forming dSphs is imprecise and a more lenient criteria could account for KKR 25. With these caveats it is difficult to convincingly argue that tidal processing cannot account for KKR 25, but it is an interesting test case that could be suggestive of merger activity. As discussed above, the normalization on the fraction of merged dwarfs is somewhat sensitive to the details of the merger criteria, primarily the upper redshift cutoff and the mass ratio of merger required. While this sensitivity and the limitations of Poisson noise limit our ability to draw conclusions about whether the two furthest bins are compatible with any merger-based dSph formation, the figure does show the range of radii over which the two formation scenarios could be active. ",
+    "The dashed blue and green lines in Figure (<>)1 take the same tidal processing criteria as the solid lines, but adds an additional constraint that the halo must experienced more than one pericentric passage inside of Rvir/2. This is slightly less restrictive in distance than the single pass criterion, since multiple weaker tidal interactions could replace a single strong interaction. As shown in the fig-ure, the fraction of halos in either simulation with two or more passages drops steeply outside of 300 kpc, and is essentially zero beyond 500 kpc. This agrees with the results of a simple orbital timescale calculation at these radii, which shows that the single orbits require a significant fraction of a Hubble time. Performing this test in a cosmological simulation accounts for more complicated factors such as the growth the main halo and the initial positions and velocities of the halos that are today found at these radii. The result of the simulation clearly shows that dwarfs such as Cetus, Tucana, and KKR 25 could not have made multiple close passages by a large galaxy; if they were transformed into dSphs by tidal forces, it must have been done by a single passage. "
+  ],
+  "3.1. Accretion History ": [
+    "In discussing Figure (<>)1 it was argued that the signifi-cant difference in the histories of halos in VL1 and VL2 was due to coherent subgroups of halos. In VL2 several of these subgroups had passed near the host galaxy, while in VL1 very few did. This difference is illustrated in Figure (<>)2, which shows the trajectories in comoving coordinates of halos that have z = 0 radii of 500-1500 kpc. The trajectories are all relative to the host galaxy, which is fixed at the origin (denoted by the red star). The trajectories of halos that have not passed inside Rvir/3 are shown in black with blue dots at their z = 0 position, while those that have are shown with green lines and red dots. In the VL2 panels, the trajectory of Halo 2 is shown in red with a large red dot. ",
+    "In both simulations it is clear that many halos are organized into small groups with correlated trajectories. The left side of the VL1 plots show one of these groupings clearly. The same effect is shown in VL2, most clearly seen in the paths, but with the distinct difference that several of these groups have passed through the main halo (or Halo 2), and have thus potentially been tidally processed. This correlated nature of the infalling halos is what causes the significant variation in the radial pro-file of processed halos, above and beyond what would be expected from pure Poisson noise on the individual ha-",
+    "los. Infall of small subgroups of dwarfs has been seen in many other simulations ((<>)Li & Helmi (<>)2008; (<>)Klimentowski (<>)et al. (<>)2010; (<>)Lovell et al. (<>)2011; (<>)Helmi et al. (<>)2011) and has been argued to be the cause of the apparent position or velocity correlations amongst satellites around the Milky Way ((<>)Lynden-Bell (<>)1976; (<>)Libeskind et al. (<>)2005; (<>)Fattahi et (<>)al. (<>)2013), M31 ((<>)Ibata et al. (<>)2013; (<>)Conn et al. (<>)2013), and more distant neighbors of the Local Group ((<>)Tully et al. (<>)2006). "
+  ],
+  "3.2. Parameter Sensitivity ": [
+    "Though our analysis includes some fixed parameters that could potentially alter the results, the robustness of the general conclusions can be shown by recalculating the results under slightly different assumptions. Figure (<>)3 shows the result of changing these assumptions. The solid green line is the same as used in Figure (<>)1, while the dashed green line shows the same calculation but under the relaxed assumption that a galaxy could be tidally affected inside Rvir/2, rather than Rvir/3. This increases the non-star forming fraction at all radii (as it must), but shows a similarly-shaped radial dependence. The solid black line in Figure (<>)3 also shows the same calculation as before, but tightening the Vmax constraint to only include halos with Vmax > 10 km/s rather than 5 km/s. This includes many fewer halos, so the resulting plot is more noisy and we have had to double the bin size accordingly, but again the radial dependence is similar. ",
+    "The most significant parameters in the merger calculation are the redshift cut-off and the required merger mass ratio. Both of these alter the absolute number of dwarfs that have undergone mergers without altering the z = 0 radial distribution. This is shown by the red lines in Figure (<>)3, where the solid line shows dwarfs with mergers more recent than 11 Gyr, the dashed shows those more recent than 10 Gyr, and the dotted corresponds to 8 Gyr ago. The number of dwarfs with mergers drops by over half in the most restrictive of these cases, but no other effects are seen. Our analysis remains cognizant of this effect and thus it should not compromise our conclusions. "
+  ],
+  "4. TRANSFORMATION TIMESCALES ": [
+    "By tracing the merger and the tidal transformation scenarios with cosmological simulations, we are able to infer the timescales on which either of these processes would have been active. The time at which star formation stopped in the dwarf is imprinted in the stellar populations and could be used to differentiate between the two scenarios for dSph formation. Figure (<>)4 shows the cumulative distribution of times at which the distant halos of our z = 0 sample (located between 500 and 1500 kpc from either host galaxy) either underwent its most recent merger (red line) or first met the tidal criteria (passing inside Rvir/3, shown as the solid blue line for VL1 and sold green for VL2). The vertical dashed line indicates the first timestep at which we are able to resolve mergers or close passages. For comparison we also show the distribution of times at which surviving halos at any present day radius first crossed Rvir/3 (dashed blue VL1, dashed green VL2). ",
+    "The distribution of merger times is clearly weighted towards early times. From the plot, roughly 50% of the observed dwarf-sized dark matter halos that experienced ",
+    "Figure 2. Trajectory of present-day distant halos in VL1 (left) and VL2 (right), in comoving coordinates relative to the motion of the main halo which is held fixed at the origin. The z = 0 location of the halos are marked with dots. Halos that have passed inside Rvir /3 are marked with green lines and a red dot, while all others are marked with black lines and a blue dot. Halo 2 in VL2 is marked by the large red dot and the red track. The clumpy nature of the accretion is clearly visible. VL1 has several subgroups which have not passed by the main halo yet, while several of the subgroups in VL2 clearly have and are receding from the main halo. ",
+    "Figure 3. Illustration of the sensitivity of our results to to various parameter choice, using the VL2 data. The solid green line is the same as in Figure (<>)1, while the dashed green line shows those that have passed inside Rvir/2 instead of Rvir /3. The black line illustrates changing the Vmax criterion to Vmax > 10 km/s rather than 5 km/s. The solid, dashed, and dotted red lines show halos that have undergone mergers in the last 11.3, 10, and 8 Gyr, respectively. All of these variations may change the normalization of the model results, but do not affect the general form. ",
+    "mergers did so more than 11 Gyr ago. This is partly due to the epoch of assembly for small halos being biased towards early times, but there is also the factor of the small halos’ infall onto the larger host increasing the relative velocities of halos to each other and thus inhibiting dynamical friction and further merging. ",
+    "Though we can directly measure the time at which dark matter halos merged in the simulation, we must also account for the fact that the baryonic components of these galaxies may require additional time for dynamical friction to bring the baryons to coalescence. This is not directly observable, but we can estimate the time lag between the merger of the dark matter and the baryons with the dynamical friction formula from (<>)Bin-(<>)ney & Tremaine ((<>)2008), ",
+    "(1) ",
+    "where σh and σs are the velocity dispersions of the “host” and “satellite” halos, r is a characteristic radius over which dynamical friction must act to bring the baryonic components together, and ln Λ is the Coulomb logarithm. Our selection of only major mergers constrains σh/σs to be roughly the square root of the mass ratio, and the Coulomb logarithm can be calculated as Λ = 23/2σh/σm ((<>)Binney & Tremaine (<>)2008). The dynamical friction time thus reduces to a small factor of crossing time. An order ",
+    "Figure 4. Cumulative distribution of the timescales at which the selected z = 0 halos first met various dSph formation criteria. The blue (VL1) and green (VL2) solid lines show when halos the halos today found between 500 and 1500 kpc from their host first crossed Rvir /3. The dashed lines show the same calculation for each simulation, but without the present-day radius restriction. The red line shows the time at which dark matter halos (those at z = 0 between 500 and 1500 kpc) first underwent a major merger. The vertical dashed line indicates the time at which we are first able to resolve mergers or close passages. ",
+    "of magnitude estimate with r ∼ 1 kpc and σ ∼ 10 km/s yields tfric = 200 Myr. Assuming a delay of 1 Gyr between the dark matter merger and the baryonic merger would be a relatively conservative estimate. ",
+    "Given that we see significant merger and accretion activity occurring at such early times, it is logical to ask why the infall of distant dwarfs (z = 0 radii of 500-1500 kpc) onto the host galaxy is so delayed. For example, the rapid rise of the VL2 cumulative infall fraction in Figure (<>)4 seems to start suddenly between 8–9 Gyr ago. Two points can help explain this. First, as discussed above, the accretion of halos onto the host galaxy is stochastic and several “clumps” of subhalos are sometimes accreted together. This effect contributes to the stochasticity of the infall rate, particularly in the VL1 simulation where there are fewer halos found at large radii at z = 0. The other effect that causes the delayed infall times is related to the distance cut we have applied. The solid green and blue lines in Figure (<>)4 only shows halos that today are found between 500 and 1500 kpc; for comparison, the dashed lines shows the same infall calculation but with that present-day radius constraint removed. In the VL2 case, by the time the infall of the present-day distant dwarfs is starting more than 70% of all surviving halos have already been accreted onto the host galaxy. These halos accreted at early times join a galaxy which is much smaller at the time of accretion, and thus fall in close to the galaxy, while satellites that fall in at later times encounter a much larger galaxy which has grown around the close-in satellites. The VL1 case is more stochastic and the accretion is weighted towards even later times, but the delay is still present. Though this is merely a rough sketch to illustrate the process, the simulation is clear in predicting late infall times for distant dwarfs. When contrasted with the timescale for the merger scenario, ",
+    "the simulations clearly point to a difference in formation times for the two channels. "
+  ],
+  "5. DISCUSSION AND CONCLUSIONS ": [
+    "We have shown that the radial distribution of galaxies of dwarf galaxies of different morphological types can be used to constrain their formation mechanisms, when combined with simple models based on cosmological simulations. The simulations show that these models produce substantially different sets of properties for the Local Group dwarfs. Mergers of dwarfs are clearly insuffi-cient to explain all of the dSphs, and tidal processes that require multiple pericenter passages cannot account for the number of dwarfs found further than 500 kpc from their host galaxy. These two points are robust. ",
+    "The fact that the simple close passage model is able to reproduce the observed radial profile of dSphs, even if it does not do so in all cosmological realizations, suggests that this model could be sufficient to create the observed dSphs. However, it hinges critically on the single-passage requirement. Many simulations have shown that multiple passages are necessary with some dwarf models ((<>)Mayer et al. (<>)2001; (<>)Kazantzidis et al. (<>)2011a), though the more recent simulations of (<>)Kazantzidis et al. ((<>)2013) suggest that a single-passage transformation is plausible if the progenitor dwarfs have shallow mass profiles in the center (cores). Such profiles contradict early predic-tions of Cold Dark Matter models ((<>)Dubinski & Carlberg (<>)1991; (<>)Navarro et al. (<>)1996, (<>)1997), but observational studies have shown that cores are prevalent in dwarf galaxies ((<>)Walker & Pe˜narrubia (<>)2011; (<>)Oh et al. (<>)2011) and simulations ((<>)Read & Gilmore (<>)2005; (<>)Governato et al. (<>)2010, (<>)2012; (<>)Zolotov et al. (<>)2012) have shown reasonable methods to create cores from baryonic processes. Cored pro-files, however, carry the risk that the halos are more susceptible to tidal stripping and even complete destruction ((<>)Pe˜narrubia et al. (<>)2010). The fine balance between tidal transformation/stirring and tidal destruction may further constrain distant dSphs to a narrow range of structural and orbital parameters. ",
+    "The alternative formation pathway we have studied, that of mergers between dwarfs, has less evidence to support it but is difficult to rule out. We show that it is unable to be the dominant pathway by which dSphs form, simply because it does not recreate the large dSph fraction at small radii to a host galaxy. However, assuming our understanding of dark matter is correct, mergers must occur. Whether these mergers leave signatures that are observable today is a challenging question that requires further study. At very high redshifts dwarfs may be able to reform gas disks and continue forming stars, which would lead us to identify them as dIrrs. At what redshift, if any, mergers cause these galaxies to no longer sustain any star formation is a complex question best answered with hydrodynamical simulations. ",
+    "We have shown that, for distant dwarfs, mergers must occur at very early times, while their infall onto a host potential occurs much later. The time at which star formation ended in the dwarf should therefore be a signature in the stellar populations that cannot be erased. Do the distant dSphs of the Local Group exhibit star formation histories that could differentiate between the early shut-off in the merger scenario and the later shut-off by tidal interactions? ",
+    "Studies of the star formation histories of Tucana and Cetus show that both dwarfs reached the peak star formation rate more than 12 Gyr ago and subsequently the star formation rates declined ((<>)Monelli et al. (<>)2010a,(<>)b), but from this history it is difficult to ascribe a specific time at which some process shut off star formation. In either case it took nearly 3 Gyr for the star formation rate to decline from its peak value to negligible levels; such a slow and gradual process does not lend itself to an easy comparison to our binary off-or-on model. This is particularly true in the case of mergers, where additional star formation may be triggered by the merger itself. More sophisticated modeling of the detailed star formation history, including the hydrodynamical processes that eventually render a dSph devoid of gas, could be able to extract conclusions from the stellar populations seen in Cetus and Tucana. ",
+    "A logical extension of our work would be to ask if there exist comparable trends outside the Local Group. The work of (<>)Geha et al. ((<>)2012) used a sample of somewhat more massive dwarfs to show that below a mass threshold of 109 M, non-star-forming galaxies do not exist in any substantial number beyond 1500 kpc of a massive galaxy. This matches well with the predictions of the tidal processing scenario, which also shows very few pro-cessed halos beyond 1500 kpc. The (<>)Geha et al. ((<>)2012) sample substantiates the hypothesis that at low masses tidal processing is sufficient to recreate the distribution of dSphs, without requiring mergers. At slightly higher masses of 109.5 − 109.75M, a small fraction of quenched halos are observed at all radii (their Figure 4), much in agreement with the expectations for mergers. If mergers are responsible at large radii, this suggests that it is only above a certain mass threshold that mergers (which must happen at all masses) are capable of quenching galaxies in the field. Such a model has been shown by (<>)Hopkins et (<>)al. ((<>)2009) to reproduce the mass dependence of the fraction of bulge-dominated galaxies in the field, and could extend to their star formation properties as well. This picture of combining tidal processes with mergers above a threshold provides a natural link between the behavior of satellites and of central galaxies. ",
+    "One difference between the (<>)Geha et al. ((<>)2012) results and the Local Group is in the fraction of quenched galaxies at small radii. In the Local Group substantially all galaxies inside 200 kpc are quenched, but the quenched fraction only reaches at most 30% in the (<>)Geha et al. ((<>)2012) sample. This could suggest a mass dependence to tidal processing, where perhaps the more massive dwarfs of the (<>)Geha et al. ((<>)2012) sample require longer timescales to shut off star formation, and thus many of their galaxies at radii are slowly on the way to quenching. Our instantaneous tidal processing model does not capture this behavior, but a more sophisticated mass-dependent model may better explain this effect. ",
+    "This work was supported by NSF grant AST 1008342. We thank the Via Lactea collaboration for making their simulation outputs available, and J. Diemand for providing the merger trees and helpful comments on their interpretation. We also thank J. Dalcanton for useful discussions. ",
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+}

jsons_folder/2013ApJ...778...80R.json

@@ -0,0 +1,191 @@
+{
+  "FORMATION OF COMPACT CLUSTERS FROM HIGH RESOLUTION HYBRID COSMOLOGICAL SIMULATIONS ": [
+    "arXiv:1308.5684v2  [astro-ph.CO]  9 Oct 2013 ",
+    "Mark L. A. Richardson 1 , Evan Scannapieco 1 , and William J. Gray 2 Accepted to ApJ 10/2013 "
+  ],
+  "ABSTRACT ": [
+    "The early Universe hosted a large population of small dark matter ‘minihalos’ that were too small to cool and form stars on their own. These existed as static objects around larger galaxies until acted upon by some outside influence. Outflows, which have been observed around a variety of galaxies, can provide this influence in such a way as to collapse, rather than disperse the minihalo gas. Gray & Scannapieco performed an investigation in which idealized spherically-symmetric minihalos were struck by enriched outflows. Here we perform high-resolution cosmological simulations that form realistic minihalos, which we then extract to perform a large suite of simulations of outflow-minihalo interactions including non-equilibrium chemical reactions. In all models, the shocked minihalo forms molecules through non-equilibrium reactions, and then cools to form dense chemically homogenous clumps of star-forming gas. The formation of these high-redshift clusters may be observable with the next generation of telescopes, and the largest of them should survive to the present day, having properties similar to halo globular clusters. "
+  ],
+  "1. INTRODUCTION ": [
+    "The observed history of large-scale structure formation is well explained by the cold dark matter model with a cosmological constant term (e.g., Spergel et al. 2007; Larson et al. 2011). This theory posits that small-scale perturbations in the dark matter density merged hierarchically over time, leading to larger perturbations that continued to coalesce into even larger structures, while underdensities became large voids (e.g., White & Rees 1978; White & Frenk 1991; Kauffmann et al. 1993; Cole et al. 2000; Bower et al. 2006). The gas dynamics were almost completely dictated by these dark matter potentials. Thus, massive baryonic objects formed at later times, while a large population of smaller objects formed early. ",
+    "At the poorly constrained redshifts before reionization, it is then expected that there existed a large population of small gravitationally bound clumps of dark matter and gas, whose masses were much smaller than galaxies today. At temperatures below ≈ 104 K, transitions in atomic hydrogen and helium are not excited, leaving gas to cool radiatively through molecular excitations and dust emission. Although some molecules may have survived from recombination and cooled the earliest structures (e.g., Abel et al. 2002; Bromm & Clarke 2002; Turk et al. 2009; Stacy et al. 2010), they would have produced stars that disassociated these molecules, sup-pressing cooling in neighboring perturbations ((<>)Galli & (<>)Palla (<>)1998). Furthermore, it is unlikely that even with some molecules surviving further, they could have effec-tively cooled such small structures (e.g. Whalen et al. 2008; Ahn et al. 2009). Thus, the subset of these low-mass objects with virial temperatures below 104 K, so-called “minihalos”, persisted as sterile objects, unable to cool and form stars without an external influence. ",
+    "Some of these minihalos may have been located near starbursting galaxies, which can drive outflows powered by supernovae, as have been observed around a variety of galaxies at a range of redshifts (e.g., Lehnert & Heck-man 1996; Franx et al. 1997; Pettini et al. 1998; Martin 1999; Heckman et al. 2000; Veilleux et al. 2005; Rupke et al. 2005; Chung et al. 2011). It is expected that these observed starbursts are a small example of a much larger, earlier population that predated, and likely drove, reion-ization (Scannapieco et al. 2002; Thacker et al. 2002; Ferrara & Loeb 2013). Although these galaxies also produced ionization fronts that disassociated their environments, and (<>)Shapiro et al. ((<>)2004) and (<>)Illiev et al. ((<>)2005) have demonstrated that minihalos that are first struck by the ionization fronts are evaporated on a timescale of 10-100 Myr, (<>)Fujita et al. ((<>)2003) showed that the outflows of such galaxies can trap this ionizing radiation, shadowing regions around the starbursting galaxies. Thus, some neutral minihalos could have been sheltered from ionization fronts, and interacted with a kinematic outflow first. Furthermore such interactions, through non-equilibrium processes, could have induced the formation of molecular gas that could cool the gas sufficiently to induce star-formation. ",
+    "Gray & Scannapieco (2010; 2011A; 2011B) (hereafter GS10, GS11A, GS11B) performed idealized simulations of this interaction, which featured a spherical isothermal gas cloud embedded in a static analytic dark matter potential. Together the dark matter and gas represented a minihalo, which followed an NFW radial density profile ((<>)Navarro et al. (<>)1997), and it was embedded in a uniform background. The starburst outflow, on the other hand, was modeled as a plane-parallel shock of material inflow-ing from the x boundary. GS10 also enacted a 14-species primordial non-equilibrium chemical network with associated cooling terms. As the shock struck the minihalo, it catalyzed the creation of H2, while mixing in some of its enriched material. As much as 100% of the baryonic material of the minihalo collapsed into a small ribbon of gas ",
+    "that extended well out of the dark matter potential, that then cooled via H2. For one simulation they included a UV background, assuming an optically thin medium, and found a reduced abundance of H2, but still suffi-cient to cool the minihalo gas. Regardless of a UV background, they found that the ribbon eventually collapsed into several distinct clumps, whose properties were remarkably similar to present-day halo globular clusters. GS11A enacted a K-L two-equation sub-grid turbulence module and metal-line cooling, which allowed for more efficient mixing of enriched shock material into the collapsed minihalo gas, and allowed this enriched material to add to the net cooling. GS11A found very similar results as GS10, producing a population of clusters very much like halo globular clusters. Finally, GS11B performed a parameter suite that looked into the effect of minihalo mass, clumping factor, and angular momentum, outflow energy and enrichment, minihalo-starburst separation, redshift, and UV background on the characteristics of the interaction and its resulting clusters. ",
+    "Cosmological simulations show that virialized structures are typically found at the nodes of a fractal-like cosmic web (e.g. Springel et al. 2005A). Thus minihalos were found at the intersections of cosmic filaments, likely with higher-mass objects nearby. Their dark matter was a dynamic background, that responded to gas dynamics. Although the average radial profile of minihalos likely did follow an NFW profile, they were not perfectly isotropic. These characteristics make minihalos quite different than the idealized gas clouds simulated in GS10, GS11A, and GS11B. ",
+    "In fact, the isotropy in their work may have been the cause of the small collapsed ribbon of material along the x-axis, resulting from the shock wave converging at the antipodal point. It is also unclear how reasonable it is to treat the dark matter as a static analytic term. As densities in the collapsing gas eventually exceeded those in the dark matter, perhaps a more dynamic treatment of the dark matter might uncover motions that significantly affect the future evolution of the gas. ",
+    "In this work, we address these issues by generating a range of minihalos in high-resolution cosmological simulations. Then, having isolated the desired objects and their immediate environments into a new simulation volume, we simulate their interactions with starburst-driven outflows. In this way we are able to understand this interaction in much more detail as it occurred in the early Universe, and contrast it with the idealized minihalo-outflow simulations previously undertaken. ",
+    "The structure of this paper is as follows. In §(<>)2 we describe the cosmological simulations, and the outflow-minihalo interaction simulations, followed by our post-processing techniques. In §(<>)3 we discuss the results from our parameter suite, and in §(<>)4 we present simulated high and low-redshift observables derived from these results. We summarize our work and give conclusions in §(<>)5. Throughout this paper we use (ΩΛ, ΩM, Ωb, n, σ8, h−1 100) (<>)et al. (<>)2011). "
+  ],
+  "2. NUMERICAL METHODS ": [],
+  "2.1. Particle Simulations ": [
+    "As a first step, we performed a low-resolution cosmological simulation using the smoothed-particle hydrodynamic code GADGET-2 (Springel et al. 2001; Springel 2005B) in a box that was 2.57 comoving Mpc on a side. This had 2 spherically nested resolution levels, the lowest resolution level spanning the whole volume, and the next level spanning a sphere centered in the box with a radius a quarter of the box size. Each level had effectively 1923 dark matter particles (with masses of 7.39 × 104 M and 9.24 × 103 M) and 1923 gas particles (with masses of 1.51×104 M and 1.87×103 M). At each level of resolution the modes of the initial spectrum are truncated to ensure there is no aliasing of high k modes into the low k values (as in Thacker & Couchman 2000; Richardson et al. 2013). Initial conditions were generated using the transfer function from CAMB ((<>)Lewis et al. (<>)2000), assuming an initial spectral slope of n = 0.963. CAMB uses a line-of-sight implementation of the linearized equations of the covariant approach to cosmic microwave background (CMB) anisotropies. This results in different transfer functions for the dark matter and baryon components, with the two weighted together to yield the total transfer function. This simulation began at z = 199 and was evolved to z = 15.4. We did not include star formation or feedback, but did include atomic and molecular cooling. We calculated the different ionization states of hydrogen and helium from the density and temperature following (<>)Katz et al. ((<>)1996). Although at such a high-redshift collisional ionization equilibrium is perhaps not appropriate, this assumption is irrelevant since the material remains neutral. Additionally, the structures on which we focus are not particularly rare and have virialized only recently. Rarer objects, with larger peak densities that virialize at earlier times and are then essentially inert require non-equilibrium chemistry to allow for the build up of molecular hydrogen. Instead, our objects have lower densities and have had less time to accumulate H2, and thus the non-equilibrium formation of H2 should not be a dominant component of their evolution. This is consistent with (<>)Richardson et al. ((<>)2013), who compared halos formed in SPH simulations, which used the same equilibrium chemistry, with the same halos formed in AMR simulations, which consider a fully non-equilibrium chemistry of H, He, and D. We assumed a primordial number density fraction of molecular hydro-gen of H2/H = 1.1×10−6 following (<>)Palla & Galli ((<>)2000) and a primordial deuterium number density fraction of D/H = 2.7 × 10−5 following (<>)Steigman ((<>)2009). Using the baryon-to-light ratio of η = 6.0 × 10−10 from (<>)Steigman ((<>)2009), we set the deuterated hydrogen number density fraction at HD/H2 = 6 × 10−4 from (<>)Palla & Galli ((<>)2000). Given these abundances, we employed the molecular cooling rates of GS10 and cooling rates for Compton scattering against CMB photons as given in (<>)Barkana & (<>)Loeb ((<>)2001). To offset runaway cooling since we do not include feedback terms, we implement a cooling temperature floor at 500 K, well below the virial temperature of any minihalos we consider. Adiabatic cooling can still cool below this floor. ",
+    "We then used the friends-of-friends algorithm ((<>)Davis ",
+    "(<>)et al. (<>)1985) to determine groups that corresponded to an overdensity of 180 with a linking length of 1.19 kpc, expected to be virialized from a spherical top-hat collapse model. We focused on three groups, with total masses of 2.0×106 M, 4.0×106 M, and 8.0×106 M, respectively. For each group, we performed a simulation statistically identical to the low-resolution simulation, but with additional resolution centered on the group. We added two additional spherically-nested resolution levels resulting in particle masses of 144 M and 29.3 M for dark matter and baryons, respectively, at the highest resolution. ",
+    "These high-resolution initial conditions were evolved to z = 14. We then located groups using the HOP group finder ((<>)Eisenstein & Hut (<>)1998) implemented in the yt visualization and analysis toolkit ((<>)Turk et al. (<>)2011) with masses, in units of 106 M, of M6 = 0.716, 1.38, 2.33, 2.72, 7.17, and 18.7. For each suitable halo, we isolated regions out to 5 virial radii, rv, of the group in the GADGET-2 snapshots and mapped these to the adaptive mesh refinement code FLASH3.2 ((<>)Fryxell et al. (<>)2000) using the procedure discussed in (<>)Richardson et al. ((<>)2013). A summary of the simulations is given in Table (<>)1. For the z ≤ 14 simulations, we extended the z = 14 datasets by scaling position, velocity and energy by the scale factor difference. The majority of these simulations were done at z = 8 as it is the most likely to be directly observable. "
+  ],
+  "2.2. AMR Simulations ": [],
+  "2.2.1. FLASH and the Dark Matter Gravitational Potential ": [
+    "The mapped GADGET-2 snapshots were treated as initial conditions for simulations performed with FLASH version 3.2, a publicly-available multidimensional adap-tive mesh refinement hydrodynamic code ((<>)Fryxell et al. (<>)2000) that solves the Riemann problem on a Cartesian grid using a directionally-split piecewise parabolic method (PPM) (Colella & Woodward 1984; Colella & Glaz 1985; Fryxell et al. 1989). FLASH also includes particles that we used to represent dark matter, which we simply moved directly from GADGET to FLASH. Dark matter mass is mapped to the grid after each hydro step using the Cloud-In-Cell (CIC) method (e.g., Birdsall & Fuss 1997), where the particles are assumed to exist in a box of the same size as the grid at the current refine-ment. The mass is distributed equally over this box and thus the percent of mass mapped into a particular cell is the percentage of the box that overlaps that cell. ",
+    "To accommodate high-resolution regions with very few particles, we sometimes moved dark matter particles to a lower resolution level, mapping them over a larger box. This was necessary to prevent any low-density gas in the high-refinement region from unrealistically collapsing onto a single dark matter particle, and similar efforts have been made in earlier work (e.g., Safranek-Shrader et al. 2012, 2013). To determine which particles needed this ‘derefinement’, a particle count was monitored for each cell. If a cell had three or more neighboring cells that did not contain particles, or if it had two neighboring cells without particles in the same direction, then the particles in that cell were flagged for derefinement, and the same criteria was checked for the parent cell. This criteria was slightly relaxed for particles in cells adjacent to block boundaries, which were always tagged for ",
+    "derefinement if the neighboring block was at a lower re-finement level. This was necessary to be consistent with the criteria used by the cells on the lower resolution block to determine if its neighbors had particles, and it is illustrative of the fact that at a lower refinement level a larger fraction of the box associated with the particles would overlap the neighboring cell. ",
+    "In all cases, once particles were derefined and mapped to that grid level using the standard CIC method, this material must then be ‘prolonged’ back onto the high-resolution level, from parent to (higher-resolution) child, and added to any density that was directly mapped to that child. The prolongation of the dark matter density into a child cell that was not near the boundary of the block, such that it could see both its parent cell and its parent’s neighbors, was determined by using linear interpolation between this cell’s parent density and its closest neighbor’s density. A quadratic interpolation scheme could have been used, but in rare circumstances this could lead to negative dark matter mapped in some cells. Figure (<>)1 shows a plot of the grid layout of a child and parent block with one dimension. If we assume the density is linearly continuous between parents P1 and P2, then: ",
+    "(1) ",
+    "where Ωij is the weighting from parent i into child j, ρC2 map is the dark matter density mapped into child C2 without requiring derefinement, ρC2 prolong is the amount of dark matter density prolonged into child C2 from derefined particles, and ρC2 final is the sum of the mapped and prolonged dark matter density, which is used for the gravity calculation. At the borders of blocks, where the child cell could not see one of its parent’s neighbors, we then used a direct mapping from the parents value, ",
+    "(2) ",
+    "Fig. 1.— Illustration of our gravity procedure in one dimension. A fraction Ωij of the density from parent PI, ρPi, is prolonged to child CJ and added to its existing density values, which were mapped from less derefined particles. ",
+    "This limited the demand of inter-processor communication, and resulted in a slight error in the dark matter field on the borders of blocks where dark matter was derefined (see Figure (<>)2). However, this error was much smaller than the error from leaving the dark matter mass at the highest refinement level, and the method still allowed for a much more efficient runtime. Ideally we would like to have filled the guard cells of parent P1 and passed that information to child C1, requiring one interprocessor communication, but in the event that the neighbor of parent P1 was itself a child block, then we would have been unable to pass the acceleration of child C1 back to the parent’s neighbor when we calculated the particle accelerations. We thus opted for a less complex weighting on the boundaries. The benefit of using this new technique for handling the dark matter density field is clearly illustrated in Figure (<>)2, which shows that individual particles were never mapped to isolated peaks in the dark matter density field. ",
+    "To cancel out the self-gravitational force from prolonged pieces of the same dark matter particle, the accelerations was ‘restricted’ up to the particle’s refinement level using identical weightings as the prolongation (see Equations (<>)1, (<>)2). Thus: ",
+    "(3) ",
+    "and then the weighting from the Cloud-in-Cell stage was applied to the acceleration from each cell onto the parti-",
+    "cle at the same grid level at which it was mapped. This resulted in an exact cancelation of the self-gravitational force, leaving only the gravitational acceleration from the gas and remaining dark matter particles. ",
+    "We tested the new particle gravity by tracing the evolution of a pressureless spherical region with a density 8 times the background density, the results of which are shown in Figure (<>)3. The radius begins to collapse slowly, then accelerates. Our new results are indistinguishable from both the results of the earlier particle gravity scheme and the analytic solution. "
+  ],
+  "2.2.2. Outflow Simulations ": [
+    "Using FLASH and the selected GADGET groups, we performed a parameter study on outflows interacting with these groups. We mapped the group region into a rectangular box with the group centered at (0,0,0) pc, with (−1.5rv ≤ x ≤ 4.5rv) and (−1.5rv ≤ y, z ≤ 1.5rv). FLASH is an AMR code with blocks of NB,X × NB,Y × NB,Z cells divided between processors. Each subsequent level in refinement increases the spatial resolution by a factor of two in each dimension. Our simulations were run with a maximum of 6 levels of refinement (except for the high and low resolution runs), allowing up to 32 blocks in each direction, where the relative difference in resolution between a block and any of its neighbors can be at most a factor of two. For our simulations we used a root grid of NB,X = 2NB,Y = 2NB,Z = 16, accommodating the rectangular box size while maintaining uniform resolution in all directions. This gives a maximum resolution of 256 cells per 3rvir. ",
+    "The outflow with positive x-velocity was added to the x-boundary, following the model of GS10. A Sedov-",
+    "Fig. 2.— Comparison of the density-weighted projection of the dark matter density field, pden, of the minihalo in the original non-derefined particle gravity routine (top) and with the new derefinement method that smooths the dark matter field (bottom). Regions where there were few dark matter particles moved those particles to lower resolution blocks, increasing the size of their mapped region. Block boundaries are not continuous to limit the number of inter-processor communications. These projections were made using the yt-toolkit ((<>)Turk et al. (<>)2011) ((<http://yt-project.org/>)http://yt-project.org/). ",
+    "Taylor solution was used to estimate the conditions of the galactic outflow. We decided on appropriate shock velocities, vs, and shock surface momentum (per unit area), µs, and used these to constrain the conditions of the outflow. We let the initial input energy for the shock be given by E = E55(1055 erg ), where E55 is the energy of the SNe driving the winds in units of 1055 erg, and the wind efficiency, , quantifies the coupling between the SNe and the winds, taken to be 0.3. To be consistent with previous work, we assumed that before reaching our box, the shock had swept up an ambient medium of material with an overdensity, δ44, in units of 44 times the background density, taken here to be 1, over the (physical) separation distance, Rs, which leads to a surface density, σ5, in units of 105 M/kpc2 . Thus, for a given shock velocity and momentum we have: ",
+    "(5) ",
+    "and ",
+    "The post-shock temperature is Ts = 1.4 × 105(vs/100 km s −1) K, the outflow is fully ionized, and it has an abundance given by Z. The fiducial values are chosen to match (<>)Scannapieco et al. ((<>)2004), with z = 8, Z = 0.12 Z, vs = 226 km s−1 , µs = 60.7 M pc−1 Myr−1 , leading to Rs = 3.6 kpc, E55 = 10, and σ5 = 2.62, and oriented such that the outflow is propagating along an accretion lane, which is the most likely direction pointing towards a neighboring starbursting galaxy. The shock lifetime is estimated from σs = ρpostvpostts, where σs is the surface density of the shock, ρpost is the post-shock density, vpost is the post-shock velocity, and ts is the shock lifetime. After 40% of the shock time, the shock was tapered off by slowly lowering the density and raising the temperature, keeping pressure constant to inhibit further refinement. The density falls off exponentially, with ",
+    "(7) ",
+    "Fig. 3.— Evolution of the radial extent of the overdensity with time. The solid black line with square points shows the analytic solution while the dotted green line with circles shows the simulated result from FLASH without derefining the dark matter, and the red dashed line with diamonds is the result with derefining the dark matter. We see no significant differences between the results of flash regardless of whether the dark matter is derefined or not, and they are consistent with the analytic solution. ",
+    "while the temperature increases as 1/ρ(t) to maintain a constant post-shock pressure. ",
+    "We allowed for refinement based on the second derivative of density and pressure. Regions that had their density or pressure profiles vary sufficiently quickly were forced to increase their resolution by a factor of two. After 7 Myr we forced derefinement beyond a cylinder with a radius of 0.8Rv aligned with the x-axis for material below 3 × 10−26 g cm−3 . This was to prevent low-density mixing from limiting the time-step. ",
+    "During the AMR simulations, we used the same cooling source terms as in the SPH runs, although we also accounted for possible non-equillibrium chemistry and corresponding cooling following GS10, itself based on (<>)Glover (<>)& Abel ((<>)2008). This is essential as the interaction between the outflow and the minihalo leads to the creation of coolants such as H2 and HD. This network follows 84 reactions including the three states of atomic hydrogen (H, H+ , H−), atomic deuterium (D, D+ , D−), and atomic helium (He, He+ , He++), two states of molecular hydrogen (H2, H+ 2 ), and molecular deuterated hydrogen (HD, HD+), and electrons (e−). We do not consider three-body reactions as these require much denser media than we expect in this work. Reactions that involve free elections are treated in the case B regime. This assumes a medium optically thick to ionizing photons produced during recombination. GS10 demonstrated that all of their clouds were in the optically thick case. Similarly, our clouds should be optically thick as well. ",
+    "For one simulation we include photo-disassociation by a UV background. We model the UV background as originating from a 105 K blackbody, and we quantify its intensity at the Lyman limit, with J(να) = J21 × 10−21 erg s−1 cm−2 Hz−1 Sr−1 . We would expect dense re-",
+    "gions with significant amount of HD and H2 to self-shield from this background, however we assume all regions are optically thin, thus the UV background’s impact will be viewed as an upper limit to the effect of this background. Including photo-disassociation expands our reaction network to 91 reactions. ",
+    "We also account for metal cooling following GS11A, which can occur once the material is enriched by the out-flow. The radiative metal cooling assumes an optically thin medium, using the tabulated results from (<>)Weirsma (<>)et al. ((<>)2008), which assumes local thermodynamic equilibrium. ",
+    "With this package in place, along with the dark matter gravitational potential calculated as described above, we ran the shock-minihalo simulations until the outflow had collapsed the minihalo material, typically leaving a ribbon of material behind the minihalo. This interaction took between a few million years, and a few tens of million years. "
+  ],
+  "2.2.3. Ballistic Evolution ": [
+    "The timescale of the evolution of this ribbon of material can be up to ten times as long as the timescale of the shock crossing the simulation volume (GS10). To avoid modeling this material for such a long period of time, we simplified its evolution by constructing a series of 64 one-dimensional point-particles, we call “cloud particles”, whose x-positions spanned the space of the ribbon. We then added the mass, momentum and metal abundance of each ribbon segment into a corresponding particle if it was within half the inter-particle spacing in the x-direction from this particle, it was denser than 150% the post-shock density, and its radial velocity away from the x-axis was sufficiently slow as to make it gravitationally bound to this axis on a timescale of 200 Myr. ",
+    "We determined if a fluid segment was bound by comparing the y-and z-component of the velocity of the fluid with the y-and z-component of the minihalo’s dark matter gravitational potential. Here we assumed a NFW profile ((<>)Navarro et al. (<>)1997): ",
+    "(8) ",
+    "where G is Newton’s gravitational constant, Mvir is the virial radius, assumed to be the same as the minihalo mass, rvir is the virial radius, set by the virial mass and redshift, F (x) = log(1 + x) − x/(1 + x), and c is the concentration parameter, assumed to be 4, slightly less than the fiducial value in GS11B since we find the halos in our Gadget simulations are typically less concentrated (e.g., Richardson et al. 2013). For each segment determined to be bound to the x-axis, we added its gravitational potential into radial bins. We then determined the best-fit NFW profile for the radial gravitational potential, fitting for mass and clumping factor, using a Gauss-Newton algorithm. We then rechecked which gas segments were bound to the x-axis using the fitted NFW profile. We iterated this process until the profile fit was self-consistent. ",
+    "Once we were satisfied with our identification of the bound material, we tracked the variance of the abundance of the particles to determine its uniformity. The cloud particles were then evolved ballistically for 200 Myr, including their mutual gravitational attraction and ",
+    "Fig. 4.— Evolution of the fiducial simulation, showing column density (first and fifth row), projection of density-weighted temperature (second and sixth row), the column density of metals (third and seventh row), and the column density of molecular hydrogen (fourth and eighth row) at 0, 2.3, 5.0, 6.7, 9.0, and 13 Myr from left to right. ",
+    "the fitted gravitational potential of the minihalo. Finally, when one particle overtook a second one, we merged them into a single new particle, conserving mass and momentum and averaging their abundance while combining their variance. "
+  ],
+  "3. RESULTS ": [],
+  "3.1. Fiducial Behavior ": [
+    "4 ",
+    "Figure shows the evolution of our fiducial run (see ",
+    "1",
+    "FID in Table ) at 6 characteristic times. This run had ",
+    "a minihalo mass of M6 = 2.72 and a virial radius of 505 pc. Our fiducial outflow had a shock speed of vs = 226 km s−1 and surface momentum of µs = 60.4 M pc−1 Myr−1 , consistent with a starburst-minihalo separation of Rs = 3.6 kpc, shock surface density of σ5 = 2.62 and energy of E55 = 10. We used a redshift of z = 8, and a shock enrichment of 0.12 Z. ",
+    "As the shock enters the volume from the left boundary, it travels freely through the diffuse medium, but stalls slightly within the inner 100 pc as it moves along ",
+    "Fig. 5.— Distribution of cloud particle masses (top left), velocity (top right), metallicity (bottom left) and relative metallicity dispersion (bottom right) vs particles positions after 200 Myr for the fiducial run. ",
+    "the denser filament. At 2.3 Myr, the shock makes contact with the dense minihalo, and molecular hydrogen begins to form in the swept-up accretion lane. By 6.7 Myr, the shock has overtaken the minihalo in the diffuse medium, and has propagated roughly 60% around the minihalo itself. The shock front has mixed in some metals and molecular hydrogen has formed along this front, most notably along the periphery of the minihalo and along accretion lanes. The minihalo begins to cool more efficiently due to molecular cooling. ",
+    "At 9 Myr, the shock has propagated around the now collapsed minihalo. What remains of the minihalo is enriched to roughly 2% of the value of the incoming material, or 2.5 × 10−3 Z, and it contains a significant amount of molecular hydrogen. The minihalo begins to cool below 103 K. Finally, by about 13 Myr, the shock has passed through the box, leaving a stream of material that is not entirely bound to the x-axis. This is because anisotropies in the minihalo lead to mismatched times at which the shock reaches the antipodal point, resulting in some material being pushed away from the axis. This is different from what is seen in GS10, GS11A and GS11B. This material is almost uniformly at a few 100 K, enriched to 2% of the shock’s metallicity, and has a mass fraction of H2 of about half a percent. During this time, we find that the dark matter of the minihalo does not respond to the outflow, although it does move in towards the halo from the outer edges of the simulation volume. This is mostly due to our choice of isolated boundary conditions, and results in a small increase in the gravitational attraction on the gas, but this movement is small and well beyond the virial radius of the halo. ",
+    "After determining the gas that is transferred to the ballistic particle scheme, we find only 24% of the baryonic mass of the original minihalo is contained in these particles, while 76% is blown away from the minihalo, out of the simulation volume. This material is not bound to the x-axis, and does not coalesce into large clumps. For our fiducial case, we consistently get 24% of the mass in particles, regardless of the number of ballistic bins, the ",
+    "density cutoff, or the timescale over which the gas must be bound to the x-axis. ",
+    "Figure (<>)5 shows the final particles whose masses are above 1% of the original minihalo’s baryons, a limit we adopt in similar figures below. The momentum from the outflow pushes this mass out of the dark matter halo, while small variations in the velocity of the original particles, along with their self-gravity, allow the particles to merge, leading to a small population of high-mass clusters. For the fiducial case, most final particles are about 1-4 × 104 M, and have a velocity profile nearly following a free expansion law, with v  4.6(x/kpc) km s −1  x/200 Myr, as expected. We also found a slight trend of increasing metallicity with position, due to increased mixing on the backside of the minihalo. "
+  ],
+  "3.2. Convergence ": [
+    "Simulations LR and HR were run with the maximum resolution in FLASH3.2 at half and double that of run FID (11.8pc and 2.46 pc, respectively). In the LR there are regions that do not meet the Truelove criterion ((<>)Tru-(<>)elove et al. (<>)1997), as the Jeans length is not resolved by at least four fluid elements. However, in both the FID and HR runs, this criterion is always met. Figure (<>)6 shows the evolution of the column density for the LR, FID, and HR runs. The increased resolution is able to better resolve the fragmentation of the cloud caused by turbulence along the shock front. This increased fragmentation leads to increased metal enrichment and general mixing of the material. Note that unlike GS11A we do not include a subgrid turbulence model in our calculations, meaning that the enrichment we compute is resolution dependent and should be considered a lower limit. ",
+    "We also performed the same ballistics evolution for each of the simulations. We compare the resulting particles in Figure (<>)7. The amount of the minihalo baryons captured in these particles is 19%, 24%, and 26% for the LR, FID, and HR runs, respectively. The increased resolution has lead to more fragmentation, leading to slightly ",
+    "Fig. 6.— Demonstration of convergence of the fiducial simulation (FID; center) with the low-resolution (LR; top) and the high-resolution (HR; bottom) column density results at 3.3, 7.7, and 14 Myr from left to right. ",
+    "Fig. 7.— A comparison between the LR (blue diamonds), FID (black squares), and HR (red circles) particle masses (top left), velocity (top right), metallicity (bottom left) and metallicity dispersion (bottom right) vs particles positions after 200 Myr. ",
+    "increased enrichment of the final particles with a slightly larger dispersion, and whose mass is in a few more less massive clumps. However, the mass dispersion is roughly 0.3 dex for all three simulations, while the average mass varies only by about 0.06 dex. Thus our statistics are still robust, even if the individual clumps are not identical with their higher resolution counterparts. Likewise, we find little dependence on the abundance of the fi-nal clumps, in their evolution, so we do not expect the slightly-increased enrichment at higher resolution to in-fluence our results. See §(<>)3.3.5 and §(<>)4.2 for more discussion on this. We are thus satisfied that the FID resolution is sufficient to model this interaction for other parameters sets. "
+  ],
+  "3.3. Parameter Study ": [
+    "The simulations run in this parameter suite are detailed in Table (<>)1, with names corresponding to the parameter that was altered from the fiducial value. PO1 has the outflow propagating through the IGM before striking the minihalo, while in all other simulations the outflow propagates along a filament. In the following subsections we discuss both the results from the FLASH3.2 simulations for each parameter as well as the evolution of the ballistic particles. "
+  ],
+  "3.3.1. Minihalo Mass ": [
+    "The minihalo mass is one of the most important parameters, as it sets not only the mass of baryons present, but the scale of the interaction, the virial temperature of the minihalo, and the depth of the gravitational potential. How this parameter affects the evolution of the interaction is shown in Figure (<>)8. Each minihalo is unique, chosen for its mass. Nevertheless, the interactions of the outflows with these minihalos are consistent. We see that the more massive minihalos create denser shock fronts as the outflow is stalled by the denser material, have denser ribbons of material after the shock overtakes the mini-halo, and they have larger wakes of swept up material. The nature of the filament along which the outflow propagates appears to influence how the shock interacts with the minihalo itself, and in §(<>)3.3.2 we explore whether this can affect the produced particle clouds. ",
+    "Figure (<>)9 shows the distribution of cloud particles 200 Myr after these simulations. As the minihalo mass increases, the cloud particles are found closer to the dark matter halo, there are more final particles, and they have larger masses. The more massive minihalos have a deeper potential well, and the innermost, most massive cloud particles are unable to escape for the very largest mini-halo. One exception to this appears to be PM7. We suspect in this case the proximity of two smaller miniha-los, as well as the orientation of a second filament directly behind the minihalo allows the gas to better escape the minihalo, while entraining the secondary filament material. We find the percent of the original minihalo’s baryons in bound cloud particles is much larger for larger minihalo mass, with only 3.7% of baryons contained in the collapsed gas for PM07, while 61% of baryons are contained in PM19. ",
+    "The metallicity again increases with increasing position of the final cloud particles. The smaller mass minihalo results in less metals penetrating into the cloud, as the shock travels more quickly around the more tenuous material. The relative spread in metallicity, σZ/Z, is mostly below 0.1 dex, except for PM19, whose increased gravity allows for more material of different enrichment to be constrained in the final ribbon of material. "
+  ],
+  "3.3.2. Orientation ": [
+    "A key component to anisotropic minihalos in this interaction is how the outflow is oriented with respect to the minihalo and its accretion lanes. Simulation PO1 looks at the effect of orientation on the shock-minihalo interaction. Figure (<>)10 compares the evolution of the fiducial run with that of PO1, which has the outflow propagating through the low-density IGM, instead of along a filament. In FID, the shock material in the filament is stalled, first collapsing the filament gas, before striking the minihalo. In PO1, the shock material along the x-axis is first to hit the minihalo, without a reduction in kinetic energy. The specifics of this interaction will be fairly stochastic, dependent on the orientation of other filaments, and the geometry of the minihalo. In PO1, we find the outflow triggers some molecular hydrogen formation in surrounding filaments, that cool and collapse, while being driven down towards the x-axis. Also, the minihalo baryons are in a more extended and bound ribbon of material at the end of the interaction. ",
+    "In Figure (<>)11 we show the ballistic particles after 200 Myr of evolution for the two different orientations. PO1 has only 14% of the minihalo’s baryons in these particles, compared with FID’s 24%. PO1 has its final particles much further out than FID, due to the undiminished kinetic energy of the outflow. PO1 also has more final particles of lower mass, suggesting that they are less ef-ficient at merging. Regardless of orientation, metallicity increases with position outside the dark matter potential. "
+  ],
+  "3.3.3. Shock Velocity ": [
+    "The shock velocity, vs, is one of the most significant parameters affecting this interaction. The outflow acts to remove the baryons from their dark matter potential well, sets the post-shock temperature, and catalyzes H2 and HD formation by ionizing the gas. Figure (<>)12 compares the evolution of the runs with different vs values. As the velocity of the shock increases, the post shock density decays quicker to maintain a constant surface momentum. At slower speeds, the minihalo baryons are slowly pushed back. The material does not get constricted to the x-axis, and instead forms a diffuse bow shock, with very little able to collapse or escape the dark matter potential. At intermediate velocities, the material collapses into extended ribbons on the x-axis, with the length of this ribbon decreasing with increasing velocity. At the largest velocity, the most material is collapsed into a single dense clump, with a diffuse envelope of gas. ",
+    "In Figure (<>)13 we show the ballistic particles after 200 Myr for the simulations that vary the shock speed. The slower outflows are unable to push the gas far from the dark matter potential, imparting little kinetic energy into the gas. As a result, these clumps are also less able to merge, resulting in more numerous cloud particles. The ",
+    "Fig. 8.— Column density of the simulations varying the minihalo mass, from top to bottom PM07, PM1, PM23, FID, PM7, and PM19, respectively, with evolution increasing from the beginning on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. All plots have x ranging from −1.5Rv to 4.5Rv, while y ranges from −1.5Rv to 1.5Rv. Thus the physical scale varies from one row to the next, but the characteristic halo scale matches. Similarly, the elapsed time varies as we increase mass since it requires more time for the shock to traverse the minihalo. ",
+    "Fig. 9.— Comparison between the PM07 (red circles), PM1 (green diamonds), PM23 (blue triangles), FID (black squares), PM7 (magenta crosses) and PM19 (cyan stars) simulations illustrating the dependence on minihalo mass. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "Fig. 10.— Column density of the simulations varying the minihalo-shock orientation, with FID on top, and PO1 on bottom, and evolution increasing from the beginning on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. ",
+    "Fig. 11.— Comparison between the PO1 (magenta crosses) and FID (black squares) simulations illustrating the dependence on minihalo-shock orientation. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "slower the outflow, the longer the timescale of the interaction, which leads to an increase in the enrichment of the baryonic material in the slow velocity cases. The most energetic outflows, on the other hand, are unable to appreciably enrich the baryons efficiently, which both lowers the average metallicity of the clumps and increases the metallicity dispersion of individual cloud particles. Finally, in Pv75 roughly 36% of the minihalo baryons are contained in the final cloud particles. In Pv125, only about 8% of the baryons are in these particles, and then for even larger speeds we asymptote to about 25%. At the lowest shock speed, the material is not efficiently re-",
+    "moved from the halo. At somewhat larger velocities the material is stripped from the minihalo potential, while not collapsed on to the x-axis. At even higher shock speeds, the material is collapsed on to the x-axis before it can be quickly removed from the potential, leading to a higher baryonic component. "
+  ],
+  "3.3.4. Outflow Surface Momentum ": [
+    "The shock surface momentum is a significant parameter that along with the shock velocity, sets the initial energy driving the outflow, while simultaneously setting the surface density of the post-shock material. Figure (<>)14 ",
+    "Fig. 12.— Column density of the simulations varying the shock velocity, vs, with Pv75, Pv125, FID, Pv340, and Pv510 from top to bottom, and evolution increasing from the first interaction with the minihalo on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. ",
+    "Fig. 13.— Comparison between the Pv75 (green diamonds), Pv125 (blue triangles), FID (black squares), Pv340 (magenta crosses), and PE30 (cyan stars) simulations illustrating the dependence on shock velocity. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "compares the evolution of the runs with different µs values. As the surface momentum of the shock increases, so does its surface density, leading to increased momentum transfer to the minihalo gas. This leads to increased fragmentation of the shock front, and confinement onto the x-axis. At the lowest surface momentum, the final ribbon of material is more extended perpendicular to the x-axis, and less extended along the x-axis. At the largest surface momentum, the final ribbon of material is the opposite, ",
+    "more constrained to the x-axis, and more extended along the x-axis. ",
+    "In Figure (<>)15, we show the ballistic particles after 200 Myr of evolution for the simulations that vary the surface momentum. The position of most of the final cloud particles is roughly the same for all surface momenta, indicating a greater dependence on the shock speed. Nevertheless, the smallest and largest momentum cases have final particles further removed from the dark matter po-",
+    "Fig. 14.— Column density of the simulations varying the shock surface momentum, µs, with Pµ3, FID, Pµ8, and Pµ9 on from top to bottom, and evolution increasing from the first interaction with the minihalo on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. ",
+    "Fig. 15.— Comparison between the Pµ3 (blue triangles), FID (black squares), Pµ8 (magenta crosses), and Pµ9 (cyan stars) simulations illustrating the dependence on shock surface momentum. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "tential. The primary cause of this in the low momentum regime is that more gas is bound to the x-axis at further distances, leading to larger clumps further away from the dark matter potential. Note that Pµ3 has 28% of the minihalo baryons in the final cloud particles. With larger momentum, less gas is ultimately bound to the x-axis at further distance, despite the ribbon of material being initially more extended. Pµ9 has about 24% of the minihalo baryons in the final cloud particles. Since we only show the final particles with more than 1% of the baryon component, there are many more extended particles for intermediate momentum that are not shown. ",
+    "The mass of the final cloud particles is roughly independent of momentum. Again, the total mass is highest at lowest momentum. The enrichment of these clouds again scales with position, for a given simulation, and ",
+    "increases with momentum, as does the dispersion. This is due to the increased fragmentation and confinement of the baryons along the x-axis at larger momentum, leading to a higher penetration of enriched material. "
+  ],
+  "3.3.5. Outflow Abundance ": [
+    "Throughout the simulations described above, the level of enrichment of the final minihalo material has been consistently a few percent of the outflow abundance. Thus by changing the outflow abundance, we expect the enrichment of the minihalo baryons to vary, which may affect its cooling efficiency as well as the metallicity of the final clusters where stars will be formed. Note that since the majority of the cooling is caused by the produced molecules, the increased metallicity may have little effect on the evolution. We explore this evolution ",
+    "Fig. 16.— Column density of the simulations varying the shock enrichment, with PZ005, PZ05, FID, and PZ5 from top to bottom, and evolution increasing from the first interaction with the minihalo on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. ",
+    "in Figure (<>)16. We see no discernible difference between the different models, with the exception of PZ5. The most enriched outflow, once a significant amount of metals has mixed into the minihalo, is able to contribute a non-negligent amount of cooling from metals, leading to a more collapsed structure starting at 7.7 Myr, and much more noticeable by 13 Myr. Also, the post-shock ambient medium is able to cool more, and fragments earlier than the metal-poor runs. ",
+    "In Figure (<>)17, we show the ballistic particles after 200 Myr of evolution for the simulations that vary the out-flow abundance. The mass distribution of final particles is almost independent of enrichment. Only in the most enriched outflow is the additional cooling sufficient to cause increased fragmentation in the pre-ballistic gas, such that these clumps do not merge. In all simulations roughly 25% of the minihalo baryons are bound in these cloud particles. The enrichment appears to only affect the abundance of the clumps, which is always roughly 2% of the outflow abundance, with a slight dependence on position of the final particles. The variance in abundance is fairly uniform, although the most metal-rich out-flow has a slight peak in its spread. This simulation’s increased fragmentation leads to a larger variance of enriched proto-clumps, which, through merging, results in clumps with higher variance. "
+  ],
+  "3.3.6. Redshift ": [
+    "The redshift of the interaction is a significant parameter that sets the minihalo density and temperature pro-files, as well as its environment. The redshift also sets the post-shock density as well as the surface momentum. We assume the surface density and momentum ",
+    "scales with (1 + z)2 , while the shock velocity is invariant with redshift, as it scales with the supernovae input energy, which we assume is independent of redshift. In Figure (<>)18 we illustrate the evolution of this interaction for various redshifts, while scaling the density color scheme with (1 + z)2 . We see little variation between the three simulations. The timescale of the interaction scales with (1 + z)−1 since vs is the same, while the physical scale of the minihalo is smaller by (1 + z). The cooling is more efficient at higher redshifts with larger densities, leading to slightly cooler, denser clumps, however this effect is minor. ",
+    "In Figure (<>)19 we show the ballistic particles after 200 Myr of evolution for these simulations. Similar to the metallicity parameter study, we see subtle effects. The increased cooling at the largest redshift leads to an increase in fragmentation of the clumps before the ballistic evolution, and this increased fragmentation leads to less merging between the final cloud particles and an increase in enrichment and enrichment variance. "
+  ],
+  "3.3.7. UV Background ": [
+    "We perform one model where a UV background is present. We allow this background to affect the chemistry rates in all cells, consistent with a optically thin medium everywhere. Thus, this is an upper limit to the effect of such a background, as the densest clumps with an appreciable amount of H2 and HD would self-shield, further delaying the effect of Lyman-Werner photons. We use a large UV flux of J21 = 0.1, as discussed in §(<>)2.2.2. This value is taken from the fiducial value in GS10, where the effect of a UV background of this intensity coupled with the gas density in these ",
+    "Fig. 17.— Comparison between the PZ005 (green diamonds), PZ05 (blue triangles), FID (black squares), and PZ5 (magenta crosses) simulations illustrating the dependence on shock metallicity. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "models produces a disassociation timescale of about 1 Myr. This value also is consistent with (<>)Ciardi & Ferrara ((<>)2005), who find at such values you should just begin suppressing structures of mass 106−7 M from collapsing. In Figure (<>)20 we compare the column density, H2, and temperature of FID and PJ01. We see little variation between these two simulations. The PJ01 run has less H2, as expected, resulting in a slightly warmer collapsed gas. However, the molecular hydrogen forms sufficiently quickly so that the amount, even after accounting for loss to disassociation, is large enough to cool the dense clumps faster than the dynamical time. We see little other differences between the two models. ",
+    "In Figure (<>)21 we show the ballistic particles after 200 Myr of evolution for these simulations. We find very little differences between the two runs. PJ01 has 25.4% of the minihalo’s baryons collapsed into the cloud particles, slightly above the fiducial value. The UV background has slightly delayed the cooling by molecular hydrogen, which delays the leading shock-minihalo interface from fragmenting, allowing for slightly more material to be compressed along the main axis. This material is also slightly more enriched since it is the leading interface with the enriched outflow, thus the metals are slightly increased in PJ01 compared with FID, and they have a larger dispersion. "
+  ],
+  "4. OBSERVATIONAL SIGNATURES ": [
+    "Our various simulations of starburst-driven outflows interacting with minihalos consistently produce dense massive objects that we expect to form stars since molecular cooling should be sufficient to cool these objects beyond the Jeans limit. While the resulting high-redshift cluster of stars are not observable with modern telescopes, their epoch of star formation should generate suf-ficient UV flux and Lyman-α photons that they may be visible with upcoming observatories. Also, their compact nature should be sufficient to survive to modern day, such that we may be able to identify presently existing objects to compare with these clusters. Here we discuss both of these possibilities. "
+  ],
+  "4.1. Direct Observations ": [
+    "To determine how bright the star-formation episode in our simulations would appear, we produced mock obser-",
+    "vations of these interactions. As we did not implement a star formation prescription in the simulations themselves, we implemented the post-processing technique of GS11B. We broke the forming ribbon of collapsed material in 175 stellar mass bins. Inside each bin we added the mass from cells with density above ([1 + z]/9)3 × 10−23 g cm−3 , consistent with GS11B and the typical peak density of the ribbon. This assumes a star-formation effi-ciency of 100% for gas above this threshold, thus our estimates are upper limits. We interpolated this stellar mass from one output to the next, yielding an effective star-formation history over the ribbon. We used the stellar population synthesis code bc03 ((<>)Bruzual & Charlot (<>)2003) to estimate fluxes from a starburst population, and convolved these outputs with our ribbon’s star-formation history as a function of frequency and age. We were also able to make estimates on the Lyman-α, H-α and H-β lines by assuming a production of Lyα photons proportional to the star formation rate, while the Balmer lines were estimate from case B ((<>)Osterbrock (<>)1989). We do not consider extinction by dust, which combined with resonant scattering of Lyα may result in a large optical depth. Again we stress that our final results are only upper limits. For more details the reader is referred to GS11B. ",
+    "We determine the fluxes expected in each of the James Webb Space Telescope (JWST ) bands, as well as from bright line emission that may be detected with future ground-based observing facilities, such as the Giant Magellan Telescope (GMT ), the Thirty Meter Telescope (TMT ), and the European Extremely Large Telescope (EELT ). The expected F115W wideband filter detections and expected observed Lyα flux are presented in units of per ribbon length in Figure (<>)22 for several parameters. The physical and angular scales both assume an edge-on viewing angle. Note that for the redshift parameter study, there is not a constant mapping between position and observed angle, thus we have set the x-axis to reflect the angular scale. We find that the final ribbon of material is typically a fraction of a kpc long, slightly smaller than those found in GS11B. This is not surprising, as the unidealized environment, including filaments, makes it more difficult for an efficient transfer of kinetic energy from outflow to minihalo gas. We tabulate the integrated flux from all bands for each simulation in Table (<>)2. Note that this is the net flux from the star formation episode, and not the expected flux from the final globular cluster-",
+    "Fig. 18.— Column density (rows 1-3) and projected temperature (rows 4-6) of the simulations varying the redshift of the interaction, along with the surface momentum, with FID shown in rows 1 and 4, Pz10 shown in rows 2 and 5, and Pz14 shown in rows 3 and 6. Evolution increases from the first interaction with the minihalo on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. ",
+    "Fig. 19.— Comparison between the FID (black squares), Pz10σ (dark blue circles), Pz10C (blue triangles), and Pz14C (magenta crosses) simulations illustrating the dependence on redshift. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "Fig. 20.— Column density (rows 1 and 2), column H2 (rows 3 and 4) and projected temperature (rows 5 and 6) of the simulations varying the UV background, with FID shown in rows 1, 3, and 5, and PJ01 shown in rows 2, 4, and 6. Evolution increases from the beginning on the left, to when the outflow is just passing the minihalo in the middle, to when the outflow reaches the end of the box on the right. ",
+    "Fig. 21.— Comparison between the PJ01 (magenta crosses) and FID (black squares) simulations illustrating the dependence on the UV background. The particle masses (left), metallicity (middle) and relative metallicity dispersion (right) vs particles positions after 200 Myr are shown. ",
+    "like clouds. ",
+    "We find that the expected flux in the JWST bands is typically around 1 nJy/kpc, or just under 1 nJy when in-",
+    "tegrated over the entire ribbon, with this flux greatest in the F115W band. These values are slightly below those of GS11B, and thus are not very optimistic for detection ",
+    "Fig. 22.— Comparison between the mock observations of several of our simulations as seen in the F115W wideband filter of JWST (first and third row), and observed Lyα (second and fourth row). We illustrate the effect of different parameters in columns, with minihalo mass, shock orientation and UV background, shock enrichment, shock velocity, shock surface momentum, and redshift, running from top left to bottom right, respectively. ",
+    "TABLE 2 Observed Flux ",
+    "by JWST, as typical observations with JWST will have sensitivity down to only 10-20 nJy for a 10σ detection after a 10,000s integration ((<>)Stiavelli et al. (<>)2008). ",
+    "Fortunately, the expected fluxes from Lyα, although a factor of a few less than those predicted in GS11B, are still well above the expected detection limit of upcoming ground-based observing facilities. For example, the proposed Near Infrared Multi-object Spectrograph on the GMT is expected to find similar sources down to a flux limit of 10−20 erg cm−2 s−1 given 25 hr of integration (McCarthy 2008; GMT Science Case). Also, the Infrared Imaging Spectrometer on the TMT will detect Lyα sources at z = 7.7 with fluxes of 10−18 erg cm−2 s−1 with a signal-to-noise ratio of 15 in only 1 hr of integration (Wright & Barton 2009; TMT Instrumentation and Performance Handbook). Finally, the planned Optical-Near- Infrared Multi-object Spectrograph for the E-ELT will detect sources with fluxes of 10−19 erg cm−2 s−1 with a signal-to-noise ratio of 8 in 40 hr of integration ((<>)Hammer et al. (<>)2010). All three of these detectors would be sufficient to observe the brightest of our objects. ",
+    "These future ground-based observatories will employ the use of adaptive optics, hoping to get angular resolution in the range of 0.1-0.3 arcsec (McCarthy 2008; Wright & Barton 2009; Hammer et al. 2010), which means our objects will likely be unresolved. However, using Equation ((<>)4) many should be within roughly 5 kpc of the starbursting galaxy driving the outflow, with masses  108 M, which will be easily detectable with JWST broadband data. Thus we expect that future observations of starbursts with ground-based narrowband imaging may see barely resolved objects around the periphery of starburst galaxies extended away from the central starburst galaxy. ",
+    "Finally, the observability of these objects are not very dependent on our parameters. The notable exceptions are minihalo mass and shock speed. For large minihalo masses, there are significantly more photons emitted for larger mass. This is because the high-mass runs result both in significantly more collapsed baryons and higher densities, leading to increased cooling and collapse. Similarly, there are significantly more photons emitted when ",
+    "the shock is faster. This is because the increased shock speed results in more compressed material along the x-axis, leading to denser material, and thus more stars. "
+  ],
+  "4.2. Modern-day Analogs ": [
+    "Figure (<>)23 shows the distribution of final cloud particles whose masses are at least 1% of their minihalo’s baryon mass for all of the simulations performed in this work. ",
+    "We find that the mass of our final cloud particles range from ≈ 103.5 to 105.5M, while the metallicity of the fi-nal cloud particles are consistent with an asymmetric log-normal distribution of log Z = −2.44−+00..36 76. Our dispersion in metallicity is typically about 0.06 dex. Our final cloud particles can be as far removed from their dark matter halo as 12 kpc, with the typical particles found removed by about 6 kpc. ",
+    "The statistical sample of the final cloud-particles from all of our simulations shares many traits with modern day globular clusters. First, the majority of our clusters are unbound from their dark matter halo, consistent with observations of globular clusters which limit the amount of dark matter at less than twice the amount of gas (e.g., Moore 1996; Conroy et al. 2011; Ibata et al. 2013). Also, their enrichment is significantly homogenous, with less than 0.1 dex for most particles. However, there is a tension between the metallicities of our final cloud particles and observations around the Milky Way and Andromeda, which find a consistent value of logZ = −1.6 ± 0.3 (Zinn 1985; Ashman & Bird 1993). If most starburst outflows at these high redshifts were more metal-rich than we assume here (cf., Scannapieco et al. 2004), with values of Z  0.3 Z, then our results would be more consistent with these observations. Additionally, we have purposefully neglected to include subgrid turbulent mixing, as we were concerned with overestimating this process. This may also explain why we only found an enrichment of about 2% of the outflow’s metallicity, which may be much lower than actually occurs in this interaction. ",
+    "Finally, our typical mass of ∼ 104 M has a large scatter, and although it is below the average mass of halo globular clusters in the Milky Way, with an observed distribution much closer to logM = 5.0 ± 0.5 ((<>)Ar-(<>)mandroff (<>)1989), this typical mass is not unreasonable given our fiducial mass. Our process of making globular cluster-like clumps seems most efficient at higher mass, and our largest mass, PM19, produced multiple fi-nal particles with masses of a few ×105 M. It would be interesting to study this parameter space further around such high-mass minihalos, keeping in mind that provided M6 < 52([1 + z]/10)−3/2 , then the virial temperature of the halo will be less than 104 K, and will be unable to cool on its own. That our objects are typically less massive and less enriched than modern-day globular clusters may be consistent with some observations that show that their metallicity may scale slightly with mass (e.g., Ashman & Bird 1993; Harris et al. 2006, 2009; Mieske et al. 2006; Strader et al. 2006; Peng et al. 2009). Additionally, since structure formation is hierarchical, we would expect a large abundance of smaller mass objects. Destructive processes then act to destroy these smaller clusters. First, the minimum radius as a function of mass is bound by mechanical evaporation (e.g., Spitzer & Thuan 1972). Second, the maximum radius as a function of ",
+    "Fig. 23.— The distribution of final cloud particles for all of our simulations. The particle masses (top left), velocity (top right), metallicity (bottom left) and relative metallicity dispersion (bottom right) vs particles positions after 200 Myr are shown. The circles’ color is indicative of the particle mass, darker for more massive particles. The solid lines show the average values for observed halo globular clusters and include a shaded region corresponding to the 1-σ spread in the observations. The dotted line and pink shaded regions mark the asymmetric log-normal distribution of our results. ",
+    "mass is bound by ram-pressure stripping as the clusters move through the plane of the Galaxy (e.g., Ostriker et al. 1972). Thus, only the largest of these objects should survive to today. Since the destructive processes set the minimum mass of the globular cluster mass distribution for a given age of the host galaxy, we would expect that at higher redshift the globular cluster mass distribution should approach the distribution found in our very high redshift models. "
+  ],
+  "5. SUMMARY AND CONCLUSIONS ": [
+    "The early Universe hosted a large population of small dark matter ‘minihalos’ that were too small to cool and form stars on their own. These existed as static objects around larger galaxies until acted upon by some outside influence. Outflows, which have been observed around a variety of galaxies, can provide this influence in such a way as to collapse, rather than disperse the minihalo gas. ",
+    "Here we performed SPH cosmological simulations using the GADGET code to produce realistic minihalos and their environment at z  10. We then implemented a derefinement technique for dark matter particles in the AMR code FLASH. With this we mapped the SPH mini-halos into AMR datasets and conducted a parameter suite studying the effect of energetic outflows, similar to those originating from high-redshift starbursting galaxies, impacting inert primordial minihalos. This was a continuation of the idealized work of GS10, GS11A, and GS11B. ",
+    "We endeavored to determine what effect the minihalo mass, outflow-minihalo environment, outflow speed, out-flow surface momentum, outflow metallicity, redshift, and UV background had on this interaction. We found that the general interaction proceeded by first shock-heating the front of the minihalo, catalyzing the production of molecular hydrogen. As the shock traversed the rest of the minihalo and molecular hydrogen continued ",
+    "to form, increasing the efficiency of cooling, while simultaneously compressing the minihalo towards the x-axis. The compressed minihalo gas continued to cool courtesy of the molecular hydrogen, while it was pushed out of the dark-matter halo. The shock then dissipated, removing roughly 75% of the baryons from the system, and collapsing the remaining 25% into a cool, relatively homogenous ribbon that was no longer bound to the dark matter halo. To compare, the idealized interaction studied in GS11B found upwards of 100% of the baryons condensed into this ribbon. Typically the resulting ribbon of gas was enriched to  2% the metallicity of the outflow, and this material was then treated ballistically, allowing for merging between separate clumps. ",
+    "The most influential parameters are the minihalo mass, orientation, and shock velocity. The minihalo mass is essential in two respects. First, changing this parameter requires changing the particular minihalo and environment mapped from the cosmological simulation. This produced stochastic effects whereby individual minihalo asymmetry and environment influenced the behavior of the interaction as well as its final cluster distribution. This was made clear by comparing models FID and PM2, which varied subtly in mass, but had significantly differ-ent shapes and environments. Second, the minihalo mass sets the abundance of gas available to the interaction, as well as the original minihalo temperature and density profile. As the minihalo mass increased in out simulations, more mass collapsed along the x-axis, but less was able to escape the dark matter potential, a trend similar to that found in GS11B. ",
+    "The orientation is also important as it sets the medium the shock interacts with before striking the minihalo. If an outflow was propagating along a filament, in our simulations, it acted to delay the initial impact, leading to less momentum transfer. Also, this delay allowed the surrounding shock to strike the periphery of the mini-",
+    "halo first, causing it to preferentially collapse before being pushed along out of the halo. Thus, we find that when the shock is oriented along a filament, we have a larger fraction of baryons collapsed into the final cloud particles. ",
+    "Finally, the shock velocity plays a dramatic role in the interaction. At very low velocities the shocks were incapable of collapsing much of the baryons into a coherent ribbon on the x-axis, leading to a large number of low-mass, enriched clumps that were still bound to the dark matter potential. As the shock speed increased, baryons were condensed more efficiently, leading to more massive final particles that were more removed from the dark matter potential. ",
+    "Our models have only considered a primordial chemistry network, and our UV background has assumed an optically thin medium everywhere. It would be interesting for future work to include additional chemical networks and a full treatment of different abundances, instead of a simple tracer for metallicity. Although the amount of enriched material mixed in to the minihalo material is roughly two orders of magnitude below the amount of molecular hydrogen formed during the shock interaction, the subsequent chemistry and cooling could have a non-negligible effect. This would be even more important when a UV background is considered, which reduces the overall impact from molecular hydrogen. Simultaneously, a full treatment of the metal chemistry could yield insights into atypical abundances in oxygen, carbon, and nitrogen, α-elements, sodium and aluminum, and heavier elements, some of which are thought to occur from enrichment from type II SNe, proton capture in the cores of massive stars, and multiple stellar populations (e.g., Pilachowski et al. 1980; Fran¸cois 1991; Colucci et al. 2013; Kacharov et al. 2013). We also encourage future work to explore a wider range of UV background intensities. These would need to be coupled with delays of incidence to insure the minihalo is not photo-evaporated before the interaction begins, and should attempt to include self-shielding, so as to better constrain the ionizing photons’ effect in the densest regions. ",
+    "We also produced simulated observations of this interaction using the post-processing technique from GS11B. We find that the final ribbon of material is typically a fraction of a kpc long, slightly smaller than those found in GS11B, and by using Equation ((<>)4) can be found around 5 kpc from the starburst galaxy driving the outflow. We find that the expected flux in the JWST bands is typically around 1 nJy/kpc, or just under 1 nJy when integrated over the entire ribbon, well below the expected sensitivity of the telescope. However, we find expected Lyα fluxes of around 10−19 erg cm−2 s−1 , well above the expected detection limit of upcoming ground-based observing facilities. Although likely unresolvable, these objects should be visible within 2” of the starburst driving the interaction. Thus future observations of dense bright ",
+    "clumps around the periphery of starburst galaxies will be a clear demonstration of outflows driving star-formation in surrounding minihalos. ",
+    "Finally, the statistical sample of the final cloud-particles from all of our simulations share many traits with modern day halo globular clusters. They are often unbound from their host dark matter halos by about 6 kpc, but by as much as 12 kpc, and are chemically homogenous. Our mass distribution has a typical value of 104 M with a large scatter, while the most massive cloud particles have masses of a few ×105 M, consistent with modern day halo globular clusters. This indicates that most present-day globular clusters are analogues of the objects created from minihalos with M6 ∼ 20 − 60, where we show the production of larger final clumps to be more efficient. Also, the enrichment of our objects is lower than seen in globular clusters. This suggests that a way of modeling subgrid mixing must be included, or that starburst galaxies may drive winds as enriched as ∼ 0.3 − 0.5 Z. ",
+    "We conclude that the interaction of starburst outflows with primordial minihalos is an energetic event that leads to several dense, uniformly-enriched clumps of gas that would be expected to undergo star formation. Such interactions may be visible with the next generation of ground-based telescopes, and may produce clusters that are the progenitors of modern-day halo globular clusters. Future observational work searching for globular clusters around younger galaxies where we expect their typical mass to be less than that found around the Milky Way, and theoretical work exploring more of the high-mass range of the parameter space, coupled with a more complete treatment of chemistry, will be crucial for further demonstrating the connection between halo globular clusters and minihalos. ",
+    "M. L. A. R. was supported by NSF grant AST11-03608 and the National Science and Engineering Research Council of Canada. E. S. was also supported by the National Science Foundation under grant AST11-03608 and NASA theory grant NNX09AD106. The authors would like to acknowledge the Advanced Computing Center at Arizona State University (URL: (<http://a2c2.asu.edu/>)http://a2c2.asu.edu/), the Pittsburg Supercomputer Center (PSC) (URL: (<http://www.psc.edu/>)http://www.psc.edu/) and the Texas Advanced Computing Center (TACC) at The University of Texas at Austin (URL: (<http://www.tacc.utexas.edu>)http://www.tacc.utexas.edu) for providing HPC resources that have contributed to the research results reported within this paper. The authors would like to thank the Extreme Science and Engineering Discovery Environment for allocation time on TACC and PSC resources. We would like to thank Robert Thacker and Paul Ricker for discussions that greatly improved this study. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 "
+  ]
+}

jsons_folder/2013ApJ...779...12B.json

@@ -0,0 +1,134 @@
+{
+  "COSMIC RAY SAMPLING OF A CLUMPY INTERSTELLAR MEDIUM ": [
+    "(<http://arxiv.org/abs/1311.0006v1>)arXiv:1311.0006v1  [astro-ph.HE]  31 Oct 2013 "
+  ],
+  "ABSTRACT ": [
+    "How cosmic rays sample the multi-phase interstellar medium (ISM) in starburst galaxies has important implications for many science goals, including evaluating the cosmic ray calorimeter model for these systems, predicting their neutrino fluxes, and modeling their winds. Here, we use Monte Carlo simulations to study cosmic ray sampling of a simple, two-phase ISM under conditions similar to those of the prototypical starburst galaxy M82. The assumption that cosmic rays sample the mean density of the ISM in the starburst region is assessed over a multi-dimensional parameter space where we vary the number of molecular clouds, the galactic wind speed, the extent to which the magnetic field is tangled, and the cosmic ray injection mechanism. We evaluate the ratio of the emissivity from pion production in molecular clouds to the emissivity that would be observed if the cosmic rays sampled the mean density, and seek areas of parameter space where this ratio di ers significantly from unity. The assumption that cosmic rays sample the mean density holds over much of parameter space; however, this assumption begins to break down for high cloud density, injection close to the clouds, and a very tangled magnetic field. We conclude by evaluating the extent to which our simulated starburst region behaves as a proton calorimeter and constructing the time-dependent spectrum of a burst of cosmic rays. "
+  ],
+  "1. INTRODUCTION ": [
+    "Starburst galaxies are complex environments with intense star formation, “clumpy,” multi-phase interstellar gas, supernovae-driven winds, and tangled magnetic fields. It is remarkable, then, that despite drastically di erent environments, both quiescent and star-forming disk galaxies have a well-established linear correlation between their far-infrared (FIR) and radio luminosities ((<>)Helou et al. (<>)1985). In these systems, the FIR-radio luminosity correlation suggests a fundamental relationship between the star formation processes, resulting in FIR emission from dust heated by young, massive stars, and the cosmic ray population, producing radio synchrotron emission from relativistic electrons spiraling along magnetic field lines. ",
+    "To explain the FIR-radio luminosity correlation, the cosmic ray calorimeter model for starburst galaxies has been explored (e.g., (<>)Voelk (<>)1989; (<>)Thompson et al. (<>)2006; (<>)Persic et al. (<>)2008; (<>)de Cea del Pozo et al. (<>)2009; (<>)Lacki et al. (<>)2011; (<>)Paglione & Abrahams (<>)2012; (<>)Yoast-Hull et al. (<>)2013). This model suggests that the energy imparted to cosmic rays by supernovae is entirely expended through observable emission within the starburst region. If this model holds for cosmic ray electrons, then the observed radio synchrotron emission should be solely dependent on the supernova rate and therefore on the star formation rate (SFR; there is, of course, also a dependence on magnetic field strength, but this too appears to be tied to the SFR; (<>)Schleicher & Beck ((<>)2013)). Likewise, if the model holds for cosmic ray protons, then we expect a similar relationship between the observed γ-ray emission from pion production and the SFR. ",
+    "In order to test the calorimeter model for starburst galaxies, it is necessary to understand how cosmic rays sample the multi-phase interstellar medium (ISM) as they undergo radiative, collisional, and advective losses within the starburst region. In an ISM consisting of cold, molecular clouds embedded in a hot, low-density medium, cosmic rays will only sample the mean density of the ISM if they are able to e ectively enter the molecular clouds. The leading theory of cosmic ray acceleration suggests that energetic particles undergo first-order Fermi acceleration ((<>)Fermi (<>)1949), or di usive shock acceleration (e.g., (<>)Bell (<>)1978; (<>)Blandford & Ostriker (<>)1978), at supernova shock fronts. Additionally, cosmic rays may undergo second-order Fermi acceleration ((<>)Fermi (<>)1949) in the di use ISM. Both first- and second-order Fermi acceleration can only occur eÿciently in low-density environments, where the acceleration mechanism can impart energies in excess of ionization losses and the small-scale magnetic field fluctuations which scatter the particles can propagate. For these reasons, the majority of cosmic rays are believed to be injected in the hot, low-density medium. ",
+    "The hot medium where cosmic rays are injected has a very large filling factor compared to the molecular gas. Additionally, the hot medium may be actively advected from the region by a galactic wind. In order for the cosmic rays to sample the mean density of the ISM, the magnetic field lines along which they propagate must intersect a suÿciently large number of molecular clouds, and the cosmic rays must remain within the region for a suÿciently long time before they are advected away. Therefore, cosmic ray sampling of the mean density of the ISM is far from a foregone conclusion. ",
+    "In this paper, we use Monte Carlo simulations to study ",
+    "TABLE 1 ",
+    "Properties of M82 ",
+    "cosmic ray sampling of an ISM with properties similar to that of the prototypical starburst galaxy M82. We selected this galaxy for our study because it has a well-studied starburst region with well-observed masses of its multi-phase ISM, galactic wind speed, and supernova rate. In M82, the ISM consists of a hot, di use medium in which dense, warm, ionized gas and dense, cold, molecular clouds are found (e.g., (<>)Westmoquette et al. (<>)2009). In particular, CO measurements suggest that the galaxy contains ∼3 ±1 ×108 M⊙of molecular gas that is largely found within clumpy clouds in the starburst region (e.g., (<>)Naylor et al. (<>)2010). Additionally, M82 has a well-observed galactic wind that travels approximately perpendicularly to the galactic plane and is believed to be primarily driven by supernova shock heating ((<>)Chevalier & Clegg (<>)1985). Estimates of the outflow velocity range from ∼500 −600 km s−1 as indicated by optical emission lines of ionized gas ((<>)Shopbell & Bland-Hawthorn (<>)1998, and references therein) to as high as ∼1400 −2200 km s−1 as suggested by X-ray observations ((<>)Strickland & Heckman (<>)2009). Although we use properties suggestive of M82 in this study (see Table 1 for a summary), our analysis is applicable to many other such systems. ",
+    "Here, we evaluate how cosmic ray sampling of the ISM in starburst galaxies is a ected by the number of molecular clouds, the galactic wind speed, the extent to which the magnetic field is tangled, and the cosmic ray injection mechanism. In Section 2, we describe our Monte Carlo simulation parameters and the calculation of an emissivity ratio used to quantify the sampling behavior of the cosmic ray population. Section 3 details the results of our simulations and highlights the region of parameter space in which the emissivity ratio is elevated by a factor of a few. In Section 4, we review our results, compare them to existing models, and discuss their implications for exploring the cosmic ray calorimeter model and constructing the time-dependent spectrum of a burst of cosmic rays. "
+  ],
+  "2. MONTE CARLO SIMULATIONS ": [],
+  "2.1. Simulation Parameters ": [
+    "The multi-phase ISM in the starburst region is modeled to consist of a hot, low-density medium in which cold molecular clouds are embedded. Observations and numerical simulations suggest that the molecular medium consists of many clumpy, fragmented clouds (e.g., (<>)Blitz (<>)1993; (<>)Inoue & Inutsuka (<>)2012). Although ∼3 ±1 ×108 M⊙of molecular gas has been detected in the star-",
+    "TABLE 2 ",
+    "Model Parameters ",
+    "burst nucleus (e.g., (<>)Naylor et al. (<>)2010), we take a conservative order of magnitude estimate of ∼1 ×108 M⊙of molecular gas within our spherical starburst region of radius R= 100 pc, corresponding to a mean number density n∼486 cm−3 . Assuming that the upper limit on the maximum mass of giant molecular clouds in the Milky Way of ∼104 −106 M⊙is applicable to M82, this implies on the order of Nc ∼103 molecular clouds. We hold the total mass of molecular gas constant while varying the number of clouds from Nc = 200 to Nc = 3000 clouds to explore both the nominal case (Nc ∼3000) as well as the limit of very small cloud numbers and very high cloud densities (Nc ∼200). Each cloud is taken to have a volume of Vc ∼27 pc 3 , and thus the clouds’ volume filling factor varies from ∼0.1% to ∼2%. ",
+    "Note that we are explicitly neglecting the contribution of the hot, low-density medium to the density sampled by cosmic rays. Due to the di usive nature of particle motion along magnetic field lines (which reduces their e ective propagation speed from cto the Alfv´en speed, vA), the contribution of the low-density gas is greater than the simple ratio nh /nc , where nh and nc are the mean densities of the hot gas and the cold molecular gas, respectively. We estimate that this is approximately a 10% e ect for the M82 environment. Likewise, warm (∼104 K) ionized gas, in addition to hot gas and cold molecular gas, is undoubtedly present and would also have a small e ect on the model. We will consider these small contributions in future work. ",
+    "Additionally, a supernova-driven galactic wind is included in the model with a linear profile and a wind speed of vadv at a height z= 100 pc above the mid-plane (v= vadv(z/100 pc)). We vary vadv from 0 to 2000 km s−1 , with 500 km s−1nominally taken as the favored value ((<>)Yoast-Hull et al. (<>)2013). We assume the wind carries away the magnetic field lines embedded in the hot gas, together with the cosmic rays loaded onto the field lines, but that the molecular component remains behind. ",
+    "Since the starburst region of M82 is highly turbulent, we expect the magnetic field to have a significant random component. Cosmic ray propagation along tangled magnetic field lines is approximated as a random walk process governed by a mean free path, λmfp, which parameterizes the magnetic correlation length. As the magnetic geometry is not well known, we vary λmfp from 0.5 pc to 25 pc. A longer value of λmfp (i.e., λmfp = 50 pc) was found to yield comparable results to the λmfp = 25 pc case. Due to scattering by short wavelength Alfv´en waves generated by the cosmic ray streaming instability, cosmic ",
+    "Fig. 1.— Summary of the cosmic ray sampling behavior during a representative run of the Monte Carlo code for each  mfp considered. From top to bottom, the figures show the distance traveled by particles before leaving the starburst region, the distance traveled inside of molecular clouds, and the average density sampled normalized to the mean density of the ISM, neglecting any contribution from the hot or warm ionized gas. The particles show a significant range of sampling behaviors; all density distributions show a peak at ˆP /ˆSB = 0, where the particles sample no clouds, as well as varying degrees of a tail at ˆP /ˆSB> 5, where they∼sample average densities greater than the mean density of the ISM by as much as an order of magnitude. These results were found for injection at the center of the starburst region, Nc = 3000 clouds, vadv = 500 km s−1 , and NP = 106 particles, although the results are broadly consistent with the full parameter space. ",
+    "rays are taken to travel along the field lines at the Alfv´en speed, vA ((<>)Kulsrud & Pearce (<>)1969). Given a magnetic field strength B= 275 µG and an average density of the hot medium n= 0.33 cm−3 ((<>)Yoast-Hull et al. (<>)2013), the Alfv´en speed is found to be vA = 960 km s−1 . ",
+    "We use three methods of injecting the cosmic rays into the starburst region. First, we consider the simple scenario where all cosmic rays are injected at the center of the region. Second, in accordance with models of distributed cosmic ray acceleration such as second-order Fermi acceleration by interstellar turbulence, we inject the particles randomly throughout the region. Finally, in agreement with models of point source cosmic ray acceleration such as first-order Fermi acceleration by supernova shocks, we inject the particles at randomly chosen supernova shock sites. We choose 30 injection sites due to observational evidence from radio interferometry for ∼30 active supernova remnants (SNRs) in M82 (e.g., (<>)Fenech et al. (<>)2010). One might expect SNRs and star-forming molecular clouds to spatially coincide, as young, massive stars are not likely to travel far from their place of birth over the course of their lifetimes. Additionally, recent observations of γ-ray emission from molecular clouds associated with SNRs (e.g., (<>)Aharonian et al. (<>)2008b,(<>)a; (<>)Abdo et al. (<>)2010, (<>)2011; (<>)Ajello et al. (<>)2012) provide evidence for a spatial correlation between SNRs and molecular clouds. Thus, for our final injection method, our injection sites are chosen randomly on spheres of radius r= 3 pc centered on clouds. For all cosmic ray injection methods, we disallow injection inside of clouds due to the reduced acceleration eÿciency expected in cold, dense environments. ",
+    "The Monte Carlo simulations are run with NP = 104 particles for a given choice of Nc, vadv, λmfp, and cosmic ray injection mechanism (see the Appendix for a discussion of the number of particles necessary to achieve convergence). At the beginning of a run, we select the cosmic rays’ initial injection sites as well as a random molecular cloud distribution, and we map the state of the ISM onto a three-dimensional grid with a resolution of 0.5 pc. Starting from its injection site, a given particle executes a random walk governed by a mean free path λmfp broken down into steps of length l= 0.5 pc. At each step, the contribution of advection to the particle motion, the component of the ISM being sampled (in/out of cloud), and the particle’s presence in the starburst region (in/out of region) are assessed. If a particle is inside of a cloud at the beginning of a step, the galactic wind does not act on the particle for that step, and the particle is taken to travel at the speed of light instead of at the Alfv´en speed. The particles are taken to free-stream inside of molecular clouds due to the destruction by ion-neutral damping of Alfv´en waves resulting from the streaming instability ((<>)Kulsrud & Pearce (<>)1969). The particle is scattered when it has traveled a distance equal to its mean free path, and the process repeats until the particle has traveled out of the region. ",
+    "Note that we do not explicitly model energy losses along the particle trajectories, deferring a discussion of it to Section (<>)4. The cloud column densities (∼5 ×1023 cm−2 , Nc = 3000 clouds; ∼7 ×1024 cm−2 , Nc = 200 clouds) are well below the characteristic column densities for energy loss (NE ∼2 ×1026 cm−2 , E= 1 GeV; ",
+    "NE ∼3 ×1025 cm−2 , E= 1 TeV) except for very small Nc and/or very high proton energies. This suggests that cosmic rays make several passes though clouds before undergoing collisional energy losses. See Table 2 for a summary of our model parameters. ",
+    "Figure 1 summarizes the sampling behavior of the cosmic rays for a single representative run of the Monte Carlo code. For each λmfp, we show distributions of the total distance traveled, the total distance traveled in molecular clouds, and the average density sampled ( ρP ) normalized to the mean density of the ISM in the starburst region ( ρSB ). It is clear from the density distributions that the particles display a diverse range of sampling behaviors. The extremes of this behavior are seen in the peaks at ρP /ρSB = 0, where no clouds are sampled, as well as in the tails at ρP /ρSB ∼>5, where the particles sample densities as high as an order of magnitude greater than the mean density of the ISM. Note that for λmfp >1, a peak appears near ρP /ρSB = 1. These trends hint that as we proceed to more precisely quantify the sampling behavior, we may reasonably expect the particles to roughly sample the mean density of the ISM over much of parameter space. "
+  ],
+  "2.2. Emissivity Calculations ": [
+    "To quantitatively assess the assumption that cosmic rays sample the mean density of the ISM in the starburst region and evaluate its e ect on γ-ray emission, we use our simulation results to construct a function ϕ(n/n)d(n/n), which gives the fraction of cosmic rays that sample gas density nrelative to the mean density n. The emissivity due to pion production by cosmic rays in molecular clouds is then given by "
+  ],
+  "(1) ": [
+    "where nand ncr are the number densities of the medium and the cosmic rays, respectively, σcoll is the cross section for pion production, vis the velocity of the particles, and Eint is the energy produced by the interaction. If the cosmic rays do indeed sample the mean density of the ISM, the emissivity is given by ",
+    "Thus, the ratio of emissivities αis given by "
+  ],
+  "(2) ": [
+    "(3) ",
+    "Although σcoll is a function of energy, αis independent of energy for all cosmic rays that satisfy the propagation assumptions given at the beginning of this section (i.e., the streaming instability results in propagation at the Alfv´en speed). αis easily obtained by appropriately normalizing, binning, and summing over the distributions of average densities sampled weighted by the densities themselves (see, e.g., Figure 1(c)). Thus, we determine αfor the range of parameters discussed in Section 2.1 and seek areas of parameter space where αdeparts significantly from unity. See the Appendix for a discussion of our determination of αfor a given choice of Nc, vadv, λmfp, and cosmic ray injection mechanism. The Appendix also details our estimation of the errors on αthat ",
+    "originate from both the finite number of particles per run as well as the changes in the random cloud distributions and injection sites from run to run. "
+  ],
+  "3. RESULTS ": [],
+  "3.1. Emissivity Ratios for all Parameters ": [
+    "Fig. 2.— Mean emissivities for all combinations of cosmic ray mean free path, injection mechanism (indicated by color), three wind speeds (shape), and two cloud numbers (fill). The lower panel is a closer view of a portion of the upper. It is clear that over the vast majority of parameter space, the emissivity ratios are clustered around = 1 and thus the cosmic rays roughly sample the mean density of the ISM. However, as discussed in Section 3.2, cosmic ray injection near the clouds in the limit of small cloud number and thus high cloud density results in emissivity ratios that are elevated by a factor of a few and the assumption that the cosmic rays sample the mean density breaks down. Additionally, cosmic ray injection randomly throughout the region results in emissivities that are suppressed by as much as a factor of ∼2; however, the suppression of the emissivity at low values of is not as dramatic as its elevation at high . ",
+    "We begin by examining the densities sampled over the entire range of parameters considered in this study (i.e., all combinations of cosmic ray mean free path, injection mechanism, two molecular cloud numbers (Nc = 200, 3000 clouds), and three wind speeds (vadv = 0, 500, and 2000 km s−1)). In Figure 2, we see that the cosmic rays roughly sample the mean density of the ISM over much of parameter space. Overall, we do not achieve emissivities suppressed below α= 1 by a factor of more than ∼2; we ",
+    "do achieve emissivities elevated above α= 1 by a factor of a few; and these modestly elevated emissivities occur only for cosmic ray injection near clouds in the limit of small cloud number and thus high cloud density. This case will be considered separately in Section 3.2. ",
+    "Although much ofover parameter space, and cosmic ray injection mechanism. We note that αthere are still clear trends relating αto Nc, λmfp, vadv, tends to increase as λmfp decreases, suggesting that cosmic rays with short λmfp generally travel along more convoluted trajectories and thus spend more time sampling the starburst region as well as the clouds that they encounter. We also note a somewhat greater spread in αat shorter λmfp that may be due to more frequent scattering allowing for more varied paths through the starburst region and thus more varied emissivity outcomes. ",
+    "For cosmic ray injection near clouds and randomly throughout the region, αtends to decrease as vadv increases. When injection occurs far from the midplane, the particle’s trajectory is immediately a ected by the wind, and advective losses dominate. However, for injection at the center of the region and short λmfp, αinstead increases with vadv. For central injection, the particle initially experiences very weak wind speeds, and advective losses are negligible. Additionally, for higher vadv, these particles may travel along more eÿcient trajectories and thus sample more clouds than for lower vadv, where they travel more convoluted trajectories and are more likely to circumvent clouds. ",
+    "The cosmic ray injection mechanism also has other effects on the value of α. At a given λmfp, emissivities from injection at the center of the starburst region exceed those of injection randomly throughout the region, while injection near clouds in the case of Nc = 3000 clouds tends to fall between these two limiting cases. It is expected that cosmic rays injected at the center have the opportunity to sample greater densities than those injected randomly because they generally spend more time within the starburst region. Additionally, cosmic rays injected near clouds in the Nc = 3000 clouds case are expected to sample greater densities than those injected randomly because of their initial proximity to clouds. However, as these cosmic rays also sample lesser densities than those injected at the center of the region, it appears that this e ect is outweighed by the relatively shorter time spent within the region. ",
+    "Finally, Nc has a clear e ect on the value of α, albeit one moderated by injection mechanism. When cosmic rays are injected near clouds and thus have ample opportunity to encounter dense gas, a smaller number of denser clouds produces a higher emissivity than a larger number of less dense clouds. However, when cosmic rays are randomly injected, they have a decreased likelihood of encountering dense gas; thus, despite the increase in cloud density, the decrease in cloud number may suppress the emissivity such that the results are comparable for both a low and high number of clouds. "
+  ],
+  "3.2. Emissivity Ratios for Injection Near Nc = 200 Clouds ": [
+    "We now discuss the region of parameter space where the cosmic rays sample the highest densities. As shown in Figure 3, the cosmic rays achieve the highest αvalues when injected the molecular clouds innear ",
+    "Fig. 3.— Mean emissivities and 68% confidence intervals for cosmic ray injection near clouds in the limit of small cloud number (Nc = 200 clouds) and high cloud density. In this region of parameter space, we achieve emissivities elevated above = 1 by a factor of a few, with the highest emissivities achieved with large vadv and small mfp. ",
+    "the limit of small cloud number (Nc = 200 clouds) and thus high cloud density. This result is not surprising, as cosmic ray injection near high-density molecular gas has the greatest likelihood of interaction between the particles and the molecular medium. As noted in Section 3.1, the value of αis highest for short λmfp (λmfp 5 pc),<∼where αvaries from ∼2 -7.5, than for longer λmfp , ",
+    "where αis ∼2 -3. In addition to spending more time sampling the starburst region, particles with short λmfp may also be more likely to enter the clouds accompanying their injection sites than those that are able to travel more eÿciently away. ",
+    "As is clear in Figure 3, the case of no galactic wind results in αvalues lower than that of high wind (vadv = 2000 km s−1) by a factor of ∼2, while the case of moderate wind (vadv = 500 km s−1) results in intermediate emissivities. At short λmfp, the cases of high and moderate vadv become comparable. Particles that are injected between the galactic plane and their accompanying cloud are likely to be advected into the cloud in the presence of a wind; the likelihood of this occurring may increase with vadv. Particles with short λmfp also have an increased likelihood of entering the clouds at their injection sites due to their inability to eÿciently travel away from these sites, rendering the emissivity less sensitive to vadv. ",
+    "In summary, cosmic ray injection near Nc = 200 clouds for short λmfp and moderate to high vadv results in αvalues that are modestly elevated above α= 1 by a factor of a few. Note that the uncertainty associated with these emissivities increases dramatically in the limit of short λmfp and high vadv. The former dependence suggests that particles that experience more frequent scattering travel along more diverse trajectories and thus have more diverse emissivity outcomes. Additionally, the latter dependence implies that a higher vadv results in greater populations of particles that are rapidly advected away (resulting in low emissivities) as well as particles that enter the clouds near their injection sites (high emissivities). Therefore, although this region of parameter space results in elevated emissivities, the nature of the random cloud and injection point distributions is important in determining the observed emissivity. ",
+    "We have now seen that cosmic rays injected near Nc = 200 high-density clouds sample densities in excess of the mean density of the ISM, while those injected near Nc = 3000 lower density clouds do not. Thus, for the case of injection near clouds, we seek an upper limit on the number of clouds necessary to achieve elevated emissivities. In Figure 4, we consider αfor vadv = 500 km s−1and a range of Nc values for which 200 ≤Nc ≤3000 clouds. It is clear that very low values of Nc are required to achieve elevated emissivities. For the shortest λmfp, decreasing Nc from 3000 to 1000 clouds increases αby only a factor of ∼2. It is only when Nc is decreased to ∼400 clouds that αbecomes elevated by a factor of a few. Thus, in the case of cosmic ray injection near clouds, a very small cloud number and thus very high cloud density is required to achieve elevated emissivities. "
+  ],
+  "3.3. Cosmic Rays that Do Not Sample Clouds ": [
+    "We now consider the fraction of cosmic rays that escape from the starburst region without sampling molecular clouds at all. This sheds light on the relationship between the sampling behavior of individual particles and the sampling of the particle population as a whole. In Figure 5, it is clear that over the full parameter space considered, the fraction fof cosmic rays that escape from the starburst region without sampling clouds ranges from near complete sampling (f∼2×10−5 , Nc = 3000 clouds, vadv = 0 km s−1 , injection at the center) to near com-",
+    "Fig. 4.— Mean emissivities and 68% confidence intervals are strongly dependent on the cloud number and thus the cloud density for cosmic ray injection near clouds. Though the emissivity is significantly elevated for short mfp in the limit of small Nc, these emissivities decrease very rapidly as Nc increases. At Nc values greater than several hundred, approaches unity for all mfp. ",
+    "Fig. 5.— Fraction of cosmic rays f that escape the starburst region without sampling molecular clouds as a function of mfp. Though the cosmic rays approximately sample the mean density of the ISM over much of parameter space, they clearly undergo a diverse range of sampling behaviors, from near complete sampling of clouds (f ∼2 ×10−5 ) to near absence of sampling (f ∼0.98). These fractions are determined from single NP = 106 particle runs, and will change slightly for di erent distributions of molecular clouds and cosmic ray injection sites. ",
+    "plete escape (f∼0.98, Nc = 200, vadv = 2000 km s−1 , random injection). As we found that cosmic rays approximately sample the mean density of the ISM over much of parameter space, we see that emissivity values of α∼1 are achieved over the full range in f. Therefore, we may find α∼1 both when the vast majority of particles sample roughly the mean density (occurring mainly for high Nc values), as well as when only a small minority of particles encounter the molecular medium (mainly low Nc values). ",
+    "When we are interested in the mean density sampled by the cosmic ray population as a whole, such as when evaluating the cosmic ray calorimeter model, these two broad sampling behaviors can be considered comparable. However, if large numbers of cosmic rays escape from the star-",
+    "burst region without losing energy to collisional processes in the molecular medium, this may have important implications for the galactic environment. It has been shown that when the cosmic rays are self-confined, meaning that they generate the waves that trap them, they may contribute to driving a galactic wind ((<>)Breitschwerdt et al. (<>)1991; (<>)Everett et al. (<>)2008). Thus, we may be more likely to observe a galactic wind under conditions for which cosmic rays are able to travel through the hot medium to escape the starburst region without undergoing energy losses in molecular clouds. "
+  ],
+  "4. DISCUSSION AND APPLICATIONS ": [],
+  "4.1. Comparison to a “Back of the Envelope” Model ": [
+    "We now discuss our Monte Carlo simulations in the context of a simple, “back of the envelope” model of cosmic ray sampling of a clumpy ISM. We refer to the model in Section 4.1 of (<>)Yoast-Hull et al. ((<>)2013) adapted to account for di usive cosmic ray propagation. This model suggests that cosmic rays will sample the mean density of the ISM if two general conditions are met. First, the magnetic field lines along which they propagate must pass through a representative sample of the varied components of the ISM. Second, they must be able to travel along or di use across field lines to encounter these components before they are advected from the region. To determine whether these conditions are met, we compare the timescale τdiff for cosmic rays to di use between clouds to the timescale τadv for them to be advected from the region. We define the former as ",
+    "(4) ",
+    "where lc is the mean distance between clouds and the factor of lc/λmfp accounts for cosmic ray di usion with a mean free path λmfp <lc. lc can be approximated as lc ∼R/Nc1/3 , where Ris the radius of the starburst region. We take lc to be the mean minimum distance that cosmic rays must travel to reach a cloud assuming that there is no spatial correlation between clouds and cosmic ray injection sites. For this reason, this model is applicable only to cosmic rays traveling along suÿciently tangled magnetic field lines (λmfp <lc) and to cosmic rays that have been injected either centrally or randomly in the starburst region. ",
+    "We define the condition under which cosmic rays will encounter molecular clouds to be ",
+    "(5) ",
+    "where τadv = 2R/vadv is the advection timescale for cosmic rays that experience a mean advecting wind speed of ∼vadv/2. Taking vA = 960 km s−1 , vadv = 500 km s−1 , and R= 100 pc, we arrive at a relationship between Nc and λmfp that predicts whether or not cosmic rays are able to encounter clouds before being advected from the starburst region: ",
+    "(6) ",
+    "We now compare this prediction with the results of our ",
+    "Monte Carlo simulations. Considering broadly the predictions of Equation (6) for central or random cosmic ray injection, vadv = 500 km s−1 , and λmfp <lc, this prediction suggests that for all but the shortest λmfp, cosmic rays should encounter dense gas for both Nc = 200 and 3000 clouds. For central injection, there is very good agreement between this prediction and our simulation results, as our αvalues are indeed close to unity. For random injection, however, there is only very broad agreement, as αis instead close to ∼0.6. This discrepancy is not surprising for the case of random injection, as our simple model does not account for the e ective decrease in the advection timescale for particles injected considerably closer than R= 100 pc to the edge of the region. ",
+    "Additionally, for λmfp = 0.5 pc, Equation (6) suggests that we require Nc ∼>350 clouds for the cosmic rays to encounter dense gas. For central cosmic ray injection, however, we find from our simulations that the cosmic rays do indeed interact with dense gas for both Nc = 200 and 3000 clouds. For random injection, we again find that the value of αis relatively insensitive to cloud number. This discrepancy is due to our simple model’s inability to account for the e ect of increasing cloud density with decreasing cloud number. In our simulations, we find that despite fewer cosmic rays sampling clouds in the limit of small cloud number, we still observe emissivities comparable to those found for larger cloud numbers due to the increase in cloud density. ",
+    "Thus, our simple model is useful for broadly considering constraints on the conditions for cosmic ray sampling of molecular clouds. However, this model solely suggests whether or not cosmic rays encounter dense gas. We have seen that the observed emissivity is dependent not only on getting cosmic rays to the gas, but on additional properties such as the gas density as well. Thus, for accurately predicting observed emissivities, our full Monte Carlo simulations are required to account for all relevant subtleties. "
+  ],
+  "4.2. Implications for Starburst Calorimeter Models ": [
+    "The starburst calorimeter model suggests that there is a direct relationship between the energy imparted to cosmic rays by supernovae and the energy lost by cosmic rays within the starburst region. Thus, there is a relationship between the supernova rate, and therefore the SFR, and observable emission in the radio (cosmic ray electrons) and γ-ray (cosmic ray protons) regimes. Here, we evaluate the extent to which our simulated starburst region behaves as a cosmic ray calorimeter under a range of physical conditions by comparing the particles’ confinement timescales τC to their energy loss timescales τE. Note that as starburst galaxies with properties like those of M82 are well established to be e ective cosmic ray electron calorimeters (e.g., (<>)Yoast-Hull et al. (<>)2013), we will consider only cosmic ray protons for the remainder of our analysis. ",
+    "The cosmic ray transport equation gives rise to the functional form of τE (e.g. (<>)Yoast-Hull et al. (<>)2013) and is given by ((<>)Longair (<>)2011): ",
+    "(7) ",
+    "Fig. 6.— To assess whether our simulated starburst region is an e ective cosmic ray proton calorimeter, we examine the ratio of the confinement timescale ˝C to the energy loss timescale ˝E. Here, we consider ˝C /˝E for E = 1 GeV and E = 1 TeV protons for a range of conditions on Nc, mfp, vadv, and the cosmic ray injection mechanism. Although the starburst region is an e ective proton calorimeter at low energies (˝C /˝E > 1, E ∼0.1 GeV), it may be at best a partial proton calorimeter for the energies considered here, where ˝C /˝E ∼< 1 over non-trivial portions of parameter space. ",
+    "Here, N(E,t)dEis the cosmic ray number density at time twith energies between Eand E+ dE, dE/dtis the rate at which radiative and collisional losses decrease a particle’s energy, and Q(E,t)dEis the rate at which particles are injected per unit volume with energies between Eand E+dE. Here, τC accounts for both di usive and advective losses and is assumed to be independent of energy. We may assume that Q(E) and N(E) are of the form Q(E) = AE−and N(E) ≈Q(E)τ(E), where τ(E)−1 ≡τC−1 + τE−1 is the total energy loss rate. For the steady state, the energy loss rate τE is then found to be ",
+    "(8) ",
+    "The energy loss rates for cosmic ray protons are due primarily to ionization and pion production, the latter of which is dominant above ∼1 GeV ((<>)Schlickeiser (<>)2002). Note that we do not account for the (negligible) contribution from Coulomb e ects. The energy loss rates from both ionization and pion production are directly proportional to the average density sampled by the particles, ",
+    "defined as the mean density of the ISM modified by a multiplicative factor of α, nP = αnSB . We define the confinement timescale τC for a given vadv, λmfp, and cosmic ray injection mechanism as the median time that NP = 106 particles take to escape from the starburst region. We calculate the ratio of the confinement to energy loss timescales τC/τE and seek physical conditions where the calorimeter model fails to hold (τC/τE <<1). ",
+    "In Figure 6, we show τC/τE for E= 1 GeV and E= 1 TeV protons over the full parameter space considered. At a given energy, the value of τC/τE ranges over more than three orders of magnitude and is strongly dependent on vadv, λmfp, and the cosmic ray injection mechanism. For the lowest energy protons (E∼0.1 GeV), τC/τE ∼>1 for all parameters considered, and the starburst region is an e ective proton calorimeter. At moderate proton energies (E∼1 GeV), however, τC/τE only exceeds unity for all λmfp in the absence of a galactic wind. Additionally, τC/τE does not exceed unity for the longest λmfp for any parameters considered. At higher energies (E∼1 TeV), τC/τE again exceeds unity in all cases except that of large Nc, high vadv, and injection throughout the region. Thus, for moderate to high proton energies, our simulated starburst region can only be deemed a partial proton calorimeter without further knowledge of the physical conditions in the region. Note that the starburst region would be calorimetric over larger portions of parameter space if we had made a more generous estimate of the molecular gas mass contained within the region. "
+  ],
+  "4.3. The Spectrum of a Cosmic Ray Burst ": [
+    "We conclude by constructing the spectrum of a cosmic ray burst from a single supernova explosion and evaluating how the time evolution of the spectrum is a ected by the density sampled by the particles. Although the steady state solution is generally preferred for the cosmic ray populations of starburst galaxies, the behavior of a burst of cosmic rays may inform our understanding of how smaller scale cosmic ray populations evolve over short timescales. Here, we again consider only cosmic ray protons, as only a small minority of a supernova’s energy is believed to be imparted to cosmic ray electrons ((<>)Blandford & Eichler (<>)1987). ",
+    "To construct the spectrum of a burst of cosmic rays, we begin by dropping both the source and the advec-tion terms from the cosmic ray transport equation; the advection term will be added later. Thus, we have ",
+    "where we define the energy loss rate to be ",
+    "(9) ",
+    "(10) ",
+    "For initial condition N(E,0) = No(E), one can show that N(E,t) takes the form: ",
+    "(11) ",
+    "where Eo(E,t) is the energy at time t= 0 of a particle with energy Eat time t. ",
+    "We now restore the advection term to the cosmic ray transport equation: ",
+    "(12) ",
+    "We consider the case where N(E,t) assumes the form N(E,t) = f(E,t)e−t/˝C . By substituting this expression into the transport equation with advective losses added, we discover that f(E,t) is a solution of this equation when advective losses are neglected. Thus, we obtain an expression for N(E,t) accounting for advective losses by multiplying our previous expression for N(E,t) by a factor of e−t/˝C . Additionally, we assume that the initial injected spectrum is a power law No(E) = AE−with spectral index γ��∼>2. Therefore, the spectrum of a burst of cosmic rays has the functional form: ",
+    "(13) ",
+    "To find the initial energy Eo given the energy Eat time t, we solve for the value of Eo that satisfies ",
+    "(14) ",
+    "This is done by selecting a value for Eo, numerically integrating backward, and evaluating the consistency of the resulting t′with the desired time t. ",
+    "Finally, we determine the value of Ain order to satisfy: ",
+    "(15) ",
+    "where ESN is the energy released by a supernova explosion, ηis the fraction of a supernova’s energy transferred to cosmic rays, and VSB is the volume of the starburst region. Therefore, Ahas the functional form: ",
+    "(16) ",
+    "where we take γ= 2.1, Emin = 0.1 GeV, ESN = 1051 erg, η= 0.1, and VSB ∼1062 cm3 . Note that we take the cosmic ray acceleration timescale in a supernova shock to be τaccel ∼<104 yr <<τC, and thus τaccel can be taken to be e ectively instantaneous. ",
+    "The time evolution of the spectrum is shown in the upper panel of Figure 7 for α= 1 and τC = 106 yr. This choice of αand τC is consistent with much of the parameter space considered. As in Section 4.2, the energy loss rates for cosmic ray protons are calculated according to (<>)Schlickeiser ((<>)2002). It is evident that the spectrum evolves rapidly with time; on timescales comparable to the confinement time, the number density decreases by several orders of magnitude at all energies. This decline is most dramatic at high energies (E∼>10 GeV), where the spectrum steepens sharply by t∼106 yr due to extreme energy loss rates as well as the initial lack of high-energy particles. ",
+    "In the lower panel of Figure 7, we show the spectrum at time t∼2×105 yr for a range of densities sampled. It is clear that increasing the value of αby a factor of a few rapidly decreases the lifetime of the particle population. ",
+    "Fig. 7.— In the upper panel, we show the time evolution of the spectrum of a burst of cosmic ray protons from a single supernova explosion under the physical conditions of M82. Here, we take = 1 and ˝C = 106 yr, values consistent with much of the parameter space considered. Other confinement times can be easily accounted for by appropriately adjusting the factor of e−t/˝C in Equation (13). The rapid evolution of the spectrum with time suggests that cosmic ray bursts are short lived in these environments. In the lower panel, we show the spectrum of a cosmic ray burst at time t ∼˝accel (dashed line) as well as at t ∼2 ×105 yr (solid lines) for a range of values of . It is clear that cosmic ray bursts that sample densities greater than the mean density of the ISM by a factor of a few have dramatically shortened lifetimes. ",
+    "For example, by comparing the top and bottom panels of Figure 7, we see that the spectrum of a cosmic ray burst with α= 1 that has evolved for t∼1.6 ×106 yr is identical to the spectrum of a burst with α= 8 that has evolved for only t∼2 ×105 yr. ",
+    "Overall, the spectrum of a burst of cosmic rays evolves rapidly under the physical conditions of a starburst galaxy like M82, and thus the cosmic ray population produced by a single supernova explosion under these conditions is a short-lived phenomenon. However, a conservative estimate of the supernova rate in M82 is ∼0.07 yr−1 ((<>)Fenech et al. (<>)2008), and thus we can expect that a supernova explosion will occur in M82 every ∼15 yr. The evolved cosmic ray spectra shown in Figure 7 will therefore never be made manifest, and instead will be regularly replenished by newly injected particles. However, in other star-forming environments where the supernova rate may be very low, such as extreme dwarf ",
+    "galaxies or OB associations, these spectra may indeed be manifested due to a lack of replenishing particles. "
+  ],
+  "5. CONCLUSIONS ": [
+    "In the interest of understanding how cosmic rays sample the clumpy ISM in a starburst environment, we have undertaken Monte Carlo simulations of cosmic ray sampling of molecular clouds under the physical conditions of the archetypal starburst galaxy M82. Here, we briefly review the results of our study: ",
+    "Though we have illustrated several applications here, cosmic ray sampling of a clumpy ISM may be applied to a wide range of science goals seeking to understand the relationship between the state of the multi-phase ISM, the star formation processes, and the cosmic ray populations of starburst galaxies. ",
+    "We gratefully acknowledge the support of NSF AST-0907837 and NSF PHY-0821899 (to the Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas). We thank Benjamin Brown, Sebastian Heinz, Dan McCammon, and Joshua Wiener for helpful discussions, as well as Masataka Okabe and Kei Ito for supplying the colorblind-friendly color palette used in this paper (see (<fly.iam.u-tokyo.ac.jp/color/index.html>)fly.iam.u-tokyo.ac.jp/color/index.html). ",
+    "This work has made use of NASA’s Astrophysics Data System. "
+  ]
+}

jsons_folder/2013IAUS..292..323D.json

@@ -0,0 +1,31 @@
+{
+  "Abstract": [
+    "Abstract. Merging systems at low redshift provide the unique opportunity to study the processes related to star formation in a variety of environments that presumably resemble those seen at higher redshifts. Previous studies of distant starbursting galaxies suggest that stars are born in turbulent gas, with a higher eÿciency than in MW-like spirals. We have investigated in detail the turbulent-driven regime of star-formation in nearby colliding galaxies combining high resolution VLA B array H i maps and UV GALEX observations. With these data, we could check predictions of our state-of-the-art simulations of mergers, such as the global sharp increase of the fraction of dense gas, as traced by the SFR, with respect to the di use gas traced by H i during the merging stage, following the increased velocity dispersion of the gas. We present here initial results obtained studying the SFR-H i relation at 4.5 kpc resolution. We determined SFR/H i mass ratios that are higher in the external regions of mergers than in the outskirts of isolated spirals, though both environments are H i dominated. SFR/H i increases towards the central regions following the decrease of the atomic gas fraction and possibly the increased star–formation eÿciency. These results need to be checked with a larger sample of systems and on smaller spatial scales. This is the goal of the on-going Chaotic THINGS project that ultimately will allow us to determine why starbursting galaxies deviate from the Kennicutt-Schmidt relation between SFR density and gas surface density. "
+  ],
+  "keywords": [
+    "Keywords. galaxies: interactions, galaxies: ISM, galaxies: starburst, stars: formation "
+  ],
+  "1. Introduction ": [
+    "The role of starbursting mergers versus quiescent evolution in the star formation (SF) budget of galaxies is one of the most debated questions in galaxy formation, both theoretically (Dekel et al., 2009) and observationally (Daddi et al., 2010). The debate has intensified in recent years after it was realized that (i) high-redshift disk galaxies can drive an active phase of star formation just by internal processes, as they are very gas–rich and (ii) their large scale interstellar medium (ISM) is highly turbulent, with turbulent speeds of several tens of km s−1(F¨orster Schreiber et al., 2006). ",
+    "ISM turbulence plays a fundamental role in driving and regulating star formation in any galaxy, from disks to mergers. On the one hand, turbulent flows can locally compress the gas, and form over–densities that subsequently cool and collapse into star–forming clouds. On the other hand, turbulence can support clouds against rapid collapse, or even disrupt local over–densities in the ISM before they have time to form stars, hence regulating star formation (Elmegreen et al., 2002). Extreme turbulence in high–velocity shocks may even suppress star–formation (Appleton et al. 2006). Di erences in the turbulent nature of the ISM in galaxies could thus lead to significantly di erent SF regimes, and this could be particularly important in colliding and merging galaxies in general, and in high–redshift galaxies in particular. ",
+    "Star formation on galactic scales can in general be seen as a two–step process: (1) formation of dense molecular gas clouds in the large scale ISM – a first step driven ",
+    "1 ",
+    "Figure 1. H i contours superimposed on the UV maps of three nearby interacting systems. The regions for which a region-to-region analysis of the SFR–H i relation are indicated with circles. ",
+    "by gravitation and cooling processes and (2) star formation in the dense cores of these molecular clouds. Whereas the conversion of dense molecular gas into stars may follow a universal eÿciency, the first phase, namely the formation of molecular complexes from large-scale atomic reservoirs, is a less studied process. ",
+    "While surveys of high-redshift disks show that they are highly turbulent, they do not resolve their gas properties down to the scale of star–forming complexes. ALMA will map the densest phases of the molecular gas, thus probing the final steps of star formation in dense clouds, but not the formation of these dense clouds from lower–density, atomic gas. Thus, surveys of the atomic gas are indispensable in order to address the following questions: how eÿcient is star formation in a more turbulent ISM than in quiescent (nearby) spirals? Are the strongest starbursts at any redshift (linked to mergers) triggered mostly by ISM turbulence, or by smaller scale processes (star formation inside dense clouds) or larger scale ones (global gas inflows)? ",
+    "In the absence in the nearby Universe of the equivalent of the distant gas–dominated and highly turbulent disks, galaxy mergers o er unique local laboratories to probe ISM physics and SF processes in such turbulent environments. Indeed, their gas velocity dispersion can be several tens of km s−1 just like in high-redshift galaxies. ",
+    "Increased ISM turbulence in interacting galaxies can now be modeled in detail in simulations with modern grid–based hydro–codes (AMR) with spatial resolutions up to one parsec (Teyssier et al. 2010). These simulations that directly resolve star–forming clouds show that this turbulence–driven star formation can trigger starbursts simply by changing the distribution of the gas between low–density phases and dense star–forming phases. Teyssier et al. (2010) thus propose that the recently observed deviation of mergers from the Kennicutt–Schmidt (KS) relation between the SFR and gas surface density (Daddi et al., 2010) can be explained mostly by turbulence. The change of the Probability Distribution Function (PDF) of the ISM density due to the increased turbulence in mergers is illustrated in Bournaud (2011). Observationally, it translates to a local increase of the Star Formation Rate to HI mass ratio during the merger. A theoretical modeling of the change of the PDF shape and its impact on the KS relation has recently been proposed by Renaud et al. (2012). ",
+    "We have checked the predictions of the simulations and models studying the spatially resolved SFR–H i relation in a sample of nearby interacting systems. "
+  ],
+  "2. Spatial evolution of the H i- SFR relation in sample of nearby colliding systems ": [
+    "High resolution maps of the H i gas were obtained with the JVLA in B configuration for a sample of 7 nearby colliding systems, as part of the Chaotic THINGS survey. We present here initial results for 3 systems: 2 interacting galaxies: Arp 105 and Arp 245 and the well known advanced merger NGC 7252 (see Fig (<>)1). According to their integrated properties and location on the KS relation, they are observed during a starburst phase. ",
+    "Their external regions, in particular their tidal tails, turn out to be gas-rich, with the H i dominating by far the baryonic budget whereas, for two galaxies, the inner regions are H i–poor. The Star Formation Rate (determined from UV emission from GALEX) and H i mass per unit area were compared at the 4.5 kpc-scale. A tight spatial correlation between the UV and H i emission was found. Fig (<>)2 plots the individual extracted regions on the SFR – H i surface density plane. For comparison, the results of the pixel-to-pixel analysis of external regions of isolated spirals, observed as part of the THINGS survey ",
+    "Figure 2. SFR − HI density relation for our sample of star forming regions in mergers. All fluxes were corrected for internal and Galactic extinction. The size of the symbols is directly proportional to the distance of the star forming region to the central galaxy. For comparison, the data obtained by the pixel-to-pixel study at 750 pc resolution of the outer discs of spiral galaxies by Bigiel et al. (2010) are plotted, together with additional data on mergers taken from the literature: Arp 158 and VCC 2062. The dashed lines represent lines of constant star formation eÿciency (or constant depletion time). The vertical dotted line represents the saturation value of H i, as measured by Bigiel et al. (2010) from a sample of spiral galaxies. ",
+    "(Bigiel et al., 2010), are also shown. The SFR/H i mass ratio in the external regions of mergers, a proxy of the Star-Formation Eÿciency (SFE) in that environment, was found to be higher than that found in H i–dominated regions of isolated systems, like the outer discs of spiral galaxies. Besides, it only weakly varies with gas density, just like the SFE of the internal disks of isolated spirals, characterized by a high molecular gas fraction (Bigiel et al., 2008). In other words, the outskirts of mergers, though they are formally H i–dominated, show a regime of Star-Formation more characteristic of the one that prevails in the H2–dominated regions of isolated spirals. ",
+    "As shown on Fig (<>)2, the SFR/H i mass ratio seems to increase towards the inner most regions, partly due to the decrease of the H i column density (following the transition of the atomic gas to a molecular phase), or possibly due to an increase of the SFE, here defined as the ratio between the SFR to the molecular gas mass. "
+  ],
+  "3. Evolution of the Star Formation Eÿciency ": [
+    "A proper study of the spatial (in-out) and temporal (along the merger sequence) evolution of the SFE would require to map the molecular gas of several systems over their full H i extent. This is now achievable with the IRAM and ALMA facilities. A few pointed CO observations towards tidal tails already exist, including for the systems studied here. These external regions of mergers have a molecular gas fraction of typically 30 to 40%, i.e., less than that measured in the disks of isolated spirals like the MW, while their star–forming regions have similar SFEs (Braine et al., 2001). This is consistent with the results obtained analyzing the H i data: the SF regime in the external parts of mergers is closer to what prevails in the inner disks of spirals than in the outer ones which is very ineÿcient at forming stars. There are some exceptions though: in shock regions such as the X–ray ridge of Stephan’s Quintet (Guillard et al., 2012), or in the collisional debris of ancient mergers, such as NGC 4694 / VCC 2062 (Lisenfeld et al., 2013, in prep.), low SFE have been measured. Arp 158 is one of the very few systems where H i, CO, UV/IR data are available over the whole system. Interestingly, Boquien et al. (2011) found enhanced SFE towards its merging nuclei, while the SFE in the other regions, in particular in the tidal tails, is constant (see Fig. (<>)2). So the two branches of the KS relation (for starbursts and normal spirals) are observed there within a single system. ",
+    "Studying the SFR-gas relation at the kpc-scale for a larger number of systems is most needed to further investigate the origin of the global enhanced SFE found in nearby and distant starbursts. "
+  ]
+}

jsons_folder/2013IAUS..295..340N.json

@@ -0,0 +1,37 @@
+{
+  "Thorsten Naab 1 ": [],
+  "Abstract": [
+    "Abstract. The discovery of a population of massive, compact and quiescent early-type galaxies has changed the view on plausible formation scenarios for the present day population of elliptical galaxies. Traditionally assumed formation histories dominated by ’single events’ like early collapse or major mergers appear to be incomplete and have to be embedded in the context of hierarchical cosmological models with continuous gas accretion and the merging of small stellar systems (minor mergers). Once these processes are consistently taken into account the hierarchical models favor a two-phase assembly process and are in much better shape to capture the observed trends. We review some aspects of recent progress in the field. "
+  ],
+  "keywords": [
+    "Keywords. galaxies: elliptical and lenticular, galaxies: formation, galaxies: evolution "
+  ],
+  "1. Introduction ": [
+    "During the formation and assembly of massive galaxies merging is a natural process in modern hierarchical cosmological models. It is expected to play a significant role for the structural and morphological evolution (e.g. (<>)Kau mann et al. (<>)1996; (<>)Kau mann (<>)1996; (<>)De Lucia et al. (<>)2006; (<>)Khochfar & Silk (<>)2006; (<>)De Lucia & Blaizot (<>)2007; (<>)Guo & White (<>)2008; (<>)Kormendy et al. (<>)2009; (<>)Hopkins et al. (<>)2010a). In the light of these theoretical expectations and direct observations of ’dry’ mergers of gas poor elliptical galaxies up to high redshift ((<>)van Dokkum (<>)2005; (<>)Tran et al. (<>)2005; (<>)Bell et al. (<>)2006a,(<>)b; (<>)Lotz (<>)2008; (<>)Jogee (<>)2009; (<>)Newman et al. (<>)2012; (<>)Man et al. (<>)2012) simulations of idealized collisionless mergers have again received attention and new studies were triggered. Merger simulations of already existing spheroidal galaxies have focused in detail on the evolution of abundance gradients, shapes and kinematics, scaling relations, sizes and dark matter fractions ((<>)White (<>)1978, (<>)1979; (<>)Makino & Hut (<>)1997; (<>)Boylan-Kolchin et al. (<>)2005; (<>)Naab et al. (<>)2006b; (<>)Boylan-Kolchin et al. (<>)2006, (<>)2008; (<>)Di Matteo et al. (<>)2009; (<>)Nipoti et al. (<>)2009b, (<>)2012a). If the progenitors were two disk galaxies (which then can include a gaseous component) the aim was to investigate the morphological transformation, i.e. the formation of new dynamically hot spheroidal elliptical galaxies from two dynamically cold progenitor spi-ral galaxies ((<>)Gerhard (<>)1981; (<>)Farouki & Shapiro (<>)1982; (<>)Negroponte & White (<>)1983; (<>)Barnes (<>)1988; (<>)Barnes & Hernquist (<>)1992; (<>)Hernquist (<>)1992). Apart from studies of the e ect of the merger mass-ratio ((<>)Barnes (<>)1998; (<>)Bekki (<>)1998; (<>)Bendo & Barnes (<>)2000; (<>)Naab & Burkert (<>)2003; (<>)Bournaud et al. (<>)2004, (<>)2005; (<>)Gonz´alez-Garc´ıa & Balcells (<>)2005) the tidal torquing of gas, its inflow to the central regions, the impact on the stellar orbits ((<>)Barnes & Hernquist (<>)1996; (<>)Naab et al. (<>)2006a; (<>)Ho man et al. (<>)2010), subsequent starbursts ((<>)Mihos & Hernquist (<>)1994, (<>)1996; (<>)Barnes (<>)2004; (<>)Di Matteo et al. (<>)2008) and the potential growth of black holes ((<>)Hernquist (<>)1989; (<>)Springel et al. (<>)2005; (<>)Di Matteo et al. (<>)2005; (<>)Johansson et al. (<>)2009a; (<>)Younger et al. (<>)2009) was investigated in numerous studies together with influential studies on the origin of early-type galaxy scaling relations ((<>)Robertson et al. (<>)2006; (<>)Dekel & Cox (<>)2006; (<>)Cox et al. (<>)2006; (<>)Hopkins et al. (<>)2008, (<>)2009c,(<>)b,(<>)d; (<>)Debuhr et al. (<>)2010; (<>)Moster et al. (<>)2011). ",
+    "1 ",
+    "However, despite the detailed insights on the stellar and gas dynamical processes in simulated galaxy mergers, the ’binary merger’ approach is limited in scope and seems not to be able to naturally explain all properties of present day massive elliptical galaxies ((<>)Naab & Ostriker (<>)2009). ",
+    "The most massive elliptical galaxies (or their progenitors) are considered to start forming their stars at high redshift (z∼6, or higher) in a dissipative environment, rapidly become very massive (∼1011M⊙) by z= 2 ((<>)Kereˇs et al. (<>)2005; (<>)Khochfar & Silk (<>)2006; (<>)De Lucia et al. (<>)2006; (<>)Kriek et al. (<>)2006; (<>)Naab et al. (<>)2007, (<>)2009; (<>)Joung et al. (<>)2009; (<>)Dekel et al. (<>)2009; (<>)Kereˇs et al. (<>)2009; (<>)Oser et al. (<>)2010; (<>)Feldmann et al. (<>)2010; (<>)Dom´ınguez S´anchez (<>)2011; (<>)Feldmann et al. (<>)2011; (<>)Oser et al. (<>)2012). A significant fraction of this high redshift population is observed to be already quiescent at z∼2, on average 4-5 times more compact (part of this apparent evolution might driven by selection e ects, see e.g. (<>)Poggianti et al. (<>)2012), and typically a factor of two less massive than their low redshift descendants ((<>)Daddi et al. (<>)2005; (<>)van der Wel et al. (<>)2005; (<>)di Serego Alighieri et al. (<>)2005; (<>)Trujillo (<>)2006; (<>)Longhetti et al. (<>)2007; (<>)Toft et al. (<>)2007; (<>)Buitrago et al. (<>)2008; (<>)van Dokkum et al. (<>)2008; (<>)van der Wel et al. (<>)2008; (<>)Cimatti et al. (<>)2008; (<>)Franx et al. (<>)2008; (<>)Damjanov et al. (<>)2009; (<>)Cenarro & Trujillo (<>)2009; (<>)Bezanson et al. (<>)2009; (<>)van Dokkum et al. (<>)2010; (<>)van de Sande et al. (<>)2011; (<>)Whitaker et al. (<>)2012). It is reasonable to assume that the high-redshift population forms the cores of at least some, if not all, present day massive ellipticals. This rapid structural evolution is supposed to happen in an inside-out fashion, mainly by adding stellar mass to the outer parts of the galaxies over time, however, without the formation of a significant fraction of new stars ((<>)Hopkins et al. (<>)2009a; (<>)van Dokkum et al. (<>)2010; (<>)Szomoru et al. (<>)2012; (<>)Saracco et al. (<>)2012). In this respect the growth of massive quiescent high-redshift galaxies is markedly di erent to the star formation driven inside-out growth of disk galaxies ",
+    "The implications of these observational findings for the formation and evolution of massive elliptical galaxies are many-fold. They are unlikely to have formed by an initial ’monolithic collapse’ followed by passive evolution as their present day counterparts would be too small and too red ((<>)van Dokkum et al. (<>)2008; (<>)Kriek et al. (<>)2008; (<>)Bezanson et al. (<>)2009; (<>)Ferr´e-Mateu et al. (<>)2012). In addition the evolution of these system cannot be explained by just a single ’binary merger of disk galaxies’. The compact high-redshift systems might have formed in such a process ((<>)Wuyts et al. (<>)2010; (<>)Bournaud et al. (<>)2011), if it were gas-rich, but the subsequent structural evolution requires additional processes which are not driven by the formation of new stars. Observational results that almost none of these massive compact galaxies were able to survive to the present day ((<>)Trujillo et al. (<>)2009; (<>)Taylor et al. (<>)2010) indicate that a general and common physical mechanism must be at work. Spectacular events alone, like major early-type galaxy mergers, might be too rare. "
+  ],
+  "2. Minor mergers vs. major mergers ": [
+    "Minor merges, however, are expected to happen frequently in the lifetime of a massive galaxy and have received particular attention as they provide a natural way to increase the size of a galaxy. With only a few assumptions the virial theorem provides a simple estimate of how a one-component system evolves during major and minor mergers ((<>)Cole et al. (<>)2000; (<>)Naab et al. (<>)2009; (<>)Bezanson et al. (<>)2009). Following (<>)Naab et al. ((<>)2009) we assume that a compact initial stellar system has formed (e.g. involving gas dissipation) with a total energy Ei, a mass Mi, a gravitational radius rg,i, and the mean square speed of the stars is vi2. According to the virial theorem ((<>)Binney & Tremaine (<>)2008) the total energy of the system is ",
+    "Figure 1. Left: Simulated size evolution as a function of bound stellar mass for mergers with mass-ratios 1:1 (blue), 5:1 (red), and 10:1 (green). The observationally expected relation is indicated by the black line ((<>)van Dokkum et al. (<>)2010). The presence of dark matter significantly boosts the size evolution of 5:1 and 10:1 mergers. Right: This also leads to a significantly stronger evolution of the Sersic index (figures taken from (<>)Hilz et al. ((<>)2012a)) ",
+    "This system then merges (on zero energy orbits) with other systems of a total energy Ea, total mass Ma, gravitational radii ra and mean square speeds2averaging va. The fractional mass increase from all the merged galaxies is η= Ma/Mi and the total kinetic energy of the material is Ka = (1/2)Mava 2, further defining ǫ= va 2/2vi . Under the assumption of energy conservation (results from ((<>)Khochfar & Burkert (<>)2006) indicate that most halos merge on parabolic orbits) the ratio of initial to final mean square speeds, gravitational radii and densities can be then written as ((<>)Naab et al. (<>)2009) ",
+    "For mergers of two identical systems, η= 1, the mean square speed would remain two, the size increases by a factor four and the density drops by a factor of 32. These estimates are, however, idealized assuming one-component systems, no violent relaxation and zero-energy orbits with fixed angular momentum. ",
+    "(<>)Hilz et al. ((<>)2012b) have recently re-investigated in detail the collisionless dynamics of major and minor mergers of systems including concentrated stellar spheroidal components embedded in extended dark matter halos. They present more accurate versions of the above equations including the e ect of escapers and the interaction of the stellar bary-onic with dark matter and describe in detail how the presence of a massive dark matter halos alter the evolution of the merging systems. One result of this study was that both minor and major mergers lead to size growth and an increase of the dark matter fraction. The physical processes are, however, di erent. Violent relaxation in major mergers mixes ",
+    "Figure 2. Left: Size evolution driven by rapid mass-loss from the idealized simulations of isolated galaxies. If 40 per cent of the mass is lost (ǫ= 0.6) the sizes can rapidly increase by 60 per cent. From the black to the green line the ejection varies from immediate ejection to an ejection time of 80 Myrs (taken from (<>)Ragone-Figueroa & Granato (<>)2011). Right: Evolution of the stellar surface density profiles of a cosmological zoom-simulation of a brightest cluster galaxy in a model with strong AGN feedback. Due to the gas explusion from the AGN the system is significantly more extended than in the no-AGN case and even develops a central core (taken from (<>)Martizzi et al. (<>)2012). ",
+    "dark matter to the central regions. Escaping, unbound, particles limit the expected size growth to values below the ones expected from the idealized equations above. In minor mergers (mass-ratios of 1:5 and 1:10), the stellar satellites are stripped at large radii where the host galaxies dominated by dark matter and the stellar e ective radii and the dark matter fractions grow more rapidly than expected from the simple virial equations (see also (<>)Laporte et al. (<>)2012). Due to the addition of stellar satellite material at large radii ((<>)Villumsen (<>)1983), the stellar mass distribution changes significantly resulting in a significant increase of the Sersic index (see Fig. (<>)1 and (<>)Hilz et al. (<>)2012a). The general results on size evolution are in agreement with similar studies by e.g. (<>)Oogi & Habe ((<>)2012). However, there is an ongoing debate of whether the size growth by minor mergers is sufficient to explain the observed cosmological size evolution of elliptical galaxies. Whereas (<>)Oogi & Habe ((<>)2012) argue that the size growth by minor mergers alone might be suÿ-cient, studies by (<>)Nipoti et al. ((<>)2012b), (<>)Cimatti et al. ((<>)2012), and (<>)Newman et al. ((<>)2012) have combined idealized numerical simulations embedded in a cosmological context and new observational constraints. They come to the conclusion that minor mergers might be able to explain the observed size growth from redshift z∼1 to the present. However, at higher redshift minor and major mergers might not be frequent enough to explain the rapid size evolution observed at z& 1 and therefore an additional physical mechanism might be required. ",
+    "A potential candidate for such an additional process is AGN driven outflow of gas from a massive high-redshift gas-rich and compact galaxy ((<>)Fan et al. (<>)2008; (<>)Hopkins et al. (<>)2010b; (<>)Fan et al. (<>)2010). In general, stellar systems su ering from central mass-loss ǫloss = Mfinal/Minitial will expand ((<>)Hills (<>)1980) and for rapid and slow mass-loss simple relations for the ratio of the final to the initial radius can be derived: ",
+    "Figure 3. Upper left: Examples for the assembly history (stellar origin) of three massive galaxies in high-resolution cosmological zoom simulations. At high redshift the formation is dominated by in-situ star formation (red colors). The low redshift assembly is dominated by merging of stellar systems (blue colors, taken from (<>)Feldmann et al. (<>)2010). Upper right: Ratio of the accreted over final stellar mass versus final stellar mass for galaxies in a cosmological simulation box (void: blue, cluster: red) including strong supernova feedback (upper panel). The fraction of accreted stars is about a factor 2 -3 lower than in the high-resolution zoom simulations of (<>)Oser et al. ((<>)2010) without strong supernova feedback (lower panel); the trend with mass is similar but less strong (taken from (<>)Lackner et al. (<>)2012). Lower left: Independent estimate of the ratio of accreted to in-situ formed stars as a function of halo mass from abundance matching studies ((<>)Moster et al. (<>)2012). Lower right: Similar estimates from a study by (<>)Behroozi et al. ((<>)2012). Both studies find a strong trend that the assembly of galaxies in more massive halos is more dominated by the accretion of stars rather than in-situ star formation. ",
+    "It is worth noting that rapid mass-loss of more than half the total mass can un-",
+    "Figure 4. Upper panels: The present day mass-size relation (left) for a sample of high-resolution zoom simulations (blue points, full symbols are quiescent galaxies) compared to observations. The evolution of the relation is driven by accretion of stars and is indicated by the location of the most massive progenitor galaxies at di erent redshifts. For all galaxies more massive than the mass limit indicated on the left plot (log(M) = 10.8) the average size evolution agrees well with observations. Lower panels: Similar plot for the evolution of the mass-dispersion relation (left). In a fixed mass range galaxies have higher dispersions at higher redshifts (right). Again, the simulated evolution is very similar to the observed one (figures are taken from (<>)Oser et al. (<>)2012). ",
+    "bind the whole system. This process is well known and has been studied for star clusters ((<>)Hills (<>)1980), galaxies ((<>)Hills (<>)1980; (<>)Hopkins et al. (<>)2010b; (<>)Ragone-Figueroa & Granato (<>)2011; (<>)Pontzen & Governato (<>)2012), as well as cores of galaxy clusters (see Fig. (<>)2 and (<>)Martizzi et al. (<>)2012). "
+  ],
+  "3. The cosmological two-phase assembly ": [
+    "The assembly histories of massive galaxies in currently favored hierarchical cosmological models are significantly more complex than a single binary merger. They grow -in particular at high redshift -by smooth accretion of gas, major mergers but also numerous minor mergers covering a large range of mass-ratios which can dominate the amount of ",
+    "assembled stars. The picture that is emerging from from semi-analytical models and high-resolution cosmological simulations of massive galaxies bears a two-phase characteristic ((<>)De Lucia & Blaizot (<>)2007; (<>)Guo & White (<>)2008; (<>)Genel et al. (<>)2008; (<>)Feldmann et al. (<>)2010; (<>)Oser et al. (<>)2010; (<>)Feldmann et al. (<>)2011; (<>)Hirschmann et al. (<>)2012). ",
+    "At high redshifts the formation is dominated by dissipative processes (i.e. significant radiative energy losses) and in-situ star formation leading compact progenitors with high phase space densities. In a second phase massive galaxies are growing by the addition of stars at large radii that have formed early outside the main galaxies in other galaxies that were accreted later-on. This assembly phase is dominated by collisionless dynamics and radiative energy losses are of minor importance (see e.g. (<>)Johansson et al. (<>)2009b; (<>)Lackner & Ostriker (<>)2010; (<>)Laporte et al. (<>)2012). ",
+    "Independent studies using cosmological simulations based on di erent numerical methods come to similar conclusions that -on average -the mass assembly of massive galaxies is dominated by minor mergers with mass-ratios ∼1 : 5 ((<>)Oser et al. (<>)2012; (<>)Lackner et al. (<>)2012; (<>)Gabor & Dav´e (<>)2012). The relative importance of accreted versus in-situ formed stars increases with galaxy mass, a result that was already predicted by semi-analytical models ((<>)De Lucia et al. (<>)2006; (<>)De Lucia & Blaizot (<>)2007; (<>)Guo & White (<>)2008) and has been confirmed by independent estimates from abundance matching techniques ((<>)Moster et al. (<>)2012; (<>)Behroozi et al. (<>)2012). The absolute fractions are model dependent and can vary e.g. by ∼50% for di erent feedback models (see Fig. (<>)3). Studies based on cosmological zoom simulations make a plausible point that the present day scaling relations might be set by the stellar accretion history of massive galaxies, i.e. the above mentioned fraction of in-situ to accreted stars ((<>)Oser et al. (<>)2012). In addition, based on still small samples, high-resolution cosmological simulations the evolution of the scaling relations appears to be in accordance with observations ((<>)Feldmann et al. (<>)2011; (<>)Oser et al. (<>)2012; (<>)Johansson et al. (<>)2012). However, in general the cosmological simulations of massive galaxies still fail to reproduce all observational constraints at the same time and are still limited with respect to either resolution and statistics as well as the algorithmic implementation of relevant feedback processes. In particular feedback from super-massive black holes might help to finally meet observational constraints for massive ellipticals ((<>)McCarthy et al. (<>)2010, (<>)2011; (<>)Puchwein & Springel (<>)2012). ",
+    "TN acknowledges support by and valuable disucssions with Peter Johansson, Ludwig Oser and Jeremiah P. Ostriker. "
+  ]
+}

jsons_folder/2013JCAP...04..022B.json

@@ -0,0 +1,74 @@
+{
+  "Andrés Balaguera-Antolínez, Cristiano Porciani ": [
+    "Argelander Institute für Astronomie, Auf dem Hügel 71, D-53121 Bonn, Germany ",
+    "E-mail: (<mailto:abalan@astro.uni-bonn.de>)abalan@astro.uni-bonn.de, (<mailto:porciani@astro.uni-bonn.de>)porciani@astro.uni-bonn.de "
+  ],
+  "Abstract": [
+    "Abstract. The halo mass function from N-body simulations of collisionless matter is generally used to retrieve cosmological parameters from observed counts of galaxy clusters. This neglects the observational fact that the baryonic mass fraction in clusters is a random variable that, on average, increases with the total mass (within an overdensity of 500). Considering a mock catalog that includes tens of thousands of galaxy clusters, as expected from the forthcoming generation of surveys, we show that the e˙ect of a varying baryonic mass fraction will be observable with high statistical significance. The net e˙ect is a change in the overall normalization of the cluster mass function and a milder modification of its shape. Our results indicate the necessity of taking into account baryonic corrections to the mass function if one wants to obtain unbiased estimates of the cosmological parameters from data of this quality. We introduce the formalism necessary to accomplish this goal. Our discussion is based on the conditional probability of finding a given value of the baryonic mass fraction for clusters of fixed total mass. Finally, we show that combining information from the cluster counts with measurements of the baryonic mass fraction in a small subsample of clusters (including only a few tens of objects) will nearly optimally constrain the cosmological parameters. "
+  ],
+  "keywords": [
+    "Keywords: cosmology: cosmological parameters, large-scale structure of universe, theory, observations, galaxies: clusters: general, methods: statistical "
+  ],
+  "1 Introduction ": [
+    "Galaxy clusters are powerful cosmological probes [(<>)1–(<>)4] which are expected to be associated with massive haloes of dark matter. To date, two di˙erent procedures have been employed to extract cosmological information from large samples of galaxy clusters. The simplest one is to measure their observed number density as a function of mass and/or redshift and compare it with theoretical models for the halo abundance which are calibrated against N-body simulations of collisionless matter [(<>)1]. The second option is to use their baryonic content within the virial radius as a sort of standard ruler [(<>)5, (<>)6]. This assumes that the baryon fraction in clusters coincides with the universal value [(<>)7] and does not scatter from object to object. The recent analysis by [(<>)8] has shown that this is a good assumption for relaxed, cool-core clusters. In this paper, we revisit the first approach and show that some modifications to the standard procedure will be needed when the forthcoming generation of cluster surveys will become available. Therefore, the second method will not be discussed any further. ",
+    "The key theoretical quantity to analyze cluster-count experiments is the halo mass function nh(M,z) which is defined so that nh(M,z) dM, gives the number of dark-matter haloes (at redshift z) with mass between M and M + dM per unit comoving volume. The calibration of the halo mass function using N-body simulations has been pushed to a precision of ∼ 5% [(<>)9–(<>)12] and can be even further improved [(<>)13]. However, this precision is somewhat illusory for direct applications to galaxy clusters. In fact, numerical simulations that, more realistically, also consider a baryonic component on top of the dark matter [(<>)14–(<>)18] have shown that gas physics can alter cluster masses in a systematic way (i.e. in one specific direction and not randomly) by up to ∼ 10% [(<>)16] with respect to pure N-body simulations. Consequently, given the steep slope of the halo mass function at cluster scales, the cluster abundance at fixed mass changes by ∼ 10 − 20% [(<>)14]. This is larger than the forecasted statistical uncertainties (∼ 1 − 10%) for the forthcoming generation of cluster surveys. ",
+    "Regrettably, due to the large uncertainties in modeling baryon physics (i.e. radiative cooling, non-thermal pressure support, star formation, and di˙erent feedback mechanisms in the presence of stars and active galactic nuclei), current gas simulations can only provide order-of-magnitude approximations of these e˙ects (see Section 2 for an extended discussion) and cannot provide robust estimates for the cluster mass function. ",
+    "State-of-the-art techniques to constrain cosmological parameters from cluster counts take into consideration the e˙ects of baryons by artificially enlarging the uncertainties in the parameters of the halo mass function extracted from N-body simulations and marginalizing over them [(<>)3]. This is a statistical trick to account for possible di˙erences between the shapes of the halo and cluster mass functions. Such an approach is adequate for the current samples of clusters which probe relatively small volumes and have large error bars [(<>)19]. Forthcoming cluster surveys will probe much larger volumes with higher sensitivities. In this paper, we show that, in order to use the new data to derive cosmological constraints that are not only precise (i.e. small statistical errors) but also accurate (i.e. unbiased estimates), it will be imperative to model the baryonic e˙ects on the cluster mass function. ",
+    "As routinely done in X-ray and Sunyaev-Zel’dovich studies, we define cluster and halo masses as spherical overdensities bounded by the radius R500 within which the mean density is Δ = 500 times the critical density of the Universe. Note the R500 is typically 1.5-2 times smaller than the virial radius (defined as in [(<>)20]) and the baryon fraction within this smaller scale, fb, is observed to be below the cosmic value (e.g. [(<>)8, (<>)21]) and vary systematically with the cluster mass [(<>)22–(<>)25]. Following a statistical approach, we describe the e˙ects of gas physics in two steps. We first use the outcome of recent numerical studies, to relate the dark-matter content of galaxy clusters with halo masses in N-body simulations. Then we reason in terms of the mean baryonic mass fraction as a function of cluster mass, fb(M), and of the corresponding dispersion around the mean σb. We focus our attention on two cosmological parameters: the matter density parameter, Ωm, and the linear rms matter fluctuation within a spherical top-hat window of radius 8 h−1 Mpc, σ8. Considering observationally motivated guesses for the shape and amplitude of the function fb(M) and of the scatter σb, we first quantify the bias in the estimates for Ωm and σ8 caused by using the halo mass function as a proxy for the cluster mass function. Subsequently, we explore the option of using extra free parameters in the models to simultaneously determine from the cluster counts both the cosmological parameters and the relation ",
+    "fb(M ). We find that this procedure increases the uncertainties on Ωm and σ8. Finally, we show that considering additional information on the baryonic mass fraction from follow-up studies of a small subsample of clusters is pivotal to recover unbiased estimates for Ωm and σ8 with small uncertainties. ",
+    "We conclude that taking into account the e˙ect of baryons on the cluster mass function is key to fully exploit the potential of forthcoming large-volume cluster surveys as cosmological probes. ",
+    "We adopt a fiducial cosmological model based on a flat ΛCDM Universe with a matter density parameter of Ωm = 0.258, a baryon density parameter of Ωb = 0.044, a dimensionless Hubble parameter h = 0.735 (in units of 100 km s−1Mpc−1), a linear rms mass fluctuation within 8 h−1 Mpc of σ8 = 0.773 and a scalar spectral index ns = 0.954. We use the transfer function of [(<>)26] to compute the linear matter power spectrum. The halo mass function is calculated using the fitting formulae of [(<>)11]. Logarithms are always taken after measuring the mass in units of h−1M. "
+  ],
+  "2 Matching cluster masses to N-body simulations ": [
+    "Many authors have compared the mass density profiles of clusters generated from hydrodynamic and collisionless simulations with identical initial conditions. The presence of the baryons generates not only a change in the total mass (defined within a fixed overdensity) of a cluster compared to the corresponding halo in a N-body simulation, but also a re-distribution of the dark-matter component [(<>)27–(<>)29]. When the gas is not allowed to radiate, infalling baryons are heated up in shocks when they cross the virial radius and subsequently exchange energy with the dark matter while the cluster undergoes dynamical relaxation. They end up having a more extended distribution than the dark matter [(<>)28, (<>)30–(<>)34]. As a matter of fact, the baryon fraction within the virial radius decreases with the cluster mass and lies below the cosmic value, fc ≡ Ωb/Ωm, even for the most massive clusters (see Fig. 5 in [(<>)28]). The dark-matter profile in spherical shells becomes slightly more concentrated than in N-body simulations (see Fig. 6 in [(<>)28]) and the total dark-matter mass within Δ = 500 increases by ∼ 1% for an object of 1014h−1M. When, instead, gas cooling and star formation are included in simulations, baryons dissipate energy radiatively and condense in the central regions pulling the dark matter along. Orbits of substructures are also altered [(<>)16]. If the energy feedback due to star formation is weak, the net e˙ect is that the concentration of the dark matter increases [(<>)16, (<>)28]. In this case, clusters exhibit dark-matter (and total) masses within R500 which are a few per cent higher than in the corresponding N-body simulations. Note, however, that the baryon fractions of the simulated clusters within the virial radius systematically lie 1-5% above the universal value. Stellar profiles also deviate substantially from the observed ones [(<>)16, (<>)29]. Observations [(<>)22–(<>)25] have shown that the baryon fraction within R500 lies below fc and varies with the cluster mass. Recent studies favour the interpretation that the “missing” baryons are located in the cluster outskirts so that the baryon fraction reaches the cosmic value near the virial radius [(<>)8, (<>)35]. This behaviour is qualitatively reproduced only by the numerical simulations that include either strong stellar feedback or active galactic nuclei (see Fig. 2 in [(<>)29]). In these simulations, the dark-matter concentration (and therefore the dark-matter mass) of the clusters coincides with what is measured in the corresponding N-body simulations to very good accuracy (see Fig. 8 in [(<>)29]). ",
+    "Let us define a cluster as the spherical region centered on a density peak and enclosing the overdensity Δ = 500 times the critical density of the universe. Each cluster will be characterized by a well defined total mass Mtot (such that Mtot = Mb + M˜ dm, where M˜ dm is the dark matter component of a cluster) and a baryon fraction fb ≡ Mb/Mtot. The same definition can be applied to identify haloes in a collisionless simulation. Note, however, that particles in N-body simulations are assigned masses proportional to the total matter content of the Universe, i.e. mp ∝ Ωm = Ωb + Ωdm (in terms of the baryonic and dark-matter components). Thus, by construction, the mass of simulated dark-matter haloes includes a baryonic fraction which coincides with fc. The total mass thus reads, Mnb = Mdm/(1 − fc), where Mdm is the corresponding dark matter mass. As discussed above, hydro simulations with strong feedback are the only ones which are able to reproduce the observed baryon distribution. Based on the fact that in these simulations the dark-matter mass of the clusters is hardly modified with respect to N-body simulations, in what follows we assume that Mdm = M˜ dm. The total mass of a cluster can be then linked with the total mass of the same halo in a N-body simulation Mnb ",
+    "via ",
+    "(2.1) ",
+    "Our assumption that Mdm = M˜ dm should be seen as a working hypothesis supported by the match between hydro simulations and observations. If future numerical simulations will evidence the need of a more complicated treatment, our analysis can be, of course, generalized by introducing a probability density function P (M˜ dm|Mdm) at the expenses of introducing a number of extra parameters "
+  ],
+  "3 The observed mass function ": [
+    "Consider now a population of galaxy clusters and a set of haloes from a N-body simulation both at the same redshift. Our goal is to write the mass function of the clusters in terms of that of the haloes (at a fixed Δ = 500). We need to keep into account that the baryon fraction of the real clusters is a stochastic quantity that varies from object to object. Based on observational studies, we assume that the conditional probability density Pb(fb|Mtot), is well approximated by a Gaussian distribution with mean ",
+    "(3.1) ",
+    "and scatter σb. We adopt the results by [(<>)22], A = 0.74 ± 0.01, B = 0.09 ± 0.03 and σb  2 × 10−3 , as fiducial values but it is worth stressing that other studies favour slightly di˙erent values for these parameters. We want to write the conditional probability density P(Mtot|Mnb) which gives the distribution of the total cluster mass for a given Mnb. This quantity satisfies the integral equation ",
+    "(3.2) ",
+    "where P(Mnb|Mtot) = (1 − fc)Pb(fb = f|Mtot)/Mtot with f ≡ 1 − (1 − fc)Mnb/Mtot. Since σb  fb|Mtot, then P(Mtot|Mnb) is a narrow function centered at Mtot|Mnb ≈ Mnb(1 − fc)/(1 − fb|Mtot), so that we can finally write ",
+    "(3.3) ",
+    "where Mnb is the solution to the equation Mtot = Mtot|Mnb and  ",
+    "(3.4) ",
+    "The conditional probability density in Eq.((<>)3.3) represents the necessary tool to associate the masses of dark matter haloes defined in N-body simulations with the total masses of galaxy clusters in the presence of a mass dependent fraction of baryons. In general, P(Mtot|Mnb) is very well approximated by a log-normal distribution with a mass-dependent log-scatter σln Mtot|Mnb ≈ ln [1 + σb/(1 − fb|Mtot)] (see panel (c) of Fig. (<>)1 for an example). ",
+    "Cluster masses are not observed directly and need to be inferred from observational proxies (e.g. optical richness, X-ray temperature or flux, Sunyaev-Zel’dovich signal, lensing shear). We assume that the observed mass, Mobs, is an unbiased estimate of the total mass, with a log-normal probability density function of the residuals P (Mobs|Mtot) [(<>)36, (<>)37], for which we use a constant log-scatter σln Mobs|Mtot = 0.1. In general the scaling relation P (Mobs|Mtot) is obtained observationally, and for this reason there is no need to explicitly emphasize its dependence on the baryonic fraction ",
+    "Figure 1. (a) Ratio between the cluster mass function n and a model assuming that the baryonic mass fraction is always equal to the cosmic value (i.e. Mtot = Mnb), n0. Line styles correspond to the observed baryon fraction reported by di˙erent authors. (b) Signal-to-noise ratio for the di˙erence n−n0 as a function of the observed cluster mass in 20 equispaced log-bins. A survey volume of 0.8 (h−1Gpc)3 centered at z = 0.1 is assumed. (c) The conditional probability density P(log10 Mtot|Mnb) at a mass scale Mnb = 1.3 × 1014h−1 M as given in Eq.((<>)3.3) ",
+    "with ",
+    "(3.6) ",
+    "Note that the conditional probability P (Mobs|Mnb) can be written as a log-normal distribution with scatter The main e˙ect of the variable baryon fraction is therefore to introduce a systematic mass-dependent o˙set between Mobs and Mnb while the correction to the intrinsic scatter plays a sub-dominant role, at least for mass proxies with broad distributions (σln Mtot|Mnb  σln Mobs|Mtot ). ",
+    "Table 1. Summary of the Bayesian-inference cases discussed in this paper. Note that n0 is obtained assuming that all clusters have Mtot ≡ Mnb (i.e. fb = fc) in Eq. ((<>)3.6) while n takes into account that the baryonic mass fraction varies from object to object. ",
+    "In panel (a) of Fig. (<>)1 we compare the cluster mass function, n(Mobs), with its counterpart obtained by neglecting the e˙ects of the varying baryon fraction (i.e. assuming that Mtot = Mnb) that we dub n0(Mobs) -note that n0 di˙ers from nh due to the mass-measurement errors. We use the observational scaling relations Pb(fb|Mtot) by [(<>)22] and [(<>)23]. The latter corresponds to Eq. ((<>)3.1) with A  0.8 and B = 0.136 ± 0.028. The main e˙ect is a reduction of the cluster counts by ∼ 5 − 15%, depending on the cluster mass and the details of Pb(fb|Mtot). ",
+    "Will the discrepancy between the actual cluster mass function, n(Mobs), and the predictions of N-body simulations (convolved with the mass-measurement error), n0(Mobs), be noticeable with future observational campaigns? As a prototype for the forthcoming cluster surveys, we consider a catalog spanning a comoving volume of 0.8 (h−1Gpc)3 (corresponding to a survey covering the full sky down to z < 0.2 or half of the sky to z < 0.25) and containing ∼ 2.79 × 104 entries in the mass range 1013.5 < Mobs/(h−1M) < 1015 (for our fiducial model) with mean redshift z = 0.1. We assume full completeness in the mass range we are probing and compute the cluster mass function in 20 mass bins of width Δlog10 Mobs = 0.075. Assuming Poisson errorbars of size σ, in panel (b) of Fig. (<>)1 we show the signal-to-noise ratio for the di˙erence n(Mobs) − n0(Mobs) as a function of the cluster mass. Highly statistically significant deviations are detectable for Mobs < 1014.5h−1M. "
+  ],
+  "4 Cosmological parameters ": [
+    "We want to quantify the bias and the uncertainty in the measurement of the cosmological parameters Ωm and σ8 obtained by fitting the observed cluster mass function, nobs, with di˙erent models. In order to do this, we use the mock cluster catalog described in the previous section and we sample the posterior distribution of the model parameters with a Markov Chain Monte Carlo algorithm. We use di˙erent models and combinations of data which are briefly summarized in Table (<>)1 and extensively described below. The (marginalized) posterior mean and rms values for Ωm and σ8 are given in Table (<>)2 together with the corresponding “figure of merit” (FoM, defined as the inverse of the area of the joint 68.3% credibility region in the {Ωm, σ8} plane). The joint 95.4% credibility regions are instead shown in panel (a) of Fig. (<>)2. ",
+    "First, we consider the mass function extracted from N-body simulations with no corrections for a varying fb (case I). Specifically, we use the function n0(Mobs) to fit the observed mass distribution. The resulting estimate for Ωm is significantly biased low. To first order, this is because the normalization of the function n0 scales proportionally to Ωm and, as shown in panel (a) of Fig. (<>)1, the e˙ect of the varying baryon fraction is to reduce the overall normalization of the observed cluster counts. On the other hand, σ8 is slightly biased high (for our fiducial model) as expected from the location of the exponential cuto˙ in the mass function. However, the bias is not very significant given the corresponding statistical uncertainty. The size and sign of the bias on σ8 markedly depends on the values adopted in Eq. ((<>)3.1) while this is not true for Ωm, which is always biased low for A < 1. ",
+    "To gain freedom in the shape of the theoretical mass function and reduce systematic e˙ects when fitting current data, it is common practice to let the parameters that define nh vary within some predefined range [(<>)3]. We have investigated what happens applying this technique to our mock sample. ",
+    "Table 2. Mean and rms value of the marginalized posterior distribution for Ωm and σ8. The third column shows the figure-of-merit, defined as the inverse of the area of the joint 68.3% credibility region. ",
+    "In this case we have allowed the parameters of the mass function to vary within a four-dimensional Gaussian prior. We built the covariance matrix of the prior by multiplying the original covariance matrix of the parameters (kindly made available by Jeremy Tinker) with a positive constant so that the halo mass function at M = 1015 h−1M is ∼ 10% uncertain (case II). With respect to case I, this method does not improve the bias of Ωm and σ8 while the corresponding FoM decreases by a factor of ∼ 3.6. ",
+    "In order to eliminate the bias, we release the assumption that Mtot = Mnb in Eq. ((<>)3.6) and replace n0 with n to fit nobs (case III). This way, we simultaneously constrain the cosmological parameters and the scaling relation P (fb|Mtot). This procedure is analogous to the “self calibration” method proposed to extract cosmological information from cluster surveys [(<>)38]. We have verified that this approach provides unbiased estimates of Ωm and σ8. However, the statistical uncertainty on the values of the cosmological parameters constrained by the cluster counts are significantly larger with respect to case I and II. ",
+    "The situation markedly improves by considering additional information on fb extracted from multi-wavelength studies of a small subset of galaxy clusters. To show this, we randomly select 30 clusters out of the full sample and imagine that the baryonic fraction of their mass content has been measured with 10% precision in an unbiased way (case IV). We then build new Markov chains assuming that the information from the measurement of the baryon fraction is independent of the cluster counts. The resulting estimates for Ωm and σ8 are unbiased and errorbars small as expected from experiments for “precision cosmology”. In this case, the parameters of the scaling relation P (fb|Mtot) are also recovered to good accuracy, namely (to 68.3% credibility), A = 0.74 ± 0.01, B = 0.09 ± 0.01 and σb = 4.5−+33..81 × 10−3 . ",
+    "Finally, we consider the ideal case in which the scaling relation P (fb|Mtot) is perfectly known from independent data (case V, not shown in Fig. (<>)2). This allows us to conclude that case IV gives cosmological constraints which are nearly optimal. ",
+    "To simplify the discussion, so far, we have assumed that the scatter of the observational mass estimates for the galaxy clusters, σln Mobs|Mnb , is perfectly known. This, however, does not accurately reflect reality where one has only limited knowledge on the actual size of the measurement error which should then be treated as a nuisance parameter in the model-fitting procedure [(<>)37]. This will generally broaden the credibility region of the cosmological parameters and, in principle, might reduce the statistical significance of the biased estimates obtained with model n0. In order to evaluate the impact of this subtlety on our results, we have repeated the measurement of the cosmological parameters (for case I and IV) after marginalizing over σln Mobs|Mnb . We have considered two cases. First, as a realistic option, we have adopted a Gaussian prior on σln Mobs|Mnb with mean 0.1 and rms error 0.02 (cases IG and IVG) -note that a 20% standard error of the standard deviation corresponds to a sample of 14 objects. As a (very) pessimistic option, instead, we have considered a flat prior between 0 < σln Mobs|Mnb < 1 (cases IF and IVF). The corresponding joint posterior distributions for Ωm and σ8 are shown in panel (b) of Fig. (<>)2. In all cases, the bias in the estimates based on the model n0 is still evident. ",
+    "Figure 2. (a) The 95.4% credibility region in the plane {Ωm, σ8} for the cases discussed in Table (<>)1. A cross indicates the input values for the cosmological parameters. (b) As in panel (a) but treating the measurement error σln Mobs|Mtot as a nuisance parameter (contrary to panel (a) where the log-scatter is assumed to be known exactly). "
+  ],
+  "5 Discussion and conclusions ": [
+    "The fractional baryon content of galaxy clusters within an overdensity of Δ = 500 is observed to be a random variable which, on average, decreases with the cluster mass [(<>)22–(<>)25]. Therefore the cluster mass function must di˙er from the predictions of N-body simulations where the baryon fraction is implicitly held constant to the cosmic value. ",
+    "The forthcoming generation of cluster surveys will provide number counts with an accuracy ranging between 1 and 10% depending on the cluster mass. Such an error is substantally smaller than the di˙erence between models of the mass function with and without baryonic physics. Considering a prototypic catalog of galaxy clusters containing 2.79 × 104 entries, we have shown that constraints on the cosmological parameters Ωm and σ8 derived from the cluster mass function would be severely biased if this signal is modelled with fitting formulae based on N-body simulations of collisionless matter. In particular, Ωm would be always biased low while the bias on σ8 depends on the details of the scaling relations between fb and the cluster mass. ",
+    "The widespread technique of artificially inflating the covariance matrix of the parameters that describe the halo mass function to gain freedom and minimize systematic e˙ect will not be of much help. Our study shows that it would enlarge the statistical uncertainties on the cosmological parameters without eliminating (or reducing) the bias. ",
+    "In order to obtain accurate estimates for the cosmological parameters, complementary information on the fraction of baryons as a function of the total mass is required. The optimal method to eliminate this systematic e˙ect requires two ingredients: I) an accurate model for the conditional probability density of finding a particular value for fb given the cluster total mass, P (fb|Mtot); II) A small, random subsample of clusters with follow-up data for which simultaneous measurements of fb and Mtot can be made. We have shown that, if the scatter around the mean fb − Mtot relation, σb, is independent of mass, nearly 30 objects would be enough for precision cosmology. The required size of the subsample should grow bigger if σb has a strong mass dependence. ",
+    "It is interesting to compare the precision we can achieve with the di˙erent methods in our fiducial case (see Table (<>)2). Using the N-body mass function (case I) returns estimates for and σ8 and Ωm with statistical errors of 1% and 2%, respectively (but with a systematic shift which is approximately ",
+    "1 and 6.5 times larger). On the other hand, accounting for the variable baryon fraction (case III) eliminates the biases but nearly doubles the rms of the marginal probabilities due to the inclusion of three additional parameters. However, combining this method with suÿcient follow-up information (case IV), we can optimally recover the same uncertainties as in case I. ",
+    "Let us now critically discuss the formalism we have outlined in this Paper. By performing an object by object comparison between collisionless and hydrodynamic simulations with the same initial conditions, recent studies have shown that the dark-matter mass of a cluster (within an overdensity of Δ = 500) does not change when baryonic physics is included, provided a strong form of feedback is considered. Our analysis is based on this result. This is a conservative assumption which, if violated, would introduce additional deviations in the cluster mass function and thus make estimates of the cosmological parameters based on the standard approach even more biased (since it is very unlikely that this e˙ect would exactly cancel the mass dependence of fb). However, in Section 2, we have indicated how our calculations could be easily generalized to that case. Independent from the detailed origin of the mass discrepancy, the take-home message of this Paper is that baryonic physics will have a sizable impact on the measurement of cosmological parameters from cluster number counts. ",
+    "To facilitate understanding, our simple analysis considers a complete sample in a narrow redshift bin and only two cosmological parameters but our results are of general value. It is straightforward to generalize them including more parameters and accounting for possible evolutionary e˙ects in the baryon fraction along the past light cone and for the radial selection function of a realistic survey. This, however, is beyond the scope of this Paper. ",
+    "We conclude that considering the e˙ect of baryons on the cluster mass function is central to extract unbiased estimates of the cosmological parameters from forthcoming large-volume surveys such as DES [(<>)39], eROSITA [(<>)40, (<>)41], ASKAP-EMU [(<>)42], CCAT [(<>)43], LSST [(<>)44] and Euclid [(<>)45]. "
+  ],
+  "Acknowledgments ": [
+    "We acknowledge support through the SFB-Transregio 33 “The Dark Universe” by the Deutsche Forschungsgemeinschaft (DFG). "
+  ]
+}

jsons_folder/2013MNRAS.428.1225S.json

@@ -0,0 +1,362 @@
+{
+  "(<http://arxiv.org/abs/1201.1104v2>)arXiv:1201.1104v2  [astro-ph.CO]  29 Oct 2012": [],
+  "ABSTRACT ": [
+    "We present numerical simulations of galaxy clusters with stochastic heating from active galactic nuclei (AGN) that are able to reproduce the observed entropy and temperature pro•les of non-cool-core (NCC) clusters. Our study uses N-body hydrodynamical simulations to investigate how star formation, metal production, black hole accretion, and the associated feedback from supernovae and AGN, heat and enrich diffuse gas in galaxy clusters. We assess how different implementations of these processes affect the thermal and chemical properties of the intracluster medium (ICM), using high-quality X-ray observations of local clusters to constrain our models. For the purposes of this study we have resimulated a sample of 25 massive galaxy clusters extracted from the Millennium Simulation. Sub-grid physics is handled using a semi-analytic model of galaxy formation, thus guaranteeing that the source of feedback in our simulations is a population of galaxies with realistic properties. We •nd that supernova feedback has no effect on the entropy and metallicity structure of the ICM, regardless of the method used to inject energy and metals into the diffuse gas. By including AGN feedback, we are able to explain the observed entropy and metallicity pro•les of clusters, as well as the X-ray luminosity-temperature scaling relation for NCC systems. A stochastic model of AGN energy injection motivated by anisotropic jet heating • presented for the •rst time here • is crucial for this success. ",
+    "With the addition of metal-dependent radiative cooling, our model is also able to produce CC clusters, without over-cooling of gas in dense, central regions. ",
+    "Key words: hydrodynamics • methods: N-body simulations • galaxies: clusters: general • galaxies: cooling •ows • X-rays: galaxies: clusters. "
+  ],
+  "1 INTRODUCTION ": [],
+  "1.1 Background ": [
+    "Clusters of galaxies are believed to be the largest gravitationally-bound objects in the Universe. Their deep gravitational potential well means that the largest clusters are •closed boxes•, in the sense that baryons ejected from cluster galaxies by supernova (SN) explosions and active galactic nuclei (AGN) do not escape the cluster completely, but instead end up in the hot, diffuse plasma that •lls the space between cluster galaxies • the intracluster medium (ICM). ",
+    "The thermal properties of intracluster gas, which can be measured with X-ray telescopes such as Chandra, XMM-Newton and Suzaku, thus provide a unique fossil record of the physical processes important in galaxy and galaxy cluster formation and evolution, such as radiative cooling, star formation, black hole accretion and the subsequent feedback from supernovae (SNe) and AGN. In addition, measurements of the ICM chemical abundances yield information about the production of heavy elements in stars in mem-",
+    "ber galaxies, providing constraints on nucleosynthesis, and the processes responsible for their transport into the ICM. ",
+    "A key diagnostic of the thermal state of intracluster gas is provided by the gas entropy1 (<>). Entropy remains unchanged under adiabatic processes, such as gravitational compression, but increases when heat energy is introduced and decreases when radiative cooling carries heat energy away, thus providing an indicator of the non-gravitational processes important in cluster formation. ",
+    "In recent years, spatially-resolved observations have facilitated a detailed examination of the radial distribution of entropy in clusters. Observed entropy pro•les are typically found to scale as K / r 1.1−1.2 at large cluster-centric radii, r & 0.1r200 2 (<>)(e.g. (<>)Ponman et al. (<>)2003; (<>)Sun et al. (<>)2009; (<>)Cavagnolo et al. (<>)2009; (<>)Sanderson et al. (<>)2009; (<>)Pratt et al. (<>)2010). This power-law scaling agrees with that predicted by simple analytical models based on ",
+    "spherical collapse ((<>)Tozzi & Norman (<>)2001) and cosmological hydrodynamical simulations that include gravitational shock heating only (e.g. (<>)Voit et al. (<>)2005; (<>)Nagai et al. (<>)2007; (<>)Short et al. (<>)2010, hereafter STY10). ",
+    "However, in the inner regions of clusters, observations have unveiled the presence of a mass-dependent entropy excess with respect to theoretical expectations, and a large dispersion in central entropy values (e.g. (<>)Ponman et al. (<>)1999; (<>)Lloyd-Davies et al. (<>)2000; (<>)Ponman et al. (<>)2003; (<>)Pratt et al. (<>)2006; (<>)Morandi & Ettori (<>)2007; (<>)Cavagnolo et al. (<>)2009; (<>)Pratt et al. (<>)2010). The source of this entropy excess is likely to be a combination of non-gravitational heating from astrophysical sources, such as SNe and AGN, and cooling processes. There is evidence that the distribution of central entropy values is bimodal, with morphologically disturbed non-cool-core (NCC) systems having an elevated central entropy compared to dynamically relaxed cool-core (CC) systems (e.g. (<>)Cavagnolo et al. (<>)2009). It is thought that the association of unrelaxed morphology with a high central entropy is an indication that either cool cores are destroyed by mergers, or that cool cores have never been able to form in these objects. ",
+    "The chemical state of the ICM is characterised by its metallic-ity, the proportion of chemical elements present heavier than H and He. X-ray spectroscopy of galaxy clusters has revealed emission features from a variety of chemical elements, O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni, all of which are synthesised in stars and transported to the ICM by processes such as ram-pressure stripping, galactic winds and AGN out•ows. Type Ia SNe produce a large amount of Fe, Ni, Si, S, Ar and Ca, but compared to Type II SNe, they only produce very small amounts of O, Ne and Mg. Type Ia SN products are found to dominate in cluster cores, whereas Type II SN products are more evenly distributed ((<>)Finoguenov et al. (<>)2000; (<>)Tamura et al. (<>)2001; see (<>)Bohringer¨ & Werner (<>)2010 for a recent review). This can be explained by early homogeneous enrichment by Type II SNe, which produce -elements in the protocluster phase, and a subsequent, more centrally-peaked enrichment by Type Ia SNe, which have longer delay times and continue to explode in the central cD galaxy long after the cluster is formed. ",
+    "The •rst detailed measurements of spatial abundance distri-butions were made by (<>)De Grandi & Molendi ((<>)2001), using data from BeppoSAX, who measured the radial Fe abundance pro-•les for a sample of massive clusters. They found that CC clus-ters have a sharp Fe abundance peak in central regions, whereas NCC clusters have •at Fe abundance pro•les. Subsequent obser-vations with XMM-Newton and Chandra have con•rmed this di-chotomy between the metallicity distribution in CC and NCC clus-ters ((<>)Tamura et al. (<>)2004; (<>)Vikhlinin et al. (<>)2005; (<>)Pratt et al. (<>)2007; (<>)Baldi et al. (<>)2007; (<>)Maughan et al. (<>)2008; (<>)Leccardi & Molendi (<>)2008; (<>)Matsushita (<>)2011). ",
+    "It is thought that cluster mergers, and the subsequent mixing of intracluster gas, are responsible for destroying the central abundance peak found in CC clusters. However, some systems with a highly disturbed morphology are also found to have a high central metallicity. (<>)Leccardi et al. ((<>)2010, see also (<>)Rossetti & Molendi (<>)2010) suggest that these objects correspond to relaxed CC systems that have undergone a major merger, or a signi•cant AGN heating event, very recently, so that mixing processes have not yet had suf•cient time to fully erase low-entropy gas and the central abundance peak. ",
+    "Explaining the observed thermal and chemical properties of the ICM from a theoretical perspective requires a detailed understanding of the complex interplay between large-scale gravitational dynamics and the various small-scale astrophysical processes ",
+    "mentioned above. Numerical cosmological hydrodynamical simulations have emerged as the primary tool with which to tackle this problem. There has been considerable effort to include the processes relevant for cluster formation and evolution in simulations in a self-consistent manner; see (<>)Borgani & Kravtsov ((<>)2009) for a recent review. However, an explicit treatment is unfeasible since these processes all occur on scales much smaller than can be resolved with present computational resources. ",
+    "Hydrodynamical simulations that include models of radiative cooling, star formation, metal production and galactic winds generally fail to reproduce observed ICM temperature, entropy and metallicity pro•les. Simulated temperature pro•les typically have a sharp spike at small cluster-centric radii, followed by a rapid drop in temperature moving further into the core (e.g. (<>)Valdarnini (<>)2003; (<>)Tornatore et al. (<>)2003; (<>)Borgani et al. (<>)2004; (<>)Romeo et al. (<>)2006; (<>)Sijacki et al. (<>)2007; (<>)Nagai et al. (<>)2007), in clear con•ict with the smoothly declining (•at) pro•les of observed CC (NCC) clusters (e.g. (<>)Sanderson et al. (<>)2006; (<>)Vikhlinin et al. (<>)2006; (<>)Arnaud et al. (<>)2010). This is due to the adiabatic compression of gas •owing in from cluster outskirts to maintain pressure support, following too much gas cooling out of the hot phase. This over-cooling causes excessive star formation in cluster cores, with predicted stellar fractions being about a factor of 2 larger than the observed value of ˘ 10% ((<>)Balogh et al. (<>)2001; (<>)Lin et al. (<>)2003; (<>)Balogh et al. (<>)2008), which in turn leads to excessive Fe production in central regions, generating steeper abundance pro•les than observed (e.g. (<>)Valdarnini (<>)2003; (<>)Tornatore et al. (<>)2004; (<>)Romeo et al. (<>)2006; (<>)Tornatore et al. (<>)2007; (<>)Dav´e et al. (<>)2008). ",
+    "It is generally accepted that the solution to the over-cooling problem in hydrodynamical simulations is extra heat input from AGN. Simple analytical arguments convincingly show that the energy liberated by accretion onto a central super-massive black hole is suf•cient to suppress gas cooling and thus quench star formation. The precise details of how this energy is transferred to the ICM are not well understood at present, but it appears that there are two major channels via which black holes interact with their surroundings (see (<>)McNamara & Nulsen (<>)2007 for a review). ",
+    "At high redshift, mergers of gas-rich galaxies occur frequently and are expected to funnel copious amounts of cold gas towards galactic centres, leading to high black hole accretion rates and radiating enough energy to support the luminosities of powerful quasars. Quasar-induced out•ows have been observationally con•rmed in a number of cases (e.g. (<>)Chartas et al. (<>)2003; (<>)Crenshaw et al. (<>)2003; (<>)Pounds et al. (<>)2003; (<>)Ganguly & Brotherton (<>)2008; (<>)Dunn et al. (<>)2010). ",
+    "Evidence for another mode of AGN feedback, not related to quasar activity, can be seen in nearby CC clusters, which often contain radio-loud X-ray cavities in the ICM. These bubbles are thought to be in•ated by relativistic jets launched from the central super-massive black hole ((<>)Blanton et al. (<>)2001; (<>)Bˆ•rzan et al. (<>)2004; (<>)McNamara et al. (<>)2005; (<>)Fabian et al. (<>)2006; (<>)Morita et al. (<>)2006; (<>)Jetha et al. (<>)2008; (<>)Gastaldello et al. (<>)2009; (<>)Dong et al. (<>)2010; (<>)Giacintucci et al. (<>)2011). Bubbles may rise buoyantly, removing some of the central cool, enriched gas and allowing it to mix with hotter gas in the outer regions of groups and clusters. Together with the accompanying mechanical heating, this can constitute an ef•cient mechanism for suppressing cooling •ows, and redistributing metals throughout the ICM. Such •ows are seen in simulations of idealised clusters, performed with hydrodynamical mesh codes (e.g. (<>)Churazov et al. (<>)2001; (<>)Quilis et al. (<>)2001; (<>)Ruszkowski & Begelman (<>)2002; (<>)Bruggen¨ et al. ",
+    "(<>)2002; (<>)Bruggen¨ (<>)2003; (<>)Dalla Vecchia et al. (<>)2004; (<>)Roediger et al. (<>)2007; (<>)Bruggen¨ & Scannapieco (<>)2009). ",
+    "Various authors have implemented self-consistent models of black hole growth and AGN feedback in cosmological simulations of galaxy groups and clusters (in addition to cooling, star formation, and thermal and chemical feedback from SNe). (<>)Springel et al. ((<>)2005a) developed a model for quasar mode AGN feedback (see also (<>)Di Matteo et al. (<>)2005), which was used in cosmological simulations of 10 galaxy groups by (<>)Bhattacharya et al. ((<>)2008). A model for radio mode AGN feedback based on bubble injection was proposed by (<>)Sijacki & Springel ((<>)2006), which was subsequently extended by (<>)Sijacki et al. ((<>)2007) to include quasar mode AGN feedback as well. Both (<>)Sijacki & Springel ((<>)2006) and (<>)Sijacki et al. ((<>)2007) performed cosmological simulations of a few massive clusters with their respective models. ",
+    "These studies demonstrated, in a qualitative manner, that AGN feedback is effective in reducing the amount of cold baryons and star formation in the central regions of groups and clusters. Furthermore, the gas density is reduced and the temperature is increased, elevating the central entropy. (<>)Sijacki et al. ((<>)2007) also showed that AGN out•ows drive metals from dense, star-forming regions to large radii, •attening ICM abundance pro•les relative to those predicted by a run without AGN feedback. Such trends are precisely what is required to reconcile simulations of galaxy clusters with observations. ",
+    "A more quantitative assessment of the impact of AGN feedback on the ICM was conducted by (<>)Puchwein et al. ((<>)2008). They resimulated a sample of 21 groups and clusters with the scheme of (<>)Sijacki et al. ((<>)2007), •nding that the model could reproduce the observed X-ray luminosity-temperature scaling relation, at least on average. However, since their sample size is quite small, it is unclear whether the model can generate a realistic population of CC and NCC systems and thus explain the observed scatter about the mean relation. In addition, the stellar fraction within the virial radii of their simulated objects appears larger than observed. ",
+    "Another detailed study was undertaken by (<>)Fabjan et al. ((<>)2010), who resimulated a sample of groups and clusters in a cosmological setting, using a model closely related to that of (<>)Sijacki et al. ((<>)2007), but with a different implementation of radio mode AGN feedback. On group scales, they found that AGN heating was able to successfully balance radiative cooling, reproducing observed stellar fractions, but the central entropy (at r2500) was about a factor of 2 too high. In addition, their predicted group Fe abundance pro•les are •at for r & 0.3r500, whereas observed pro•les have a negative gradient out to the largest radii for which measurements are possible (e.g. (<>)Rasmussen & Ponman (<>)2009). There is also an indication that the Fe distribution may be too sharply peaked in central regions compared to observations. The effect of AGN feedback on galaxy groups was also investigated by (<>)McCarthy et al. ((<>)2010), who implemented the AGN feedback scheme of (<>)Booth & Schaye ((<>)2009) in a cosmological simulation. With this model they were able to explain the observed entropy, temperature and Fe abundance pro•les of groups, as well as observed X-ray scaling relations. ",
+    "For massive clusters, (<>)Fabjan et al. ((<>)2010) showed that their model can reproduce the entropy structure of the ICM, but a factor of 3•4 too many stars were formed. The cluster Fe abundance pro•les they obtained have a shape consistent with that of observed pro•les, although with a higher normalisation, but the central Fe abundance may be over-estimated. (<>)Dubois et al. ((<>)2011) also examined the role of AGN feedback in establishing the properties of the ICM, using a cosmological AMR simulation of a massive cluster ",
+    "with a prescription for jet heating by AGN. The entropy pro•le of their cluster agrees well with that of observed CC clusters if metal-cooling is neglected, and when metals are allowed to contribute to the radiative cooling, the resulting pro•le resembles that of a NCC cluster instead. However, the metallicity pro•le of their cluster appears steeper than observed. "
+  ],
+  "1.2 This work ": [
+    "In this work, we pursue a different, but complementary, approach to the theoretical study of galaxy clusters. Instead of undertaking self-consistent hydrodynamical simulations, we adopt the hybrid approach of (<>)Short & Thomas ((<>)2009, hereafter SHT09) which couples a semi-analytic model (SA model) of galaxy formation to a cosmological N-body/smoothed-particle hydrodynamics (SPH) simulation. In this model, the energy imparted to the ICM by SNe and AGN is computed from a SA model and injected into the bary-onic component of a non-radiative hydrodynamical simulation; see SHT09 for details. The main advantage of this approach is that feedback is guaranteed to originate from a realistic population of galaxies, since SA models are tuned to reproduce the properties of observed galaxies. As a consequence, the stellar fraction in massive clusters agrees with observations ((<>)Young et al. (<>)2011), which is not the case in self-consistent hydrodynamical simulations. ",
+    "We have extended the model of SHT09 to follow the metal enrichment of the ICM. Note that (<>)Cora ((<>)2006, see also (<>)Cora et al. (<>)2008) have already used a similar hybrid technique to study the pollution of intracluster gas by heavy elements. However, they did not include energy injection from SNe and AGN, which are likely to affect the distribution of metals in the ICM. ",
+    "In the model of SHT09, the energy liberated by SN explosions and black hole accretion is assumed to be distributed uniformly throughout the diffuse gas of the host halo. With this rather ad hoc heating model they were able to reproduce observed X-ray scaling relations for NCC clusters, but ICM entropy pro•les were found to be •atter than observed within 0.5 times r500 (STY10). These simulations do not well resolve the core (r ˘ < 0.1 r500), nor do they include radiative cooling that is likely to be important in this region, at least for CC clusters. However, we would expect that they should be able to provide a much better •t to X-ray observations of NCC clusters outside the core. ",
+    "The primary goal of this paper is, therefore, to formulate a new feedback model that has a clear physical motivation and that is better able to explain the radial variaton of both the thermal and chemical properties of intracluster gas outside the core of the cluster. To help us do this we test a wide variety of different models for SN and AGN feedback and metal enrichment, using a selection of X-ray data (namely, entropy and metallicity pro•les and the luminosity-temperature scaling relation) to identify the features that a model should possess in order to reproduce the data. ",
+    "Our conclusion is that a stochastic heating model, motivated by observations of anisotropic AGN out•ows, provides a better •t to the observed properties of the ICM than more commonplace models, such as heating a •xed number of neighbours or heating particles by a •xed temperature. Using entirely plausible duty cycles and opening angles for the jets, it is possible to provide an acceptable •t to all available observations with our model. ",
+    "Note that the use of SA models means that the feedback is not directly coupled to the cooling of the gas • that is why our previous work and the bulk of this paper uses non-radiative simulations and restricts its attention to NCC clusters. However, towards the end of the paper we introduce radiative cooling in an attempt to repro-",
+    "duced CC clusters. We estimate the degree to which the SA model fails to supply the required feedback energy and show that there can be a substantial short-fall at high redshift, but that it averages to under 10 per cent over the lifetime of the cluster. We are able to qualitatively reproduce some CC pro•les, but we do not provide a detailed quantitative analysis here. ",
+    "In this work, we neglect many physical effects such as magnetic •elds, cosmic rays, thermal conduction, turbulent mixing, etc.. Our principal reason for doing this is to keep the model simple and ease interpretation of our results. Some of these may be important in the central regions of CC clusters (r < ˘ r500) but there is little evidence that they play a signi•cant role at the larger radii that we use to constrain our models. We discuss this further at the end of the paper. ",
+    "The layout of this paper is as follows. In Section (<>)2, we present the details of our hybrid numerical model and describe our cluster simulations. We investigate the effect of SN feedback on the thermal and chemical properties of the ICM in Section (<>)3, and assess how our results are affected by different choices of SN feedback and metal enrichment models. We show, in agreement with previous work, that SN have little impact on the entropy structure of the intracluster gas. In Section (<>)4 we examine the impact of additional heating from AGN: these can reproduce the correct scaling relations but give entropy pro•les that are too •at. Our results motivate a new, stochastic feedback model based on jet heating, which is described in Section (<>)5. In this section, we also discuss what this model predicts for the thermal and chemical properties of the ICM, and we conduct an exhaustive comparison with observational data in Section (<>)6. In Section (<>)7 we demonstrate that our model is capable of producing both CC and NCC clusters with the inclusion of metal-dependent radiative cooling. Our conclusions are presented in Section (<>)8. ",
+    "For those readers who are mostly interested in the •nal model itself, rather than the steps used to motivate it, we recommend skipping Sections (<>)3 and (<>)4, at least on •rst reading. "
+  ],
+  "2 SIMULATIONS ": [
+    "We make use of hydrodynamical resimulations of a sample of massive galaxy clusters extracted from the dark-matter-only Millennium Simulation ((<>)Springel et al. (<>)2005b). Our sample consists of 25 objects with 9 × 1013h−1 M⊙ . M500 . 7 × 1014h−1 M⊙ and forms a subset of the larger sample of 337 groups and clusters res-imulated by STY10 for their so-called FO simulation, one of the Millennium Gas Simulations3 (<>). See STY10 for details of the cluster selection procedure. Basic properties of our clusters are listed in Table (<>)1. ",
+    "Following STY10, the feedback model we adopt in our simulations is the hybrid scheme of SHT09, where a SA model of galaxy formation is used to compute the number of stars formed and the ",
+    "Table 1. The masses, M (in units of h−1 M⊙), and dynamical temperatures, kBTdyn (in units of keV), of the 25 clusters used in this study within r500 (second and third columns, respectively), and r200 (third and fourth columns, respectively). Cluster C1 is our “ducial cluster, used for most of the plots in this paper. ",
+    "energy transferred to the ICM by SNe and AGN. We refer the reader to STY10 for a full description of the modelling process and simulation parameters. ",
+    "Brie•y, we •rst perform dark-matter-only simulations of each region containing a cluster in our sample using the massively parallel TreePM N-body/SPH code GADGET-2 ((<>)Springel (<>)2005). Viri-alised dark matter haloes are identi•ed at each simulation output using the friends-of-friends (FOF) algorithm, with a standard linking length of 20% of the mean inter-particle separation ((<>)Davis et al. (<>)1985). Only groups with at least 20 particles are kept, yielding a minimum halo mass of 1.7 × 10 10 h−1 M⊙. Gravitationally bound substructures orbiting within these FOF haloes are then found with a parallel version of the SUBFIND algorithm ((<>)Springel et al. (<>)2001). From the stored subhalo catalogues we construct dark matter halo merger trees by exploiting the fact that each halo will have a unique descendant in a hierarchical scenario of structure formation; see (<>)Springel et al. ((<>)2005b) for further details. ",
+    "The second stage is to generate galaxy catalogues for each resimulated region by applying the Munich L-Galaxies SA model of (<>)De Lucia & Blaizot ((<>)2007) to the halo merger trees. A full description of the physical processes incorporated in L-Galaxies and model parameters is given in (<>)Croton et al. ((<>)2006) and (<>)De Lucia & Blaizot ((<>)2007). For each galaxy in these catalogues, we use its merger tree to compute the change in stellar mass, M∗, and mass accreted by the central black hole, MBH, between successive model outputs. Knowledge of M∗ enables us to incorporate ",
+    "         M∗  MBH               ESN   EAGN       ",
+    "                                 43%                      (<>)   (<>)                                           ",
+    "                                                   ",
+    " ",
+    "                                       MZ,ICM               zn           MZ,ICM     zn+1   MZ,ICM          MZ,ICM                          zn+1 ",
+    " ",
+    "  MZ,ICM                  ",
+    "                                                                                                                               T & 2   ",
+    "                                                   Nstar = M∗/mgas               Nstar                                                      ",
+    "                         X         ",
+    "     z = 0           (<>)   (<>)            ",
+    "                                                     (<>)                                                 "
+  ],
+  "3 FEEDBACK FROM TYPE II SUPERNOVAE ": [
+    "                                         (<>)(<>)       (<>)  (<>)                                                       "
+  ],
+  "3.1 Supernova feedback models ": [
+    "             thermal               (<>) (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>)  kinetic         (<>)   (<>) (<>)   (<>) (<>) (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) ",
+    "                                                           (<>)                 "
+  ],
+  "3.1.1 Thermal models ": [
+    "                        ESN    ",
+    "                         Nheat = 1 10  100                     ",
+    "                               frad      r200    frad = 0.1 0.32  1    Nheat                                ",
+    "            ftemp      T200   ",
+    " ",
+    "   ftemp     1 3.2  10                ",
+    " ",
+    "                 ",
+    " ",
+    " ui           ˆi           Ai    A     X   K  K = µmH(µemH)γ−1A  µemH ˇ 1.90 × 10−27          ",
+    "                   ",
+    "        ",
+    " ",
+    " ",
+    "       fb     ˆ200              Nheat        r200                       fbˆ200   [max (fbˆ200, ˆi)]γ−1         (<>)               ui(ˆi/fbˆ200)γ−1 < ui                      ˆi< fbˆ200 ",
+    "                           ",
+    " ",
+    "                   ",
+    "    vwind               vwind = 1  −1  300  −1  600  −1  1000  −1                    4 (<>)    v200     vwind = 1  −1                Nkick         r              Nkick  r         Nkick   Nkick                 ",
+    " ",
+    " nˆ                            ",
+    "                           (<>)   (<>) (<>)   (<>) (<>)    (<>)                     (<>) (<>) (<>)   (<>)           (<>)   (<>) "
+  ],
+  "3.2 Metal enrichment models ": [
+    "                                         fZ,rad       fZ,rad = 0.1 0.32  1                          mZ,i     ",
+    " ",
+    " Nenrich          ",
+    "                  ",
+    " ",
+    "      particle metallicity          smoothed metallicity (<>)   (<>) (<>)   (<>)   ",
+    " ",
+    "      ˆZ,i          P   "
+  ],
+  "3.1.2 Kinetic models ": [
+    "                                    ",
+    " ",
+    " Nsph = 64     P    W        ",
+    "Figure 1.                                                       X  PP ",
+    "     i  j |ri− rj|       i hi            P                                         "
+  ],
+  "3.3 Naming conventions ": [
+    " (<>)   23                                "
+  ],
+  "3.4 Entropy pro•les ": [
+    "                              (<>)                      X  (<>)P   (<>)  PP                  M500  20%      ",
+    "   ",
+    "",
+    "   ",
+    "",
+    "                                      K / r1.2  r & 0.1r500       (<>)   (<>)             r . 0.1r500              ",
+    "         ",
+    "Figure 2.                                                              ",
+    "           r & 0.1r500                               ",
+    "                                          "
+  ],
+  "3.5 Metallicity pro•les ": [
+    "         fZ,rad                           fZ,rad                     vwind = 600  −1   (<>)                    (<>) (<>)            80%                                  ",
+    "                                                                                                        ",
+    "                ",
+    "     (<>)                  r . 0.2r180         fZ,rad = 0.1                                      fZ,rad = 1                                                                        ",
+    "                                                                              (<>)             25            M200 > 1011h−1 M⊙                             5%                                                        ",
+    "                              (<>)    (<>)                                                         (<>)   (<>) ",
+    "                              (<>) ",
+    "Figure 3.                fZ,cent                 M200 > 1011h−1 M⊙              25        5%                      ",
+    " fZ,rad = 1     (<>)                      ",
+    "                                     fZ,rad = 0.1                                  ",
+    "              (<>)   (<>)                             (<>)   (<>)            ",
+    "Figure 4.                                                    "
+  ],
+  "3.6 Summary ": [
+    "                                     ",
+    "                                vwind = 600  −1         (<>)    (<>)     600  −1        (<>)   (<>)  z ˘ 2  (<>)   (<>)   ",
+    "                                                                                  ",
+    "                     "
+  ],
+  "4 FEEDBACK FROM ACTIVE GALACTIC NUCLEI ": [
+    "                                                                                                ",
+    "  (<>)                 (<>)                                           (<>) "
+  ],
+  "4.1 AGN feedback models ": [
+    "        EAGN                              X                                         "
+  ],
+  "4.1.1 Thermal models ": [
+    "",
+    "                           ESN   EAGN              (<>)   (<>) (<>)    (<>) (<>)   (<>) (<>)   (<>) "
+  ],
+  "4.1.2 Kinetic models ": [
+    "                  (<>)            (<>)           EAGN        ESN         vwind = 1000  −1  4500  −1  20000  −1         (<>)P   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) "
+  ],
+  "4.1.3 Naming conventions ": [
+    " (<>)                            "
+  ],
+  "4.2 Entropy pro•les ": [
+    "                             15   4     "
+  ],
+  "4.2.1 Thermal models ": [
+    "            (<>)                            ",
+    "                       ",
+    "Table 3.                              600  −1                ",
+    "Figure 5.                                                          X  PP ",
+    "                    r1.1−1.2                   r ˘ 0.5 − 0.6r500                                   z = 0   "
+  ],
+  "4.2.2 Kinetic models ": [
+    " (<>)                       (<>) ",
+    "   r ˘ r500                     vwind = 1000  −1                                        vwind = 20 000 ",
+    "Figure 6.                                                        X  PP ",
+    " −1                           ",
+    "                                            r500                   z = 0      vwind = 20 000  −1                          r500        vwind = 1000  −1                                                      (<>) "
+  ],
+  "4.3 Summary ": [
+    "                       ",
+    "                                                       15            ",
+    "                                                                       ",
+    "             1/vwind 2                                   vwind = 20 000  −1                       ",
+    "                                                                               "
+  ],
+  "5 A NEW MODEL FOR FEEDBACK FROM ACTIVE GALACTIC NUCLEI ": [
+    "                              X                (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>)                                       ",
+    "   z ˘ 2 − 3                      0.2%            (<>)   (<>) (<>)                                    z ˇ 2    (<>)   (<>)               ",
+    "                                                                                        (<>)   (<>) ",
+    "  (<>)           (<>)       X        "
+  ],
+  "5.1 Stochastic AGN feedback model ": [
+    "                                      frad                           t        ",
+    " ",
+    " fduty               tduty       tduty = 108   (<>)   (<>) (<>)   (<>) (<>)   (<>)            2 . t/tduty . 4  z < 3 ",
+    "          r          Pheat  r < Pheat        ",
+    " ",
+    "  r > Pheat           Pheat      (<>)                     fduty ",
+    "                                  ",
+    "        frad  fduty             frad = 0.1 0.32  1  fduty = 10−4  10−3  10−2  10−1       fduty = 1       frad ",
+    "       fduty                            2     cos  = 1 − fduty       fduty      1◦ .  . 26◦  ",
+    " (<>)                            "
+  ],
+  "5.2 Entropy pro•les and scaling relations ": [
+    "                  ",
+    "Figure 7.                   frad               fduty    10−2                  X  PP      ",
+    "             ",
+    "         frad                fduty                                             "
+  ],
+  "5.2.1 The effect of changing frad ": [
+    " ",
+    "      frad           fduty     10−2                   frad                    frad = 1            ",
+    " ",
+    "   LXTsl     25        frad                LXTsl       LXTsl  frad    ",
+    "Figure 8.  X            frad = 0.1  0.32   1       fduty   10−2        X     r500                  X  P ",
+    "       frad                               frad = 1        "
+  ],
+  "5.2.2 The effect of changing fduty ": [
+    "           fduty       fduty = 10−4  10−3  10−2  10−1    frad                 (<>)       fduty             frad  fduty    10−4  10−1          r . 0.4r500     fduty = 10−4                    fduty = 10−1    fduty = 10−3  fduty = 10−2             ",
+    "Figure 9.                   fduty             frad                          X  PP ",
+    "         fduty                        fduty = 10−4                       Pheat       (<>)                r & r500                   fduty    10−1              Pheat                                 ",
+    "    fduty         LXTsl        (<>)     LXTsl               fduty = 10−4         X                                             fduty       LXTsl                LXTsl     fduty = 10−2      fduty                                    "
+  ],
+  "5.2.3 Identifying optimal parameter values using observations ": [
+    "                               25  ",
+    "Figure 10.  X            fduty = 10−4  10−3  10−2   10−1       frad          X     r500          X P    ",
+    "            (frad, fduty)     frad = 0.1 0.32  1  fduty = 10−4  10−3  10−2  10−1      12    ",
+    "                                     r1000   0.7r500              r1000      0.1r200        X           X                           ",
+    "                               ",
+    " ",
+    " xc           xcom          r500  (<>)   (<>)         S > 0.1    ",
+    "            ",
+    "   h n  in i h ˜2 ii ",
+    "h Ncsim i h n  ) i  n Y = K(r1000) K(r1000)/K(0.1r200)  LX nin n h in in ni h nii C0 n  h niin n       h nin  in ",
+    "in  in h  hn in in h (<>)i  h (<>)) in   in in n h  in h TXobs n Y obs  h niin C0 h ni  h−1/3 keV 2 n 1044h−2 erg s−1  Y = K(r1000) n LX i n i inin  Y = K(r1000)/K(0.1r200) h  E(z)ni in   h i ii in h h in n = 4/3 0 n −1  h K(r1000)TX K(r1000)/K(0.1r200)TX n LXTX in i ",
+    "h    ii nini ˙stat i ",
+    "h ",
+    ") ",
+    ") ",
+    "n n  h  in n Yiobs  i ",
+    " i h   ˙raw in ih in  h in in ",
+    "h wi= ˙stat2 /˙i2 n Ncobs i h n     in h  ",
+    "in h inini  ˙int  h  n in i i  ",
+    ") ",
+    " in h     h    h n in  in h in )   in i h i  h  n i   n  h  iiin in h  ",
+    " (<>) n (<>) h h iii p)  h   12  in  h ˜2 in (<>)) n   i  h   h LXTX in h        hihih in   i in h   ih fduty 6 10−3       hi i in n n h  i n  h  h h n  in n h i  ",
+    " h   i   n n h nin   h K(r1000)TX n K(r1000)/K(0.1r200)TX in  i n h h ˜2   h K(r1000)TX in      h  ih (frad, fduty) = (1, 10−3) n ",
+    "Table 5. ˜2  ii   h LXTsl in in ",
+    "Table 6.   ii   h LXTsl in in ",
+    "(1, 10−2) h h       ih fduty = 10−4  fduty = 10−1  n h   h K(r1000)/K(0.1r200)TX in h h ˜2 n       ih fduty = 10−1  nin    h  h ih n  h  ",
+    " h in h    6  2  h  h 3 in in) in ih h  inin p h  iii   12   i in  (<>)  i in h n n  i n  h  ih (frad, fduty) = (1, 10−2) h  h  i   h   h hi    10−2  ",
+    " hi h h   hi in h n n  n  i ii ni    i  ih n iniin  h in      h i   h in  h   i    ni     in in  n h h  i i innn h  hih  n  h  "
+  ],
+  "5.3 Metallicity pro•les ": [
+    "P    n i ni  nin ih i   h n in  h n h i in in h nih  i nin   in  n  n      (<>)n   (<>) (<>)iin   (<>) (<>)ii   (<>)) i hni iin h  n h   in  h  nihn  in   (<>)ii   (<>) (<>)   (<>) (<>)n   (<>) (<>)i   (<>)) ",
+    "  in (<>) h   n h  ni",
+    "Table 7. in ii    h in in ",
+    "Figure 11. iinih ii     i ih  i hi     ih in  nihn h i  in  n   i) h  in   n ih n  n i hn  in    h     h  in) n  i  in)   h    ",
+    "i i n h iiin   in h    h  in hih h i n i in in h i   n ini hh h inin   n in     ii    hi  h i   ih  i      10−2) in h  fZ,rad in   nihn h  h hi   h i  h hi in    ihin hih   in) ",
+    "i (<>)  h in iinih ii  ih h     h      h  h  h in  h      i hn   ii ni hh h ni h fZ,rad = 1)  fZ,rad i    h n   h n nn  h i in ni ih h in   h  ii  nihn  i i in h   ninnin  iin i h    in h    h hn in    ",
+    "in h ii  i      h in  h  i  n  n  h iin    h in i    n  in in      h  i  hi i  n   in  h i in h   h   in   n h i  in  n    h n in   in h i  ih i hin in h  "
+  ],
+  "5.4 Summary ": [
+    " h   n    h h n i in in in  in  hi nn   i hii n h     frad hih  h i  h hi in ihin hih n i in n fduty hih i h in  i in hi in h  h     ",
+    " h n h  n  n h LXTsl in in  i innii  iin in frad  n n n fduty     fduty h in n     h in   n ih   n iin h  hin h i  in hi  hi i  n   i  h n h i  n  hih  h  i n   in  h  n in h i  n  hin ",
+    " fduty i in h ii   i in h  in hn  i in h   h h  in   n inin n  h  n  n  in  h h  n h  ni  in h in  h in n    h ",
+    " h  h  in in  ini n i hi  h    in   (frad, fduty) = (1, 10−2) in fduty = 10−2 h n    nin n  16◦  ih h  hi   n   10−2  n in h  n  n LXT in    ",
+    "in   10−2   i     h n h  hin h i i n h iiin   in h   in    ih ini n  n hn h     in i  ii ni hh h ni h h   ) h in nn in i   h  h  in   ",
+    " h in  hi   h       i    in  in  h h n i  n   "
+  ],
+  "6 COMPARISON WITH OBSERVATIONS ": [
+    "n hi in  n  i n  h   i   ) n    h n hi i  in  "
+  ],
+  "6.1 Thermal properties of the ICM ": [
+    "i (<>)  h i n    25  ) in   ih h     in h   n h    i) i   hn  i )  in ",
+    "i iin  h  i  n  h n    ih h     h in   niin n in h n n i  hih in h       h  i  i       nii  n in h h n  niin n h  ih   ",
+    "i (<>) h h n  niin n  h n  r1000)   nin  ii  i n) i n   i)  h h n in  n ) in     in h X   hn h   h nin i n   in  i in  (<>)  h  n ni   in   hn in h  n     h  hn in h  i in h h K(r1000)Tsl in i    i   h  h  ",
+    "Figure 12. n   25  i ih  i hi    h    i)   hn  i )  in     h  in) n  i  in)  in h X  PP)   i  i  h   n h   n   i n ",
+    "Figure 13. h in  n  niin K(r1000) ih  i   i hi      h ii  ihin r500 i n) i n   i)  in  i   n h i  in i h  in niin   n h  in    in h X  PP) i  hn  n  n  i  in ",
+    "in h  n niin  h ihin 1˙  h   n h   h n in i  ",
+    "n i (<>)  i h iin  h i K(r1000)/K(0.1r200)    h n  h) ih  h    i in i nin ih h  h  in n h  i ini  h     (<>)  h n",
+    "Figure 14. h in  n  h K(r1000)/K(0.1r200) ih  i   i hi    h ii  i  ihin r500  i)  in  i    hn   n) i h i  in i h  in in in    n  in   i h  in     h X PP n  n  in) ",
+    "iin i ih  h   n  hi  i n     h n n    K(r1000)/K(0.1r200) hih  h niin  h i K(r1000)/K(0.1r200)Tsl in hi  n  h   ih n i n n in i (<>) n h  h   i ni  n   i  n h K(r1000)/K(0.1r200)Tsl n hi   i h niin  h  in i  h i n hh i    in X h   h   n n inin     i (<>) ih h i h i   n n h i n  K(r1000)/K(0.1r200)Tsl in ",
+    "in  n  i LXTsl in in ih h X   in in i (<>)  i ih    h n in hn     h niin n   h  in  ihin 1˙  i in  (<>)  n h  i  i n LXTsl in h i   h  h  in    "
+  ],
+  "6.2 Chemical properties of the ICM ": [
+    "h i iinih ii    25  in    i in i (<>) n ih  nn     n    h     n  i in  n  h     h i in h  n nn   i  in i )  in n   i)   in h   h iiin   ii    n  nihn n nn iiin n     n    h i i in h h    i   in n n ih h    ",
+    "Table 8.   ih 1˙ )  z = 0 in in in     i  n  h X in  PP  h  n ni   in   hn iin i in     in h  hn in h ",
+    "C0 n  h in niin n   h in i  in (<>)) n ˙int i h inini   h n in in (<>)) ",
+    "Figure 15. h X ini in in i   i hi    X i   ihin r500 i n) i n   i)  in  i   n h i  in i h  in    n  i     h  in    in h X  P  n i  in) ",
+    " h in   niin n  ih h in  h     h h  h n nn  hih    nn (<>)i   (<>) (<>)i  ni (<>))  n hi  i  n ini h h ii  h  ih  ",
+    "h   ii  h   i h i  h ii   i  0.25r180  h   i  0.045r180  h h i ii in n   h  in h    h  ii  n  hi i n h iiin h n     n   iin  ",
+    "i (<>) h h i in  h i Z(0.25r180)/Z(0.045r180) ih ii  h nin  in    i  hn  in n h   h  in  n in  (<>)   h  in  ihin 1˙  h i niin i  hn  n h  i   h in    n ",
+    "Figure 16. iinih ii   25  i ih  i hi    h    i)   hn  i )  in  in   h     h  in) n  i  in)  in h X  PP)  n h   ih   in h  n   i  ",
+    "h i n   h i ni   h h hih i   in h niin  h  in i  h   "
+  ],
+  "7 INCLUDING RADIATIVE COOLING: A FIRST ATTEMPT ": [
+    "n  h iin n in hi  h  in in  n hi in       n  hi  h  in    ii  i i      hih n  both  n   hi iin hi in   in n  in  hi h hi  i  inn   n h h   i i ih  h ",
+    "h iin   in i i    in n h iin  ini n h  h h h n n n in  i nnii n  i i n  innin h  n n hi ",
+    "Figure 17. h in  iinih ii  h Z(0.25r180)/Z(0.045r180) ih  i   i hi    h  n) i n   i)  in  i   h i  in i h  in in hn niin  h   in   h  in    in h    i  i  n i  in) ",
+    "in  in   hn in   in   hi    ",
+    " in   in h 2 hi hin   in h in (<>) h   h  h i  hi hn ih h iin  in) n    i      i nihin    in  i in  n iin ih    600  −1) n  nihn     in i  ni ii hh h ni h h) ",
+    "nn ii in i in in  iin    h  i  n i h) ii Zsm,i in (<>)) n  n  i   i n Ai n ni ˆi ih hi inin  hn  h in  in h in nin  (<>)hn  i (<>)) n  h n  h  i in ",
+    "i (<>)  h n     in  n ih  i    ) ih n ih in  i n h h hin   n  h n n in  n in in n  in h i  h  in    r . 0.3r500 in    in in h n  n h i n n in   ii   h ni  in in   i  inin   in h  ",
+    "A priori h i n n   h h n   n  hin i  h nin     in  i n ii in in h iin hi i  i   i in i  n h in h h h  hii ih  iiin hih i i n h  in hni iin  h i in    in h i  in  h in h iin in h n   h ",
+    "Figure 18. n     i ih  i hi    ih in i  in) n ih nn ii in i  in)    ii  h  in) n  i  in)  in h X  PP)   i  i  ",
+    "n     n  n n  h n h   n  h in in  in  i h i i ni  in     ih in h iin ",
+    "  hi   h  n ad hoc nin   hi    h  in  n in      nin  iin  hin h  h in  nhn  h in    in in h  h i i i h  n in i  n ii in i   in  h iin i  h   ",
+    "h i        h     ini   i in h iin iin in h n in  h r < 0.1r200)  h n i   i n  h i h    hh   3 × 104  i h h  i hi    i ftemp  h ii  T200 in (<>))  hi h h  h i  i  nin in hi hin ni h n   i h  hih in h i  i nin in h  i  n h  i  ",
+    "n h    h i  n inin in       ni frad = 1)  hn h    h in  i h     fduty n ftemp hih n h   i in    h   n  h   in h  n h n iiin in       i in  (<>) h  h in h h    hi h h in nn ii in ",
+    "Table 9. hi    ih nn ii in n  iin  iin hin    in   n h  n  i in in  ini  h i nihin    in  i in  n iin ih i 600  −1  n n   h in ihin  i  r200 frad = 1 n fZ,rad = 1 i) n hi  h in  i h     i fduty = 10−1  n  i in    h     ftemp = 2.5 i h h ii  ",
+    "Figure 19. n     i ih  hi    inin nn ii in  i hi  h  fduty  in  n   i  n h h i in  fduty = 10−4 h   iin  h   hin hih )    h n   inin in   i h  2.5 i h h ii   in   h h     h  in) n  i  in)  in h X  PP) "
+  ],
+  "7.1 The effect of changing fduty ": [
+    "i (<>) i h h n     i   in fduty in ftemp   2.5 ih h in  fduty = 10−1     fduty  n  h hii in  in hi i  n   in   i  h    in h    n  in in h   n ih h inin  iin n hn  in fduty  10−1   h   in   i  h    in  i n  n i  h ii in h n n h  hn  i   fduty  10−2  10−1  hih n     nin n   52◦  "
+  ],
+  "7.2 The effect of changing ftemp ": [
+    "",
+    "h   in h  ftemp n h n     i hn in i  h   ftemp  ni  1 2.5 4.5 n 20 in fduty = 0.1 in h    i ",
+    "Figure 20. n     i ih  hi    inin nn ii in n in h   in h n in   i h   i ftemp  h h ii  i  in  n   i) h h   fduty i   10−1  h     h  in) n  i  in)  in h X  PP)   i  in ",
+    "   h h n n nn n   h  i   in   z ˇ 0.8)  i i  i ni  in    i in h  ftemp i   20  1 h n  n in i  i h     hi n n  in       ftemp  i in   h h i n iin n in    i  hi n  i hn hn ftemp i   h h n n h  h  hih  n h hi in i i h h  ftemp i  h n   n  in   in in    n n n    ",
+    " nin  n in i   i hh  hin  i ni i  ni hi  n fenergy  h i  h n   h n i  h iin i  h    h   h iin  n fenergy      i  z = 0  ftemp = 1 2.5 4.5 n 20  h fenergy ˇ 0.6 0.15 0.18 n 0.5 i   i h  ih fheat = 1 n 20 n ni n    fheat fheat = 1)      n in  h ",
+    "Figure 21. h X ini in in i   i hi    ih nn ii in n iin hin    in   X i   ihin r500  )  in    hn   ) i hi  n)  n h   i   i)   i     in    in) n  )  in h X  P) ",
+    " i    n i i in  in n i hn h in  n  hin n  i  h in hi    n hn fheat i  fheat = 20)   hin n  i  n   i h  h hih  h i in i   n  h  n  n n  h   h hih  n h fenergy i in  ",
+    " h in  hi in  h h  ih (frad, fduty, fheat) = (1, 10−1 , 2.5)   i  in hi i  i n      n i n  n in  ˘ 15%  h i  h    h i  25  in   ih hi  n  n in h i h i  h  "
+  ],
+  "7.3 Thermal properties of the ICM ": [
+    "i (<>) h  X ini in h h ini n ii  h n  ihin r500  ) i n  )  n  n)  n   i)   i     i h    h n  in    in h X PP)   hn 1˙ 7   25  i hi iin  i    h in    in) n  )  in h X ",
+    " i in i n   h  h in  in h n h h    n h  ",
+    "Figure 22. n n    h   in n    n h   in    h i in    i ih  i hi     nn ii in n iin hin    in   h h in      in h X  PP) h  h   n ",
+    "n   ih  hih ini hh hi    in   h in in i h     n h  n   ih  in     h i ni i ih nin hni iin hi nin  n h n    in   ",
+    "h n n n ii       in    i in i (<>) n (<>) i h    )   hn   ) in ih i h) in nin  i )   h h iin  inii   h n in i i  i  h    h i  n  i     i  n i i ih in  ih    in   niin  ",
+    "h   n  in n h i n   i h h  n  i      in h   h n   i   h h     hih  niin   r500 in h i  n  h n in  nin  h  ii h    h  hin  i    n h h  h  iin hin  n  h   nh i i in h hi   h      iin in in h n   h     ",
+    "",
+    "in   h n in    n i   h h i fenergy   nin  hi    25  h i ) in h h ini i) in n in  h ii   in   in) n   in)  h  in  n i h  z = 0 h    n in i ˘ 15%  h i  h   hi i      n    hih h fenergy ˇ 0.25) hih i n   i    n in hih i    in h  in i in h n in ",
+    "Figure 23. n ii     h   in n    n h   in    h i in    i ih  i hi     nn ii in n iin hin    in   h h in      in h X  PP) h  h   n ",
+    "Figure 24. in  h i  h iin n in i   ii in in    h i   n      25  in    h i   in  ) n  )  h i ) in h h ini i) in ",
+    " h  i h hn in    h in i  nin  hi z . 3 h i i  iinih n h  h in in   hih hi z ˘ 3 − 8 h n  h  iin n i in in h     hn   hi   n iniin  n i  hi    "
+  ],
+  "8 CONCLUSIONS ": [
+    "n hi   h  ni iin  ini h  in  h in n h i    n  h n nih in   i i    h in inin  h    h h n hi i  h  in  in    X in i  nin   ",
+    " h i    25 i     h inni iin n h iin h n n  in in h    n  i        in in h hi h   hi n h  iin   ii  in h  nin hni iin n i i  in n   ",
+    " in hin h n    n     h i h hi i n   inin  nn in i     h h  n   h  i n n  h  h in  n  i  n hi nii hin  h  hih i i  in in h  hin i i   iin h hn ii ",
+    " nin    ",
+    " i hi hin  i   in h h h n hi i  in        in   h    i  in  h niin n h  n  h X ini in in n h h  ii  h  i   h  n  ",
+    "h ini    ih vwind = 20 000  −1   h h n  in hi i ",
+    "  h   h   i  i  h n  n  hi  in hi  hi   n  n  h     niin i h   h  i i i h hi i    in hi h  ini h in  nin  hi  ",
+    "ni  n i  i h  i    in h  h n  n h   n   ii  in  h nih   inn niin    h in h  in (<>)ni (<>)) i h n     i    in  i (<>)nn    (<>) (<>)  P (<>)) ii h n ni  i    hn   hnh  h  h h n  h   n h h ii  n h   ni   h inin  i  i n  (<>)   (<>)) n P (<>)   (<>)) iin  h  n h ni n     i in in h  ",
+    "ni  nh in h    n       n  µ  (<>)n   (<>) (<>)   (<>) n n hin) n  h    h  h   n n in    in h in h n i  (<>)n   (<>)) n ini i    µ hi  ih hi i  (<>)n   (<>))  hi  h ni n ni i  n  in ni    n)  h  n ni  h  ",
+    "nin h n ini  n h ini     in h in  in    (<>)  h (<>) (<>)Pih   (<>) (<>)i  h ",
+    "(<>) (<>)i  h (<>) (<>)Pih   (<>)) i in  nin i h  i  n  ii  hi   h   ii  n h in    in nin   h     (<>)   (<>) (<>) P   (<>) (<>)n   (<>) (<>)   (<>))  i i h h   n  ni hh h ii nin  h in  h   hi  h i in i h   hih ni     nin n h  n h  i n hi i n n h i in  in  ni in n h iin  i n inin  ",
+    "in h  ni n    (<>)ihinin   (<>)) n in nin  h i  hn i i i  i h i   hih  n  h   hi n  i  in h    i    )−1  r > 0.1r500     ) in h  in  h i  i i hn ni h n  h ii i  in  h n  nii  n h h     h  ihin h  n     ii h nin h n in n h n inin h n in hi  ",
+    " h n h  i hi hin  n in  in in i  i     h  ih n X ih  ih h inin  nn ii in n  i iin  iin hin   in h n in    h n     in    h  n   ih  in    n nin  hni iin  h  inni  500h−3 3) ih h  h i i     ii     n  h i  nin ih h i X  n   n in iin  h     in h in nin  X   (<>)hn   (<>)) hi i ni  i h      i   h nin hi  h ni "
+  ],
+  "ACKNOWLEDGEMENTS ": [
+    "      P n  hi  in  ih hi in    hn  in  iin h    h i in i  in h  i   n  nin  h   n inii niin h in  hi    n h   hin hih i   h i ii in n  h in n hn iii ni h  iii i n   n h nii in  n   h in n hn iii ni n n ) "
+  ]
+}

jsons_folder/2013MNRAS.428.2529H.json

@@ -0,0 +1,238 @@
+{
+  "ABSTRACT ": [
+    "(<http://arxiv.org/abs/1209.2413v2>)arXiv:1209.2413v2  [astro-ph.CO]  15 Oct 2012Accepted 2012 October 15. Received 2012 October 9; in original form 2012 September 10 ",
+    "High-redshift submillimetre galaxies (SMGs) are some of the most rapidly star-forming galaxies in the Universe. Historically, galaxy formation models have had dif•culty explaining the observed number counts of SMGs. We combine a semi-empirical model with 3-D hydrodynamical simulations and 3-D dust radiative transfer to predict the number counts of unlensed SMGs. Because the stellar mass functions, gas and dust masses, and sizes of our galaxies are constrained to match observations, we can isolate uncertainties related to the dynamical evolution of galaxy mergers and the dust radiative transfer. The number counts and redshift distributions predicted by our model agree well with observations. Isolated disc galaxies dominate the faint (S1.1 . 1 mJy, or S850 . 2 mJy) population. The brighter sources are a mix of merger-induced starbursts and galaxy-pair SMGs; the latter subpopulation accounts for ˘ 30 −50 per cent of all SMGs at all S1.1 & 0.5 mJy (S850 & 1 mJy). The mean redshifts are ˘ 3.0−3.5, depending on the •ux cut, and the brightest sources tend to be at higher redshifts. Because the galaxy-pair SMGs will be resolved into multiple fainter sources by ALMA, the bright ALMA counts should be as much as 2 times less than those observed using single-dish telescopes. The agreement between our model, which uses a Kroupa IMF, and observations suggests that the IMF in high-redshifts starbursts need not be top-heavy; if the IMF were top-heavy, our model would over-predict the number counts. We conclude that the dif•culty some models have reproducing the observed SMG counts is likely indicative of more general problems • such as an under-prediction of the abundance of massive galaxies or a star formation rate•stellar mass relation normalisation lower than that observed • rather than a problem speci•c to the SMG population. ",
+    "Key words: galaxies: high-redshift • galaxies: starburst • infrared: galaxies • radiative transfer • stars: luminosity function, mass function • submillimetre: galaxies. "
+  ],
+  "1 INTRODUCTION ": [
+    "Submillimetre galaxies (SMGs; (<>)Smail et al. (<>)1997; (<>)Barger et al. (<>)1998; (<>)Hughes et al. (<>)1998; (<>)Eales et al. (<>)1999; see (<>)Blain et al. (<>)2002 for a review) are amongst the most luminous, rapidly star-forming galaxies known, with luminosities in excess of 1012 L⊙and star formation rates (SFR) of order ˘ 102 − 103 M⊙yr−1 (e.g., (<>)Kov´acs et al. (<>)2006; (<>)Coppin et al. (<>)2008; (<>)Micha›owski et al. ",
+    "(<>)2010, (<>)2012; (<>)Magnelli et al. (<>)2010, (<>)2012; (<>)Chapman et al. (<>)2010). They have stellar masses of ˘ 1011 M⊙, although recent estimates ((<>)Hainline et al. (<>)2011; (<>)Micha›owski et al. (<>)2010, (<>)2012) differ by a factor of ˘ 6, and typical gas fractions of ˘ 40 per cent ((<>)Greve et al. (<>)2005; (<>)Tacconi et al. (<>)2006, (<>)2008; but cf. (<>)Narayanan, Bothwell, & Dav´e (<>)2012a). ",
+    "The most luminous local galaxies, ultra-luminous infrared galaxies (ULIRGs, de•ned by LIR > 1012 L⊙), are almost exclusively late-stage major mergers (e.g., (<>)Lonsdale et al. (<>)2006) because the strong tidal torques exerted by the galaxies upon one another when they are near coalescence cause signi“cant gas in”ows and, consequently, bursts of star formation (e.g., (<>)Hernquist ",
+    "(<>)1989; (<>)Barnes & Hernquist (<>)1991, (<>)1996; (<>)Mihos & Hernquist (<>)1996). Thus, it is natural to suppose that SMGs, which are the most luminous, highly star-forming galaxies at high redshift, are also late-stage major mergers undergoing starbursts. There is signi•cant observational support for this picture (e.g., (<>)Ivison et al. (<>)2002, (<>)2007, (<>)2010; (<>)Chapman et al. (<>)2003; (<>)Neri et al. (<>)2003; (<>)Smail et al. (<>)2004; (<>)Swinbank et al. (<>)2004; (<>)Greve et al. (<>)2005; (<>)Tacconi et al. (<>)2006, (<>)2008; (<>)Bouch´e et al. (<>)2007; (<>)Biggs & Ivison (<>)2008; (<>)Capak et al. (<>)2008; (<>)Younger et al. (<>)2008, (<>)2010; (<>)Iono et al. (<>)2009; (<>)Engel et al. (<>)2010; (<>)Bothwell et al. (<>)2010, (<>)2012; (<>)Riechers et al. (<>)2011a,(<>)b; (<>)Magnelli et al. (<>)2012). However, there may not be enough major mergers of galaxies of the required masses to account for the observed SMG abundances ((<>)Dav´e et al. (<>)2010). Consequently, explaining the abundance of SMGs has proven to be a challenge for galaxy formation models. ",
+    "Much observational effort has been invested to determine the number counts and redshift distribution of SMGs (e.g., (<>)Chapman et al. (<>)2005; (<>)Coppin et al. (<>)2006; (<>)Knudsen et al. (<>)2008; (<>)Chapin et al. (<>)2009; (<>)Weiß et al. (<>)2009; (<>)Austermann et al. (<>)2009, (<>)2010; (<>)Scott et al. (<>)2010; (<>)Zemcov et al. (<>)2010; (<>)Aretxaga et al. (<>)2011; (<>)Banerji et al. (<>)2011; (<>)Hatsukade et al. (<>)2011; (<>)Wardlow et al. (<>)2011; (<>)Roseboom et al. (<>)2012; (<>)Yun et al. (<>)2012) because this information is key to relate the SMG population to their descendants and to understand SMGs in the context of hierarchical galaxy formation models. Various authors have attempted to explain the observed abundance of SMGs using phenomenological models (e.g., (<>)Pearson & Rowan-Robinson (<>)1996; (<>)Blain et al. (<>)1999b; (<>)Devriendt & Guiderdoni (<>)2000; (<>)Lagache et al. (<>)2003; (<>)Negrello et al. (<>)2007; (<>)B´ethermin et al. (<>)2012), semi-analytic models (SAMs; e.g., (<>)Guiderdoni et al. (<>)1998; (<>)Blain et al. (<>)1999a; (<>)Granato et al. (<>)2000; (<>)Kaviani et al. (<>)2003; (<>)Granato et al. (<>)2004; (<>)Baugh et al. (<>)2005; (<>)Fontanot et al. (<>)2007; (<>)Fontanot & Monaco (<>)2010; (<>)Lacey et al. (<>)2008, (<>)2010; (<>)Swinbank et al. (<>)2008; (<>)Lo Faro et al. (<>)2009; (<>)Gonz´alez et al. (<>)2011), and cosmological hydrodynamical simulations ((<>)Fardal et al. (<>)2001; (<>)Dekel et al. (<>)2009; (<>)Dav´e et al. (<>)2010; (<>)Shimizu et al. (<>)2012). ",
+    "(<>)Granato et al. ((<>)2000) presented one of the •rst SAMs to self-consistently calculate dust absorption and emission by coupling the GALFORM SAM ((<>)Cole et al. (<>)2000) with the GRASIL spectrophotometric code ((<>)Silva et al. (<>)1998). This was a signi•cant advance over previous work, which effectively treated the dust temperature as a free parameter. Self-consistently computing dust temperatures made matching the submm counts signi•cantly more dif•cult: the submm counts predicted by the (<>)Granato et al. model were a factor of ˘ 20 − 30 less than those observed ((<>)Baugh et al. (<>)2005; (<>)Swinbank et al. (<>)2008). ",
+    "The work of (<>)Baugh et al. ((<>)2005, hereafter B05) has attracted signi•cant attention to the •eld because of its claim that a •at IMF is necessary to reproduce the properties of the SMG population, which we will discuss in detail here. B05 set out to modify the (<>)Granato et al. ((<>)2000) model so that it would reproduce the properties of both z ˘ 2 SMGs and Lyman-break galaxies (LBGs) while also matching the observed z = 0 optical and IR luminosity functions. Adopting a •at IMF1 (<>)in starbursts rather than the (<>)Kennicutt ((<>)1983) IMF used in (<>)Granato et al. ((<>)2000) was the key change that enabled B05 to match the observed SMG counts and redshift distribution while still reproducing the local K-band luminosity function. A more top-heavy IMF results in both more ",
+    "luminosity emitted and more dust produced per unit SFR; consequently, the submm •ux per unit SFR is increased signi•cantly (see B05 and (<>)Hayward et al. (<>)2011a, hereafter H11, for details). The B05 modi•cations increased the S850 per unit SFR for starbursts by a factor of ˘ 5 (G.-L. Granato, private communication), which caused starbursts to account for a factor of ˘ 10 3 times more sources at S850 = 3 mJy than in (<>)Granato et al. ((<>)2000). As a result, in the B05 model, ongoing starbursts dominate the counts for 0.1 . S850 . 30 mJy. Interestingly, these starbursts are triggered predominantly by minor mergers (B05; (<>)Gonz´alez et al. (<>)2011). (<>)Swinbank et al. ((<>)2008) present a detailed comparison of the properties of SMGs in the B05 model with those of observed SMGs. The far-IR SEDs, velocity dispersions, and halo masses (see also (<>)Almeida et al. (<>)2011) are in good agreement; however, recent observations suggest that the typical redshift of SMGs may be higher than predicted by the B05 model and, contrary to the B05 prediction, brighter SMGs tend to be at higher redshifts ((<>)Yun et al. (<>)2012; (<>)Smolˇci´c et al. (<>)2012). Furthermore, the rest-frame K-band •uxes of the B05 SMGs are a factor of ˘ 10 lower than observed; the most plausible explanation is that the masses of the SMGs in the B05 SAM are too low ((<>)Swinbank et al. (<>)2008), but the top-heavy IMF in starbursts used by B05 makes a direct comparison of masses dif•cult. These disagreements are reasons it is worthwhile to explore alternative SMG models. ",
+    "(<>)Granato et al. ((<>)2004) presented an alternate model, based on spheroid formation via monolithic collapse, that predicts submm counts in good agreement with those observed and reproduces the evolution of the K-band luminosity function. However, the typical redshift they predict for SMGs is lower than recent observational constraints ((<>)Yun et al. (<>)2012; (<>)Smolˇci´c et al. (<>)2012), and this model does not include halo or galaxy mergers. ",
+    "The (<>)Fontanot et al. ((<>)2007) model predicts SMG number counts in reasonable agreement with those observed using a standard IMF; they argue that the crucial difference between their model and that of B05 is the cooling model used (see also (<>)Viola et al. (<>)2008 and (<>)De Lucia et al. (<>)2010). However, their SMG redshift distribution peaks at a lower redshift than the redshift distribution derived from recent observations ((<>)Yun et al. (<>)2012; (<>)Smolˇci´c et al. (<>)2012). Furthermore, the (<>)Fontanot et al. ((<>)2007) model produces an overabundance of bright galaxies at z < 1. However, this problem has been signi•cantly reduced in the latest version of the model ((<>)Lo Faro et al. (<>)2009), which provides a signi•cantly better •t to the galaxy stellar mass function at low redshift ((<>)Fontanot et al. (<>)2009). In the revised model, the submm counts are reduced by ˘ 0.5 dex, primarily because of the change in the IMF from Salpeter to Chabrier, but the redshift distribution is unaffected. Thus, the submm counts for the new model are consistent with the data for S850 . 3 mJy, but they are slightly less than the observed counts at higher •uxes ((<>)Fontanot & Monaco (<>)2010). No •ne-tuning of the dust parameters has been performed for the new model. ",
+    "A compelling reason to model the SMG population in an alternative manner is to test whether a top-heavy IMF is required to explain the observed SMG counts. Matching the submm counts is the primary reason B05 needed to adopt a •at IMF in starbursts.2 (<>)Using the same model, (<>)Lacey et al. ((<>)2008) show that the •at IMF is necessary to reproduce the evolution of the mid-IR luminosity function. Others (e.g., (<>)Guiderdoni et al. (<>)1998; (<>)Blain et al. (<>)1999a; (<>)Dav´e et al. ",
+    "(<>)2010) have also suggested that the IMF may be top-heavy in SMGs, but they do not necessarily require variation as extreme as that assumed in B05. However, the use of a •at IMF in starbursts remains controversial: though there are some theoretical reasons to believe the IMF is more top-heavy in starbursts (e.g., (<>)Larson (<>)1998, (<>)2005; (<>)Elmegreen & Shadmehri (<>)2003; (<>)Elmegreen (<>)2004; (<>)Hopkins (<>)2012; (<>)Narayanan & Dav´e (<>)2012), there is to date no clear evidence for strong, systematic IMF variation in any environment ((<>)Bastian et al. (<>)2010 and references therein). Furthermore, in local massive ellipticals, the probable descendants of SMGs, the IMF may actually be bottom-heavy (e.g., (<>)van Dokkum & Conroy (<>)2010, (<>)2011; (<>)Conroy & van Dokkum (<>)2012; (<>)Hopkins (<>)2012). Finally, the large parameter space of SAMs can yield multiple qualitatively distinct solutions that satisfy all observational constraints ((<>)Bower et al. (<>)2010; (<>)Lu et al. (<>)2011, (<>)2012), so it is possible that a top-heavy IMF in starbursts is not required to match the observed submm counts even though it enables B05 to match the submm counts.3 (<>)Thus, it is useful to explore other methods to predict the submm counts and to determine whether a match can be achieved without using a top-heavy IMF. ",
+    "Another reason to model the SMG population is to investigate whether, like local ULIRGs, they are predominantly merger-induced starbursts. Some observational evidence suggests that some SMGs may be early-stage mergers in which the discs have not yet coalesced and are likely not undergoing starbursts (e.g., (<>)Tacconi et al. (<>)2006, (<>)2008; (<>)Engel et al. (<>)2010; (<>)Bothwell et al. (<>)2010; (<>)Riechers et al. (<>)2011a,(<>)b), and massive isolated disc galaxies may also contribute to the population (e.g., (<>)Bothwell et al. (<>)2010; (<>)Carilli et al. (<>)2010; (<>)Ricciardelli et al. (<>)2010; (<>)Targett et al. (<>)2011, (<>)2012) In H11 and H12, we suggested that the inef•cient scaling of (sub)mm •ux with SFR in starbursts results in an SMG population that is heterogeneous: major mergers contribute both as coalescence-induced starbursts and during the pre-coalescence in-fall stage, when the merging discs are blended into one (sub)mm source because of the large (˘ 15•, or ˘ 130 kpc at z ˘ 2 − 3) beams of the single-dish (sub)mm telescopes used to perform large SMG surveys. We refer to the latter subpopulation as •galaxy-pair SMGs•. Similarly, compact groups may be blended into one source and can thus also contribute to the population. The most massive, highly star-forming isolated discs may also contribute (H11). Finally, it has been observationally demonstrated that there is a contribution from physically unrelated galaxies blended into one source ((<>)Wang et al. (<>)2011). It is becoming increasingly clear that the SMG population is a mix of various classes of sources; if one subpopulation does not dominate the population, physically interpreting observations of SMGs is signi•cantly more complicated than previously assumed. ",
+    "Narayanan et al. ",
+    "2010b",
+    "Micha•owski et al. ",
+    "2012",
+    "In previous work, we demonstrated that major mergers can reproduce the observed 850-µm •uxes and typical SED ((<>)Narayanan et al. (<>)2010b); CO spatial extents, line-widths, and excitation ladders ((<>)Narayanan et al. (<>)2009); stellar masses (; H11; ); LIR• effective dust temperature relation, IR excess, and star formation ef•ciency ((<>)Hayward et al. (<>)2012, hereafter H12) observed for SMGs. In this work, we present a novel method to predict the (sub)mm counts from mergers and quiescently star-forming disc galaxies. We utilise a combination of 3-D hydrodynamical simulations, on which we perform radiative transfer in post-processing to ",
+    "calculate the UV-to-mm SEDs, and a semi-empirical model (SEM) of galaxy formation • both of which have been extensively validated in previous work • to predict the number counts and redshift distribution of SMGs in our model. We address four primary questions: 1. Can our model reproduce the observed SMG number counts and redshift distribution? 2. What are the relative contributions of merger-induced starbursts, galaxy pairs, and isolated discs to the SMG population? 3. How will the number counts and redshift distribution of ALMA-detected SMGs differ from those determined using single-dish surveys? 4. Does the SMG population provide evidence for a top-heavy IMF in high-redshift starbursts? ",
+    "The remainder of this paper is organised as follows: In Section (<>)3, we present the details of the simulations we use to determine the time evolution of galaxy mergers and to translate physical properties of model galaxies into observed-frame (sub)mm •ux densities. In Section (<>)4, we discuss how we combine the simulations with a SEM to predict the (sub)mm counts for merger-induced starburst SMGs (Section (<>)4.1) and isolated disc and galaxy-pair SMGs (Section (<>)4.2). In Section (<>)5, we present the predicted counts and redshift distribution of our model SMGs and the relative contribution of each subpopulation. We discuss implications for the IMF, compare to previous work, and highlight some uncertainties in and limitations of our model in Section (<>)6, and we conclude in Section (<>)7. "
+  ],
+  "2 SUMMARY OF THE MODEL ": [
+    "Predicting SMG counts requires three main ingredients: 1. Because SFR and dust mass are the most important properties for predicting the (sub)mm •ux of a galaxy (H11), one must model the time evolution of those properties for individual discs and mergers. 2. The physical properties of the model galaxies must be used to determine the observed-frame (sub)mm •ux density of those galaxies. 3. One must put the model galaxies in a cosmological context. Ideally, one could combine a cosmological hydrodynamical simulation with dust radiative transfer to self-consistently predict the (sub)mm counts. However, this is currently infeasible because the resolution required for reliable radiative transfer calculations cannot be achieved for a cosmological simulation large enough to contain a signi•cant number of SMGs (see, e.g., (<>)Dav´e et al. (<>)2010).4 (<>)",
+    "Here, we develop a novel method to predict the number counts and redshift distribution of high-z SMGs while still resolving the dusty ISM on scales of ˘ 200 pc. We predict (sub)mm counts using a combination of a simple SEM ((<>)Hopkins et al. (<>)2008a,(<>)c) and ide-alised high-resolution simulations of galaxy mergers. The method we use for each of the three model ingredients depends on the subpopulation being modelled. The physical properties of the isolated disc galaxies and early-stage mergers are determined using the SEM. For the late-stage mergers, hydrodynamical simulations are used because of the complexity of modelling a merger•s evolution. Dust radiative transfer is performed on the hydrodynamical simulations to translate the physical properties into observed (sub)mm •ux density. For the isolated discs and early-stage mergers, •tting functions derived from the simulations are used, whereas ",
+    "Table 1. Summary of methods ",
+    "for the late-stage mergers, the (sub)mm light curves are taken directly from the simulations. Finally, the isolated galaxies are put in a cosmological context using an observed stellar mass function (SMF). For the mergers, merger rates from the SEM and duty cycles from the simulations are used. The methods are summarised in Table (<>)1, and each component of the model is discussed in detail below. ",
+    "We emphasize that we do not attempt to model the SMG population in an ab initio manner. Instead, we construct our model so that the SMF, gas fractions, and metallicities are consistent with observations. This will enable us to test whether, given a demographically accurate galaxy population, we are able to reproduce the SMG counts and redshift distribution. If we are not able to reproduce the counts and redshift distribution, then our simulations or radiative transfer calculations must be incomplete. If we can reproduce the counts and redshift distribution, then it is possible that the failure of some SAMs and cosmological simulations to reproduce the SMG counts may be indicative of a more general problem with those models (e.g., a general under-prediction of the abundances of massive galaxies) rather than a problem speci•c to the SMG population. ",
+    "In the next two sections, we describe our model in detail. Readers whom are uninterested in the details of the methodology may wish to skip to Section (<>)5. "
+  ],
+  "3 SIMULATION METHODOLOGY ": [],
+  "3.1 Hydrodynamical simulations ": [
+    "We have performed a suite of simulations of isolated and merging disc galaxies with GADGET-2 ((<>)Springel et al. (<>)2001; (<>)Springel (<>)2005), a TreeSPH ((<>)Hernquist & Katz (<>)1989) code that computes gravitational interactions via a hierarchical tree method ((<>)Barnes & Hut (<>)1986) and gas dynamics via smoothed-particle hydrodynamics (SPH; (<>)Lucy (<>)1977; (<>)Gingold & Monaghan (<>)1977; (<>)Springel (<>)2010).5 (<>)It explicitly conserves both energy and entropy when appropriate ((<>)Springel & Hernquist (<>)2002). Beyond the core ",
+    "Schmidt ",
+    "1959",
+    "Kennicutt ",
+    "1998",
+    "gravitational and gas physics, the version of GADGET-2 we use includes radiative heating and cooling ((<>)Katz et al. (<>)1996). Star formation is implemented using a volume-density-dependent Kennicutt-Schmidt (KS) law (; ), ˆSFR / ˆNgas, with a low-density cutoff. We use N = 1.5, which reproduces the global KS law and is consistent with observations of high-redshift disc galaxies ((<>)Krumholz & Thompson (<>)2007; (<>)Narayanan et al. (<>)2008, (<>)2011; but see (<>)Narayanan et al. (<>)2012b). ",
+    "Furthermore, our simulations include a two-phase sub-resolution model for the interstellar medium (ISM; (<>)Springel & Hernquist (<>)2003) in which cold dense clouds are in pressure equilibrium with a diffuse hot medium. The division of mass, energy, and entropy between the two phases is affected by star formation, radiative heating and cooling, and supernova feedback, which heats the diffuse phase and evaporates the cold clouds ((<>)Cox et al. (<>)2006b). Metal enrichment is calculated assuming each particle behaves as a closed box the yield appropriate for a (<>)Kroupa ((<>)2001) IMF. The simulations also include the (<>)Springel et al. ((<>)2005) model for feedback from active galactic nuclei (AGN), in which black hole (BH) sink particles, initialised with mass 10 5 h−1 M⊙, undergo Eddington-limited Bondi-Hoyle accretion ((<>)Hoyle & Lyttleton (<>)1939; (<>)Bondi & Hoyle (<>)1944; (<>)Bondi (<>)1952). They deposit 5 per cent of their luminosity (L = 0.1 ˙ 2mc , where m˙ is the mass accretion rate and c is the speed of light) to the surrounding ISM. This choice is made so that the normalisation of the MBH − ˙ relation is recovered ((<>)Di Matteo et al. (<>)2005). Note that our results do not depend crucially on the implementation of BH accretion and feedback for two reasons: 1. the AGN typically do not dominate (but can still contribute signi“cantly to) the luminosity of our model SMGs because the SEDs during the phase of strong AGN activity tend to be hotter than during the starburst phase (e.g., (<>)Younger et al. (<>)2009, Snyder et al., in preparation), so the mergers are typically not SMGs during the AGN-dominated phase. 2. Even in the absence of AGN feedback, the SFR decreases sharply after the starburst simply because the majority of the cold gas is consumed in the starburst. ",
+    "Each disc galaxy is composed of a dark matter halo with a (<>)Hernquist ((<>)1990) pro•le and an exponential gas and stellar disc in which gas initially accounts for 80 per cent of the total bary-onic mass. At merger coalescence, the baryonic gas fractions are typically 20-30 per cent, which is consistent with the estimates of (<>)Narayanan et al. ((<>)2012a). The mass of the baryonic component is 4 per cent of the total. The galaxies are scaled to z = 3 following the method described in (<>)Robertson et al. ((<>)2006). Dark matter particles have gravitational softening lengths of 200h−1 pc, whereas gas and star particles have 100h−1 pc. We use 6×104 dark matter, 4×104 stellar, 4 × 104 gas, and 1 BH particle per disc galaxy. The detailed properties of the progenitor galaxies are given in Table (<>)2. Note that we have chosen galaxy masses such that most of the mergers, based upon our simulations, will contribute to the bright SMG population (i.e., at some time during the simulation they have observed 850-µm •ux density S850 > 3 mJy). More massive galaxies ",
+    "Table 2. rogenitor disc gl properties ",
+    "Table 3. erger prmeters ",
+    "ill lso contriute ut re incresingl more rre so our simultions should e representtie o ll ut the rightest rrest s (<>)ichosi et l. (<>). ote lso tht e he included some slightl loer mss mergers or completeness. ",
+    "",
+    "hochr  urert ",
+    "",
+    "e simulte ech disc gl listed in le (<>) in isoltion or 1.5h−1 r nd use these isolted disc simultions s prt o our simultion suite. ur suite lso includes  numer o simultions o mor nd minor gl mergers. or the merger simultions to o the progenitor disc glies re plced on prolic orits hich re motited  cosmologicl simultions (<>)enson   ith initil seprtion Rinit = 5R200/8 nd pericentricpssge distnce eul to tice the disc scle length Rperi = 2Rd(<>)oertson et l. (<>). he eolution o the sstem is olloed or 1.5h−1 r hich is sucient time or the glies to colescence nd or signicnt str ormtion nd  ctiit to cese. he detils o the merger simultions re gien in le (<>). or ech comintion o progenitor discs in le (<>) e simulte  suset o the ip orits o (<>)o et l. (<>). pecicll e use the ip orits or the mor mergers  .. nd  nd the i nd  orits or the uneulmss mergers .  nd  ecuse the ltter he shorter dut ccles nd the rition in dut ccles mongst orits is not  primr source o uncertint. onseuentl e use  totl o   simultions. "
+  ],
+  "3.2 Dust radiative transfer ": [
+    "n postprocessing e use the  onte rlo rditie trnser code  6 (<>)to clculte the tomm s o the simulted glies. e he preiousl simulted glies ith colours/s consistent ith locl  (<>)ennicutt et l. (<>) (<>)le et l. (<>) glies (<>)onsson roes  o (<>) locl s (<>)ounger et l. (<>) mssie uiescent compct ",
+    "z ˘ 2 glies (<>)uts et l. (<>) (<>)  µmselected glies (<>)rnn et l. (<>) /poststrurst glies (<>)nder et l. (<>) nd etended  discs (<>)ush et l. (<>) mong other popultions so e re condent tht  cn e used to model the high  popultion. s discussed oe preious or hs demonstrted tht mn properties o our simulted s gree ith osertions (<>)rnn et l. (<>) (<>) (<>)rd et l. (<>) (<>) ut e he et to put our simulted s in  cosmologicl contet. e rie reie the detils o  here ut e reer the reder to (<>)onsson et l. (<>) (<>)onsson et l. (<>) nd (<>)onsson  rimc (<>) or ull detils o the  code. ",
+    " uses the output o the  simultions to speci the detils o the rditie trnser prolem to e soled specicll the input rdition eld nd dust geometr. he str nd  prticles rom the  simultions re used s sources o emission. tr prticles re ssigned  (<>)eitherer et l. (<>) s ccording to their ges nd metllicities. e consertiel use the (<>)roup (<>)  hen clculting the simple stellr popultion  templtes. tr prticles present t the strt o the  simultion re ssigned ges  ssuming tht their stellr mss s ormed t  constnt rte eul to the str ormtion rte o the initil snpshot ut the results re insensitie to this choice ecuse e discrd the erl snpshots nd the strs present t the strt o the simultion ccount or  smll rction o the luminosit t lter times. he initil gs nd stellr metllicities re Z = 0.015 ˘ Z⊙ (<>)splund et l. (<>). e he chosen this lue so tht the strursts lie roughl on the osered mssmetllicit reltion hoeer the results re irl roust to this choice ecuse  ctor o  chnge in dust mss chnges the summ u  onl ˘ 50 per cent ecuse summ u scles pproimtel s Md0.6 utions (<>) nd (<>).  prticles re ssigned luminositdependent templtes deried rom osertions o unreddened usrs (<>)opins et l. (<>) here the luminosit is determined using the ccretion rte rom the  simultions s descried oe. ",
+    "he dust distriution is determined  proecting the totl gsphse metl densit in the  simultions on to   dptie mesh renement grid ssuming  dusttometl rtio o . (<>)e (<>) (<>)mes et l. (<>). e he used  mimum renement leel o  hich results in  minimum cell sie o h−1 pc. his renement leel is sucient to ensure the s re conerged to ithin  e per cent ecuse the structure present in the  simultions is sucientl resoled i the resolution o the  simultions ere ner the rditie trnser ould reuire correspondingl smller cell sies. ote tht e ssume the  is smooth on scles elo the  resolution nd do not me use o the (<>)roes et l. (<>) suresolution photodissocition region model. he detils o motition or nd implictions o this choice re discussed in sections .. nd . ",
+    "o . e ssume the dust hs properties gien  the il  R = 3.1 dust model o (<>)eingrtner  rine (<>) s updted  (<>)rine  i (<>). he summ ues re similr i the  or  dust models re used. ",
+    "nce the str nd  prticles re ssigned s nd the dust densit eld is specied  perorms the rditie trnser using  onte rlo pproch  emitting photon pcets tht re scttered nd sored  dust s the propgte through the . he energ sored  dust is rerdited in the . ust tempertures hich depend on oth grin sie nd the locl rdition eld re clculted  ssuming the dust is in therml euilirium. he  o our simulted glies cn oten e opticll thic t  elengths so  clcultes the eects o dust selsorption using n itertie method. his is crucil or ensuring ccurte dust tempertures. ",
+    "he  clcultion ields sptill resoled s nlogous to integrl eld unit spectrogrph dt o the simulted glies ieed rom dierent ieing ngles. ere e use  cmers distriuted isotropicll in solid ngle. e use the  µm  .mm nd  nds  nd  lter response cures to clculte the summ u densities. epending on the mss nd the  u cut the simultions re selected s s or ˘ 0 − 80 snpshots nd ech is ieed rom  ieing ngles. onseuentl e he  smple o ˘ 3.7 × 104 distinct snthetic  s tht e use to derie tting unctions or the isolted disc nd glpir s nd dut ccles or the strurst s. "
+  ],
+  "4 PREDICTING (SUB)MM NUMBER COUNTS ": [
+    "o clculte the totl  numer counts predicted  our model e must ccount or ll supopultions including the inllstge glpir s discussed in  nd  ltestge mergerinduced strursts nd isolted discs. o clculte the counts or the to supopultions ssocited ith mergers e must comine the dut ccles o the mergers the time the merger hs summ u greter thn some u cut ith merger rtes ecuse the numer densit is clculted  multipling the dut ccles  the merger rtes. or the isolted discs e reuire the numer densit o  disc gl s  unction o its properties nd the summ u ssocited ith tht gl. e descrie our methods or predicting the counts o ech supopultion no. "
+  ],
+  "4.1 Late-stage merger-induced starbursts ": [
+    "o predict the numer counts or the popultion o ltestge mergerinduced strurst s e comine merger rtes  hich depend on mss mss rtio gs rction nd redshit  rom the  ith summ light cures rom our simultions. e use the summ light cures rom the simultions directl ecuse it is dicult to nlticll model the dnmicl eolution o the mergers hich cn depend on the gl msses merger mss rtio progenitor redshit gs rction nd oritl properties. or the  supopultion ttriutle to mergers the numer densit o sources ith u densit greter thn Sλt redshit z is ",
+    "here dN/dV dtd log Mbardµdfg(Mbar, µ, fg, z) is the numer o mergers per comoing olume element per unit time per de ronic mss per unit mss rtio per unit gs rction hich is  unction o progenitor ronic mss Mbar merger mss rtio µ gs rction t merger fg nd redshit z nd ˝(Sλ, Mbar, µ, fg, z) is the mount o time dut ccle or hich  merger ith mostmssieprogenitor ronic mss Mbar mss rtio µ nd gs rction fgt redshit z hs u densit > Sλ. "
+  ],
+  "4.1.1 Duty cycles ": [
+    "e clculte the dut ccles ˝(S850) nd ˝(S1.1) or rious S850 nd S1.1 lues or the ltestge mergerinduced strurst phse o our merger simultions. e neglect the dependence o dut ccle on gs rction ecuse smpling the rnge o initil gs rctions in ddition to msses mss rtios nd orits is computtionll prohiitie. nsted s descried oe e initilise the mergers ith gs rction fg= 0.8 so tht sucient gs remins t merger colescence.7 (<>)",
+    "imilrl ecuse o computtionl limittions e scle ll initil disc glies to z ˘ 3. e ill see elo tht ll else eing eul the dependence o summ u densit on z is smll . 0.13 de or the redshit rnge o interest z ˘ 1 − 6 so e ssume the dut ccles re independent o redshit nd plce the mergers t z = 3 hich is pproimtel the medin redshit or our model s hen clculting the dut ccles. ote hoeer tht the summ dut ccles or the strursts m dier or mergers ith progenitor disc properties scled to dierent redshits ut our model does not cpture this eect. oeer ecuse most s in our model he z ˘ 2 − 4 see elo this uncertint should e sudominnt. ",
+    "or ech Sλ e erge the dut ccles or ech set o models ith identicl (Mbar, µ) nd then t the resulting ˝(Mbar, µ) surce ith  seconddegree polnomil in Mbar nd µ to estimte the dut ccle or (Mbar, µ) lues not eplicitl smpled  our simultions. "
+  ],
+  "4.1.2 Merger rates ": [
+    "he other ingredient needed to predict the counts or mergerinduced strursts is the merger rtes. e use rtes rom the  descried in detil in (<>)opins et l. (<>)c (<>)(<>)(<>)c hich e ill rie summrise here. he model strts ith  hlo mss unction tht hs een clirted using highresolution Nod simultions. lies re ssigned to hloes using n osered  or strorming glies nd the hlo occuption ormlism (<>)onro  echsler (<>). e use  ducil  tht is  comintion o multiple osered s in hich ech coers  suset o the totl redshit rnge. or z < 2 e use the  o strorming glies rom (<>)lert et l. (<>). or 2.0 6 z 6 3.75 e use the  o (<>)rchesini et l. (<>) ecuse their sure is mongst the idest nd deepest ille nd ecuse the he perormed  thorough nlsis o the rndom nd sstemtic uncertinties ecting the  determintion. or z > 3.75 e use the (<>)ontn et l. (<>)  prmeterition though the onl ",
+    "Figure 1. umer densit o disc glies dN/dV d log(M⋆/M⊙) pc−3 de−1 ersus M⋆(M⊙) or integer redshits in the rnge z = 0 −6 or our composite . or z < 2 e use the  or strorming glies rom (<>)lert et l. (<>). or 2 6 z 6 3.75 e use the (<>)rchesini et l. (<>)  nd or z > 3.75 e use the (<>)ontn et l. (<>) prmeteristion o the . ",
+    "constrined the  out to z ˘ 4 the etrpoltion grees resonl ell ith the 4 < z < 7 constrints rom (<>)onle et l. (<>) so this etrpoltion is not unresonle. ecuse the  t z & 4 is uncertin it m e possile to constrin the  t those redshits  using the osered  redshit distriution nd reltie contriutions o the supopultions e discuss these possiilities elo. he interested reder should see (<>)rd (<>) or  detiled eplortion o ho the choice o  ects the predictions o our model. e do not correct or the pssie gl rction eond z > 2 ut this rction is reltiel smll t z ˘ 2 nd decreses rpidl t higher redshits e.g. (<>)uts et l. (<>) (<>)rmmer et l. (<>). ur composite  t integer redshits in the rnge z = 0 − 6 is plotted in ig. (<>). inll e use hlohlo merger rtes rom highresolution Nod simultions nd trnslte to glgl merger rtes  ssuming the glies merge on  dnmicl riction timescle. ",
+    "he merger rtes  nd osered gs rctions re ll uncertin. he merger rtes re uncertin t the ctor o ˘ 2 leel the rious sources o uncertint nd eects o modiing the model ssumptions re discussed in detil in (<>)opins et l. (<>)(<>). t the redshits o interest the rndom nd sstemtic uncertinties in the  re comprle to the totl uncertint in the merger rtes. "
+  ],
+  "4.1.3 Predicted counts ": [
+    "sing the oe ssumptions ution (<>) ecomes ",
+    " ",
+    "o clculte the oserle cumultie counts deg−2 e must multipl  dV/d dz the comoing olume element in solid ngle d nd redshit interl dz nd integrte oer redshit: ",
+    " ",
+    "here ",
+    " "
+  ],
+  "4.2 Isolated discs and early-stage mergers ": [
+    "e tret the isolted discs nd erlstge mergers hich re dominted  uiescent str ormtion in  semiempiricl mnner in hich e ssign gl properties sed o osertions. o clculte the osered summ u densities using scling reltions similr to those o  e must determine the  nd dust mss o  gl s  unction o stellr mss nd redshit. e then use  nd merger rtes to clculte the summ counts or these popultions. "
+  ],
+  "4.2.1 Assigning galaxy properties ": [
+    "olloing (<>)opins et l. (<>)(<>)c e ssign gs rctions nd sies s  unction o stellr mss using osertionll deried reltions. e present the relent reltions elo ut e reer the reder to (<>)opins et l. (<>)(<>)(<>)c or ull detils including the list o osertions used to derie the reltions nd ustictions or the orms used. (<>)opins et l. (<>)c he shon tht this model reproduces glol constrints such s the  luminosit unction t rious redshits nd the str ormtion histor o the nierse mong others these results support the ppliction o the model in this or. ",
+    "he ronic gs rction fgas = Mgas/(Mgas + M⋆) o  gl o stellr mss M⋆nd redshit z s determined rom the osertions listed in (<>)opins et l. (<>)c is gien  ution  o (<>)opins et l. (<>)c ",
+    " ",
+    "here ˝(z) is the rctionl looc time to redshit z. t  gien mss gl gs rctions increse ith redshit. t ed redshit the decrese ith stellr mss. sing fgas(M⋆, z) e cn clculte the gs mss s  unction o M⋆nd z ",
+    " ",
+    "imilrl e prmeterie the rdius o the gs disc s  unction o mss nd redshit using the osertions listed in (<>)opins et l. (<>)c. ote tht the stellr disc rdii re signiicntl smller. he reltion ution  o (<>)opins et l. (<>)c see lso (<>)omerille et l. (<>) is ",
+    "e ssume the uiescentl strorming discs oe the  reltion (<>)chmidt (<>) (<>)ennicutt (<>) ",
+    " ",
+    "here ˙ ⋆nd gas re the  nd gs surce densities respectiel nd nK= 1.4 (<>)ennicutt (<>) t ll redshits ",
+    "Figure 2.   M⊙yr−1 ersus M⋆( M⊙) or model disc glies t integer redshits in the rnge z = 0 −6 solid lines nd rom the osertionll deried tting unction o (<>)hiter et l. (<>) t z = 0, 1, nd  dshed lines. he normlistion o the reltion increses ith redshit oth ecuse gs rctions re higher nd glies re more compct. he model grees resonl ell ith the osertions ecept t z ∼0 ut e shll see tht the z ∼0 contriution to our model  popultion is smll.  the s rom (<>)hiter et l. (<>) ere used insted o those clculted rom ution (<>) the z ∼0 contriution ould e een less so the discrepnc is unimportnt. ",
+    "roup ",
+    "",
+    "s is supported  osertions e.g. (<>)rnn et l. (<>) (<>)ddi et l. (<>) (<>)enel et l. (<>) (<>)rnn et l. (<>) ut c.. (<>)rnn et l. (<>). e normlise the reltion ssuming   . ssuming gas ˇ Mgas/(ˇRe2) nd ˙ ⋆ˇ M˙ ⋆/(ˇRe2) here M˙ ⋆is the  e nd ",
+    "",
+    "",
+    " ",
+    "hich cn e recst in terms o M⋆rther thn Mgas using utions  nd . ig. shos the M⋆reltion gien  ution (<>) or integer redshits in the rnge z = 0 − 6 nd the osered reltions rom (<>)hiter et l. (<>) or z ˘ 0  nd . he greement eteen our reltion nd those osered or z ˘ 1 nd  is resonle or the msses M⋆& 1011 M⊙ relent to the  popultion. he greement is less good or z ˘ 0 ut s e shll see elo this is unimportnt ecuse the rction o s t z . 1 is smll.  the (<>)hiter et l. (<>) s ere used insted o those clculted rom ution (<>) the z ˘ 0 contriution ould e een smller. ",
+    "n ddition to the  e reuire the dust mss to clculte the summ u densities. o determine the dust mss e must no the gsphse metllicit. sertions he demonstrted tht metllicit increses ith stellr mss this reltionship hs een constrined or redshits z ˘ 0 − 3.5 (<>)remonti et l. (<>) (<>)glio et l. (<>) (<>)r et l. (<>) (<>)ele  llison (<>) (<>)iolino et l. (<>). (<>)iolino et l. (<>) prmeteried the eolution o the mssmetllicit reltion  ith redshit using the orm ",
+    " ",
+    "he determine the lues o log M0 nd K0 t redshits z = ",
+    ". . . nd . using the osertions o (<>)ele  llison (<>) (<>)glio et l. (<>) (<>)r et l. (<>) nd their on or respectiel. o crudel cpture the eolution o the  ith redshit e t the lues o log M0 nd K0 gien in le  o (<>)iolino et l. (<>) s poer ls in (1 + z) the result is log M0(z) ˇ 11.07(1 + z)0.094 nd K0(z) ˇ 9.09(1 + z)−0.017 . ",
+    "he ",
+    "e ssume the dust mss is proportionl to the gsphse metl mss Md= MgasZfdtm. hus ",
+    "here e use  dusttometl rtio fdtm = 0.4 (<>)e (<>) (<>)mes et l. (<>). ",
+    "otited  eution  o  e t the summ u densities o our simulted glies s poer ls in  nd Md. e nd tht ",
+    "S1.1 = 0.35 mJy ",
+    " ",
+    " ",
+    "is ccurte to ithin 0.13 de or z ˘ 1 − 6. he u or glies t z . 0.5 is underestimted signicntl  these eutions ut such glies contriute little to the oerll counts ecuse o the smller cosmologicl olume proed nd the signicntl loer gs rctions nd s so this underestimte is unimportnt or our results. he summ u is insensitie to redshit in this redshit rnge ecuse s redshit increses the decrese in u cused  the incresed luminosit distnce is lmost ectl cncelled  the increse in u cused  the restrme elength moing closer to the pe o the dust emission this eect is reerred to s the negtie  correction see e.g. (<>)lin et l. (<>).  comining utions (<>) nd (<>) ith utions (<>) nd (<>) e cn clculte S850(M⋆,z) nd S1.1(M⋆, z) ",
+    "Figure 3. seredrme µm S850 top nd .mm S1.1 ottom u densit in m ersus M⋆( M⊙) or isolted discs t integer redshits in the rnge z = 1 −6 see utions (<>) nd (<>). he summ u o  disc o ed M⋆increses ith redshit or to resons: . s shon in ig. (<>) the normlistion o the M⋆reltion increses ith redshit. . or ed M⋆ gs rction increses ith redshit. or ed Z  higher gs rction corresponds to  higher gsphse metl mss. oeer ecuse the normlistion o the  decreses s z increses the increse o the gsphse metl mss ith gs rction is prtill mitigted. oth the incresed  nd incresed dust mss cuse the summ u to increse. ",
+    "here e cn sustitute the pproprite epressions or Mgas Re nd Z to epress S850 nd S1.1 in terms o M⋆nd z onl. ",
+    " ",
+    "ig. shos the S850 − M⋆nd S1.1 − M⋆reltions gien  utions (<>) nd (<>) respectiel or isolted discs t integer redshits in the rnge z = 1 − 6. s redshit increses glies ecome more gsrich nd compct oth eects cuse the  or  gien M⋆to increse see ig. (<>). or ed Z  higher gs rction corresponds to  higher gsphse metl mss. oeer ecuse the normlistion o the  decreses s z increses the increse o the gsphse metl mss ith gs rction is prtill mitigted.8 (<>)he incresed  nd Md oth result in  higher summ u or  gien M⋆. o produce n isolted disc  S850 & 3 − 5 m or S1.1 & 1 − 2 m t z ˘ 2 − 3 e re",
+    "uire M⋆& 1011 M⊙. his lue is consistent ith the results o (<>)ichosi et l. (<>) (<>). ",
+    "ote lso tht e cn use these reltions to clculte the epected S850/S1.1 rtio S850/S1.1 ˇ 2.3 this is similr to osertionl estimtes e.g. (<>)ustermnn et l. (<>). or simplicit e ill use this rtio to derie pproimte S850 lues to lso sho n S850 is on the relent plots. "
+  ],
+  "4.2.2 Infall-stage galaxy-pair SMGs ": [
+    "uring the inll stge o  merger the discs re dominted  uiescent str ormtion tht ould occur een i the ere not merging. nl or nucler seprtion . 10 pc9 (<>)do the discs he s tht re signicntl eleted  the mutul tidl interctions  this result is consistent ith osered  eletions in mergers e.g. (<>)cudder et l. (<>). hus during the inll stge e ssume the discs re in  sted stte i.e. the he constnt  nd dust mss een ithout  source o dditionl gs this is  resonle pproimtion or the inll stge to ithin  ctor o . 2 see g.  o . or  merger o to progenitors ith stellr msses M⋆,1 nd M⋆,2 the totl u densit is Sλ= Sλ(M⋆,1) + Sλ(M⋆,2). he tpicl em sies o singledish summ telescopes re  or ˘ 130 pc t z ˘ 2 − 3 schemticll hen the proected seprtion is less thn this distnce the sources re lended into  single source. 10 (<>)o predict singledish counts e ssume the glies should e treted s  single source i the phsicl seprtion is < 100 pc. rom our simultions hich use cosmologicll motited orits e nd tht this timescle is o order ˘ 500 r. hough the timescle depends slightl on the mostmssieprogenitor mss e neglect this dependence ecuse it is sudominnt to rious other uncertinties. oeer this timescle is deried rom the z ˘ 2 − 3 simultions nd thus m e too long or mergers t higher z. ien the oe ssumptions the dut ccle or  gien Sλ′nd merger descried  moremssie progenitor mss M⋆,1 nd stellr mss rtio µ = M⋆,2/M⋆,1 is . r i Sλ(M⋆,1) + Sλ(M⋆,1µ) > Sλ′nd  otherise. ith the dut ccle in hnd e cn use utions (<>) nd (<>) to clculte the predicted numer densit nd counts. ",
+    "o predict counts or  e simpl ssume tht the to discs re resoled into indiidul sources nd thus tret them s to isolted disc glies s descried elo. "
+  ],
+  "4.2.3 Isolated disc counts ": [
+    " ",
+    "",
+    "or  gien Sλnd z e inert the Sλ(M⋆, z) unctions utions nd  to clculte the minimum M⋆reuired or  gl t redshit z to he summ u densit > Sλ M⋆(Sλ|z). o clculte the numer densit n(> Sλ,z) e then simpl use the strorming gl  to clculte ",
+    " ",
+    "Figure 4. redicted cumultie numer counts or the unlensed  popultion s osered ith singledish summ telescopes N(> S1.1) in deg−2  ersus S1.1 m. he counts re decomposed into the three  supopultions e model: the green longdshed line corresponds to isolted disc glies the lue dshed to glpir s i.e. inllstge prestrurst mergers nd the red dshdotted to mergerinduced strursts. he lc solid line is the totl or ll  supopultions e model. he model predictions o (<>)ugh et l. (<>) n dotted (<>)rnto et l. (<>) mgent dotted nd (<>)ontnot et l. (<>) mroon dotted re shon or comprison. he points re osered .mm nd nd µm counts see the tet or detils. he nd µm counts he een conerted to .mm counts  ssuming S850/S1.1 ≈S870/S1.1 = 2.3. his rtio hs lso een used to sho the pproimte S850 on the top is. he htched re shos the regime here e lensing is epected to signicntl oost the counts or oerdense elds (<>)retg et l. (<>). he counts predicted  our model gree er ell ith the counts tht re not thought to e oosted signicntl  lensing. .. he steepness o the cuto in the strurst counts t S1.1 & 4 m is rticil see the tet or detils. ",
+    "nd e use ution (<>) to clculte the predicted counts. o predict counts or singledish summ telescopes here the glpir s re lended into  single source e sutrct the rction o glies ith M⋆> M⋆(Sλ|z) tht re in mergers rom the isolted disc counts to oid doule counting. "
+  ],
+  "5 RESULTS ": [
+    "ere e present the e results o this or the  cumultie numer counts the reltie contriutions o the supopultions nd the redshit distriution predicted  our model. e ocus on the  (<>)ilson et l. (<>) .mm counts here ecuse to our noledge the estconstrined lneld counts i.e. those rom the deepest nd idest sures he een determined using tht instrument (<>)ustermnn et l. (<>) (<>)retg et l. (<>). oeer ecuse or our simulted s S850/S1.1 = 2.3 to ithin ˘ 30 per cent e cn esil conert the .mm counts to µm counts. hus e include oth S1.1 nd S850 lues on the relent plots nd conert osered µm counts to .mm counts  ssuming the sme rtio holds or rel s. "
+  ],
+  "5.1 SMG number counts for single-dish observations ": [
+    "ig. (<>) shos the totl cumultie .mm numer counts lc solid line hich re clculted rom the cumultie numer densit using ution (<>). e decompose the counts into isolted ",
+    "discs green longdshed gl pirs lue dshed nd strursts induced t merger colescence red dshdotted the reltie contriution o ech supopultion is discussed in ection (<>).. he dt points in ig. (<>) re osered counts rom rious sures: .mm counts rom (<>)retg et l. (<>) circles (<>)ustermnn et l. (<>) sures (<>)tsude et l. (<>) dimonds nd (<>)cott et l. (<>) tringles µm counts rom (<>)nudsen et l. (<>) steriss nd (<>)emco et l. (<>) plus signs nd µm counts rom (<>)ei et l. (<>) s. he nd µm counts he een conerted to .mm counts  ssuming S850/S1.1 ˇ S870/S1.1 = 2.3. he model predictions o (<>)ugh et l. (<>) (<>)rnto et l. (<>) nd (<>)ontnot et l. (<>) re shon or comprison. ",
+    "he predicted nd osered counts re in good greement t the loest ues ut the predicted counts re less thn some o those osered t the right end. he (<>)ustermnn et l. (<>) nd (<>)retg et l. (<>) sures re the to lrgest ˘ 0.7 deg−2 so their counts should e lest ected  cosmic rince nd thus most roust. hus it is encourging tht the greement eteen our predicted counts nd those o (<>)ustermnn et l. (<>) is er good t ll ues. he disgreement eteen our predicted counts nd those osered  (<>)retg et l. (<>) is signicnt een or the loer u ins  ctor o ˘ 2 or the S1.1 > 2 m in. oeer (<>)retg et l. (<>) conclude tht the ecess o sources t S1.1 & 5 m compred ith the  eld osered  (<>)ustermnn et l. (<>) is cused  sources modertel mplied  glgl nd glgroup lensing. t higher ues the eect o lensing is more signicnt (<>)egrello et l. (<>) (<>)cig et l. (<>) (<>)im et l. (<>) nd it ould e incredil dicult to eplin the sources ith mm u densit >> 10 m osered  (<>)ieir et l. (<>) nd (<>)egrello et l. (<>) i the re not strongl lensed. e do not include the eects o grittionl lensing in our model so it is unsurprising tht e signiicntl underpredict the counts o (<>)retg et l. (<>) despite the ecellent greement eteen our counts nd those osered  (<>)ustermnn et l. (<>). ",
+    "dditionll it is importnt to note tht the steepness o the cuto in the strurst counts t S1.1 & 4 m is rticil: ecuse e determine the ues o the isolted discs nd gl pirs in n nltic  e cn etrpolte to ritrril high msses or those popultions. or the strursts hoeer e re limited  the prmeter spce spnned  our merger simultions. one o our strurst s rech S1.1 > 6.5 m or S850 & 15 m so the dut ccle or ll strursts or S1.1 > 6.5 m is ero.  e ere to simulte  gl more mssie thn our most mssie model  the simultion ould rech  correspondingl higher u so the predicted counts or S1.1 > 6.5 m ould no longer e ero. oeer the rrit o such oects does not usti the dditionl computtionl epense. hus or S1.1 & 4 m or S850 & 9 m the strurst counts should e considered  loer limit.  simple etrpoltion rom the loeru strurst counts suggests tht our model m een oerpredict the counts o the rightest sources. oeer the osered numer densit o sources ith S1.1 & 5 m is highl uncertin ecuse o the eects o smll numer sttistics cosmic rince nd lensing nd the uncertint in the model prediction is signicnt ecuse o uncertinties in the undnces nd merger rtes o such etreme sstems. hus the counts or the rightest sources should e interpreted ith cution. ",
+    "urthermore e do not ttempt to model some other potentil contriutions to the  popultion. n prticulr e do not include contriutions rom mergers o more thn to discs clus",
+    "Table 4. ingledishdetected  cumultie numer counts ",
+    "Figure 5. rctionl contriution o ech supopultion to the totl cumultie counts ersus S1.1. he lines re the sme s in ig. (<>). t the loest ues the isolted discs dominte heres t the highest ues the strursts dominte. he gl pirs re ∼ per cent o the popultion t ll ues plotted here. ",
+    "ters or phsicll unrelted sources lended into  single summ source see (<>)ng et l. (<>) or eidence o the lst tpe. ",
+    "ien these cets nd the modelling uncertinties our predicted counts re clerl consistent ith those osered nd including lensing nd the preiousl mentioned dditionl possile contriutions to the  popultion ould tend to increse the numer counts. lso e stress tht our model is consertie in the sense tht it uses  roup  rther thn tophe or t   nd is tied to osertions heneer possile. he consistenc o the predicted nd osered counts suggests tht the osered  counts m not proide eidence or  rition this ill e discussed in detil in ection (<>).. "
+  ],
+  "5.2 Relative contributions of the subpopulations ": [
+    "n preious or  (<>)rd et l. (<>)  e rgued tht the  popultion is not eclusiel ltestge mergerinduced strursts ut rther  heterogeneous collection o strursts inll",
+    "stge mergers glpir s nd isolted discs. oeer so r e he onl presented the phsicl resons one should epect such heterogeneit. t is crucil to unti the reltie importnce o ech supopultion so e do this no. ",
+    "he counts shon in ig. (<>) re diided into supopultions ut the reltie contriutions cn e red more esil rom ig. (<>) hich shos the rctionl contriution o ech supopultion to the totl cumultie counts. t the loest ues the isolted disc contriution is the most signicnt. t S1.1 ˘ 0.8 m S850 ˘ 2 m the three supopultions contriute lmost eull. s epected rom conentionl isdom the strursts dominte t the highest ues. oeer contrr to conentionl isdom the right s re not eclusiel mergerinduced strursts: rom ig. (<>) e see tht t ll ues plotted the gl pirs ccount or ˘  per cent o the totl predicted counts so the re  signiicnt supopultion o s in our model. s eplined in  the glpir s re not phsicll nlogous to the mergerinduced strurst s thus their potentill signicnt contriution to the  popultion cn complicte phsicl interprettion o the osered properties o s. ",
+    "t is interesting to compre the reltie contriutions o the isolted disc nd glpir supopultions ecuse the reltie contriutions cn e understood  t lest schemticll  in  simple mnner. or  mor merger o to glies ith M⋆= Miso the u o the resulting glpir  is pproimtel tice tht o the indiidul isolted discs 2S1.1(Miso). ecuse S1.1 depends sulinerl on M⋆see ig. (<>) or n isolted disc to he S1.1 eul to tht o the gl pir it must he M⋆& 3Miso. hus the reltie contriution o the to supopultions depends on hether the numer densit o M⋆= 3Miso discs diided  tht o M⋆= Miso discs n(3Miso)/n(Miso) is greter thn the rction o M⋆= Miso discs undergoing  mor merger hich is the merger rte times the dut ccle o the inll phse ˘ r.  the ormer is lrger the M⋆= 3Miso discs ill dominte the pirs o M⋆= Miso discs heres i the merger rction is higher thn the reltie numer densit the gl pirs ill dominte. ",
+    "he ltter scenrio is liel or right s hich re on the eponentil til o the . or emple t z ˘ 2 − 3  gl ith M⋆= 1011 M⊙undergoes ˘ 0.3 mergers per ",
+    "r. hus i e ssume  dut ccle o  r or the glpir phse pproimtel  per cent o such glies ill e in gl pirs. or the (<>)rchesini et l. (<>)  the numer densit o M⋆= 3 × 1011 M⊙glies is ˘ 8 per cent tht o M⋆= 1011 M⊙glies. hereore  the oe logic the pirs o M⋆= 1011 M⊙glies ill contriute more to the summ counts thn the isolted M⋆= 3 × 1011 M⊙discs. his simple rgument demonstrtes h the gl pirs ecome dominnt oer the isolted discs or S1.1 & 0.7 m S850 & 1.6 m. oeer the threshold or dominnce depends on oth the S1.1 −M⋆scling nd the shpe o the  t the highmss end. hus osertionll constrining the rction o the  popultion tht is gl pirs cn proide useul constrints on oth the summ uM⋆reltion nd the shpe o the mssie end o the . ",
+    "nortuntel the reltie contriution o the strurst supopultion cnnot e eplined in s simple  mnner. he dut ccles or the mergerinduced strursts depend sensitiel on progenitor mss nd merger mss rtio so the mpping rom merger rte to numer densit is not s simple s it is or the isolted discs nd gl pirs. ortuntel the  uncertint hich is er signicnt or the oerll counts is reltiel unimportnt or the reltie contriution o strursts nd gl pirs. hus the reltie contriutions o strursts nd gl pirs depend primril on their reltie dut ccles. o chiee  gien u densit one reuires  less mssie strurst thn gl pir ecuse the strurst increses the summ u densit modertel. hus the reltie numer densit lso mtters. oeer the inecienc o strursts t incresing the summ u densit o the sstem preents signicntl less mssie ut more common strursts rom dominting oer more mssie nd rrer gl pirs. he dut ccles re uncertin ut gien tht in our ducil model the gl pirs contriute ˘ 30 − 50 per cent o the totl counts nd the uncertint in the dut ccles is denitel less thn  ctor o 2 − 3 the prediction tht oth the strurst nd gl pir supopultions re signicnt i.e. more thn  e per cent o the popultion is roust. ",
+    "hough there he een mn osertionl hints suggesting the importnce o the glpir contriution see  nd  or discussion the phsicl importnce o this supopultion hs to dte not een ull pprecited nd the rctionl contriution o glpir s to the totl counts remins reltiel poorl constrined. oeer cler osertionl eidence supporting the signicnce o this supopultion is ccumulting: o the  s presented in (<>)ngel et l. (<>)  he  emission tht is resoled into to components ith inemtics consistent ith to merging discs. n to o the cses the proected seprtion o the to components is > 20 pc such oects re prime emples o the glpir supopultion. ee lso (<>)cconi et l. (<>) (<>) (<>)othell et l. (<>) (<>)iechers et l. (<>)(<>). (<>)molcic et l. (<>) presented  lrger smple o s ith summintererometric detections. he ound tht hen osered ith intererometers ith . 2 resolution ˘ 15 − 40 per cent o singledish s ere resoled into multiple sources hich is consistent ith our prediction or the reltie contriution o the glpir supopultion.  osertions ill signiicntl increse the numer o s osered ith ˘ 0.5 resolution nd thus etter constrin the glpir contriution to the  popultion. ",
+    "urther eidence or  glpir contriution consistent ith ht e predict is the rction o the s ith multiple counterprts t other elengths. ne o the erliest osertionl indictions o this popultion cme rom the  m sure: o ",
+    "Figure 6. op: the predicted redshit distriution o .mm sources ith S1.1 > 1.5 m S850 & 3.5 m lc solid line compred ith the osered distriution rom (<>)un et l. (<>) lue dshed line. he men redshits re . nd . or the model nd osered s respectiel. ottom: the predicted redshit distriution or sources ith S1.1 > 4 m S850 & 9 m lc solid line compred ith the osered distriution rom (<>)molcic et l. (<>) lue dshed line. he men redshits re . nd . or the model nd osered s respectiel. n oth pnels the u limits ere chosen to pproimtel mtch those o the osertions. he righter s tend to e t higher redshits. ",
+    "this smple o µm sources (<>)ison et l. (<>) ound tht ˘ 25 per cent he multiple rdio counterprts. pproimtel ten per cent o the  µm (<>)ope et l. (<>)  .mm (<>)hpin et l. (<>)  −µm (<>)ison et l. (<>) (<>)lements et l. (<>) nd  .mm (<>)un et l. (<>) sources he multiple counterprts. hese rctions re someht smller thn the ˘  per cent contriution shon in ig. (<>) ut oth the predicted nd osered rctions re uncertin. s eplined oe the predicted rction depends sensitiel on the shpe o the upperend o the  nd the reltion eteen summ u nd M⋆. sertions on the other hnd m miss the more idel seprted counterprts nd cses hen one o the counterprts is signicntl more oscured or is rdiouiet. "
+  ],
+  "5.3 Redshift distribution ": [
+    "n ddition to the numer counts  successul model or the  popultion must reproduce the redshit distriution. ig. (<>) shos the redshit distriution o .mm sources predicted  our model or dierent .mm u cuts S1.1 > 1.5 m or S850 & 3.5 ",
+    "Table 5. ingledishdetected  redshit distriution ",
+    "m in the top pnel nd S1.1 > 4 m or S850 & 9 m in the ottom long ith some osered distriutions tht he similr u limits. he redshit distriutions re reltiel rod nd the pe in the rnge z ˘ 2 − 4 nd decline t loer nd higher redshits. he S1.1 > 1.5 m sources he men redshit . heres the S1.1 > 4 m sources he men redshit . so there is  tendenc or the righter sources to e t higher redshits this trend grees ith osertions (<>)ison et l. (<>) (<>)un et l. (<>) (<>)molcic et l. (<>). ",
+    "or the S1.1 > 1.5 m s top pnel o ig. (<>) compred ith the osertions our model predicts  higher men redshit nd  greter rction o s t z ˘ 3 − 4. his discrepnc m suggest tht the etrpoltion o the (<>)ontn et l. (<>)  e use or z > 3.75 oerpredicts the numer o mssie glies t the highest redshits. urthermore merger timescles m e shorter t high redshit nd the dust content m e loer thn in our models oth o these eects ould decrese the highredshit contriution. dditionll constrining the redshit distriution is complicted  selection eects counterprt identiction nd in some cses  lc o spectroscopic redshits. picll the selection eects nd counterprt identiction me identiing higherredshit s more dicult. inll the signicnt dierences mongst osered distriutions see (<>)molcic et l. (<>) or discussion demonstrte the dicult o determining the redshit distriution. hus the dierences in the distriutions m not e signicnt spectroscopic olloup o  sources should clri this issue ut note tht the redshit distriution o  sources hich is shon in the net section should dier slightl. he tpicl redshit or the righter s ottom pnel o ig. (<>) is lso someht higher thn tht osered . compred ith . nd the pe t z ˘ 1 − 2 is not reproduced. oeer the osered distriution is sed on  smple o  sources so smllnumer sttistics might eplin the dierences. "
+  ],
+  "5.4 Predicted ALMA-detected SMG number counts and redshift distribution ": [
+    "n the oe sections e he presented our model predictions or sures perormed ith singledish summ telescopes such s the ",
+    "Figure 7. redicted cumultie numer counts or the  supopultion osered ith telescopes such s  tht he resolution sucient to resole the glpir supopultion into multiple sources. he green longdshed line corresponds to isolted disc glies the dshdotted red to strursts nd the lc solid to the totl counts. he singledish counts rom ig. (<>) re shon or comprison lue dsh dot dot dot. he top is shos pproimte S850 lues. ecuse some o the right sources ould e resoled into multiple sources ith  the counts o right  sources re s much s  ctor o  less thn the singledish counts. ",
+    "Figure 8. redicted redshit distriutions or detected s ith S1.1 > 1.5 m S850 & 3.5 m lc solid line z¯ = 3.0 nd S1.1 > 4 m S850 & 9 m lue dshed line z¯ = 3.5. s or the singledish sources the righter s tend to lie t higher redshit. ",
+    " or hich the ˘ 15 rcsec em cuses the glpir s to e lended into  single source or much o their eolution.  lrger singledish summ telescopes such s the  nd  re used then the glpir s ill e lended or  smller rction o the inll stge o the merger. hus the dut ccle or the glpir phse ill e shorter nd the numer counts o the right sources conseuentl less. or intererometers ith ngulr resolution . 0.5 rcsec or ˘ 4 pc t z ˘ 2 − 3 such s  essentill ll glpir s ill e resoled into multiple sources ecuse or such seprtions the mergers re tpicll dominted  the strurst mode . hus the gl pirs ould contriute to the numer counts s to uiescentl strorming glies rther thn one lended source. ",
+    "o predict the counts nd redshit distriution o  sources e modi our model  remoing the glpir con",
+    "Table 6. detected  cumultie numer counts ",
+    "Table 7. detected  redshit distriution ",
+    "triution nd redistriuting those glies into the isolted disc supopultion. he predicted cumultie numer counts re shon in ig. (<>) in hich the totl singledish counts re lso plotted or comprison. he lues o the counts nd the rctionl contriutions o the isolted discs nd strursts or rious u ins re gien in le (<>). o cilitte comprison ith osertions the tle includes pproimte u densities or  nds  nd  clculted using the men rtios or our simulted s SALMA−6/S1.1 = 0.8 ± 0.06 nd SALMA−7/S1.1 = 1.6 ± 0.2. ",
+    "s or the singledish counts the isolted discs dominte t the loest ues S1.1 . 1 m or S850 . 2 m nd the rightest sources re predominntl strursts. ecuse the glpir s re resoled into multiple inter sources the cumultie numer counts or detected s re loer t ll ues  ˘ 30 − 50 per cent nd the dierentil counts should e steeper. t ues inter thn those shon or hich the isolted discs completel dominte nd the right sources contriute negligil ",
+    "to the cumultie counts the singledish nd  cumultie counts ill e lmost identicl. his eect hs lso een discussed  (<>)ocs et l. (<>) nd (<>)molcic et l. (<>). ",
+    "he redshit distriutions or to u cuts re shon in ig. (<>) nd the lues re gien in le (<>). he men redshits or the S1.1 > . nd  m S850 & 3.5 nd  m ins re . nd . respectiel. he men lues re lmost identicl to those or the singledish counts nd there is lso the sme tendenc or the rightest s to e t higher redshits. he redshit distriutions re similr ut the distriution or the S1.1 > 4 m sources is less strongl peed thn or the singledish sources. he ltters redshit distriution is more strongl peed ecuse the redshit distriution o the right gl pirs pes t z ˘ 3.5. "
+  ],
+  "6 DISCUSSION ": [],
+  "6.1 Are modi•cations to the IMF required to match the observed SMG counts? ": [
+    "ne o the primr motitions or this or is to reemine the possiilit tht  numer counts proide eidence or  t   (<>)inn et l. (<>) (<>)e et l. (<>). o test this clim e he ssumed the null hpothesis  tht the  in s does not dier rom ht is osered locll  nd used  roup . urthermore our model is constrined to mtch the presentd mss unction  or more ccurtel to not oerproduce z ˘ 0 mssie glies   construction this is n importnt litmus test or puttie models o the  popultion. he counts predicted  our model gree ell ith the osered counts or elds elieed not to e signicntl ected  grittionl lensing e.g. (<>)ustermnn et l. (<>). hus our model does not reuire modictions to the  to mtch the osered counts. s n dditionl chec e crudel pproimte the eect o ring the  in strursts in our model  multipling the summ ues o our strursts  ctors o  to represent  mildl tophe  nd  to represent  t  ecuse this is the ctor pproprite or the  used in  .. rnto prite communiction. ",
+    "ig. (<>) shos the rnge in numer counts predicted or this ",
+    "Figure 9. redicted cumultie numer counts or the unlensed  popultion s osered ith singledish summ telescopes N(> S1.1) in deg−2  ersus S1.1 m here e he crudel pproimted the eects o using  mildl tophe t  in strursts  multipling the .mm u o the strurst s   ctor o  . he region lled ith cn lines indictes the rnge spnned   oost ctors eteen  nd . he counts or our stndrd model hich uses  roup  re shon or comprison. he points nd gre htched region re the sme s in ig. (<>). he strurst nd totl counts re incresed signicntl  the tophe  ut the isolted disc nd gl pir counts re not ected ecuse their ues re not ltered. he strursts dominte the  popultion or S1.1 & 1 m S850 & 2 m. or S1.1 & 2 m S850 & 5 m the mildl tophe  model oerpredicts the counts tht re thought not to e oosted  lensing nd the t  model oerpredicts ll the osered counts hich suggests tht  signicntl tophe  is ruled out. .. he lc o  oost in the counts or S1.1 . 1 m is rticil see the tet or detils. ",
+    "rnge o  rition. his modiction cuses strursts to completel dominte the counts or S1.1 (S850) & 1 (2) m s is the cse or the  model nd the predicted counts re signicntl greter thn most o the osered counts or unlensed s.11 (<>)t the loer ues the similrit eteen the strursts counts or the rious  ctors is n rticil eect cused  the limited prmeter spce spnned  our simultion suite.  the suite included mergers o loermss glies dopting  tophe  ould cuse them to contriute to the counts t these ues nd thus oost the counts t ll ues. urthermore the strength o the eect t the highest ues is underestimted ecuse o the orementioned rticil cuto o our strurst counts t S1.1 & 4 m see (<>). or detils. ppling the t  ctor cuses the model to signicntl oerpredict ll the osered counts or S1.1 & 2 m S850 & 5 m nd s eplined oe the lc o n eect or loer ues is n rticil conseuence o our merger simultion suite not including loermss glies. he cler conclusion is tht in our model signicnt modiction to the  in strursts is unustied. ",
+    "dmittedl the oe rguments ginst  rition depend on the detils nd ssumptions o our model. oeer there is  much simpler rgument ginst the  in strursts eing t or signicntl tophe: s discussed oe nd in detil ",
+    "in  nd  there is groing osertionl eidence tht  signicnt rction o the singledishdetected  popultion is ttriutle to multiple sources lended into one summ source. n some cses the s re erlstge mergers ith components seprted  & 10 pc see (<>)ngel et l. (<>) nd (<>)iechers et l. (<>)(<>) or ecellent emples. drodnmicl simultions suggest tht t such seprtions  strong strurst is tpicll not induced  this is consistent ith osertions o locl gl pirs e.g. (<>)cudder et l. (<>). hen the glies eentull merge their s ill increse   ctor o  e t the lest tpicll signicntl more or mor mergers ut e ill e consertie nd i the  is t in strursts the summ u per unit  produced ill increse   ctor o ˘ 5. hus the summ u o the glies should increse   ctor o & 10 during the strurst. he reltie dut ccles o the glpir nd strurst phses re similr to ithin  ctor o  e so or  gien mss nd mss rtio the numer densit o strursts nd mergers in the glpir phse should e similr. hus i the summ u is & 10 times greter in the strurst phse thn in the uiescentl strorming glpir phse mergers during the glpir phse should contriute negligil to the right  popultion s is the cse in ig. (<>) een hen  more modest oost  ctor o  is used. his is in str contrdiction ith osertionl eidence. ndeed the eistence o the glpir supopultion is  nturl conseuence o strursts eing er inecient t oosting the summ u o merging glies see the discussion in ection (<>).. he onl mens to circument this rgument is to rgue tht the multiplecomponent s osered re ll strursts ut s eplined oe this is unliel. ",
+    "he oe rgument does not rule out the possiilit o  mildl tophe  in strursts or sstemtic glol eolution o the  ith redshit s suggested  e.g. (<>)n oum (<>) (<>)e (<>) (<>)rnn  e (<>) it onl reuires tht the s in strurst nd glpir s t  gien redshit e similr. urthermore the rgument does not rule out the possiilit o  ottomhe  in strursts hich hs een suggested recentl or locl mssie ellipticls the descendnts o high strursts e.g. (<>)n oum  onro (<>) (<>) (<>)onro  n oum (<>) (<>)opins (<>).  the  ere ottomhe in strursts the scling eteen summ u nd  ould e eer thn ht e he shon in  nd here. he eer scling ould urther increse the contriution o glpir s to the  popultion. nortuntel the model nd osertionl uncertinties re sucientl lrge tht e cnnot use the osered glpir rction to rgue or or ginst  ottomhe  in strursts ut the oe rguments suggest tht  signicntl tophe  is unliel. "
+  ],
+  "6.2 Differences between our model and other work ": [
+    "ecuse e nd tht contrr to some preious suggestions  (<>)inn et l. (<>) (<>)e et l. (<>)  tophe  is not reuired to mtch the osered  counts it is orthhile to emine h our results dier rom those ors. here re multiple resons our results m dier: the cosmologicl contet undnces nd merger rtes the eolution o  nd dust mss or indiidul mergers the rditie trnser clcultion the eects o lending nd dierences in the osered counts used. e eplore these in turn no. "
+  ],
+  "6.2.1 Radiative transfer calculation ": [
+    "n  e demonstrted tht the summ u densit o our simulted glies cn e ell prmeteried s  poer l in  nd dust mss see utions (<>) nd (<>).  the sme reltion does not hold in the  model then dierences in the rditie trnser m e one cuse o the discrepnc eteen our counts nd theirs. hile e he een unle to compre directl ith the  model e he compred our results ith those o   tht uses  similr rditie trnser tretment (<>)enson (<>). e nd tht reltions similr to utions (<>) nd (<>) hold or the s in the  so it ppers tht the rditie trnser is not the primr cuse o the discrepnc een though some spects o the rditie trnser dier signicntl e.g. the geometr used in the  clcultions is ten directl rom the   simultions heres the geometr ssumed   is nlticll specied nd imuthll smmetric the  clcultions include  suresolution model or oscurtion rom the irth clouds round oung strs ut e opt not to use the corresponding suresolution model tht is implemented in  (<>)roes et l. (<>) or the resons discussed in sections .. nd . o . ",
+    "(<>)e et l. (<>) did not perorm rditie trnser insted the ssumed tht the most rpidl strorming glies in their simultion ere s. oeer s noted preiousl  this simple nst is not necessril true ecuse o dierences in dust mss mongst glies nd the eects o lending. hus i dust rditie trnser ere perormed in or our tting unctions ere pplied to the (<>)e et l. (<>) simultions the conclusions might dier. "
+  ],
+  "6.2.2 Merger evolution ": [
+    "erhps the time eolution o the  or dust mss in the   nd our model diers.  prmeterie the  in ursts s M˙ ⋆= Mgas,c/˝⋆ here Mgas,c is the cold gs mss nd ˝⋆is   timescle gien  ˝⋆= max[fdyn˝dyn, ˝⋆burst,min]. ere fdyn = 50 ˝dyn is the dnmicl time o the nel ormed spheroid nd ˝⋆burst,min = 0.2 r. he mor merger shon in g.  o  hs Mgas ˘ 1011 M⊙hen the glies re t colescence. et us suppose tht ll the gs is cold. hen the mimum  possile gie the  prescription is 1011 M⊙/0.2 r   M⊙yr−1  ˘ 9 times less thn tht o the simultion.  the dust mss is ept constnt utions (<>) nd (<>) impl tht  ctor o  decrese in  results in  ctor o ˘ 2.5 decrese in summ u hich ould signicntl ect the predicted counts. his is o course onl  crude comprison ut it demonstrtes tht the s o strursts in the  model m disgree ith those in our simultions nd dierences in the dust content m lso e importnt. ",
+    "urther eidence tht the phsicl modelling o mergerinduced strursts m ccount or some o the discrepnc is proided  the dierent importnce o strursts in the to models. n the  model strursts dominte the summ counts   lrge mrgin nd contriute signicntl to the  densit o the unierse the dominte oer uiescentl strorming discs or z & 3. n our model isolted discs dominte the summ counts t the loest summ ues nd uiescentl strorming glpir s proide  signicnt contriution to the right counts. urthermore in our model mergerinduced strursts ccount or . 5 per cent o the  densit o the unierse t ll redshits (<>)opins et l. (<>)c this is consistent ith the strurstmode contriution inerred rom the stellr densities surce rightness ",
+    "proles inemtics nd stellr popultions o osered merger remnnts (<>)opins et l. (<>) (<>)(<>) (<>)opins  ernuist (<>). ",
+    "ierences in the s o mergers m lso contriute to the discrepnc eteen our model nd tht o (<>)e et l. (<>). t is not cler tht the resolution o the (<>)e et l. (<>) simultion 3.75h−1 pc comoing is sucient to resole the tidl torues tht drie mergerinduced strursts.  it is not the s during mergers o their simulted glies ould e underestimted nd prt o the discrepnc eteen their simulted s s nd those osered could e ttriuted to resolution rther thn  rition. urthermore their ind prescription m rticill suppress the  enhncement in mergerinduced strursts (<>)opins et l. (<>). ig.  o (<>)e et l. (<>) shos tht all their simulted glies lie signicntl under the osered M⋆reltion so it is perhps not surprising tht the cnnot reproduce the s o s hich re  mi o mergerinduced strursts tht re outliers rom the M⋆reltion nd er mssie uiescentl strorming glies tht lie ner the reltion  (<>)gnelli et l. (<>) (<>)ichosi et l. (<>). "
+  ],
+  "6.2.3 Cosmological context ": [
+    "he third mor component o the models tht cn disgree is the cosmologicl contet hich includes the  nd merger rtes. n (<>)rd (<>) e demonstrted tht the predicted numer densities nd redshit distriution o isolted disc s re er sensitie to the ssumed . hus it is orthhile to compre the  in the s to the osertionll deried  e he used. hile  direct comprison o the   to those in the literture is complicted  the  models use o the t  in strursts see section . o (<>)ce et l. (<>) (<>)inn et l. (<>) he shon tht the  model underpredicts the restrme Knd ues o s hich suggests the msses o their model s re loer thn osered. his ould e  nturl result o n underprediction o the undnce o mssie glies. ",
+    " the  model underpredicts the  then the must compenste  ming the strurst contriution signicntl higher the do this  enling er gsrich minor mergers to cuse strong strursts in their model minor mergers hich onl produce  strurst i the mostmssie progenitor hs ronic gs rction greter thn  per cent ccount or pproimtel threeurters o the  popultion (<>)onle et l. (<>) nd  modiing the  in strursts such tht or  gien  the produce signicntl greter summ u. n underprediction o the undnce o ll mssie glies nd suseuent need to strongl oost the strurst contriution ould eplin h the reltie contriutions o strursts nd uiescentl strorming glies dier so signicntl. "
+  ],
+  "6.2.4 Blending ": [
+    "n dditionl reson or the discrepnc is tht neither  nor (<>)e et l. (<>) ccount or the lending o multiple glies into one summ source hich cn e signicnt or oth merging discs   nd phsicll unrelted glies (<>)ng et l. (<>). ur model suggest tht glpir s cn ccount or ˘ 30 − 50 per cent o the  popultion ttriutle to isolted discs nd mergers. he tpes o sources (<>)ng et l. (<>) osered could lso e importnt. hus not ccounting or lending could ccount or  ctor o ˘ 2 discrepnc eteen the predicted nd osered counts. "
+  ],
+  "6.2.5 Revised counts ": [
+    "inll  compred ith nd (<>)e et l. (<>) utilised numer counts tht he since een superseded  sures coering signicntl lrger res. he ne counts re s much s  ctor o  loer thn those o e.g. (<>)hpmn et l. (<>) so the dierence in counts is nother nontriil ctor tht cn eplin prt o the discrepnc eteen our conclusion nd tht o some preious ors. "
+  ],
+  "6.3 Uncertainties in and limitations of our model ": [
+    "ur model hs seerl dntges: the  enles us to isolte possile discrepncies eteen our model nd other or tht originte rom dierences in the dnmicl eolution o gl mergers nd the dust rditie trnser clcultion rther thn more generl issues such s n oerll underprediction o the  t z ˘ 2−4.  constrining the  nd gs rctions to mtch osertions nd including no dditionl gs in our models e mtch the z ˘ 0 mss unction  construction. ecuse e use  hdrodnmicl simultions comined ith  dust rditie trnser clcultions e cn more ccurtel clculte the dnmicl eolution o glies nd the summ u densities thn cn either s or cosmologicl simultions. urthermore e consertiel ssume  roup  rther thn inoe d hoc modictions to the . ",
+    "oeer our model lso hs seerl limittions: rst computtionl constrints preent us rom running simultions scled to dierent redshits. nsted e scle ll initil disc glies to z ˘ 3. dell e ould run simultions ith structurl prmeters nd gs rctions scled to rious redshits ecuse the rition in the glies phsicl properties ith redshit m cuse the summ light cures to depend on redshit. n uture or e ill run  lrge suite o simultions tht ill more ehustiel smple the relent prmeter spce such  suite could e used to more ccurtel predict the  counts nd redshit distriution. oeer ecuse our predicted counts re dominted  glies t z ˘ 3 our conclusions ould liel not dier ulittiel. ",
+    "econd to he the resolution necessr to perorm ccurte rditie trnser on  sucient numer o simulted glies e must use idelised simultions o isolted disc glies nd mergers rther thn cosmologicl simultions. n principle including gs suppl rom cosmologicl scles e.g. (<>)eres et l. (<>) could chnge the results. oeer such gs suppl is implicitl included in our model or the isolted discs nd glpir supopultions ecuse e use osertionll deried gs rctions or these supopultions. ecuse the dut ccles or mergers re clculted directl rom the merger simultions hich do not include dditionl gs suppl the gs contents nd thus s o the strurst s could e incresed i cosmologicl simultions ere used. oeer ecuse the summ u densit depends onl el on   ctor o  increse in the  increses the summ u densit  ˘ 30 per cent  this ould not chnge our results ulittiel. imilrl dierences in the dust content could ect the results ut  ctor o  decrese in the dust mss decreses the summ u densit  . 50 per cent. ",
+    "hird our predictions re ected  uncertinties in the osertions used to constrin the model.  prticulr importnce re uncertinties in the normlistion nd shpe o the  hich re especill signicnt t z & 4. or z . 3 the merger rtes predicted  our model re uncertin   ctor o . 3 ut the uncertinties re higher t higher redshits.  decrese in the normlistion o the  or merger rtes ould decrese the counts ",
+    "predicted  our model. oeer the most interesting conclusions ould remin: .l pirs ould still proide  signicnt contriution to the  popultion. . epending on the ctor  hich the undnces re decresed  mildl tophe  might not e ruled out. oeer  t  ould still oerpredict the counts een i the  normlistion nd merger rtes ere decresed  & 10 times hich is surel n oerestimte o the uncertint. ",
+    "ourth e do not include the contriution rom phsicll unrelted i.e. nonmerging glies lended into  single summ source. rom osertions it is non tht such glies contriute to the  popultion (<>)ng et l. (<>). hether such sources contriute signicntl to the popultion is n open uestion tht should e ddressed  otining redshits or s osered ith .  the do contriute signicntl inclusion o this supopultion ould increse the numer counts predicted  our model chnge the reltie contriutions o the supopultions nd potentill lter the redshit distriutions hoeer this ould onl strengthen the eidence ginst  tophe . ",
+    "inll e do not model the eects o grittionl lensing. heres the inter sources re liel dominted  unlensed s the right counts S1.1 & 5 m or S850 & 11.5 m re liel oosted signicntl  lensing (<>)egrello et l. (<>) (<>) (<>)cig et l. (<>) (<>)im et l. (<>) (<>)ieir et l. (<>). urthermore the liel cuse o the discrepnc eteen the counts osered  (<>)ustermnn et l. (<>) nd (<>)retg et l. (<>) is tht the ltter counts re oosted  glgl e lensing see the discussion in (<>)retg et l. (<>) so the discrepnc eteen our predicted counts nd the (<>)retg et l. (<>) counts might e resoled i e included the eects o lensing rom  oreground oerdensit o glies. gin our model predictions re consertie ecuse inclusion o grittionl lensing ould oost the counts thus inclusion o lensing ould strengthen the rgument ginst  tophe . "
+  ],
+  "7 CONCLUSIONS ": [
+    "e he presented  noel method to predict the numer counts nd redshit distriution o s. e comined  simple  ith the results o  hdrodnmicl simultions nd dust rditie trnser to clculte the contriutions o isolted discs gl pirs i.e. inllstge mergers nd ltestge mergerinduced strursts to the  numer counts. ur model is constrined to osertions s much s possile conseuentl e re le to isolte the eects o uncertinties relted the dnmicl eolution o mergers nd the dust rditie trnser  hich re perhps uniuel relent to the  popultion  rom more generl issues tht ect the highredshit gl popultion s  hole such s the . urthermore e he consertiel used  roup  s opposed to t or tophe   ecuse e ish to test hether e cn mtch the osered counts ithout modiing the  rom ht is osered locll. ur principl results re: ",
+    "cept t the loest ues S1.1 . 1 m or S850 . 2 m mergerinduced strursts ccount or the ul o the popultion not ccounted or  glpir s nd the rightest sources re predominntl mergerinduced strursts. hus isolted discs contriute negligil to the right  popultion. he ",
+    "contriution o isolted discs to the  popultion is  roust testle prediction o our model. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "e thn ndre enson omeel e r inn nd oi oshid or comments on the mnuscript cott hpmn ich ichosi ierluigi onco le ope sc oseoom nd osh ounger or useul discussion rlton ugh edric ce io ontnot inuigi rnto ernes molcic el ei nd in un or proiding dt ith hich e he compred nd or useul discussion nd oler pringel or proiding the nonpulic ersion o  used or this or.  cnoledges support rom  tionl cience oundtion rnt .  s supported   through ule elloship grnt ..  cnoledges support   grnt rom the . . ec oundtion. he simultions in this pper ere perormed on the dsse cluster supported  the  eserch omputing roup t rrd niersit. "
+  ]
+}

jsons_folder/2013MNRAS.429..799V.json

@@ -0,0 +1,133 @@
+{
+  "ABSTRACT ": [
+    "The spatial distribution of gas matter inside galaxy clusters is not completely smooth, but may host gas clumps associated with substructures. These overdense gas substructures are generally a source of unresolved bias of X-ray observations towards high density gas, but their bright luminosity peaks may be resolved sources within the ICM, that deep X-ray exposures may be (already) capable to detect. In this paper we aim at investigating both features, using a set of high-resolution cosmological simulations with ENZO. First, we monitor how the bias by unresolved gas clumping may yield incorrect estimates of global cluster parameters and affects the measurements of baryon fractions by X-ray observations. We •nd that based on X-ray observations of narrow radial strips, it is dif•cult to recover the real baryon fraction to better than 10 -20 percent uncertainty. Second, we investigated the possibility of observing bright X-ray clumps in the nearby Universe (z 6 0.3). We produced simple mock X-ray observations for several instruments (XMM, Suzaku and ROSAT) and extracted the statistics of potentially detectable bright clumps. Some of the brightest clumps predicted by simulations may already have been already detected in X-ray images with a large •eld of view. However, their small projected size makes it dif•cult to prove their existence based on X-ray morphology only. Preheating, AGN feedback and cosmic rays are found to have little impact on the statistical properties of gas clumps. ",
+    "Key words: galaxy clusters, ICM "
+  ],
+  "1 INTRODUCTION ": [
+    "The properties of gas matter in more than two-thirds of the galaxy cluster volume are still largely unknown. In order to further improve our use of clusters as high-precision cosmological tools, it is therefore necessary to gain insight into the thermodynamics of their outer regions (see (<>)Ettori & Molendi (<>)2011, and references therein). The surface brightness distribution in clusters outskirts has been studied with ROSAT PSPC (e.g. (<>)Eckert et al. (<>)2012, and references therein) and with Chandra (see (<>)Ettori & Balestra (<>)2009, and references therein). A step forward has been the recent observation of a handful of nearby clusters with the Japanese satellite Suzaku that, despite the relatively poor PSF and small •eld of view of its X-ray imaging spectrometer (XIS), bene•ts from the modest background associated to its low-Earth orbit (see results on PKS0745-191, (<>)George et al. (<>)2009; A2204, (<>)Reiprich et al. (<>)2009; ",
+    "A1795, (<>)Bautz et al. (<>)2009; A1413, (<>)Hoshino et al. (<>)2010; A1689, (<>)Kawaharada et al. (<>)2010; Perseus, (<>)Simionescu et al. (<>)2011; Hydra A, (<>)Sato et al. (<>)2012; see also (<>)Akamatsu & Kawahara (<>)2011). The •rst results from Suzaku indicate a •attening and sometimes even an inversion of the entropy pro•le moving outwards. The infall of cool gas from the large-scale structure might cause the assumption of hydrostatic equilibrium to break down in these regions, which could have important implications on cluster mass measurements ((<>)Rasia et al. (<>)2004; (<>)Lau et al. (<>)2009; (<>)Burns et al. (<>)2010). However, as a consequence of the small •eld of view (and of the large solid angle covered from the bright nearby clusters) observations along a few arbitrarily chosen directions often yield very different results. ",
+    "In addition to instrumental effects (e.g. (<>)Eckert et al. (<>)2011), or non-gravitational effects (e.g. (<>)Roncarelli et al. (<>)2006; (<>)Lapi et al. (<>)2010; (<>)Mathews & Guo (<>)2011; (<>)Battaglia et al. (<>)2010; (<>)Vazza et al. (<>)2012; (<>)Bode et al. (<>)2012), there are •simpler• physical reasons to expect that properties of the ICM derived close to ˘ R200 may be ",
+    "more complex than what is expected from idealized cluster models. ",
+    "One effect is cluster triaxiality and asymmetry, which may cause variations in the ICM properties along directions, due to the presence of large-scale •laments in particular sectors of each cluster (e.g. (<>)Vazza et al. (<>)2011c; (<>)Eckert et al. (<>)2012), or to the cluster-to-cluster variance related to the surrounding environment (e.g. (<>)Burns et al. (<>)2010). ",
+    "A second mechanism related to simple gravitational physics is gas clumping, and its possible variations across different directions from the cluster centre ((<>)Mathiesen et al. (<>)1999; (<>)Nagai & Lau (<>)2011). ",
+    "In general, gas clumping may constitute a source of uncertainty in the derivation of properties of galaxy clusters atmospheres since a signi•cant part of detected photons may come from the most clumpy structures of the ICM, which may not be fully representative of the underlying large-scale distribution of gas (e.g. (<>)Roncarelli et al. (<>)2006; (<>)Vazza et al. (<>)2011c). Indeed, a signi•cant fraction of the gas mass in cluster outskirts may be in the form of dense gas clumps, as suggested by recent simulations ((<>)Nagai & Lau (<>)2011). In such clumps the emissivity of the gas is high, leading to an overestimation of the gas density if the assumption of constant density in each shell is made. The recent results of (<>)Nagai & Lau ((<>)2011) and (<>)Eckert et al. ((<>)2012) show that the treatment of gas clumping factor slightly improves the agreement between simulations and observed X-ray pro•les. ",
+    "The gas clumping factor can also bias the derivation of the total hydrostatic gas mass in galaxy clusters at the ˘ 10 percent level ((<>)Mathiesen et al. (<>)1999), and it may as well bias the projected temperature low ((<>)Rasia et al. (<>)2005). Theoretical models of AGN feedback also suggest that overheated clumps of gas may lead to a more ef•cient distribution of energy within cluster cores ((<>)Birnboim & Dekel (<>)2011). ",
+    "Given that the effect of gas clumping may be resolved or unresolved by real X-ray telescopes depending on their effective resolution and sensitivity, in this paper we aim at addressing both kind of effects, with an extensive analysis of a sample of massive (˘ 1015M⊙) galaxy clusters simulated at high spatial and mass resolution (Sec.(<>)2). First, we study in Sec.(<>)3.1 the bias potentially present in cluster pro“les derived without resolving the gas substructures. Second, in Sec.(<>)3.2 we derive the observable distribution of X-ray bright clumps, assuming realistic resolution and sensitivity of several X-ray telescopes. We test the robustness of our results with changing resolution and with additional non-gravitational processes (radiative cooling, cosmic rays, AGN feedback) in Sec.3.3. Our discussion and conclusions are given in Sec.(<>)4. "
+  ],
+  "2 CLUSTER SIMULATIONS ": [
+    "The simulations analysed in this work were produced with the Adaptive Mesh Re•nement code ENZO 1.5, developed by the Laboratory for Computational Astrophysics at the University of California in San Diego 1 (<>)(e.g. (<>)Norman et al. (<>)2007; (<>)Collins et al. (<>)2010, and references therein). We simulated twenty galaxy clusters with masses in the range 6 · 1014 6 M/M⊙6 3 · 1015 , extracted from a total cosmic volume of Lbox ˇ 480 Mpc/h. With the use of a nested grid approach we achieved high mass and spatial resolution in the region of cluster formation: mdm = 6.76 · 108M⊙for the ",
+    "Figure 1. 2-dimensional power spectra of X-ray maps for three simulated clusters at z = 0 (E1, E3B and E15B, as in Fig.(<>)2). Only one projection is considered. The long-dashed lines show the power spectra of the total X-ray image of each cluster, while the solid lines show the spectrum of each image after the average X-ray pro•le has been removed. Zero-padding has been considered to deal with the non-periodic domain of each image. The spectra are given in arbitrary code units, but the relative difference in normalization of each cluster spectrum is kept. The vertical grey line shows our •ltering scale to extract X-ray clumps within each image. ",
+    "Table 1. Main characteristics of the simulated clusters at z = 0. Column 1: identi•cation number; 2: total virial mass (Mvir= MDM + Mgas); 3: virial radius (Rv); 4:dynamical classi“cation: RE=relaxing, ME=merging or MM=major merger; 5: approximate redshift of the last merger event. ",
+    "Figure 2. Top panels: X-ray •ux in the [0.5-2] keV (in [erg/(s · cm2)]) of three simulated clusters of our sample at z=0 (E15B-relax, E1-post merger and E3B-merging). Bottom panels: X-ray ”ux of clumps identi“ed by our procedure (also highlighted with white contours). The inner and outer projected area excluded from our analysis have been shadowed. The area shown within each panel is ∼ 3 × 3 R200 for each object. ",
+    "DM particles and ˘ 25 kpc/h in most of the cluster volume inside the •AMR region• (i.e. ˘ 2 − 3 R200 from the cluster centre, see (<>)Vazza et al. (<>)2010; (<>)Vazza (<>)2011a; (<>)Vazza et al. (<>)2011a for further details). ",
+    "We assumed a concordance CDM cosmology, with 0 = 1.0, B = 0.0441, DM = 0.2139,  = 0.742, Hubble parameter h = 0.72 and a normalization for the primordial density power spectrum of ˙8 = 0.8. Most of the runs we present in this work (Sec.3.1-3.2) neglect radiative cooling, star formation and AGN feedback processes. In Sec.3.3, however, we discuss additional runs where the following non-gravitational processes are modelled: radiative cooling, thermal feedback from AGN, and pressure feedback from cosmic ray particles (CR) injected at cosmological shock waves. ",
+    "For consistency with our previous analysis on the same sample of galaxy clusters ((<>)Vazza et al. (<>)2010, (<>)2011a,(<>)c), we divided our sample in dynamical classes based on the total matter accretion history of each halo for z 6 1.0. First, we monitored the time evolution of the DM+gas mass for every object inside the ŽAMR regionŽ in the range 0.0 6 z 6 1.0. Considering a time lapse of t = 1 Gyr, Žmajor mergerŽ events are detected as total matter accretion episode where M(t + t)/M(t) − 1 > 1/3. The systems with a lower accretion rate were further divided by measuring the ratio between the total kinetic energy of gas motions and the ther-",
+    "mal energy inside the virial radius at z = 0, since this quantity parameter provides an indication of the dynamical activity of a cluster (e.g. (<>)Tormen et al. (<>)1997; (<>)Vazza et al. (<>)2006). Using this proxy, we de•ned as •merging• systems those objects that present an energy ratio > 0.4, but did not experienced a major merger in their past (e.g. they show evidence of ongoing accretion with a companion of comparable size, but the cores of the two systems did not encounter yet). The remaining systems were classi•ed as •relaxed•. According to the above classi•cation scheme, our sample presents 4 relaxed objects, 6 merging objects and 10 post-merger objects. ",
+    "Based on our further analysis of this sample, this classi•cation actually mirrors a different level of dynamical activity in the subgroups, i.e. relaxed systems on average host weaker shocks ((<>)Vazza et al. (<>)2010), they are characterized by a lowest turbulent to thermal energy ratio ((<>)Vazza et al. (<>)2011a), and they are characterized by the smallest amount of azimuthal scatter in the gas properties ((<>)Vazza et al. (<>)2011c; (<>)Eckert et al. (<>)2012). In (<>)Vazza et al. ((<>)2011c) the same sample was also divided based on the analysis of the power ratios from the multi-pole decomposition of the X-ray surface brightness images (P3/P0), and the centroid shift (w), as described by (<>)Bohringer¨ et al. ((<>)2010). These morphological parameters of projected X-ray emission maps were measured inside the innermost projected 1 Mpc2 . This leads to decompose our sample into 9 •non-cool-core-like• (NCC) systems, and 11 •cool-core-",
+    "like• systems (CC), once that •ducial thresholds for the two parameters (as in (<>)Cassano et al. (<>)2010) are set. We report that (with only one exception) the NCC-like class here almost perfectly overlap with the class of post-merger systems of (<>)Vazza et al. ((<>)2010), while the CC-like class contains the relaxed and merging classes of (<>)Vazza et al. ((<>)2010). ",
+    "Table 1 lists of all simulated clusters, along with their main parameters measured at z = 0. All objects of the sample have a •nal total mass > 6 · 1014M⊙, 12 of them having a total mass > 1015M⊙. In the last column, we give the classi“cation of the dynamical state of each cluster at z = 0, and the estimated epoch of the last major merger event (for post-merger systems). "
+  ],
+  "2.1 X-ray emission ": [
+    "We simulated the X-ray •ux (SX) from our clusters, assuming a single temperature plasma in ionization equilibrium within each 3D cell. We use the APEC emission model (e.g. (<>)Smith et al. (<>)2001) to compute the cooling function (T, Z) (where T is the temperature and Z the gas metallicity) inside a given energy band, including continuum and line emission. For each cell in the simulation we assume a constant metallicity of Z/Z⊙= 0.2 (which is a good approximation of the observed metal abundance in cluster outskirts, (<>)Leccardi & Molendi (<>)2008). While line cooling may be to “rst approximation not very relevant for the global description of the hot ICM phase (T ˘ 108K), it may become signi“cant for the emission from clumps, because their virial temperature can be lower than that of the host cluster by a factor ˘ 10. Once the metallicity and the energy band are speci“ed, we compute for each cell the X-ray luminosity, SX= nHne(T, Z)dV , where nHand neare the number density of hydrogen and electrons, respectively, and dV is the volume of the cell. "
+  ],
+  "2.2 De•nition of gas clumps and gas clumping factor ": [
+    "Although the notion of clumps and of the gas clumping factor is often used in the recent literature, an unambiguous de•nition of this is non-trivial 2 (<>). In this work we distinguish between resolved gas clumps (detected with a •ltering of the simulated X-ray maps) and unresolved gas clumping, which we consider as an unavoidable source of bias in the derivation of global cluster parameters from radial pro•les. On the theoretical point of view, gas clumps represent the peaks in the distribution of the gas clumping factor, and can be identi•ed as single •blobs• seen in projection on the cluster atmosphere if they are bright-enough to be detected. While resolved gas clumps are detected with a 2-dimensional •ltering of the simulated X-ray images (based on their brightness contrast with the smooth X-ray cluster emission), the gas clumping factor is usually estimated in the literature within radial shells from the cluster centre. The two approaches are not fully equivalent, and in this paper we address both, showing that in simple non-radiative runs they are closely related phenomena, and present similar dependence on the cluster dynamical state. "
+  ],
+  "2.2.1 Resolved gas clumps ": [
+    "We identify bright gas clumps in our cluster sample by post-processing 2-dimensional mock observations of our clusters. We do not consider instrumental effects of real observations (e.g. degrading spatial resolution at the edge of the •eld of view of observation), in order to provide the estimate of the theoretical maximum amount of bright gas clumps in simulations. Instrumental effects depends on the speci•c features of the different telescope, and are expected to further reduce the rate of detection of such X-ray clumps in real observations. In this section we show our simple technique to preliminary extract gas substructures in our projected maps, using a rather large scale (300 kpc/h). •X-ray bright gas clumps•, in our terminology, correspond to the observable part of these substructures, namely their small (6 50 kpc/h) compact core, which may be detected within the host cluster atmosphere according the effective resolution of observations (Sec.(<>)3.2). ",
+    "Based on the literature (e.g. (<>)Dolag et al. (<>)2005, (<>)2009), the most massive substructures in the ICM have a (3-dimensional) linear scale smaller than < 300−500 kpc/h. We investigated the typical projected size of gas substructures by computing the 2-dimensional power spectra of SXfor our cluster images. In order to remove the signal from the large-scale gas atmosphere we subtracted the average 2-dimensional cluster pro“le from each map. We also applied a zero-padding to take into account the non-periodicity of the domain (see (<>)Vazza et al. (<>)2011a and references therein). The results are shown in Fig.(<>)1 for three representative clusters of the sample at z = 0: the relaxed cluster E15B, the post-merger cluster E1 and the merging system E3B-merging (see also Fig.(<>)2). The long-dashed pro“les show the power spectra of the X-ray image of each cluster, while the solid lines show the spectra after the average 2-dimensional pro“le of each image has been removed. The power spectra show that most of the residual substructures in X-ray are characterized by a spatial frequency of k > 10 − 20, corresponding to typical spatial scales l0 < 300 − 600 kpc/h, similar to three-dimensional results ((<>)Dolag et al. (<>)2009). A dependence on the dynamical state of the host cluster is also visible from the power spectra: the post-merger and the merging clusters have residual X-ray emission with more power also on smaller scales, suggesting the presence of enhanced small-scale structures in such systems. We will investigate this issue in more detail in the next sections. ",
+    "To study the •uctuations of the X-ray •ux as a result of the gas clumps we compute maps of residuals with respect to the X-ray emission smoothed over the scale l0. The map of clumps is then computed with all pixels from the map of the residuals, where the condition SX/SX,smooth > is satis“ed. By imposing l0 = 300 kpc/h (˘ 12 cells) and = 2, all evident gas substructures in the projected X-ray images are captured by the algorithm. We veri“ed that the adoption of a larger or a smaller value of l0 by a factor ˘ 2 does not affect our “nal statistics (Sec.(<>)3.2) in a signi“cant way. In Figure (<>)2 we show the projected X-ray ”ux in the [0.5-2] keV energy range from three representative clusters of the sample (E1-post merger, E3B-merging and E15B-relaxed, in the top panels) at z = 0, and the corresponding maps of clumps detected by our “ltering procedure (lower panels). The visual inspection of the maps show that our “ltering procedure ef“ciently removes large-scale “laments around each cluster, and identi“es blob-like features in the projected X-ray map. The relaxed system shows evidence of enhanced gas clumping along its major axis, which is aligned with the surrounding large-scale “laments. Indeed, although this system is a relaxed one based on its X-ray morphology within R200/2 (based on the measure of X-ray morpho-",
+    " s (<>)ss   (<>)   s     s  (<>)   (<>) s s  ss   s  s ss  s         s s R500  s  s     sss s        s ss     s   s      s   s  s sss    ss "
+  ],
+  "2.2.2 The gas clumping factor ": [
+    "    s   Cρ s      s s     s ",
+    " ",
+    "       s           s ss s R        ss  s       s R    25 kpc/h     ss   ˇ 1.5 R200 s    s   s  s   s s   s s s ss  s ss (<>)s   (<>) (<>)   (<>)    s ss   Cρ(R) s     s   ss  s  ss   s s s s    s s   s    s          s    s   s s  (<>)   s s  s s s    ss   s   s    s   sss  s s   s  s ss  s          ss                6 300 kpc/h ss   s  (<>) s s  s ss s   s s     ss   s       s     s  s s    s        s  s   s s   s      s   s    ss  s s    s  sss  ss "
+  ],
+  "3 RESULTS ": [],
+  "3.1 Gas clumping factor from large-scale structures ": [
+    "     s  ss s          s  s ss     (<>)   (<>) (<>)s   (<>) (<>)   (<>) (<>)   (<>) ",
+    "  s s       s    (<>) ",
+    " ",
+    " ss     Cρ(R)     sss    s     s   sss   s      Cρ< 2 ss s   s   s   s Cρ˘ 3 − 5 s R200 s   ",
+    "Figure 3.     s  s   s  s ss  z = 0   s s  1˙    s s    sss      s   s    s ss ",
+    "sss s  ss     s       s      ss s s  ss    ss  (<>)   (<>)    s   s s   s s   s  (<>)     s  s         s  s s     s   s  s  s        s ss s     s sss    ",
+    "     s  s     s  s s          ss  ss s       s   s  ss     ",
+    " (<>)  s   s  s      s  s s ˆcr,b < 50 50 6 ˆcr,b < 102  102 6 ˆcr,b < 103  ˆcr,b > 103   ˆcr,b s ˆ/(fbˆcr  fb s    ˆcr  s  s  s  T < 106  106 6 T < 107  107 6 T < 108   T > 108   z = 0 ",
+    "         ss   s s s  s   s sss     s s   s s s  s    s s    s s    s  sss 6 300 kpc/h  s s   ss  s  s   s   s s   s s  s   (<>)        s 1 Mpc/h 3 (<>)  (<>)  s s  s ss    ",
+    "Figure 4. Average profiles of gas clumping factor and gas mass distribution for different phases across the whole cluster sample at z = 0, for relaxed clusters (left panels) and for merging clusters (right panels). The average gas clumping factor is computed for different decompositions of the cluster volume in gas­density bins (top 4 panels; lines are colour-coded as described in the legend in the top 2 panels) and temperature bins (bottom 4 panels with colour-coded as detailed in paesl in the third row). The gas over-density is normalized to the cosmological critical baryon density. ",
+    "Figure 5. Top panels  s      ss   s  z = 0      s     s   s   s          s s  s   s  s ss   s  Second row  s   s         ss s  s s s  s   s s  s       s s Third row  s s s   s s s   s Last row s  s s ss    s s  s    s s     s      s   s  ",
+    "Figure 6.  s   s    s  s  s        ss  s    ss  s     Suzaku ROSAT  XMM  s s     s  s s     ss ",
+    "s s   ss  s ss s    s     ss s    s     s s       ss  s  s     sss  s   s s ss     < 106    106 6 T < 107 s  s   sss      s  s s s ss    s    s (<>)          s  ss  ",
+    " s s   ˆcr,b < 50  T 6 106 − 107 s   s s (<>)   (<>) (<>)   (<>) (<>)   (<>)  s  s  s s   s ss s   s              sss s s s  s   s s            s sss   s   s ss   ss    s s  (<>)    s s   ss     s s    s s s      s  s  s s  s   s    sss (<>)s   (<>)   s    s  ss s s     s           s s   s    s sss  ss     s     s   s        s  s s  ss  sss   s    s ss s  ss  ss       s  ss (<>)   (<>) s         s ˘ Gyr   s s ",
+    "  s  s     ss  s s    (<>)   s     s s      s ss s  (<>)  s     s    s s   ss     s   ss   s sss  s        s ss   ss s s s        s  ss s     ss  ss (<>)s   (<>) (<>)   (<>) (<>)   (<>)   s s  s   s s  ss   ˘ 500 kpc s  ss (<>)s   (<>) (<>)   (<>)   s    s ˘ 8 Mpc     s  s ss s ˘ 20     s    s s  s  s   s       ",
+    " s   s       s    s (<>)   (<>) s  R s          s     s    s     s 0.02 R200 6 R 6 R200 ",
+    "   ss s s  s  s     s 0.8R200      s           ˘ R200  s s s ss  s  s       > 0.6R200   s   s s          s s       s       s ss   s s     (<>) ss  s  s s s  s  s  s s s   s   (<>)   (<>) ",
+    " s       s  ss  s    s    sss s   s  (<>)     s  s   s  ss        ˘ 30 − 40   R200    ss s    s s s    (<>)     s s  s > 40         s      s ss ",
+    "s s    s ss  s ss s  s s   s s        s  s     ss   ss (<>)s   (<>) (<>)   (<>) (<>)   (<>) (<>)   (<>) ",
+    " (<>)  s      s   Ygas(< R)  fbar(< R)/fb   s  s  fb s  s      s ",
+    "s  s  Ygas s s  s s s  s       s  s s s s s  s     s     ss sss   ss ",
+    "   ",
+    "",
+    "   ",
+    "",
+    "            s     s  ss (<>)   (<>)    Yg s     s    s  s  R200   s   s < 1.2 R200 s ±5    s    s ±10 − 20     s   ss ",
+    "  s   s   s s     s  ss  s s  s    s     s   s     ±10     s   s   s   ss s   s  s     ˘ 25   ss    s  ss  ss     ss       ˘ 10    ˘ 50 ",
+    "  ss  ss  s     s   ˘ 10 − 20     ss    R200 s     ˘ 5  ",
+    "  ss     s s          s       s   s    s  s      s  (<>)     s s   ss  s s   s   s s      s s s  s          s   s  s  ss  > 0.4 R200    s   s   ",
+    "   s s   Cρ˘ 2 − 3   s ss  s      s   s  s ss   sss   s   s s  s   s  s  s   s   s s      ss          s s  s  s     s   s    s s    s  s       s  s s ss   ss  s s     s  s        ss s    s  s   ss s    s s   s ss  s   s ss   s        ",
+    "s    s        s   s   s   s      s   s    s ss   s > 0.4R200      s   s          s         ss   s  s    ˘ 5−10         s      s   s   ",
+    "s s     s   s s   larger   s    ˘ R200  s  ss (<>)s   (<>) smaller   s   s  ss (<>)   (<>)     s     ss  (<>)   (<>) (<>)   (<>) s ss    s   s  ss s            s   s      ±10 − 20       s  ",
+    "           sss s ss lower  ˘ 30 − 40          s s ss   s s            s  s   s  s  s ss  sss (<>)   (<>) (<>)   (<>)    s  ss s s  s ss s  s  s    s s             lower   s  R ss  s s     s       s s  s s s (<>)   (<>) s s s ss   ",
+    "Figure 8.  s s  s    s  s    ss SX,low = 2·10−15 erg/(s·cm 2) ′′   s s  ≈ 10     s  XMM  s s     s  s s     ss    s s    s   s s            ss  ss   s    ss   s s s    s    ss      ",
+    "ss (<>)   (<>) (<>)   (<>)   s  s s  s  (<>)   (<>)    s s (<>)   (<>)   ss     s s s s s  ss   s   s     s        ss s    s s "
+  ],
+  "3.2 Properties of gas clumps ": [
+    "  ss       s s s  s  s s     s   (<>)   s    s   s     sss    ss  s s    s s    ss  s    ss z = 04 (<>) z = 0.1  z = 0.3       s  / (1 + z)4      s     s  s   s s s    ss   ss SX,low   s  s    s ss        s   ss  s s    ss s    s  s    (<>)Rs   (<>) (<>)   (<>) (<>)   (<>)        s    s s  ssss      s       s  s    s  s s s   s ss   ss  s                 s s      ss s  s  s  s s s ",
+    " s  s ss sss   s  s  s   s  s   (<>)  s  s    s    s ss   s ss  s    s      s  s  ss   SX,low = 2 · 10−15erg/(s · cm2)  XMM ss   SX,low = 3 · 10−14erg/(s · cm2)  ROSAT ss    SX,low = 10−13erg/(s · cm2)  Suzaku ss  s  s        ss   s   XMM s    s ss  s      s s s s        s s  s s  s         s      s s s   ",
+    "s   ss  s   s      ss    ss ˘ 20 − 30  s  ROSATSuzaku  ˘ 102  s  XMM s ss  s  ss  s the whole s s 1.2 × 1.2 R200    s s     s  ˘ 2 − 3         s s  s s    s s   z = 0.3  XMM ss  s  s s ˘ 30  s  s s   s s  s ss s ˘ 5 · 10−12erg/(s · cm2)  Suzaku  ROSAT  ˘ 10−12erg/(s · cm2)  XMM 5 (<>) ",
+    "    s ss    s  ",
+    "Figure 7.  s s  s    s  s    ss SX,low = 2 · 10−15erg/(s · cm2)    s  ≈ 10 ′′    s  XMM      s  s          s   s    s    s   s   s   s   s      s   s     sss    s s   ss        s   ss   s s ss    s   s  sss      ",
+    "z = 0.1 ss  XMM   s  ss ss  s    ",
+    "  (<>)  s  s s   s s                     s    s ss     s  SX6(<>)   s   s        s    s           s      s     s     ",
+    " s ss  s   s  ",
+    " s s  s  s   ss         s  s s   s   ˘ 2−3 s     ss    ˘ 2 − 4 ss   s       ss   s  s s  s sss      ˘ 2 s    sss  s    s  s  s     s  ss  s   ss s    s  s    s  s s s  s s   s s s s   s   s s        s (<>)   (<>)  s    s  s  s 6 50 kpc/h s s s    s   s  ss     s s   s       s  s   s s ss     s ",
+    " (<>)  s     s   s     s          s ss      s s   s 0.6 6 R/R200 6 1.2 s > 70    s   s   s   s s    s  s    ",
+    "Figure 11.    s  s  s s        s s s    ss   R s       (<>)   (<>)  s s s  ss s 0.1 6 R/R200 < 0.6  s s s  s s 0.6 6 R/R200 < 1.2     s  s s   ss   s ss ",
+    "    s    s s ss s s s s       sss     ss   ss ",
+    "       s    ss     s ss  XMM Suzaku ROSAT  Chandra       ss      s   (<>) "
+  ],
+  "3.3 Tests with additional physics and at higher resolution ": [
+    " s   s      s   s  ss  s ",
+    "(<>)   (<>)  s     s  ss       s  s  s s     s  s   s          s (<>)   (<>) R  s       s s             s       s    s  s     s  s    sss          s   s  s  s s   s ss     ss      s ss    s      (<>)   (<>) ",
+    " s s  ssss     ss s  s  s ss   ss s s s s    sss   s ss   s  s    ˘ 3 − 4 · 104  s   s     s s    s      s   ss  s    s  s ss    (<>) (<>)  s     ss   ss  ˘ 2 − 3 · 1014M⊙     ss  s    s  s     s  s       s ss  s     ss   s     s  25 kpc/h        s  s         s   s  z = 1     Wjet ˇ 1044erg/s     s  s         100 keVcm2 s  z = 10    s        s  z = 1     Wjet ˇ 1043erg/s         s   ss    ss  s  s   s      s 12 kpc/h ",
+    " ss       (<>) (<>)     s       s s  (<>)   (<>)        s  s  ss s     s s s s s  s      s    ss  (<>)   (<>)    s    s ss           s      s  s       s     sss       sss s   s    s        s   s ss      s s s ss          s s    sss s  (<>)   (<>)  s    s        s    s    ˘ 2   s s s    s  s 0.1R200   ss  s   s s s  s        ",
+    "   s s s s   (<>)   (<>)  s   s  s s   (<>)  s (<>)  s ss     s   ",
+    "Figure 9.  s    log10LX s   ss   ∼ 3 · 1014M⊙  s s s    s  s  ss    s s    ",
+    "Rs       Ł = 4/3 ss     s s  s     s       s s  s ss       ss  (<>)  s (<>)  ss   Rs  s s s s ˘ 0.05 − 0.1 s R200   s ss  z = 0 ",
+    "  s sss     ss   s    s   s  (<>)  ss (<>) (<>)   (<>) (<>)s   (<>)     s   s s  ss         ss    s s    ",
+    " (<>) ss    s  ss  s   ss     s ",
+    " s s      s s  s s  s     s  s  s  (<>)     s s s     ss  s   ss   s       s s   ss   s   s s    s   s              s     s           s   s  6 0.3R200 s  s       s  s  s   s s   10 − 102 s     s            s         s  ss ss     s   ss       s   s    ",
+    "      s     s    s  R   s ss s      s  sss    s s    s     ss    Rs s    ss       R  s    ˘ 10 − 20   s       s s  s  ss  s   s    Rs   s   s        s s  (<>)       sss   s s       Rs  ss s  ss ",
+    "  s    s s s   s     s     s    s s       s     s  ssss s     s s   s s s     s  s    ss s s   s s  s    sss s    s  (<>)R   (<>) s     s   s       s     s ss  s      ˘ R200  z = 0   s  s    s    ss  s     s     sss s ss  ss   s ss      s   s s  s   s        s   s   s s   s  s  s  s   s s  s   s   ",
+    "Figure 10.  s  s               s   ss  ∼ 2 − 3 · 1014M⊙s  s s s s  s   s R s s s s   s s    s ",
+    "s  s s s s s      s sss s   s          s ss  ss   s    ˘ 2 − 3   s   s s   s     s   s  s  (<>)  s    6 50 kpc/h s  s s   s    s s    s   s s s    s  s  s      s ",
+    " s      s      s  s   ss s ss  (<>)   (<>)    s     s  s    s   s  ss   ss  s      s s    s  ",
+    "   s  ss     s   s   s  s  sss    s    s  s   s    unresolved s s       ss   ss "
+  ],
+  "4 DISCUSSION AND CONCLUSIONS ": [
+    " s   s  s  s s ss  ss  ss    sss  s  s s sss    s    ss   s s sss       s  s ss      s ss  ss ss  s  ",
+    "         s     ss s   ss ",
+    " s  s   s   ss sss ˘ 1015M⊙ s   s     (<>)   (<>) (<>)s   (<>)          s      s    s s    ss   s   s   s   s  s   ss    (<>)   (<>)  s ss     s s s  ss  C(ˆ) ˘ 3 − 5    s   sss  sss      s sss          s      s  s ss  ss   s  s  s s s ss    s  ss    s   s    sss  s s    s   s s  s       s ss       s      s  s     ss   s s    s      s  s   s     s  ±10    sss   ±20   sss  s ss  ss ss   s ",
+    "   s      s s   s  s     s   ss         ss   s    s s s   s     s  s     s  ss   s    s s   s s   s  s   s s s   s    s   s   s    s ss s     ss     s   s s      s   ss  s sss      s  s       s    s   s s   s  sss s     ˘ 2 − 10  s     ss    s  sss   s s ss     s       s   s ss  s   ˘ 0.3         s s      0.6 6 R/R200 6 1.2    s     s   s  s     s < 0.6R/R200     s  s  s s     s 6 50     ss s    ss   s ss   s  Rss     s  s   ss  s   s s R   ss  s   s  (<>)   (<>)     s   ss      s     s   s      sss  s  ss  s  s s  s   s    s   s       ss   s   ˘ 2 − 3       s      ssss     s   ss     ss s   s   ",
+    "s    s s       s          6 50 kpc/h ",
+    "     s   ss   sss   s (<>)  ss           s  s  ss     R     ss      sss     s    ss  s s    ss  s       s s  s < 50 kpc/h   s      ss    s     ss s      s    ",
+    "     s      ss      ss     R ss  (<>)   (<>)  (<>)  s  s    s   ss   R s     s s sss   s   s s   s s   s    s  s ss      s 0.1 6 R/R200 < 0.6  0.6 6 R/R200 < 1.2 ",
+    "    ss    s s ˘ 1.5 − 2 s    s s  s     s s s s  s   s ss  ss  s   s s   ss       s s s s    s  s   s   s       s  ss   ss    s s     s       s s s    ss s    s s    s ss     ss   R s    (<>)   (<>) s  s s sss     ss  R   ss     s s    s ss      ss   ˘ 3 · 10−14erg/(s · cm2)    s ˘ 20/2  s          ss   R     (<>)   (<>)        s  (<>)   (<>)       ss s ˘ 6 − 8 s R200 s s     ss            s s       ˘ 40  R200   s    s  s   s  s         s s    s s  (<>)   (<>) (<>)s   (<>) s       ss           s s   s  ",
+    " s ss   s   s  ss     s s s  ss   s       s       s s   s  s Chandra s   ss  s ss  s s     s  s s    s     s s s       s   s s s      ss ss s s  ss  s s s  s 6 100 − 200 kpc    s   Chandra ss (<>)s   (<>) ",
+    "    ss        s    s    s  s s    s  "
+  ],
+  "ACKNOWLEDGEMENTS ": [
+    "     s s        s     s   R   s sss   s  ss              s                    s s   s  s        s s s           s    s ss s             s s       "
+  ]
+}

jsons_folder/2013MNRAS.429.3068T.json

@@ -0,0 +1,112 @@
+{
+  "ABSTRACT ": [
+    "The presence of a dark matter core in the central kiloparsec of many dwarf galaxies has been a long standing problem in galaxy formation theories based on the standard cold dark matter paradigm. Recent simulations, based on Smooth Particle Hydrodynamics and rather strong feedback recipes have shown that it was indeed possible to form extended dark matter cores using baryonic processes related to a more realistic treatment of the interstellar medium. Using adaptive mesh refinement, together with a new, stronger supernovae feedback scheme that we have recently implemented in the RAMSES code, we show that it is also possible to form a prominent dark matter core within the well-controlled framework of an isolated, initially cuspy, 10 billion solar masses dark matter halo. Although our numerical experiment is idealized, it allows a clean and unambiguous identification of the dark matter core formation process. Our dark matter inner profile is well fitted by a pseudo-isothermal profile with a core radius of 800 pc. The core formation mechanism is consistent with the one proposed recently by Pontzen & Governato. We highlight two key observational predictions of all simulations that find cusp-core transformations: (i) a bursty star formation history (SFH) with peak to trough ratio of 5 to 10 and a duty cycle comparable to the local dynamical time; and (ii) a stellar distribution that is hot with v/σ ∼ 1. We compare the observational properties of our model galaxy with recent measurements of the isolated dwarf WLM. We show that the spatial and kinematical distribution of stars and HI gas are in striking agreement with observations, supporting the fundamental role played by stellar feedback in shaping both the stellar and dark matter distribution. ",
+    "Key words: galaxies: formation, dwarf – cosmology: dark matter – methods: numerical "
+  ],
+  "1 INTRODUCTION ": [
+    "Dwarf galaxies, although very numerous and common in our present day universe, are also very faint and difficult to observe. Nevertheless, it is now established that star formation proceeds at a very inefficient rate in dwarf galaxies, making them ideal laboratories to study the spatial distribution of their parent dark matter halo. Indeed, if dwarf galaxy are dark matter dominated, a stellar kinematic analysis gives direct constraints on the dark matter mass distribution. Although theoretical predictions of pure N-body models favor the formation of a cusp in the inner region of dark matter ha-",
+    "los ((<>)Moore (<>)1994; (<>)Navarro et al. (<>)1997), the observed rotation curve of dwarf and low surface brightness galaxies was shown to be more consistent with a shallower profile, even a constant density core ((<>)de Blok & McGaugh (<>)1997; (<>)de Blok et al. (<>)2001; (<>)de Blok & Bosma (<>)2002; (<>)Kuzio de Naray et al. (<>)2008). This apparent disagreement led to the so-called “cusp-core” problem, a serious challenge for the currently favored Cold Dark Matter (CDM) paradigm ((<>)Moore (<>)1994; (<>)Flores & Pri-(<>)mack (<>)1994). Many solutions to this problem have been proposed in the recent years – for example a warm dark matter particle ((<>)Kuzio de Naray et al. (<>)2010; (<>)Villaescusa-Navarro & (<>)Dalal (<>)2011; (<>)Macci`o et al. (<>)2012) or self-interacting dark matter ((<>)Spergel & Steinhardt (<>)2000; (<>)Rocha et al. (<>)2012) – but the only explanation consistent with CDM relies on the effect of ",
+    "baryonic physics, and more precisely on stellar feedback, to modify substantially the dark matter distribution. ",
+    "(<>)Mashchenko et al. ((<>)2008) were the first to find a cusp-core transformation effect in a cosmological simulation, modeling a dwarf galaxy of mass ∼ 109 M down to redshift z ∼ 5. This has been seen again in more recent work at higher masses and reaching lower redshifts ((<>)Governato et al. (<>)2010; (<>)Macci`o et al. (<>)2012; (<>)Martizzi et al. (<>)2012). A long history of work has looked at the possibility of baryonic physics generating such a transformation: for instance (<>)Navarro et al. ((<>)1996) showed that impulsive mass loss leads to irreversible expansion of orbits near the centre, (<>)Read & Gilmore ((<>)2005) suggested that repeated epochs of outflows could produce a strong enough effect to generate cores and (<>)Mashchenko (<>)et al. ((<>)2006) pointed out that internal bulk motions of gas (not necessarily outflows) could have the same effect. Finally, (<>)Pontzen & Governato ((<>)2012) (hereafter PG12) produced an analytic model of impulsive heating which was able to make quantitative predictions for the rate of cusp flatten-ing, agreeing with the simulated results of (<>)Governato et al. ((<>)2010). This demonstrated that impulsive gas motions were the dominant cause of the simulated cusp-core transformations as opposed to, for example, heating due to dynamical friction (e.g. (<>)El-Zant et al. (<>)2001; (<>)Goerdt et al. (<>)2010). ",
+    "Although cosmological simulations provide realistic environments and mass accretion histories for the model galaxies, they are often challenging to analyze because of their geometrical and evolutionary complexity. Moreover, since they are time consuming, the force resolution is currently limited to ∼ 80 pc, which is only one tenth of the measured core radius ((<>)Governato et al. (<>)2010). It is therefore quite important to perform additional simulations with both a simpler set up and a higher resolution, which is precisely the goal of our paper. In (<>)Mashchenko et al. ((<>)2006), a similar approach was proposed with an isolated NFW halo stirred by 3 arbitrarily moving gas clumps. Although the proposed set-up was quite simplistic, it provided a well controlled experiment of cusp-to-core evolution with a better force resolution of 40 pc. Very recently, (<>)Cloet-Osselaer et al. ((<>)2012) have performed a series of isolated NFW halo simulations with a more realistic treatment of star formation, stellar feedback and the induced gas motions based on the SPH technique. This work, following up on a series of papers reproducing many properties of the gas and stellar distribution in dwarf galaxies ((<>)Valcke et al. (<>)2008; (<>)Schroyen et al. (<>)2011), also confirmed the formation of a dark matter core. ",
+    "In this paper, we will also perform idealized simulations of an isolated NFW halo, with a more realistic treatment of the ISM physics, and, for the first time, with the Adaptive Mesh Refinement (AMR) code RAMSES ((<>)Teyssier (<>)2002). It is indeed important to verify that core formation can also be recovered using a different type of code than the one used so far in all the previously cited papers, namely SPH in two different implementations, GADGET by (<>)Springel ((<>)2005) and GASOLINE by (<>)Wadsley et al. ((<>)2004). As shown by (<>)Agertz (<>)et al. ((<>)2007) and (<>)Wadsley et al. ((<>)2008), both code types suffer from different systematic effects that might affect the numerical solution, especially when trying to resolve the clumpy ISM (see also (<>)Read et al. ((<>)2010) and (<>)Read & Hay-(<>)field ((<>)2012)). ",
+    "The paper is organized as follows: in the first section, we describe the set up of our numerical experiment, with ",
+    "3 different simulations that we would like to compare. We then present and discuss our new stellar feedback implementation in the RAMSES code, which allows us to have a much stronger dynamical effect on the surrounding gas than we were previously able to achieve, without invoking extra sources of energy. In the third section, we present our results, with emphasis put on the dark matter distribution and how the formation of the core correlates with strong potential fluctuations triggered by powerful gas expulsion phases. Finally, we discuss and interpret our results in the light of the recently proposed mechanism by PG12, and confront our findings with observations. "
+  ],
+  "2 SIMULATION SET-UP ": [
+    "We consider an isolated halo in hydrostatic equilibrium with fgas = 15 %. Both gas and dark matter follows the same NFW density profile, with concentration parameter c = 10. The halo circular velocity is chosen to be V200 = 35 km/s, corresponding to the virial radius R200 = 50 kpc (or 35 kpc/h) and the virial mass M200 = 1.4 × 1010 M (or 1010 M/h). The halo is truncated at 112.5 kpc, so that the total enclosed mass is Mtot = 2 × 1010 M. Following now rather standard prescriptions, such as in (<>)Kaufmann et al. ((<>)2007) and (<>)Dubois & Teyssier ((<>)2008), we initialized the gas temperature by solving the hydrostatic equilibrium equation (see Eq. 1 in (<>)Kaufmann et al. (<>)2007, for example), and we set the gaseous halo in slow rotation around the z-axis, using the average angular momentum profile computed from cosmological simulation ((<>)Bullock et al. (<>)2001) and a spin parameter λ = 0.04. For more details on the set-up, the reader can refer to (<>)Dubois & Teyssier ((<>)2008). We use 1 million dark matter particles to sample the phase space of our dark matter halo. Initial positions and velocities were computed using the density-potential pair approach of (<>)Kazantzidis et al. ((<>)2004), later refined by (<>)Read et al. ((<>)2006). To test the stability of our gas-dark matter equilibrium system, we ran a first simulation with only adiabatic gas dynamics, without cooling nor star formation. As can be seen in Figure (<>)1, our dark matter halo is stable during 2 Gyr of evolution and does not deviate by more than 10% from the initial NFW distribution, except within 60 pc from the center (corresponding roughly to twice the cell size), where the deviation can be as high as a factor of 2. ",
+    "All the simulations presented here have been run using the RAMSES code ((<>)Teyssier (<>)2002; (<>)Teyssier et al. (<>)2006; (<>)Fro-(<>)mang et al. (<>)2006). We used a quasi-Lagrangian refinement strategy to build the initial AMR grid, as well as refining and de-refining cells during the course of the simulation: each cell is individually refined if it contains more than 8 dark matter particles or if it contains a baryonic mass (gas mass + star particle mass) larger than 8×mres, where mres = 1500 M. Note that our gas mass resolution corresponds initially to 2 million gas resolution elements across the whole gaseous halo. The box size being set to L = 300 kpc (in our terminology this corresponds to the first AMR level  = 1), we used isolated boundary conditions for the Poisson solver and zero-gradient boundary conditions for the hydro solver. For the latter, we used the HLLC Riemann solver and the MinMod slope limiter (see (<>)Fromang et al. ((<>)2006) for related details). ",
+    "Without cooling and star formation, we do not need to specify a maximum level of resolution: we just let the code refine the grid until it runs out of mass in the smallest AMR cell. In our adiabatic simulation, we have indeed reached “only” level  = 13 at the very centre of the halo, corresponding to a cell size Δx = 36 pc. If cooling and star formation are activated, gas dynamics becomes strongly dissipative and nothing can prevent the collapse. It is therefore crucial to set a maximum level of refinement, or a minimum grid resolution. In this paper, we use max = 14 or Δx = 18 pc, which is only a factor of 2 better than in the dark matter only case, therefore avoiding two-body relaxation in the dark matter component. Our limited spatial resolution requires a careful treatment of our thermal model, in order to avoid numerical difficulties. As is now customary in galaxy and star formation simulations, we use an artificial pressure floor designed to enforce that the effective Jeans length is equal to 4 computational cells ((<>)Truelove et al. (<>)1997). This extra-pressure, equal to PJ  16GΔx2ρ2 , is added to the thermal pressure in the Euler equation, gas cooling being applied only to the thermal internal energy. We use standard H and He cooling ((<>)Katz et al. (<>)1996), with an additional contribution from metals based on the (<>)Sutherland & Dopita ((<>)1993) model above 104 K and metal fine-structure cooling below 104 K as in (<>)Rosen & Bregman ((<>)1995). Metallicity is modeled as a unique, passively advected quantity, noted Z, representing the mass fraction of metals, and seeded by individual supernovae event with a yield y = 0.1. The initial metallicity in the halo is set to Z = 10−3 Z, enabling from the start cooling down to very low temperatures. With these ingredients and for our spatial resolution of 18 pc, gas will cool efficiently down to TJ  600 K and reach a density of nJ  60 H/cc, before hitting the Jeans-length related pressure floor (the index J standing for Jeans-length related quantities). This is a conservative estimate of the maximum gas density we can reach before being affected by finite resolution effects. ",
+    "Star formation (SF) is modeled using a Schmidt law ((<>)Schmidt (<>)1959), for which the SF rate is given by ",
+    "(1) ",
+    "The SF efficiency per free-fall time tff is usually chosen close to a few percent ((<>)Krumholz & Tan (<>)2007); we used here ∗ = 0.01. The density threshold for SF, above which gas is considered to be dense enough to be eligible to form stars, has to be chosen carefully. In order to mimic as closely as possible realistic SF in dense molecular clouds, we want to choose this threshold as high as possible. On the other hand, as discussed previously, the gas density distribution in the simulation will be affected by finite resolution effect close to the Jeans density, in our case nJ  60 H/cc. It is therefore quite natural to choose the SF threshold density close to the Jeans density. In the present paper, we conservatively picked n∗ = nJ /3 = 20 H/cc. These recipes have been all implemented in the RAMSES code and used for many galaxy formation studies in the recent years ((<>)Agertz et al. (<>)2009; (<>)Teyssier et al. (<>)2010; (<>)Bournaud et al. (<>)2011; (<>)Agertz et al. (<>)2011; (<>)Scannapieco et al. (<>)2012). We will now present in more details the main ingredient of the present study, namely our new implementation of stellar feedback. ",
+    "Figure 1. Evolution of the dark matter density profile over the 2 Gyr of evolution for the control run with adiabatic (no cooling and no star formation) hydrodynamics. We see that the dark matter halo density profile remains stable (with at most 10% deviations), except within the central 60 pc, which corresponds to twice the cell size in this case, in which we see less than a factor of two deviations from the initial profile. "
+  ],
+  "3 STELLAR FEEDBACK IMPLEMENTATION ": [
+    "The last but probably most important ingredient in galaxy formation simulations is stellar feedback. Stars, especially young stars, interact quite strongly with their environment. Among many possible physical processes, HII regions, stellar winds, type II and type Ia supernovae explosions have been the most popular. These various mechanisms are believed to be responsible for SF regulation in dwarf galaxies ((<>)Dekel (<>)& Silk (<>)1986), and they contribute collectively to roughly a couple of 1051 erg of energy injection into the surrounding ISM, for an average 10 M massive star and for a standard stellar initial mass function (IMF) ((<>)Piontek & Steinmetz (<>)2011). Since all these processes occur at very small, sub-pc scales, we have to rely on rather approximate numerical implementations. The simplest approach is clearly to inject directly thermal energy into each gas cell containing young stars. It turns out that feedback is very inefficient in that case because it occurs mostly in dense gas where cooling immediately radiates away the added thermal energy. It is usually considered that this strong cooling is a spurious numerical effect ((<>)Ceverino & Klypin (<>)2009). But supernovae explosions, and more generally feedback from young stars, takes place in very dense environment (such as molecular ",
+    "Figure 2. Maps of gas density (left, in logarithmic scale between 0.1 et 1000 H/cc), gas temperature (middle, in logarithmic scale between 300 and 106 K) and stellar column density (right, logarithmic scale in arbitrary units), seen face-on (lower plot) and side-on (upper plot), with (upper half) and without (lower half) feedback after 2 Cyr of evolution. The images are all 10 kpc across. ",
+    "clouds) so that strong radiative effects are likely to take place anyway. More recently, radiative pressure from young stars has been also proposed as a new possible mechanism ((<>)Murray et al. (<>)2010) to drive momentum into the interstellar medium (ISM). This approach is very promising since gas momentum does not suffer directly from gas cooling. It is however quite difficult to model since it requires detailed radiative transfer calculation of the infrared radiation reprocessed by dust. It was also shown recently that, for dwarf galaxies such as the ones studied here, supernovae feedback likely dominates over other sources of feedback energy ((<>)Hop-(<>)kins et al. (<>)2012) : radiative effects become inefficient due to the lower column densities. ",
+    "Physical processes associated to stellar feedback are probably even more complex than the ones quoted here so far. For example, we know from X-ray observations of supernovae remnants than they are strongly magnetized and turbulent. Moreover, cosmic rays acceleration occurs very rapidly and the energy density stored in the relativistic component is large enough to affect significantly the dynamics of the propagating shock wave ((<>)Ellison et al. (<>)2004; (<>)Ferrand (<>)et al. (<>)2010). These non-thermal processes have much longer dissipation time-scales than the thermal component, so they can store feedback energy longer than the rapidly cooling gas and release it to the gaseous component more gradually. Modeling unresolved turbulence, magnetic field amplifica-tion and cosmic ray propagation and radiative losses in the framework of galaxy formation is at its infancy, although some recent progresses have been reported ((<>)Hanasz et al. (<>)2006; (<>)Jubelgas et al. (<>)2008; (<>)Scannapieco & Br¨uggen (<>)2010; (<>)Uhlig et al. (<>)2012). We propose here a much simpler formalism that captures very crudely these various non-thermal processes and couple more efficiently the energy associated with stellar feedback to the gas component. ",
+    "The idea is to introduce a new variable for the energy density in these non-thermal components. We note this new variable eturb for simplicity, although it doesn’t have to be associated to turbulence only, but also to cosmic rays and magnetic fields. The specific turbulent energy turb is defined by eturb = ρturb. We model the time evolution of this non-thermal energy using the following simple equation ",
+    "(2) ",
+    "where we have only 2 terms, the non-thermal energy source E˙inj due to stellar feedback and the energy dissipation modeled classically as a damping term with dissipation timescale tdiss. The time scale depends on the exact underlying dissipation mechanism, such as radiative losses for cosmic rays ((<>)Enßlin et al. (<>)2007) or eddy turn-over time for turbulence. In what follows, we just need to accumulate enough feedback energy to drive strong outflows and to regulate our SF efficiency across the galactic disk. In this paper, we used a fixed dissipation time scale ",
+    "(3) ",
+    "comparable to the typical molecular cloud life time, as expected from their observed internal SF efficiency ((<>)Williams (<>)& McKee (<>)1997). Other options are possible, such as, for example, tdiss  λJ/σturb, where λJ could be the typical Jeans length or, equivalently, the typical cell size, or even more exotic, the cosmic rays mean free path or magnetic ",
+    "dissipation length scale. The turbulence velocity dispersion σturb is defined here as ",
+    "(4) ",
+    "(5) ",
+    "which corresponds to a maximally efficient model for which 1051 erg per 10 M massive star is injected into non-thermal energy. For a typical IMF, the mass fraction of stars going supernovae is roughly ηSN = 0.1. Although these numbers are determined by stellar evolution models, we believe that they can be considered as free parameters. Indeed, both the IMF and stellar evolution models are poorly constrained at low metallicity and/or at high redshift, and more generally in extreme galactic environments ((<>)Marks et al. (<>)2012). Note that this energy is injected in the gas cell only 10 Myr after the star particle has been created. ",
+    "The final step of our feedback model is to compute the non-thermal pressure using Pturb = ρσturb 2 and add it to the thermal pressure to get ",
+    "(6) ",
+    "This obviously requires to modify the Euler equation by adding the non-thermal pressure term, and this could impact more or less deeply the hydrodynamics solver. One even simpler alternative is to actually add directly to the thermal energy the injected non-thermal energy as ",
+    "(7) ",
+    "and shut down gas cooling to mimic the contribution of the non-thermal pressure to the total pressure. turb becomes a completely independent variable (like a passive Lagrangian tracer) used only to re-activate cooling when the non-thermal contribution becomes comparable or smaller than the thermal energy. In practice, we shut down cooling everywhere the turbulence velocity dispersion is large enough, using ",
+    "(8) ",
+    "Our final model does not require any modification to the hydro solver. It just requires to shut down cooling in each cell, if the velocity dispersion is above a chosen threshold (here 10 km/s). The other advantage is that it is qualitatively very similar to the “delayed cooling” approach used in other recent studies ((<>)Stinson et al. (<>)2006; (<>)Governato et al. (<>)2010; (<>)Agertz et al. (<>)2011), although our current approach is motivated by non-thermal astrophysical processes for which a detailed modeling would be far beyond the scope of the present study. "
+  ],
+  "4 EVOLUTION OF THE DARK MATTER DENSITY PROFILE ": [
+    "Now that we have presented our numerical set-up and parameters, we now describe in more details our results. We have performed 3 different simulations, in order to highlight the effect of stellar feedback on the mass distribution within the halo. The first simulation, already presented in the previous sections, was a pure adiabatic gas evolution of our initial ",
+    "Figure 3. Star formation history in the runs without (left plot) and with (right plot) feedback. ",
+    "hydrostatic equilibrium halo. We checked that our initial setup was indeed stable over 2 Gyr time, as it should be since no gas cooling was considered in this case (see Fig. (<>)1). We would like to stress that this is a very important step in our methodology, since it demonstrates that any evolution in the dark matter density profile has to be related to the dissipative nature of baryons, through gas cooling, star formation or feedback. The second simulation was run with (metal dependent) gas cooling and star formation. No stellar feedback was included. In this case, the gas loses pressure support and rains down towards the centre of the halo, quickly reaching the centrifugal barrier and sets up into a centrifugally supported disc. As one can see in Figure (<>)2, the final disk is very thin and fragments into dense gas clumps that form stars actively. This gives rise to the formation of dense bound star clusters that survive for long times. We also see the formation of a massive bulge in the centre of the galaxy, leading to an overall highly concentrated baryons distribution. The associated SF history can be seen on Figure (<>)3: it is on average very high, around 1 M/yr, with short bursts reaching 4 to 6 M/yr, associated to the formation of dense gas clumps. Such a high SF rate is usually associated to massive galaxies at low redshift. This is quite unrealistic for dwarf galaxies we see today ((<>)Hopkins et al. (<>)2002). The effect of this strongly dissipative evolution on the dark matter profile can be seen on Figure (<>)4. After 1 Gyr, the dark matter distribution has been adiabatically contracted very significantly by baryons. The inner slope of the dark matter density profile is close to -2, and no core is visible. It is worth mentioning that although we have a very clumpy structure in the ISM and in the stellar distribution, it does not trigger the formation of ",
+    "a dark matter core in our case: the mechanism proposed by (<>)Mashchenko et al. ((<>)2006) (see also (<>)El-Zant et al. (<>)2001) does not work here, probably because our clumps are not massive enough. ",
+    "We now move to our final run with gas cooling, SF and stellar feedback. The evolution of the star forming disk is dramatically different from the “no feedback” run. We see in Figure (<>)2 that the final gas distribution shows a very thick, turbulent disk, with strong outflows made of shredded clouds and filaments. The face-on view reveals that many gas clouds form in the outskirts of the disk, while the central region has been evacuated by stellar feedback, giving rise to the wind. The temperature map illustrates nicely the hot gas in the wind, segregating from the cold gas in the ISM. Star formation still proceeds within dense clouds, but these are not long-lived anymore. This is why we don’t see any massive star clusters in the stellar surface density map. Only a few managed to survive. This is one of the key qualitative features of our stellar feedback implementation: gravitational instability and shock compression trigger the formation of star forming clouds, which are then quickly disrupted by stellar feedback, recycling the unused gas into the ISM and giving rise to the galactic wind. ",
+    "The SF rate plotted in Figure (<>)3 is one order of magnitude lower in average than the “no feedback” case. It exhibits strong bursts followed by quiescent phases. When gas cools down and sinks towards the central region, SF rises sharply and triggers a starburst. Stellar feedback then removes the gas into the hot wind, leaving the central kpc almost devoid of gas. This explains the very low star formation episodes. Gas then rains back down from the corona and ",
+    "Figure 4. Evolution of the dark matter density profile over the 2 Gyr of evolution for the control run with cooling, star formation but no feedback. The dark matter halo has been strongly adiabatically contracted. ",
+    "triggers a new SF episode. These cycles are clearly visible in the SF history. They are at the origin of strong potential fluctuations due to massive periodic gas outflows and inflows. ",
+    "In Figure (<>)5, we plot the evolution of the dark matter density profile. As a technical side note, we would like to stress that these profiles have been computed using the highest dark matter density peak as centre, defined using the “shrinking sphere” algorithm. This minimizes spurious features in the density profiles due to poor centering. We clearly see in the “feedback” run that a large dark matter core develops. We tried to fit the resulting profile using a “pseudo-isothermal” profile defined as ",
+    "(9) ",
+    "This analytical shape has traditionally been used in rotation curve fitting and has proven to work extremely well in nearby dwarf galaxies ((<>)Begeman et al. (<>)1991; (<>)Kuzio de Naray (<>)et al. (<>)2006, (<>)2008). As can be seen in Figure (<>)5, this is also true in our simulation, for which the pseudo-isothermal fit is remarkably good within the central 3-4 kpc. We have measured core radii ranging from 500 pc at early time (0.5 Gyr) to 800 pc at late time (1.6 Gyr). We do see a systematic increase of the core radius with time. We have also tried to fit our dark matter profile with other popular cored den-",
+    "Figure 5. Evolution of the dark matter density profile over the 2 Gyr of evolution for the control run with cooling, star formation and stellar feedback. We see the formation of a large core. We also show for comparison the analytical fit (dashed line) based on a pseudo-isothermal profile (see text for details) ",
+    "sity distributions ((<>)Burkert (<>)1995, for example) but with less success. ",
+    "To quantify even more the time evolution of the dark matter distribution, we have fitted the density profile between 200 pc and 800 pc with a single power law. This is obviously a poor fit to our cored distribution, but this captures the essence of the dark matter flattening in the centre. At t = 0, we measure for the slope α = −1.2, which is the average value of the NFW profile between the 2 chosen radii. At the beginning, gas cools down and adiabatic contraction of the halo can be measured as a decrease of the inner slope to α = −1.8. But stellar feedback processes very quickly develop and trigger strong potential fluctuations, leading to a gradual flattening of the slope. We end up after 2 Gyr of evolution with a slope between α = −0.3 and α = −0.5, in excellent agreement with the measurement reported by PG12 in the context of a lower resolution cosmological simulation. ",
+    "As proposed by PG12, this strongly suggests that the core formation mechanism is related to violent gas outflows triggered by a succession of starbursts. In order to validate this idea in our simulation, we have computed the time evolution of the enclosed gas mass within spheres of increasingly large radii, from 200 pc for the smallest to 1600 pc for the largest. The results are shown in Figure 7 and illustrate ",
+    "that gas is repeatedly removed from the central region of the galaxy, giving rise to strong coherent potential fluctuations. As more gas cools down from the halo, the SF bursts become more violent and large mass fluctuations propagate to larger radii. This explains why we see a systematic increase in the dark matter core size as a function of time. At the end of the simulation, only scales up to ∼800 pc are affected by these strong fluctuations, corroborating nicely the measured core size of 800 pc. ",
+    "While these results are qualitatively consistent with the analysis of PG12, there is a difference in the quantitative details. In our case, many potential fluctuations are not only established in under a dynamical time (as in PG12) but also are erased before a full dynamical time has elapsed (unlike in PG12). The effect of these short-time transients is ignored by the PG12 toy model, since it starts by sampling the potential only once per dynamical time. Applying the PG12 algorithm directly therefore leads to incorrect predictions for our present simulation. We verified, however, that consistent predictions can be made by changing the sampling method to pick out, at each dynamical time step, the most extreme potential jump that occurred within the simulation. While this is a heuristic method, we believe it shows that the essential ingredient of impulsive potential changes is at play in our new simulations. It is in principle possible to extend the PG12 work to track phases of particles, thus giving a complete description of the impulsive changes which does not require the problematic quantization of time. However this approach would lose the attractive simplicity of the PG12 model and is certainly beyond the scope of the present investigation. ",
+    "We should also emphasis that the core forms after only 0.5 Gyr in our reference feedback run, when only 10% of the stars have formed. We have indeed measured a total stellar mass of M∗  5 × 107 M at that time. This means that the final total energy liberated in supernovae explosions is not the limiting factor. This is in fact consistent with the estimates of energy required to form cores in (<>)Pe˜narrubia (<>)et al. ((<>)2012). The question of what limits star formation requires full cosmological runs to tackle further, since our ”monolithic collapse” models do not reflect the interplay between gas inflow, outflow and feedback that presumably regulate star formation as of function of redshift in the real universe. "
+  ],
+  "5 OBSERVATIONAL GALAXY PROPERTIES ": [
+    "We have shown that cusp-core transformations are expected if there are strong (order unity) potential fluctuations on dynamical timescales. Such fluctuations are non-adiabatic, non-reversible, and heat both the dark matter and stars. We discuss here the observational consequences of such fluctu-ations; these can then be used to constrain or rule out the presence of such fluctuations in real systems. "
+  ],
+  "5.1 The stellar distribution ": [
+    "(<>)Read & Gilmore ((<>)2005) found from their toy models that, when cusp-core transformations occur, the resulting surface brightness of the stars is well-approximated by an exponential over many scale lengths, sometimes with a break radius ",
+    "Figure 6. Time evolution of the slope of the dark matter density profile measured between 200 and 800 pc for the simulation with feedback. ",
+    "at large radii and a core at small radii. This is exactly what we see in the present simulation: in Figure (<>)8, we have plotted the stellar surface density with and without feedback. In the latter case, we see a prominent bulge with high Sersic index and a weak exponential disk extending up to 6 kpc, while in the feedback case, we see a smaller exponential disk, with no bulge in the center and a clear signature of a stellar core within the central 500 pc. We have fitted this stellar distribution with a pure exponential disk with scale length Rd = 1.1 kpc (see Figure (<>)8). In our simulation without feedback, the stars form in a razor-thin, rotationally supported disc. ",
+    "Note that simulations of the formation and evolution of isolated dwarf galaxies generically end up with near-exponential surface brightness profiles, with rather thick gas and stellar disks ((<>)Springel & Hernquist (<>)2003; (<>)Valcke et al. (<>)2008; (<>)Dubois & Teyssier (<>)2008). These simulations can be however divided into 2 main categories: quiescent feedback models, in which small scale effects are captured by an effective equation of state, leading to a quiescent star formation history where outflows are obtained through a quasi-stationary galactic wind (see e.g. (<>)Springel & Hernquist (<>)2003; (<>)Dubois & Teyssier (<>)2008); and bursty models, in which the star formation history is not stationary and shows violent fluctuations (see e.g. (<>)Stinson et al. (<>)2007; (<>)Valcke et al. (<>)2008; (<>)Revaz et al. (<>)2009). The first category of simulations give rise to moderately thick disk, and very weak potential fluctua-",
+    "Figure 7. Time evolution of the total enclosed gas mass within spheres of radius 200 (blue), 400 (green), 800 (red) and 1600 (black) pc for the simulation with feedback. ",
+    "tions. The stellar disk is still well defined with an aspect ratio close to h/R  0.1 (see Fig. 11 in (<>)Springel & Hern-(<>)quist (<>)2003, for example). Therefore, we should not expect any dark matter core in this case. The second type of simulations, however, gives much thicker disks, in some case almost spheroidal galaxies. They show violently time-varying outflows, and they should lead to the formation of a dark matter core. Our present model, with strong stellar feedback, belongs to the second category: the resulting stellar distribution is oblate and quite hot, with v/σ  1 and a scale height to scale length ratio close to 0.5 (see Figure (<>)2 and Figure (<>)10). ",
+    "Unfortunately, it can be difficult to conclusively test the above expectations. Exponential surface brightness profiles can form through a variety of physical processes not related to violent potential fluctuations (e.g. (<>)Lin & Pringle (<>)1987). Similarly, hot stellar distributions with v/σ ∼ 1 need not be a smoking gun for cusp/core transformations. Galactic mergers (e.g. (<>)Searle & Zinn (<>)1978; (<>)Read et al. (<>)2006), and col-lisionless heating from a strong tidal field (e.g. (<>)Mayer et al. (<>)2001; (<>)Lokas et al. (<>)2011) both lead to stellar distributions with low v/σ. ",
+    "We can avoid all of the above complications, however, if we focus on isolated low mass dwarf galaxies. The best-studied system to date is WLM. Despite being extremely tidally isolated, WLM does indeed have a hot, oblate spheroidal, stellar distribution (with v/σ  1 and ",
+    "Figure 8. Stellar surface density of the final dwarf galaxy with (red line) and without (black line) feedback. In blue is shown the exponential fit of the stellar disk with feedback with scale length Rd = 1.1 kpc. ",
+    "h/Rd  0.5) that is reasonably approximated by an exponential surface brightness fall-off ((<>)Leaman et al. (<>)2012). Note that in this case too, a flattening on the stellar surface density profile is seen in the centre, reminiscent of a stellar core 1 (<>). (<>)Leaman et al. ((<>)2012) point out that it may be difficult to understand why the stellar distribution in WLM is so hot without recourse to strong and bursty stellar feedback. We can confirm that view here. In our model of an isolated dwarf galaxy, only the simulation with very strong feedback managed to form a hot thick-disc-like stellar distribution. This same simulation found a significant cusp-core transformation in the underlying dark matter distribution. In order to push the comparison with WLM even further, we have analyzed the kinematic properties of our dwarf galaxy. These are shown on Figure (<>)10. One can see immediately that the stellar rotation curve is slowly rising, while the stellar velocity dispersion is slowly declining. Both curves intersect at around 2 kpc, at a value close to 20 km/s. These features are in striking agreement with WLM data as exposed in (<>)Lea-(<>)man et al. ((<>)2012). The gas kinematic properties are also very similar, as shown in Figure (<>)10. Using our kinematic analysis, we are in a good position to test one important method to derive the total mass profile in dwarf galaxies from their ",
+    "Figure 9. Kinematic analysis of our dwarf galaxy without feedback: circular velocities (black solid line), stellar tangential velocity (red solid line) and stellar tangential velocity dispersion (green solid line), compared to the gas tangential velocity (red dotted line) and gas tangential velocity dispersion (green dotted line). ",
+    "kinematic properties, namely the Asymmetric Drift (AD) model. This method, based on the Jeans equation, follows a few reasonable simplifying assumptions to derive the relation between the circular velocity and the velocity moments. Following (<>)Hinz et al. ((<>)2001) and (<>)Leaman et al. ((<>)2012), we used vcirc 2 = vθ2 + σθ2 (2r/Rd − 1) with Rd  1.1 kpc, as measured in our simulation. We see in Figure (<>)10 that AD is overall a good approximation to recover the underlying mass profile, except perhaps in the very center where it is underestimated. The total mass inferred from this analysis by (<>)Leaman et al. ((<>)2012) for WLM, Mtot  2 × 1010 M is therefore accurate, and again very close to our simulated halo mass. ",
+    "Although our spatial and kinematic properties are in striking agreement with the relatively isolated dwarf WLM, the total stellar mass that we obtained in our simulation is too large by one order of magnitude. We have plotted in Figure (<>)11 the cumulative stellar mass profile in spherical shells. One sees clearly that without feedback, almost all baryons are converted into stars after 1 Gyr, since we get M∗  109 M. With our strong stellar feedback model, we managed to reduce this number by one order of magnitude, down to M∗  108 M. This is quite an achievement, but it falls short by one order of magnitude to explain the stellar ",
+    "Figure 10. Kinematic analysis in the feedback case: circular velocities (black solid line), stellar tangential velocity (red solid line) and stellar tangential velocity dispersion (green solid line), compared to the gas tangential velocity (red dotted line) and gas tangential velocity dispersion (green dotted line). Also shown as the blue solid line is the predicted circular velocity curve based on the Asymmetric Drift (AD) approximation. ",
+    "mass observed in WLM, which has been measured by (<>)Jack-(<>)son et al. ((<>)2007) to be M∗  1.1 × 107 M. We are therefore overproducing stars to a level comparable to most current galaxy formation simulations ((<>)Piontek & Steinmetz (<>)2009; (<>)Governato et al. (<>)2010; (<>)Agertz et al. (<>)2011), when compared to individual galaxies or to an ensemble of galaxies using the abundance matching technique ((<>)Guo et al. (<>)2010; (<>)Moster (<>)et al. (<>)2010), although recently (<>)Munshi et al. ((<>)2012) argue differently. Although solving this issue is beyond the scope of the present paper, we have a conceptually simple way to solve this problem, by lowering the star formation efficiency parameter ∗ by one order of magnitude, and in the same time, increasing the mass fraction of massive star going supernovae by also one order of magnitude. The first idea could be justified by the low metallicity we find in dwarf galaxies, leading to a inefficient regime of star formation, for which dust shielding is less efficient at promoting H2 molecule formation ((<>)Krumholz & Dekel (<>)2011). The second idea could be justified by recent observations of low metallicity star clusters in the Galaxy, which are consistent with a top-heavy IMF ((<>)Marks et al. (<>)2012). Using these two non-standard but plausible ingredients, we will straightforwardly obtain the same energy input from supernovae, and therefore the same ",
+    "Figure 11. Cumulative stellar mass profile as a function of spherical radius for the fiducial star formation efficiency (1%) without (black line) and with (red line) stellar feedback at t  1 Gyr. Also shown are the stellar mass profiles with a very low star formation efficiency (0.2%) and a top heavy initial mass function, without (green line) and with (blue line) stellar feedback. Only the latter model can match the observed stellar mass in the dwarf galaxy WLM. ",
+    "hydrodynamical model, with however ten times less long-lived star formed. A different model based on early radiative stellar feedback has been recently proposed by (<>)Brook et al. ((<>)2012) that could solve this very same issue, although the quantitative effect would not be as straightforward as the one proposed here. ",
+    "Since complex non-linear hydrodynamical processes are at play, it is not obvious that lowering ∗ (while increasing the feedback energy per stellar mass formed) will result in decreasing the total stellar mass formed. We therefore run 2 additional simulations with ∗ = 0.2% and a top-heavy IMF so that 50% of the mass of a given stellar population (or star particle) will be in massive stars going supernovae. The first simulation was run without stellar feedback (only metal enrichment) and the second simulation was run with our new stellar feedback scheme and a top-heavy IMF. We have plotted in Figure (<>)11 the cumulative stellar mass pro-files of these 2 additional runs. Interestingly, although we have decreased by a factor of 5 the SFE, the run without feedback gives also rise to the formation of M∗  109 M of stars, like in the fiducial case. This means that, without stellar feedback, the gaseous disk always manages to cool and contract enough to reach high gas densities and trans-",
+    "form most of its baryons into stars. With stellar feedback, however, we form only M∗  2×107 M of stars after 1 Gyr, in much better agreement with the observed stellar mass in WLM. We have also checked (not shown here) that, in this last simulation, all of the galaxy properties discussed above are also recovered, namely a large dark matter core, thick stellar and gaseous disks and a bursty SF history, with large amount of gas moving in and out of the central kpc of the galaxy. This last model gives very encouraging results, but requires a significantly top-heavy IMF together with a very low star formation efficiency. We would like also to stress again (see Section 4) that star formation might be also regulated or even stopped after only 0.5 Gyr of evolution, due to the effect of a more realistic cosmological accretion history, which is not captured here in this idealized set-up. "
+  ],
+  "5.2 Star formation histories ": [
+    "A second key observational prediction of cusp-core transformations is the star formation history (SFH). In the category of feedback models where cusp-core transformations are expected ((<>)Stinson et al. (<>)2007; (<>)Valcke et al. (<>)2008; (<>)Revaz et al. (<>)2009; (<>)Cloet-Osselaer et al. (<>)2012, and this paper), the SFH is extremely bursty with peak to trough variations of 10 and a duty cycle of roughly one dynamical time. Although our average star formation rate of 0.02 to 0.2 M/yr for a total gas mass of 109 M is consistent with observations of blue compact dwarf galaxies in the local universe ((<>)Hopkins et al. (<>)2002), the bursty nature of its time evolution needs to be tested observationally. There are two possibilities: (i) measure the SFH for individual systems; and (ii) estimate the variance in the star formation statistically for a large population of like-galaxies. The former is cleaner, but requires very high time resolution in the derived SFH; the latter has potentially high time resolution but relies on assumptions about the equivalence of large populations of galaxies. We discuss each in turn, next. "
+  ],
+  "5.2.1 Individual star formation histories ": [
+    "The best SFHs come from the most nearby systems. These have resolved color magnitude diagrams (CMDs) that reach the oldest main sequence turn-offs, which is vital for correctly recovering the intermediate age stars (e.g. (<>)No¨el et al. (<>)2009). More distant systems have SFHs derived via spectral energy distribution (SED) fitting of the unresolved stars that is degenerate and less accurate than CMD fitting (e.g. (<>)Zhang (<>)et al. (<>)2012). ",
+    "The best-studied system to date is the nearby dwarf spheroidal galaxy Sculptor that orbits the Milky Way (e.g. (<>)Mateo (<>)1998; (<>)Lux et al. (<>)2010). Unfortunately, even for excellent data, CMD fitting has a temporal resolution poorer than ∼1 Gyr ((<>)Dolphin (<>)2002), where the errors come from a mix of photometric uncertainty, spread in distance modulus, and errors in the stellar population evolution libraries ((<>)Dolphin (<>)2012). (<>)de Boer et al. ((<>)2012) have recently attempted to improve this situation by simultaneously fitting the CMD and spectroscopic metallicities of red giant branch stars. They explicitly consider how well their methodology could recover a bursty star formation history. Using simulated data, they show that their method would recover a smooth continuous ",
+    "star formation history (as observed for Sculptor) from an input bursty history. Thus, the very best data remain inconclusive. It is interesting to note, however, that the very latest dynamical models for Sculptor appear to favor a cored rather than cusped mass distribution ((<>)Battaglia et al. (<>)2008; (<>)Walker & Pe˜narrubia (<>)2011; (<>)Amorisco & Evans (<>)2012). This motivates a continued effort to attempt to confirm or deny a highly bursty star formation history for Sculptor. "
+  ],
+  "5.2.2 The star formation history of a population of dwarf galaxies ": [
+    "An alternative approach to studying individual galaxies is to study a population statistically. If we assume that all dwarf galaxies of a given mass and type are statistically equivalent, then we can treat these has individual sample points along the SFH. If the SFH is smooth and continuous then the variance in the measured SFH for the population will be small; if, however, it is bursty then the variance will be larger. (<>)Weisz et al. ((<>)2012) have recently used this idea to test a simple bursty star formation history against a population of 185 galaxies from the Spitzer Local Volume Legacy survey. They find that their more massive galaxies (M∗  107 M) are better fit (on average) by a smooth and continuous SFH, while the lower mass systems (M∗  107M ) favour a bursty SFH with bursts of ∼ 10’s of Myrs, inter-burst periods of ∼ 250 Myrs, and peak to trough burst amplitude ratios of ∼ 30. These numbers are in total agreement with the SFH we obtained for our model with a cusp-core transformation (see Figure (<>)3). WLM is again interesting here. It has a stellar mass of 1.1 × 107 M and a dynamical mass of ∼ 1010 M ((<>)Leaman et al. (<>)2012). As we have shown, it is comparable to our simulated halo, and statistically in the stellar mass range where bursty star formation in dwarf galaxies is observationally favored. ",
+    "It seems that all of the currently available data favor a bursty SFH for dwarf galaxies with stellar mass  107 M and dynamical mass  1010 M. As we have shown here, such a bursty SFH will naturally heat the stars producing a hot stellar distribution even in isolated systems, consistent with recent observations of the isolated dwarf galaxy WLM. It also drives cusp-core transformations in the dark matter that can explain the now long-standing cusp-core problem ((<>)Flores & Primack (<>)1994; (<>)Moore (<>)1994). "
+  ],
+  "6 DISCUSSION ": [
+    "In this paper, we have simulated an isolated dwarf galaxy using the now traditional set-up of the cooling halo. Using a new implementation of stellar feedback within the RAMSES code, we have modeled the formation of a dwarf galaxy of 1010 M halo mass, whose evolution has been shown to be strongly dominated by feedback processes. We have observed the formation of a 800 pc dark matter core, the size of which corresponds roughly to 40 resolution elements. We have analyzed in details the stellar distribution and kinematics of our model galaxy, observable properties that compare successfully to the local isolated dwarf WLM. In our fidu-cial model, the total stellar mass is too large by one order of magnitude, suggesting that we need to lower the long-lived ",
+    "star formation efficiency, while keeping the same overall feedback efficiency to match all constraints. We have shown that this might be indeed achieved, if one uses a very low value for the Schmidt law parameter ∗  0.2%, together with a top-heavy initial mass function. ",
+    "Our simulation with feedback and AMR clearly con-firms previous works performed with various SPH codes, both for isolated haloes and in a cosmological context, at a somewhat lower resolution than the one used here. The temporal variations and systematic evolution of the inner slope of the dark matter profile correlate nicely with bursts seen in the SF history of our dwarf galaxy. We noted that there are several observational diagnostics which point to the cusp-flattening process driven by bursty star formation. The most obvious place to look is in star formation histories. Unfortunately for individual cases, it is unlikely to be possible to achieve sufficient time resolution (e.g. (<>)Dolphin (<>)2012; (<>)de Boer et al. (<>)2012). On the other hand, statistical studies of populations encouragingly point to bursts of exactly the right nature for cusp-flattening, and in agreement with our work, especially at low masses ((<>)Weisz et al. (<>)2012). There may be less direct evidence of a cusp-flattening process in the final kinematics of the stars. Since stars behave as colli-sionless particles, like dark matter, they should be heated by the irreversible process proposed by (<>)Read & Gilmore ((<>)2005), (<>)Mashchenko et al. ((<>)2006) and (<>)Pontzen & Governato ((<>)2012). Indeed when cusp-flattening occurs, we also obtain hotter, more oblate stellar distributions with v/σ  1. More directly related to the proposed mechanism, we also obtain a core in the stellar distribution. Promisingly, this also agrees well with the recent observations of the isolated dwarf galaxy WLM ((<>)Leaman et al. (<>)2012). ",
+    "Although these observations tend to favor bursty SF histories as a plausible origin to cusp-core transformations, we would like to stress that this is only a necessary condition for these to occur, not a sufficient one: other physical mechanisms could be at play to explain cusp-core transformations, not related to baryonic processes, but, for example, to warm or self-interacting dark matter particles. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "We thank our anonymous referee for helpful suggestions that greatly improved the quality of the paper. We thank Pascale Jablonka for interesting discussions on the star formation history of dwarf galaxies. Justin Read would like to acknowledge support from SNF grant PP00P2 128540/1. The simulations presented here were performed on the COAST cluster at IRFU, CEA Saclay. "
+  ]
+}

jsons_folder/2013MNRAS.430..105P.json

@@ -0,0 +1,169 @@
+{
+  "arXiv:1208.3026v1  [astro-ph.CO]  15 Aug 2012 ": [
+    "Annika H. G. Peter,1 Miguel Rocha,1† James S. Bullock,1‡ and Manoj Kaplinghat1§ "
+  ],
+  "ABSTRACT ": [
+    "If dark matter has a large self-interaction scattering cross section, then interactions among dark-matter particles will drive galaxy and cluster halos to become spherical in their centers. Work in the past has used this effect to rule out velocity-independent, elastic cross sections larger than σ/m  0.02 cm2/g based on comparisons to the shapes of galaxy cluster lensing potentials and X-ray isophotes. In this paper, we use cosmological simulations to show that these constraints were off by more than an order of magnitude because (a) they did not properly account for the fact that the observed ellipticity gets contributions from the triaxial mass distribution outside the core set by scatterings, (b) the scatter in axis ratios is large and (c) the core region retains more of its triaxial nature than estimated before. Including these effects properly shows that the same observations now allow dark matter self-interaction cross sections at least as large as σ/m = 0.1 cm2/g. We show that constraints on self-interacting dark matter from strong-lensing clusters are likely to improve significantly in the near future, but possibly more via central densities and core sizes than halo shapes. ",
+    "Key words: galaxies: halos — methods: numerical "
+  ],
+  "1 INTRODUCTION ": [
+    "The nature of dark matter is one of the most compelling mysteries of our time. On large scales, the behavior of dark matter is consistent with what cosmologists of yore called “dust” (e.g., (<>)Tol-(<>)man (<>)1934), meaning its behavior is consistent with being colli-sionless and non-relativistic (“cold”) for the vast majority of the Universe’s history ((<>)Reid et al. (<>)2010). This consistency has been of great interest to the particle-physics community because the most popular candidate for dark matter, the supersymmetric neutralino, displays exactly this behavior ((<>)Steigman & Turner (<>)1985; (<>)Griest (<>)1988; (<>)Jungman, Kamionkowski & Griest (<>)1996). While the super-symmetric neutralino paradigm is attractive in many ways, there are two outstanding problems with it. First, astroparticle searches have yet to turn up evidence for the existence of the neutralino, though searches are rapidly increasing their sensitivity to interesting neutralino parameter space ((<>)Geringer-Sameth & Koushiappas (<>)2011; (<>)Ackermann et al. (<>)2011; (<>)Cotta et al. (<>)2012; (<>)Fox et al. (<>)2011; (<>)Bertone et al. (<>)2012; (<>)Atlas Collaboration (<>)2012; (<>)Koay (<>)2012; (<>)Baudis (<>)2012; (<>)Baer, Barger & Mustafayev (<>)2012; (<>)XENON100 Collabora-(<>)tion et al. (<>)2012). Second, there are predictions for the structure of dark-matter halos that have not been observationally verified at a ",
+    "quantitative level ((<>)Dubinski & Carlberg (<>)1991; (<>)Diemand et al. (<>)2008; (<>)Vogelsberger et al. (<>)2009; (<>)Stadel et al. (<>)2009; (<>)Navarro et al. (<>)2010). In fact, there are hints of tension with the neutralino paradigm on sub-galactic scales ((<>)Dobler & Keeton (<>)2006; (<>)Gentile et al. (<>)2007; (<>)de Blok (<>)et al. (<>)2008; (<>)Kuzio de Naray, McGaugh & de Blok (<>)2008; (<>)Kuzio de (<>)Naray et al. (<>)2010; (<>)Zwaan, Meyer & Staveley-Smith (<>)2010; (<>)Boylan-(<>)Kolchin, Bullock & Kaplinghat (<>)2011; (<>)Papastergis et al. (<>)2011). And yet, most of the effort to characterize the evolution of the Universe (experimentally, observationally, and theoretically) has been in the context of this dust-like cold dark matter (CDM). In the absence of evidence for any dark-matter candidate, much less the neutralino, it is important to explore the structure and evolution of the Universe for dark-matter phenomenology beyond cold and collisionless. ",
+    "One intriguing possibility is that the dark matter belongs to and interacts with a “dark” or “hidden” sector ((<>)Khlopov, Stephan & (<>)Fargion (<>)2006; (<>)Feldman, Kors & Nath (<>)2007; (<>)Foot (<>)2007; (<>)Pospelov, (<>)Ritz & Voloshin (<>)2008; (<>)Feng & Kumar (<>)2008; (<>)Arkani-Hamed et al. (<>)2009; (<>)Feng et al. (<>)2009; (<>)Sigurdson (<>)2009; (<>)Cohen et al. (<>)2010). The Standard Model has rich intra-sector phenomenology; it is not unreasonable to speculate that a complex dark sector only tenuously connected to the Standard Model might exist as well. The simplest kind of dark-matter interaction is a hard-sphere interaction of identical dark-matter particles. Such an interaction – with an isotropic, velocity-independent, elastic scattering cross section – was first introduced in an astrophysical context by (<>)Spergel & Stein-(<>)hardt ((<>)2000). Interactions of this type were invoked to ameliorate the tensions between observations and CDM predictions on small ",
+    "scales (on the scales of individual dark-matter halos) while leaving the large-scale successes of CDM intact. In this paper we revisit this basic class of self-interacting dark matter (SIDM) using cosmological simulations to explore its effect on dark matter halo shapes as a function of cross section. In a companion paper (Rocha et al. 2012) we investigate implications for dark matter halo substructure and density profiles. ",
+    "We are reinvestigating this simple SIDM model, which had been decreed “uninteresting” in several studies a decade ago, for two primary reasons. First, we suspected that the constraints that indicated that the SIDM cross section was too small to meaningfully alter the morphology of dark-matter halos, were not as tight as claimed. Second, there is a wealth of new data (e.g., from near-field cosmology, lensing studies of galaxies and clusters) that may be better places to either look for SIDM or constrain its properties. In this paper and our companion paper, Rocha et al. (2012), we reevaluate past constraints on SIDM and suggest several new places to look for the effects of SIDM on halo structure. ",
+    "There was a burst of work on SIDM before its untimely demise ((<>)Yoshida et al. (<>)2000a,(<>)b; (<>)Kochanek & White (<>)2000; (<>)Hogan & Dal-(<>)canton (<>)2000; (<>)Dalcanton & Hogan (<>)2001; (<>)Dave´ et al. (<>)2001; (<>)Col´ın (<>)et al. (<>)2002; (<>)Hennawi & Ostriker (<>)2002). The death of isotropic, velocity-independent, elastically scattering SIDM largely came from the interpretation of three types of observations: halo evaporation in galaxy clusters ((<>)Gnedin & Ostriker (<>)2001), cores in galaxy clusters ((<>)Yoshida et al. (<>)2000b; (<>)Meneghetti et al. (<>)2001), and halo shapes ((<>)Miralda-Escude´ (<>)2002). The Y2K-era constraints from the former two classes of observations were at the level of σ/m  0.3 cm2/g and σ/m  0.1 cm2/g respectively. However, we show in a companion paper, Rocha et al. (2012), that the evaporation and cluster-core constraints are likely overestimated. ",
+    "The most stringent constraints on dark matter models with large isotropic, elastic self-scattering cross sections emerged from the shapes of dark-matter halos, in particular from lens modeling of the galaxy cluster MS 2137-23 by (<>)Miralda-Escude´ ((<>)2002). This massive galaxy cluster has a number of radial and tangential arcs within ∼ 200 kpc of the halo center ((<>)Mellier, Fort & Kneib (<>)1993; (<>)Miralda-Escude (<>)1995). (<>)Miralda-Escude´ ((<>)2002) argued that self interactions should make dark-matter halos round within the radius r where the local per-particle scattering rate equals the Hubble rate Γ(r) = H0, or equivalently, where each dark-matter particle experiences one interaction per Hubble time. The scattering rate per particle as a function of r in a halo scales in proportion to the local density and velocity dispersion, ",
+    "(1) ",
+    "where ρ is the local dark-matter mass density and vrms is the rms speed of dark-matter particles. Using the fact that the lens model needs to be elliptical at 70 kpc, (<>)Miralda-Escud´e ((<>)2002) set a constraint of σ/m  0.02 cm2/g on the velocity-independent elastic scattering cross section. This constraint is one to two orders of magnitude tighter than other typical constraints on velocity-independent scattering ((<>)Yoshida et al. (<>)2000b; (<>)Gnedin & Ostriker (<>)2001; (<>)Randall et al. (<>)2008). It rendered velocity-independent scattering far too small to form cores in low surface brightness galaxies and other small galaxies ((<>)Kuzio de Naray, McGaugh & de Blok (<>)2008; (<>)de Blok et al. (<>)2008). This is unfortunate because the main reason SIDM was interesting at the time was that it was a mechanism to create cores in such galaxies ((<>)Spergel & Steinhardt (<>)2000). ",
+    "The tightness of the SIDM constraints on cluster scales has meant that the focus of SIDM studies has shifted to those on velocity-dependent cross sections, such that SIDM may signifi-",
+    "Table 1: Summary of simulations. ",
+    "cantly alter dwarf-scale or smaller dark-matter halos while leaving cluster-mass halos largely untouched ((<>)Feng et al. (<>)2009; (<>)Buckley (<>)& Fox (<>)2010; (<>)Loeb & Weiner (<>)2011; (<>)Vogelsberger, Zavala & Loeb (<>)2012). In recent times, such velocity-dependent interactions have arisen in hidden-sector models designed to interpret some charged-particle cosmic-ray observations as evidence for dark-matter annihilation ((<>)Pospelov, Ritz & Voloshin (<>)2008; (<>)Fox & Poppitz (<>)2009; (<>)Arkani-Hamed et al. (<>)2009; (<>)Feng, Kaplinghat & Yu (<>)2010). Constraints on other hidden-sector dark-matter models have been made using X-ray isophotes of the gas in the halo of the elliptical galaxy NGC 720 ((<>)Buote et al. (<>)2002; (<>)Feng et al. (<>)2009; (<>)Feng, Kaplinghat & (<>)Yu (<>)2010; (<>)Buckley & Fox (<>)2010; (<>)Ibe & Yu (<>)2010; (<>)McDermott, Yu & (<>)Zurek (<>)2011; (<>)Feng, Rentala & Surujon (<>)2012). ",
+    "However, as we show below, reports of the death of isotropic, velocity-independent elastic SIDM are greatly exaggerated. In this paper, we show that these earlier studies did not correctly account for the fact that the observed ellipticity (of the mass in cylinders or the projected gravitational potential) gets contributions from mass well outside the core, and the region outside the core retains its triaxiality. We also show that for ellipticity estimators that are relevant observationally, there is significant amount of scatter and the overlap between CDM and SIDM ellipticities is substantial even for σ/m = 1 cm2/g. Lastly, we find that in the regions where SIDM particles have suffered (on average) about one or more interactions, the residual triaxiality is larger than what has been previously estimated ((<>)Dav´e et al. (<>)2001). Along with the analysis in Rocha et al. (2012), we find that studies of the central densities of dark-matter halos are likely to yield tighter constraints on the SIDM cross section than the morphology of the halos. ",
+    "We briefly summarize our simulations in Sec. (<>)2. We present results on the three-dimensional shapes of SIDM dark-matter halos compared to their CDM counterparts in Sec. (<>)3. We reexamine the previous SIDM constraints based on halo shapes in light of our simulations in Sec. (<>)4. In particular, we reexamine the (<>)Miralda-(<>)Escud´e ((<>)2002) constraint in Sec. (<>)4.2 and from the shapes of the X-ray isophotes of NGC 720 ((<>)Buote et al. (<>)2002) in Sec (<>)4.3. In Sec. (<>)4.4, we show how other lensing data sets may constrain SIDM in the future. We summarize the key points of this paper and present a few final thoughts in conclusion in Sec. (<>)5. "
+  ],
+  "2 SIMULATIONS ": [
+    "We modeled self interactions by direct-simulation Monte Carlo with a scattering algorithm derived in Appendix A of Rocha et al. (2012) and implemented within the GADGET-2 ((<>)Springel ",
+    "Figure 1. Surface density of a halo of mass Mvir = 1.2 × 1014M projected along the major axis of the moment-of-inertia tensor – the orientation that dominates the lensing probability. The left column shows the halo for CDM, while the middle and right columns show the same halo simulated using SIDM with σ/m = 0.1 cm2/g and 1.0 cm2/g, respectively. The bottom row shows the same information, now zoomed in on the central region. The surface density stretches logarithmically from ≈ 10−3g/cm2 (blue) to ≈ 10 g/cm2 (red). ",
+    "(<>)2005) cosmological N-body code. Once the code passed accuracy tests, we performed cosmological simulations of CDM and SIDM with identical initial conditions for cubic boxes of 25h−1Mpc on a side and 50h−1Mpc on a side, each with 5123 particles. For the SIDM runs we explored cross sections of σ/m = 1, 0.1, and 0.03 cm2/g, though the lowest cross section run (with σ/m = 0.03 cm2/g) provided results that were so similar to CDM that we have not included them in any of the figures below. The initial conditions were generated using the MUSIC code at z = 250 ((<>)Hahn & Abel (<>)2011) with a year seven WMAP cosmology ((<>)Ko-(<>)matsu et al. (<>)2011): h = 0.71, Ωm = 0.266, ΩΛ = 0.734, Ωb = 0.0449, ns = 0.963, σ8 = 0.801. A summary of our simulation parameters, including particle mass and resolution is provided in Table 1. We adopt a naming convention where the simulations denoted SIDM0.1 and SIDM1 have subscripts corresponding to their cross sections in units of cm2/g. In all cases the self-interaction smoothing length as defined in Rocha et al. (2012) was set to 2.8 times the force softening. ",
+    "We locate and characterize halos using the publicly available Amiga Halo Finder (AHF; (<>)Knollmann & Knebe (<>)2009) package. The total mass of a host halo Mvir is determined as the mass within a radius rvir using the virial overdensity as defined in (<>)Bryan & (<>)Norman ((<>)1998). Though most of our analysis focuses on distinct (field) halos, we also explore subhalo shapes. For these objects their masses are measured within the radius at which the radial density ",
+    "profile of the subhalo begins to rise again because of the presence of the host. ",
+    "We present results on the shapes of halos at z = 0 in a radial range rmin to rvir, where rmin is the minimum radius within which we trust the shape measurements. Since our two sets of simulations have different resolution, we can check the convergence of our shape estimates. For integral measures of shape (e.g., the moment-of-inertia tensor for all particles within a given radius), we find that although the density profiles look largely converged outside of the numerical-relaxation radius rrelax defined in (<>)Power et al. ((<>)2003), the shapes do not converge until at least rmin = 2rrelax. This radius is roughly rmin ≈ 20 kpc for the halos in the 50h−1Mpcsized simulations, with only modest dependence on halo mass and scattering cross section, and rmin ≈ 10 kpc for the 25h−1Mpc boxes. Below rmin we find that the halo shapes are systematically too round. However, shapes are more robust if found in shells (either spherical or ellipsoidal) because they are less contaminated by the effects of the overly round and numerically relaxed inner regions. Shape estimates, especially integral estimates, are most reliable if there are at least ∼ 104 particles within the virial radius (or tidal radius for subhalos), consistent to what has been found in earlier work (e.g., (<>)Allgood et al. (<>)2006; (<>)Vera-Ciro et al. (<>)2011). ",
+    "Figure 2. Surface density profiles for the same halo shown in Fig. (<>)1, now projected along the intermediate axis. Deviations from axisymmetry are highest along this projection. ",
+    "Figure 3. Host halo shapes in shells of radius scaled by the virial radius in three virial-mass bins as indicated. The black solid lines denote the 20th percentile (lowest), median (middle), and 80th percentile (highest) value of c/a at fixed r/rvir for CDM. The blue dashed lines show the median and 20th/80th percentile ranges for σ/m = 1 cm2/g, and the green dotted lines show the same for σ/m = 0.1 cm2/g. There are 440, 65, and 50 halos in each mass bin (lowest mass bin to highest). "
+  ],
+  "3 SIMULATED HALO SHAPES ": [],
+  "3.1 Preliminary Illustration ": [
+    "Before presenting a statistical comparison of CDM and SIDM halo populations, we provide a pictorial illustration of how an individual halo changes shape as we vary the cross section. The columns ",
+    "of Figs. (<>)1 and (<>)2 show surface density maps for the same halo simulated in CDM, SIDM0.1, and SIDM1 from left to right. In Fig. (<>)1, we project the halo along the major axis, which is the orientation that maximizes the strong-lensing cross section ((<>)van de Ven, (<>)Mandelbaum & Keeton (<>)2009; (<>)Mandelbaum, van de Ven & Kee-(<>)ton (<>)2009). In Fig. (<>)2, we project the halo along the intermediate ",
+    "axis, which maximizes the deviation of the surface density from axisymmetry. This particular halo is one of the most massive halos identified in the 50h−1Mpc box runs, with Mvir = 1.2 × 1014M and rvir = 1.27 Mpc. The top row in each figure shows the surface density on the scale of the virial radius, while the lower row shows the inner 300h−1kpc of the halo (side-to-side). The surface-density stretch is the same between the two figures. ",
+    "The major and minor axes for the projections in these figures were determined using the moment-of-inertia tensor of all particles within a sphere of radius rvir in the halo. If modeling the mass distribution as an ellipsoid, the principal axes a(major) > b(intermediate) > c(minor) are the square roots of the eigenvalues of this tensor. ",
+    "In comparing Figs. (<>)1 and (<>)2, note that Fig. (<>)1 is the most relevant for strong-lensing studies (Sec. (<>)4) and shows the smallest differences, especially at large radii. Indeed, only the zoomed view of the σ/m = 1 cm2/g run is visibly rounder than the CDM case. Even for the intermediate projection (Fig. (<>)2), which maximizes the visual difference, the inner regions of the halo are only slightly rounder and less dense than their CDM counterparts for σ/m = 0.1 cm2/g. The σ/m = 1 cm2/g case is indeed less dense and rounder within ∼ 100h−1 kpc, but even in this case, some ellipticity is clearly evident. ",
+    "A final point of interest in these visualizations concerns the substructure. The subhalos apparent in the CDM halo are similarly abundant in the SIDM cases, and even approximately match in their positions. There are minor differences in substructure densities and locations (especially in the central regions) but overall it is difficult to distinguish among the runs by comparing their substructure content (see Rocha et al. 2012 for a more quantitative comparison of substructure). "
+  ],
+  "3.2 Three-dimensional halo shapes ": [
+    "We quantify halo shapes by examining ellipsoidal shells centered on the radial slices identified by AHF ((<>)Knollmann & Knebe (<>)2009) for profile measurements. We use shells instead of enclosed volume because it is less sensitive to numerical relaxation effects at the center and because it is a better estimate of the effects of local dark-matter scattering. In each shell of material, we calculate a modified moment-of-inertia tensor (defined and used in (<>)Allgood et al. (<>)2006) in ellipsoidal shells, ",
+    "(2) ",
+    "and (x1,n, x2,n, x3,n) are the coordinates of the nth particle in the frame of the principal axes (major, intermediate, minor) of this tensor. This is the same moment-of-inertia tensor from which shapes are inferred in (<>)Dubinski & Carlberg ((<>)1991) and (<>)Dave´ et al. ((<>)2001). The principal axes (a, b, c) are computed as the square roots of the eigenvalues of I˜ijell.The weighting of the moment-of-inertia tensor is chosen such that the outermost particles in the shell do not dominate the shape estimate. We begin by finding the moment-of-inertia tensor in a spherical shell, setting a = b = c = 1 for this initial estimate of I˜ijell , and iterate to find I˜ijell with convergent (a, b, c) values. In each iteration, the ellipsoidal shell volume is defined using the (a, b, c) found in the previous iteration. We experiment with either keeping the semi-major axis a of the shell fixed between iterations or allowing a to float such that the volume in the shell ",
+    "Figure 4. Median subhalo shape vs. radius for galaxy-mass systems compared to host halos of the same mass. Bold lines denote subhalos and lighter lines denote host halos. The radii are normalized by rvir for hosts and rtidal for subhalos. Line colors and styles have the same meanings as in Fig. (<>)3: dashed blue is SIDM1, dotted green is SIDM0.1, and solid black is CDM. ",
+    "remains fixed as we iterate to find I˜ij (a), but find that c/a is insensitive to these choices. Throughout this section, we show c/a for fixed volume in the shell. We only show results for c/a because the trends for b/a are similar but less informative, since c/a indicates the deviation of the halo shape from sphericity. ",
+    "In order to understand trends, we split our analysis of host dark-matter halos and subhalos, and bin halos by virial (or tidal) mass. Host halos are those whose centers do not lie within the virial radius of a more massive halo. In Fig. (<>)3, we show the minor-to-major axis ratio c/a as a function of radius normalized by the halo virial radius, r/rvir, for host halos in three mass bins. Larger values of c/a imply more spherical halos. For the two lower mass bins, we used halos selected from the 25 h−1Mpc boxes since these have the higher resolution. For the highest mass bin, we used halos identified in the 50 h−1Mpc boxes in order to gain better statistics. We checked to make sure that the results were convergent between boxes where the relevant mass resolutions overlap. The shaded region corresponds to the 20th to 80th percentile for c/a of the halo population for fixed r/rvir, and the central line shows the median value of c/a. The black solid lines and yellow shaded regions denote shapes of CDM halos, the blue dashed lines and regions correspond to σ/m = 1 cm2/g, and the green dotted lines and regions correspond to σ/m = 0.1 cm2/g. The regions extend down in r/rvir to the largest value of rmin/rvir in the given mass bin. ",
+    "We reproduce the well-known trend that galaxy-mass halos in CDM are more spherical than cluster mass halos and that CDM halos become more spherical in their outer parts ((<>)Allgood et al. (<>)2006). SIDM halos deviate most strongly from CDM at smaller radii, where the scattering rates are highest for a fixed cross section. For SIDM1, halos are actually more spherical in their centers than their edges, with c/a rising with decreasing r for r/rvir < 0.5. For SIDM0.1, differences from CDM are only apparent for r/rvir < 0.1. ",
+    "In Fig. (<>)4, we compare the shapes of subhalos (thick lines) and ",
+    "host halos (thin lines) of similar mass by plotting the median axis ratio c/a as a function of r/router where router = rtidal for subha-los (as defined by the AHF halo finder) and router = rvir for host halos. All halos have masses within router between 1011h−1M and 1012h−1M. Though not shown, the 20th to 80th percentile ranges are similar in size as in Fig. (<>)3. We find that the subhalo interiors in the σ/m = 1 cm2/g cosmology are systematically rounder than host halos. We speculate that there are are at least three effects that drive this trend. First, subhalos are typically more evolved than field halos of the same mass, with fewer recent mergers. (<>)Allgood (<>)et al. ((<>)2006) find that halos that form earlier are more spherical than halos that form later, which is attributed to directional merging, and more generally to the highly non-spherically-symmetrical way in which halos form and accrete. Second, these subhalos are the remains of more massive halos, which are more susceptible to the effects of self interactions at fixed r/rvir, as we showed in Fig. (<>)3. Moreover, the outer radius of the subhalos is truncated with respect to its virial value, thus increasing r/router for fixed r. Since halos tend to be rounder in the outer parts with respect to the interiors for CDM halos, this boosts the initial c/a for fixed r/rvir, beyond which SIDM boosts c/a even more. We see this trend for the CDM and σ/m = 0.1 cm2/g halos in Fig. (<>)4. ",
+    "To see how the shape of dark-matter halos changes as a function of the typical local scattering rate (Eq. (<>)1), we plot c/a as a function of ρ(r)vrms(r) ∝ Γ(r)(σ/m)−1 in Fig. (<>)5. The proportionality constant in relating ρvrms to the scattering rate is O(1) and depends on the distribution function of dark matter particles. Thus it is reasonable to use ρvrms as a proxy for the local scattering rate modulo the actual cross section. To simplify the interpretation further, we multiply this quantity by 10 Gyr cm2/g in Fig. (<>)5. In these units, if ρ(r)vrms(r) > 1 for σ/m = 1 cm2/g, most particles will have scattered after 10 Gyr. For σ/m = 0.1 cm2/g, this quantity needs to be 10 times larger to achieve the same scattering rate. Generally, ρvrms increases as one goes in towards the halo center, so particles tend to scatter more frequently in the core than in the outer parts of the halo, where interactions are uncommon over a Hubble time. ",
+    "Fig. (<>)5 shows that deviations in the halo shape from CDM begin when ρvrms(σ/m) × (10 Gyr) ∼ 0.1, independent of halo mass. This corresponds to approximately 10% of particles having scattered over a Hubble time at this radius. However, the changes are small compared to the change where Γ × (10 Gyr)  1. We note here that the most massive halos in (<>)Dav´e et al. ((<>)2001) also seem to show the same qualitative behavior. However, even for large values of ρvrms, the deviation from sphericity is significant, a fact that is in some disagreement with the simulation results of (<>)Dav´e et al. ((<>)2001) where c/a  0.9 for their most massive halo. We speculate that part of this could be due to the differences in the way the ellipticity was estimated and part could be due to the smaller box run by (<>)Dav´e et al. ((<>)2001), which implies a quieter merger history. It is well known that CDM halos have anisotropic velocity ellipsoids and elongated shapes that are driven partially by directional merging ((<>)Allgood et al. (<>)2006). These mergers provide a source of anisotropy that needs to be overcome by scattering in order for halos to reach sphericity. We also note that the energy transfer facilitated by self-interactions would lead to an isotropic velocity dispersion tensor and that does not necessarily imply a rounder halo. To make this connection between isotropic velocity dispersion tensor and a rounder halo, previous analytic estimates have relied on the simulations of (<>)Dave´ et al. ((<>)2001). ",
+    "The difference may also be a numerical artifact: we find that halo shapes only converge if there are at least 104 particles in the ",
+    "halo and only for radii r > 2rrelax (see Sec. (<>)2). Most of the halos used for shape estimates in (<>)Dave´ et al. ((<>)2001) only have 103 particles in the virial radius. Their largest halo does have more than enough particles for reliable shape estimates. However, for this massive halo, (<>)Dave´ et al. ((<>)2001) show shape measurements at radii much smaller compared to the convergence radius than we do. In our simulations, we find that halos appear artificially round below the convergence radius. Our shape measurements are consistent with (<>)Dav´e et al. ((<>)2001)’s massive halo for radii above the convergence radius. ",
+    "The other major effect of energy transfers due to scattering is to create a core (see Rocha et al. (2012)) and deep inside a constant density core, we must have c/a → 1. Hence we expect the log slope of the density profile to correlate strongly with the halo shape. Thus, instead of the density profile scaling as ρ ∼ r−1 in the interior as expected for CDM ((<>)Navarro, Frenk & White (<>)1997; (<>)Navarro (<>)et al. (<>)2004, (<>)2010), the density profile of SIDM halos plateaus close to the center. We use the following proxy for the negative log slope of the density profile: ",
+    "(3) ",
+    "where M(r) is the mass enclosed within radius r and γ = −d log ρ/d log r for a power-law density profile. Based on the previous figures, we expect halo shapes to become increasingly round as γ  1, and that the CDM and σ/m = 0.1 cm2/g halos should not dip below γ ≈ 1. In Fig. (<>)6, we show c/a as a function of the log slope of the density profile, as approximated using Eq. ((<>)3), for host halos in our highest mass bin. We obtain similar results for halos of smaller mass, but only show the highest mass bin because these halos are the best resolved. ",
+    "We find that, indeed, SIDM1 halos become significantly rounder as γ < 1 and become almost completely round when γ gets much smaller than 0.5. Interestingly, we also see that c/a deviates strongly from CDM even for relatively large values for the log slope, in regions of the halo in which the scattering is not efficient at changing the radial density profile. This is a consequence of the fact, as shown in Fig. (<>)5, that it does not take a lot of scatters to start rounding out the halos, although it takes multiple scatters for the halos to acquire c/a axis ratios in excess 0.8. Thus, the effects of scattering are apparent for σ/m = 1 cm2/g even when ρ ∼ r−2 and the density profile is unaffected by scatterings. However, the observational importance of this behavior is mitigated by two factors – the change for γ  1 is mild and easily within the scatter in ellipticities seen in CDM. ",
+    "In summary, we find that it only takes a modest local scattering rate per particle, Γ(r)  0.1H0, to start changing the three-dimensional halo shape within radius r with respect to CDM. We find that SIDM1 halos gets significantly rounder compared to CDM predictions when the negative log-slope of the density profile γ  1 in regions where dark matter particles (on average) have had at least interactions in a Hubble time (Γ × (10 Gyr) > 1) . Our results show that even in the limit of one or more scatterings, the halo shapes retain some of their initial triaxiality. "
+  ],
+  "4 COMPARISONS TO OBSERVATIONS ": [],
+  "4.1 Defining Observables ": [
+    "There are a number of ways of quantifying deviations of mass distributions from spherical or axial symmetry. In the previous section, we quantified the deviations in terms of c/a, the ratio of ",
+    "Figure 5. Median axis ratio c/a for host halos as a function of the local scattering rate modulo the cross section: ρvrms ∼ Γ(σ/m)−1 . Smaller values correspond to the outer halo, where the density and scattering rate are low. The quantity is scaled by 10 Gyr cm2/g, such that 1 in these units means that each particle has roughly one interaction per 10 Gyr in SIDM1 (blue dashed line) and one interaction per 100 Gyr in SIDM0.1 (green dotted line). The black solid line is CDM. ",
+    "the semi-minor to semi-major axes determined from the modified three-dimensional moment-of-inertia tensor, Eq. ((<>)2). This is rarely a practical shape estimate observationally. Instead, there is a more suitable measure of halo ellipticity or triaxiality for each type of observation. The relationship between these measures is non-trivial, so care must be taken to compare theory to observation appropriately. From paper to paper, the definition of “ellipticity” can change significantly. In order to facilitate these comparisons, we define three distinct measures of asymmetry in this section and go on to use them for specific comparisons to observational studies in Sec. (<>)4.2, (<>)4.3, and (<>)4.4. The symbols we use for these shape definitions are summarized in Table 2. ",
+    "For strong lensing, which we discuss in Secs. (<>)4.2 and (<>)4.4, what matters is the deviation of the convergence from axial symmetry. The convergence is κ = Σ/Σcr, where Σcr is the critical surface density for creating multiple images. For an axially symmetric system the convergence will be κ(θ), and depend only on the angular distance on the sky θ from then lens center. Once axial symmetry is broken, one must consider κ(θ, φ), where φ is the azimuthal angle that rotates on the sky. (<>)Miralda-Escude´ ((<>)2002) used the following quadrupole approximation to fit the surface density of MS 2137-23, ",
+    "(4) ",
+    "where κ0(θ) is the convergence averaged along azimuthal angle and ε quantifies the amplitude of deviation of the convergence from axial symmetry. Since the normalization of κ and the angle θ depend on the source, lens, and source-to-lens distances, which generically vary, we quantify deviations from axial symmetry in terms of surface density Σ(R, φ), where R is the two-dimensional physical radius in projection. Using Eq. ((<>)4), we define the measure of ellipticity ",
+    "(5) ",
+    "which should be equivalent to ε cos(2φ) if the quadrupole expansion of the two-dimensional surface density is approximately correct. Here, Σ0(R) is the azimuthally averaged surface density. ",
+    "The second type of measure used to quantify deviations from ",
+    "spherical or axial symmetry in lensing arises from the extension of the double pseudo-isothermal sphere, ",
+    "(6) ",
+    "to allow for deviations of the surface-mass density from axial symmetry (double pseudo-isothermal elliptical, or dPIE; see (<>)Richard (<>)et al. (<>)2010), ",
+    "with ",
+    "The dPIE profile has the properties that ρ ∼ const for r  rcore, ρ ∝ r−2 for rcore  r  rcut, and ρ ∝ r−4 for r  rcut, so that the total mass is finite. The center of the halo in projection is denoted by (xc, yc), with the x-direction aligned with the major axis of the distribution. This surface-density profile is often used in fits of the shapes of galaxies or dark-matter halos in clusters that strongly lens background galaxies. ",
+    "The third way we will quantify halo shapes observationally is in terms of similar spheroids (see, e.g., Section 2.5 of (<>)Binney & (<>)Tremaine (<>)2008). For spheroids, we can define an ellipticity parameter ",
+    "(9) ",
+    "where b is the semi-minor and a the semi-major axis. If the z-axis is the symmetry axis, the semi-major axis is given by ",
+    "(10) ",
+    "(11) ",
+    "for prolate spheroids. Similar spheroids are those for which the ",
+    "(7) ",
+    "Table 2: Summary of shape definitions used in observational comparisons ",
+    "Figure 6. Median halo shapes as a function of the estimated log slope of the radial density profile. Lines have the same meaning as in Fig. (<>)3. ",
+    "density profile may be described in terms of ρ(a) and  is fixed throughout the body. The isopotential surfaces of such spheroids are rounder at large distances if the body is more centrally concentrated (see the discussion in Sec. 2.5 of (<>)Binney & Tremaine (<>)2008). ",
+    "As summarized in Table 2, e is the surface-density shape definition we use in Sec. (<>)4.2,  is the X-ray motivated shape definition we use in Sec. (<>)4.3, and e is the lensing-fit shape definition used in Sec. (<>)4.4. "
+  ],
+  "4.2 Revisiting (<>)Miralda-Escude´ ((<>)2002) ": [
+    "Galaxy clusters are great places to look for the effects of velocity-independent SIDM because one may typically achieve much higher values of ρ(r)vrms(r) for fixed r/rvir. In addition, there are many different probes of the mass distribution of clusters that span an enormous dynamic range of radial scale—stellar kinematics and strong lensing towards the center of the cluster, weak lensing and X-ray gas distributions throughout the halo volume, and weak + strong lensing maps of the matter distribution around individual galaxies in the cluster ((<>)Sand et al. (<>)2008; (<>)Newman et al. (<>)2009, (<>)2011; (<>)Kneib & Natarajan (<>)2011). It is no surprise the tightest constraints on velocity-independent SIDM emerged from cluster studies, and a revisit of the tightest of these constraints is the subject of this section. ",
+    "The strongest published constraint on velocity-independent SIDM, σ/m  0.02 cm2/g came from (<>)Miralda-Escude´ ((<>)2002)’s study of the galaxy cluster MS 2137-23. This cluster has an esti-",
+    "mated virial mass of ∼ 8 × 1014M ((<>)Gavazzi (<>)2005), and its mass distribution has also been studied by (<>)Fort et al. ((<>)1992), (<>)Mellier, Fort (<>)& Kneib ((<>)1993), (<>)Miralda-Escude ((<>)1995), (<>)Gavazzi et al. ((<>)2003), and (<>)Sand et al. ((<>)2008). There are two strongly lensed galaxies that produce a total of five distinct images: one source has a radial image at θ ∼ 5 from the center of the brightest cluster galaxy and an arclet at θ = 22.5 . The other source has a large tangential arc and two arclets all at about θ = 15 from the brightest cluster galaxy center, which corresponds to 70 kpc. In order to reproduce both the relative magnifications and the alignments of the images in the sky, the surface density must deviate from axial symmetry at 70 kpc. Quantitatively, it means that the parameter ε in Eq. ((<>)4), which corresponds to the amplitude of e given in Eq. ((<>)5), must be ε ≈ 0.2 at R = 70 kpc. This figure is largely driven by the tangential arcs and associated arclets ((<>)Miralda-Escude (<>)1995) ",
+    "Based on the ellipticity at 70 kpc and an argument that the dark-matter surface density should be approximately axial for a typical particle collision rate Γ  H0, (<>)Miralda-Escud´e ((<>)2002) asserts that Γ(70 kpc)  H0. Using the fact that the tangential arc should lie at approximately where the mean interior convergence κ¯ = 1 (or an estimated critical density Σcr = 1 g/cm2) and the rough approximation ρ(r) ∼ Σ(r)/r, (<>)Miralda-Escude´ estimates the three-dimensional density ρ(70 kpc). Using the velocity dispersion of the brightest cluster galaxy at the center of the halo as a proxy for vrms, (<>)Miralda-Escude´ uses Eq. ((<>)1) to determine a limit on σ/m, which is found to be σ/m  0.02 cm2/g. ",
+    "We get a sense that this line of reasoning may be flawed when we examine the surface-density plots of one of our most massive halos in Figs. (<>)1 and (<>)2 and our findings of Sec. (<>)3. First, recall that our results show (cf., Fig. (<>)5) that the inner halo shape retains some triaxiality even when Γ  H0. Second, the surface density includes all matter along the line of sight, not just the material within r < R. Thus, the surface density at small R/rvir includes a lot of material with large r, far out in the halo where SIDM scatters are unimportant. This material is still quite triaxial. Moreover, SIDM also creates cores, which means that the outskirts of the halo have an even greater weight in the total surface density than if the halo were still cuspy at the center. Empirically, we see that the simulated surface densities in Figs. (<>)1 and (<>)2 are quite elliptical. This point becomes more and more important as the size of the core becomes smaller. All of these things suggest that the constraint reported in (<>)Miralda-(<>)Escud´e ((<>)2002) is far too high. ",
+    "When attempting to quantify the constraints on SIDM from MS 2137-23 using our simulations, we run into the following problem: the largest halo in our simulations has a virial mass Mvir = 2.2 × 1014M, a factor of approximately four smaller than the estimated virial mass of MS 2137-23. Moreover, we do not know the orientation of the principal axes of the cluster with respect to the line of sight. In order to make the comparison, we do two things. First, we can use virial scaling relations to estimate the radius at which ρ(r)vrms(r), a proxy for the scattering rate (see Fig. (<>)5), has the same value as it would for a radius of 70 kpc in MS 2137-23, in other words, we look for the radius at which the ",
+    "Figure 7. The surface-density ellipticity e(R, φ) as defined in Eq. (<>)5 for the same halo as in Figs. (<>)1 and (<>)2. Shown are projections along the three principle axes, evaluated at R = 35 kpc and plotted as a function of azimuthal angle. As in the figures in Sec. (<>)3, the solid black line corresponds to CDM, the blue dashed line to σ/m = 1 cm2/g, and the green dotted line to σ/m = 0.1 cm2/g. The dot-dashed red line shows the minimum amplitude of e(φ) required in order to explain the image positions of MS 2137-23. We do not show the lines for the σ/m = 0.03 cm2/g simulation because it is indistinguishable from the CDM line. The angle φ is defined such that φ = 0 corresponds to the longer axis of the surface-density distribution. ",
+    "SIDM scattering rate should be comparable to the radius at which (<>)Miralda-Escude´ ((<>)2002) finds the constraint for MS 2137-23. For our Mvir ∼ (1 − 2) × 1014M halos, r = 35 kpc is roughly the point at which the scattering rate is similar to that at 70 kpc in MS 2137-23. This is outside rmin for these halos, so we trust the shape measurements. Second, we look at several projections of the halos. We calculate Σ0(R), Σ(R, φ), and hence e(φ) for the various projections of the halos. ",
+    "We show an example of e(φ) curves for lines-of-sight along the principal axes of the halo moment-of-inertia tensors of one of our largest halos in Fig (<>)7, the same halo shown in Figs. (<>)1 and (<>)2. As in previous figures, the solid black line denotes the CDM result, the blue dashed line the result for σ/m = 1 cm2/g, and the green dotted line the result for σ/m = 0.1 cm2/g. We do not show the curve for σ/m = 0.03 cm2/g even though it is the cross section closest to the (<>)Miralda-Escude´ ((<>)2002) constraint because it is indistinguishable from the CDM line. The red dotted line shows the minimum amplitude of e(φ) required for the lens model of MS 2137-23. The e(φ) curves of the other massive halos look similar to the curves for the halo shown in Fig. (<>)7. What we find is that even the σ/m = 1 cm2/g curve generally satisfies the MS 2137-23 constraint. Therefore, we find that the (<>)Miralda-Escude´ ((<>)2002) constraint is in fact overly constraining by two orders of magnitude. While we do not simulate cosmologies with σ/m > 1 cm2/g, and thus cannot set a quantitative upper limit on the SIDM cross section, we may conclude that σ/m = 1 cm2/ g is not ruled out by MS 2137-23. ",
+    "There are a few caveats to this conclusion, which we do not believe will significantly alter our claim. First, none of our simulated clusters are as massive as MS 2137-23. This precludes us from doing a detailed comparison of the projected densities in σ/m = 1 cm2/g to that required to explain the arcs in MS 2137-23. It is, however, informative to do a simple calculation to gauge the importance of this effect. We appeal to the results in the companion paper (Rocha et. al. 2012) that show that the density profile in SIDM for σ/m = 1 cm2/g is well fit by a Burkert profile ((<>)Burk-",
+    "(<>)ert (<>)1995), and that this profile deviates from CDM density profiles at radii smaller than half the Burkert scale radius. At this point, rb/2 or 0.35(rmax/21.6 kpc)−0.08 , the density profile becomes almost constant. We use the Vmax − rmax relation seen in our CDM simulations and the NFW profile to compute the projected mass within 70 kpc as the CDM prediction and compare that to the SIDM prediction by computing the same projected density but assuming that ∀ r < rb/2, ρSIDM(r) = ρCDM(rb/2). This computation reveals that the projected density in σ/m = 1 cm2/g model should be about 30% lower than in CDM for the median (1−5)×1015 M halos. Even for the CDM case, however, the projected density is about a factor of 2 smaller than the estimated Σcr = 1 g/cm2 . Clearly, the estimated projected density (as opposed to the shape) could be a significant constraint on the σ/m = 1 cm2/g model. This simple computation motivates further work along these lines with more realistic SIDM density profiles, inclusion of scatter and the uncertainty in the halo virial mass. ",
+    "We have started much larger-scale simulations in order to study clusters in more detail, which will include an investigation of strong-lensing cross sections as well as ellipticity. In terms of the ellipticity function e(φ), it is not clear in which direction our results will go for simulated 8×1014M halos. On one hand, large halos are more triaxial than small halos, so we would expect that if anything, we would be underestimating the degree of ellipticity in the surface-density distribution. On the other hand, large halos have larger and rounder cores for velocity-independent SIDM compared to their lower-mass cousins. This might drive the constraints the other way, although a larger core implies that the outskirts of the halo get weighted more heavily along the line-of-sight integral of the density for the surface-density calculation. Finally, several authors have noted that MS 2137-23 is actually unusually round for a galaxy cluster ((<>)Gavazzi (<>)2005; (<>)Sand et al. (<>)2008). And intriguingly, the modeling of both (<>)Miralda-Escude ((<>)1995) and (<>)Sand et al. ((<>)2008) indicate that a cored dark-matter radial density profile is preferred over a strongly, CDM-like cuspy profile for the dark-matter halo. Such a cored profile is more in line with what we would expect ",
+    "Figure 8. Distribution of halo ellipticity  as defined in Eq. (<>)9 from fits for halos with M = (3 − 10) × 1012M. The black histograms indicate ellipticities for CDM halos, and the blue shaded histograms show the ellipticities for halos with σ/m = 1 cm2/g, and green dashed histogram shows ellipticities if σ/m = 0.1 cm2/g. The dark blue line with arrow shows the center and width of the best-fit  and uncertainty from (<>)Buote (<>)et al. ((<>)2002). The shapes are found in using the (<>)Dubinski & Carlberg ((<>)1991) weighted moment-of-inertia method described in Sec. (<>)2 and approximated as oblate or prolate spheroids. The initial minimum radius of the shell for the shape measurement is set to rmin = 8.5 kpc, and the maximum radius to rmax = 14 kpc. See text for details. ",
+    "for SIDM. Tighter constraints on σ/m, or a measurement should it be non-zero, will come from an ensemble of clusters, including the most triaxial of them, a point to which we return in Sec. (<>)4.4. "
+  ],
+  "4.3 Shapes from X-ray observations of elliptical galaxies ": [
+    "Constraints on dark-matter scattering have also been made using the shapes of significantly smaller dark-matter halos, Mvir ∼ 1012 − 1013M ((<>)Feng et al. (<>)2009; (<>)Feng, Kaplinghat & Yu (<>)2010; (<>)Buckley & Fox (<>)2010; (<>)McDermott, Yu & Zurek (<>)2011). In this case, the observations consist of X-ray studies of the hot gas halos of elliptical galaxies ((<>)Buote et al. (<>)2002). ",
+    "One may use the shape and twisting of the X-ray isophotes to learn about the three-dimensional shape of the dark-matter halo. Interestingly, halo shapes may be constrained with imaging data alone and do not rely on temperature-profile modeling, which is required for mass-density determinations. This “geometric argument” was first made by (<>)Binney & Strimpel ((<>)1978) and subsequently applied by a number of authors in the study of elliptical galaxies and galaxy clusters ((<>)Fabricant, Rybicki & Gorenstein (<>)1984; (<>)Buote & Canizares (<>)1994, (<>)1996, (<>)1998b; (<>)Buote et al. (<>)2002). The geometric argument is the following: for a single-phase gas in hydrostatic equilibrium, the three-dimensional surfaces in the gas temperature T , gas pressure pg , gas density ρg and gravitational potential Φ all have the same shape ((<>)Binney & Strimpel (<>)1978; (<>)Buote (<>)& Canizares (<>)1998a). Surfaces of constant emissivity jX ∝ ρ2g have the same three-dimensional shape as the isopotential surface. ",
+    "On the other hand, if the spectral data are available (as they ",
+    "typically are with the Chandra telescope), then the temperature-profile data may be used with the assumption of hydrostatic equilibrium to fit the X-ray isophotes. (<>)Buote et al. ((<>)2002) use both approaches to model NGC 720. ",
+    "X-ray isophotes are a good probe of the shape of the local matter distribution for the following reasons. First, the total mass profile (galaxy + gas + dark-matter halo) is nearly isothermal (ρ ∼ r−2) for elliptical galaxies ((<>)Humphrey et al. (<>)2006; (<>)Gavazzi (<>)et al. (<>)2007). This means that the shape of the isopotential contours reflects the shape of the matter distribution at the same radius, although typically the isopotential surfaces are significantly rounder than the isodensity contours (see, e.g., (<>)Binney & Tremaine (<>)2008). Second, the density profile of gas tends to be pretty sharply cuspy (ρg ∼ r−1.5). Since the emissivity goes as jX ∝ ρ2g , and the morphology of jX traces that of the gravitational potential (see the discussion on the geometric argument above), this means that most of the X-ray emission along the line of sight is concentrated at radii close to the projected radius. Thus, the X-ray isophotes indicate the shape of the matter distribution at radii similar to the projected radius. ",
+    "In this section, we focus on the shape measurement of the X-ray emission about the elliptical galaxy NGC 720. The inferred shape of the matter distribution of this system has been used to set constraints on self-interacting dark matter in the recent past ((<>)Feng (<>)et al. (<>)2009; (<>)Feng, Kaplinghat & Yu (<>)2010; (<>)Buckley & Fox (<>)2010; (<>)McDermott, Yu & Zurek (<>)2011). The data set used by (<>)Buote et al. ((<>)2002) for the shape measurement of NGC 720 is a 40 ks exposure of the inner 5 of the galaxy with the ACIS-S3 camera on the Chandra telescope. The data included in the fit are contained within a 35 − 185 annulus from the center of the galaxy, which corresponds to ≈ 4.5 − 22.4 kpc. (<>)Buote et al. ((<>)2002) estimate the three-dimensional isopotential shapes in the following way. First, they investigate a mass-follows-optical light (M ∝ L∗) mass profile for the gravitating mass using the geometric argument. They use a spheroidal (<>)Hernquist ((<>)1990) model for the stellar mass of the galaxy, with structural parameters determined by deprojecting the optical image to three dimensions. This is to test if the stars in the galaxy may be sufficient to provide a gravitational potential for the gas. They find that the isophotes are rounder than observed beyond about Re (≈ 50 or 5 kpc). This suggests that there must be significant ellipsoidally distributed mass extending well beyond the effective radius of stars, since isopotential contours become round as the distance to the main ellipsoidal mass profile increases. ",
+    "Next, (<>)Buote et al. ((<>)2002) use the fact that they find the temperature profile of the halo gas to be isothermal to find the three-dimensional X-ray emissivity distribution (jX ∝ ρg2 ) directly from the equation of hydrostatic equilibrium: ",
+    "(12) ",
+    "where µ is the molecular weight of the gas atoms and mp is the proton mass. They used three similar spheroid models for the mass distribution of the galaxy (baryons plus dark matter) to find the gravitational potential Φ(r). The three models were pseudoisother-mal (ρ(a) ∝ 1/(1 + (a/ap)2) where a is defined in Eqs. ((<>)10-(<>)11)), Navarro-Frenk-White ((<>)Navarro, Frenk & White (<>)1997) and Hern-quist ((<>)Hernquist (<>)1990). They fit both oblate and prolate spheroids, and assumed that the symmetry axis was in the plane of the sky, as this leads to the most elliptical isophotes for a given spheroid. Once the potential was found, they calculated the emissivity distribution ",
+    "in three dimensions and integrated along the line of sight. A χ2 ",
+    "statistic was used to test the quality of the model fits to the X-ray surface-brightness map. ",
+    "The best-fit models were the pseudoisothermal ones, with the oblate and prolate spheroids having nearly identical goodness-of-fit. The best-fit ellipticity  = 0.37 ± 0.03 for the oblate spheroid, and  = 0.36 ± 0.02 for the prolate spheroid. The flatness of the ellipticity as a function of radius in the region of interest drives the best-fit density-profile for isothermality. Only for a similar isothermal spheroid are the X-ray isophotes so constant in ellipticity assuming density profiles that are similar spheroids. ",
+    "We compare our simulations to the (<>)Buote et al. ((<>)2002) results by using the weighted moment-of-inertia tensor ellipsoidal shape estimator of Sec. (<>)2. This method weights particles in the region of interest equally in estimating the shape of the mass distribution, and does not preferentially weight particles near the edge as the true moment-of-inertia tensor does. The initial region in which the ellipsoidal shapes are estimated is a spherical shell of radius rmin < r < rmax, where rmin is our numerical limit on the shape convergence radius and rmax = 14 kpc. We choose this value of rmax as a compromise between finding the ellipticity at small radii, where differences with CDM are highest, and having enough particles in the region of interest for a robust and unbiased shape estimate. The shape of the region of interest is deformed in each iteration of the weighted moment-of-inertia calculation to reflect the major axes of the morphology of the tensor at that iteration, keeping the morphology of the region of interest ellipsoidal and fixing its volume. This region is within the core radii of the σ/m = 1 cm2/g halos, and is our best approximation to the shape of the innermost part of the dark-matter halos, the parts relevant to the study of NGC 720. For reference, the 1012 , 1013M halos have median core radii 16, 43 kpc, respectively (Rocha et. al., 2012). ",
+    "In order to find the spheroidal ellipticity (described in Eq. ((<>)9)) from these ellipsoidal fits, we use the ellipsoidal axis ratios to decide if the halo is oblate or prolate. If prolate, we√take axis ratio of the spheroid 1 − , cf. Eqs. ((<>)10) & ((<>)11), to be bc/a, i.e., the spheroidal semi-minor axis is the geometric mean of the ellipsoidal √ minor and intermediate axes. If oblate, we set 1 −  = c/ ab, i.e., the semi-major axis of the oblate spheroid is set to be the geometric mean of the major and intermediate axes of the ellipsoid. Both these choices set the spheroidal volume equal to the ellipsoidal volume. A more realistic analysis would compute the integrated jX directly from the potential of the simulated halo and compare that to the observations. However, there are significant other uncertainties (discussed below) that argue against such an approach being more fruitful. ",
+    "In Fig. (<>)8, we show the ellipticity distribution for all halos in our 25 h−1Mpc boxes for CDM and SIDM1 that have a virial mass within the 1σ uncertainties of the mass modeling in (<>)Humphrey (<>)et al. ((<>)2006) for NGC 720, Mvir = (6.6+2−3..40) × 1012M. Note that we do not weigh the  distribution by the error distribution for the virial mass presented in (<>)Humphrey et al. ((<>)2006). However, the  distribution in our simulated halos is not a strong function of virial mass in this mass range. We show the CDM  distributions with the black histograms, the σ/m = 1 cm2/g  distributions with the cyan shaded histograms, and σ/m = 0.1 cm2/g with dashed green histograms. We find that the inferred ellipticities are approximately independent of rmax out to approximately 25 kpc, with there being a small tail at higher  for the σ/m = 1 cm2/g halos since the core radii are in the 20-40 kpc range and halo shapes are less affected by scatterings at radii larger than roughly the core radius. For σ/m = 0.1 cm2/g, the core sizes are of order rmin or smaller, so the shape measurements are relatively insensitive to rmax range. A ",
+    "quick review of Fig. (<>)3 also shows that the relative independence of the ellipticity estimate out to 0.1rvir is to be expected in each cosmology. For the σ/m = 1 cm2/g halos, we exclude those halos for which either poor centering of the halo or ongoing merging makes the halos appear artificially flattened. For the other cosmologies, the relative cuspiness of the central density leads to more accurate halo centering. ",
+    "Although there are significant differences in the ellipticity distributions of the CDM and SIDM halos, the observed ellipticity (downward arrow) is just within the ellipticity distribution for σ/m = 1 cm2/g. The fact that this magnitude of ellipticity is still in the distribution for σ/m = 1 cm2/g is also apparent from the middle panel of Fig. (<>)3, which shows that the three-dimensional axis ratios at r/rvir  0.04 (approximately the radius corresponding to the 2D region of interest for NGC 720) can accommodate significant ellipticity. Note that radius is also close to the typical core radius where there we expect roughly 1 interaction per particle on average. This implies that NGC 720 could be an extreme outlier in SIDM1 model and thereby consistent with observations. ",
+    "However, there are some issues with this interpretation. One issue is that the ellipticity measured for the dark matter halo seems to be constant down to roughly ∼ 5 kpc in the data, which is about 1% of the virial radius for the mean virial mass for NGC 720 ((<>)Humphrey et al. (<>)2006). The middle panel of Fig. (<>)5 shows a sharp rise in axis ratio when the number of interactions gets above unity and hence our results are likely to change if we were able push deeper into the core with higher-resolution simulations. A second issue is that the measured halo mass for dark matter within 10 kpc ((<>)Humphrey et al. (<>)2006) is a factor of 2-3 larger than even the median mass in our CDM simulations for halos with virial mass in the range preferred by (<>)Humphrey et al. ((<>)2006) fits. Thus we should also cut the histogram in Fig. (<>)8 based on, say, the mass within 10 kpc (or some other measure of the concentration). These halos, by virtue of their larger densities, will also be rounder. The discrepancy in average dark-matter density within 10 kpc may also be a sign that the inner part of the dark-matter halo has been compressed as a consequence of assembly of the elliptical galaxy, a compression that has been observed in other studies of elliptical galaxies ((<>)Schulz, Man-(<>)delbaum & Padmanabhan (<>)2010; (<>)Dutton et al. (<>)2011). Moreover the presence of the stars and gas increase the velocity dispersion of the dark matter in the central parts and increase the scattering rate – an effect that is not captured in our SIDM simulations. ",
+    "The resolution of these issues lies in a better comparison to the data, which in turn requires a bigger box higher-resolution simulation to probe deeper into the halo and gain more statistics. It will be important to include baryons to see how their presence may affect halo properties. With such a halo catalog in hand, it will be interesting to do a more careful comparison to the X-ray data of NGC 720 and other large nearby ellipticals. The addition of other ellipticals would be crucial. With only one object, the spread we see in ellipticities may be hard to overcome (although it may be smaller if we also cut on concentration as discussed above). If we had an ensemble of shape measurements, we would be able to set tighter limits on the SIDM cross section. ",
+    "While our comparison to (<>)Buote et al. ((<>)2002) is not sufficiently sharp, the weight of the arguments suggests that σ/m = 1 cm2/g is not likely to be consistent with the measured shape of NGC 720. However, based on our existing simulations, σ/m = 0.1 cm2/g is as consistent as CDM for the shape of the NGC 720 isophotes. It is interesting to note in this regard that there is no hint of a large core (∼ 30 kpc) in the results of (<>)Buote et al. ((<>)2002) or (<>)Humphrey et al. ((<>)2006). The core sizes for σ/m = 0.1 cm2/g are smaller, ∼ 7 kpc, ",
+    "for the same virial mass range (Rocha et al, 2012), comparable to the effective radius of the stars in NGC 720. Thus the inferred dark matter density profile in NGC 720 may be a better way to search for effects of self-interactions. ",
+    "To amplify the point about the dark matter density further, we note that the median central (maximum) density for SIDM with σ/m = 0.1 cm2/g is 0.05M/pc3 , while (<>)Humphrey et al. ((<>)2006) infer an average density of 0.04M/pc3 within 10 kpc. At 5 kpc, the inferred average density is 0.1M/pc3 , still within a factor of two (expected from scatter) of the predictions. This lends credence to the argument that an analysis focused on SIDM predictions of an ensemble of nearby X-ray-detected elliptical galaxies could be a fruitful way to look for signatures of or constrain SIDM. It is also worth noting that the shape distribution of σ/m = 0.1 cm2/g is visibly different from CDM and perhaps an ensemble of X-ray-shape measurements could resolve the differences. ",
+    "Our analysis argues for the conclusion that SIDM cross sections with σ/m  0.1 cm2/g can be hidden in X-ray data, and that previous constraints on SIDM using these data are overly stringent. (<>)Feng, Kaplinghat & Yu ((<>)2010) assumed that the (<>)Buote et al. ((<>)2002) ellipticities described the halo shape at the inner radius of R = 4.5 kpc and that Γ ∼ H0 was required to make the halo spherical as indicated by the results of (<>)Dave´ et al. ((<>)2001). Our results indicate that this interpretation is flawed because (a) SIDM halos retain significant triaxiality in the region where Γ ∼ H0 and (b) the scatter in SIDM halo ellipticities is large. In order to use analytic arguments to constrain self-interacting dark matter models, they should be tuned to reproduce the the distribution of axis ratios seen in simulations. "
+  ],
+  "4.4 The future of cluster lensing constraints ": [
+    "In the future, far better constraints on SIDM will come from statistical studies of galaxy-cluster lens samples rather than the analysis of individual objects. In this section, we focus on statistical studies of the shapes of relaxed clusters. ",
+    "There are a number of ongoing and future observational programs designed to characterize the mass function of and mass distribution within galaxy clusters (e.g., (<>)LSST Science Collabora-(<>)tions (<>)2009; (<>)Gill et al. (<>)2009; (<>)Plagge et al. (<>)2010; (<>)Richard et al. (<>)2010; (<>)Planck Collaboration et al. (<>)2011a,(<>)b,(<>)c; (<>)Pillepich, Porciani & (<>)Reiprich (<>)2012; (<>)Marriage et al. (<>)2011; (<>)Viana et al. (<>)2012; (<>)Postman (<>)et al. (<>)2012). Modulo the effects of baryons, a smoking-gun sign of SIDM would be for the mass function of galaxy clusters to look identical to CDM, but with lower mass density and rounder surface-mass distributions at the centers of the clusters. One would use the ensemble of galaxy-cluster data to compare with simulations of clusters in CDM and SIDM (with various elastic scattering cross sections). ",
+    "In this study, we will consider shape-based constraints from the initial results of the Local Cluster Substructure Survey (Lo-CuSS; PI: G. Smith), a multi-wavelength follow-up program of 165 low-redshift clusters selected from the ROSAT All-sky Survey catalog ((<>)Ebeling et al. (<>)2000; (<>)Bohringer¨ et al. (<>)2004; (<>)Richard (<>)et al. (<>)2010). Twenty clusters were used for the first mass-modeling study ((<>)Richard et al. (<>)2010). These were selected because they had been observed with the Hubble Space Telescope (HST), could be followed up spectroscopically at Keck, and were confirmed to have strongly lensed background galaxies. The details of the mass modeling of these clusters are presented in Sec. 3 of (<>)Richard et al. ((<>)2010). For our purposes, the key fact is that the surface density of the cluster-mass dark-matter-halo component of the lens model was ",
+    "parametrized in terms of the dPIE profile, Eq. ((<>)7). This study should be taken as an example of the power of using statistical studies of clusters for SIDM constraints, with an emphasis on the constraints on halo shapes. ",
+    "In order to compare the LoCuSS clusters to simulations, we fit the surface densities of our most massive clusters in the 50 h−1Mpc boxes for our CDM, SIDM0.1, and SIDM1 runs using the dPIE surface-density profile, Eq. ((<>)7). We fit the surface densities of the halos projected along the principal axes of the moment-of-inertia tensors of the mass within the virial radius, and perform the fits within annuli Rmin < R < Rmax. The inner radius of the annuli is chosen to be Rmin = 20 kpc/h, since this is the three-dimensional shape convergence radius (see Sec. (<>)2). We set the outer radius Rmax = 50 kpc/h since most of the lensing arcs in Lo-CuSS are in the range 20 kpc < R < 100 kpc if projected into the plane of the sky at the position of the galaxy clusters. We fix rcut = 1000 kpc, which is what is typically done with the LoCuSS clusters. In practice, the parameter constraints are insensitive to this choice, as all the data are well within this radius if projected onto the sky. The free parameters that we fit are: σ0, the characteristic velocity dispersion of the cluster; rcore, the pseudoisothermal core radius; e, the cluster ellipticity (as defined in Eq. ((<>)8)); and the position angle θ. We fix the center of the cluster to that inferred by AHF. The surface-density parameters were fit using the downhill simplex algorithm in the scipy python module using the likelihood ",
+    "(13) ",
+    "where P (Nobs|N(σ0, rcore, e, θ)) is the Poisson probability of finding Nobs simulation particles within the annulus given a dPIE model with parameters (σ0, rcore, e, θ), for which N simulation particles are expected. Li is the probability of finding a simulation particle i at position (x, y) given those same parameters, ",
+    "(14) ",
+    "where Σ(x, y) is defined in Eq. ((<>)7). ",
+    "Examples of the dPIE fits are shown in Figs. (<>)9 and (<>)10, in which we show the surface densities of one massive halo (Mvir = 1.8 × 1014M) along the major and intermediate principal axes of the halo moment-of-inertia tensor as well as the best-fit dPIE surface densities. The central regions of the halos are masked for R < rmin, the region where the shape profiles in three dimensions are not converged. The halo appears rounder and more dense if projected along the major axis rather than the intermediate axis, just as we saw for another halo in Figs. (<>)1 and (<>)2. While there are noticeable differences between the CDM and σ/m = 1 cm2/ g surface densities at small projected radii, the differences between CDM and σ/m = 0.1 cm2/g are more subtle. ",
+    "To make a quantitative comparison between our simulations and the LoCuSS observations, we examine only those LoCuSS clusters that have σ0 and rcore in a similar range as the fits to the five most massive halos in our simulations. This restricts the number of relevant LoCuSS cluster to five. In Fig. (<>)11, we show the ellipticity e distribution of the five most massive clusters in the CDM (black), σ/m = 1 cm2/g (cyan), and σ/m = 0.1 cm2/g (green hatched) simulations for lines of sight along the three principal axes of the moment-of-inertia tensors. The dark blue points with error bars show the central values and 1-σ uncertainties in e for the cluster halos in the lens-model fits for the five similar LoCuSS clusters. As expected, the ellipticities are highest for the ",
+    "Figure 9. Top row: Surface density of a simulated galaxy cluster of mass Mvir = 1.8 × 1014M in CDM (left), σ/m = 0.1 cm2/g (center) and σ/m = 1 cm2/g (right) cosmologies. The central regions in which the projected radius R < rmin are masked as they are in the fits. These surface densities result from viewing the halo along the major axis of the moment-of-inertia tensor of all particles in the halo. Bottom row: Best-fit dPIE surface-density fits for the surface densities above. The ellipticities of the dPIE fits are: CDM, e = 0.28; σ/m = 0.1 cm2/g, e = 0.25; σ/m = 1 cm2/g, e = 0.29. ",
+    "intermediate-axis line of sight. In this instance, the ellipticities of the CDM and σ/m = 0.1 cm2/g halos are more consistent with the LoCuSS sample than the σ/m = 1 cm2/g halos. However, the lensing probability is highest for lines of sight closely aligned to the major axis ((<>)van de Ven, Mandelbaum & Keeton (<>)2009; (<>)Man-(<>)delbaum, van de Ven & Keeton (<>)2009), and in this case even the CDM halos appear slightly rounder than the LoCuSS clusters. The σ/m = 1 cm2/g halos are definitely too round. ",
+    "Based on this initial set of LoCuSS halos, we believe it is safe to say that σ/m = 0.1 cm2/g is at least as consistent with observations as CDM, but that there is significant tension with σ/m = 1 cm2/g. There are several things that preclude us from making any statements stronger than this. First, we have a small sample of both simulated and observed galaxy-cluster halos. Second, we do not know the virial mass or alignment of the LoCuSS galaxy clusters, nor do we have a good handle on the selection function of the survey. This means that we cannot make a direct comparison between the simulations and the observations. Third, we do not have any galaxy-cluster-mass halos with Mvir > 2.2 × 1014M in our simulations, and thus our ellipticity probability distributions for the lowest-σ0 LoCuSS clusters are almost certainly biased, although it is not clear in which direction that bias goes. Based on the X-ray data, it appears likely that several of the LoCuSS clusters in our subsample are more massive than any simulated cluster even though σ0 and rcore are similar to the simulated clusters ((<>)Richard (<>)et al. (<>)2010). Given that the dPIE fits are made based on the very cen-",
+    "tral regions of the clusters, it is not unexpected that virial masses of the clusters can be very different even if the inner regions look similar. Finally, we do not include baryons in our simulations; it remains unclear how the presence of baryons alters the density profile and shape of galaxy clusters ((<>)Scannapieco et al. (<>)2012). ",
+    "However, it is fair to say that this ensemble of observed galaxy clusters already places stronger constraints on the SIDM cross section than the other constraints we considered in this section, in particular the constraint from MS 2137-23. While σ/m = 1 cm2/g is easily allowed by our reanalysis of the MS 2137-23 constraint (modulo the uncertainty in the normalization of the convergence), this value of the SIDM cross section is in some tension with the LoCuSS cluster sample. A more quantitative limit, though, will only be possible with better theoretical predictions for the shapes of cluster-mass halos and a careful analysis of observed cluster selection functions. In the future, we will simulate larger dark-matter halos and perform mock observations of them to find a better quantitative mapping between observations and SIDM cross-section limits. ",
+    "It may be difficult to probe cross sections as small as σ/m = 0.1 cm2/g based on cluster halo shapes alone, though. We get a sense of how hard it may be to use strong lensing to probe halo shapes, and hence small self-interaction cross sections, in Fig. (<>)9, in which the shapes of the simulated CDM and σ/m = 0.1 cm2/g halos do not look very different on the scales to which strong lensing is sensitive. Moreover, in Rocha et al. (2012), we estimated that core sizes for cluster-mass halos should be  20 kpc if ",
+    "Figure 10. Same as Fig. (<>)9 but with the line-of-sight along the intermediate axis of the halo. The ellipticities here are: CDM, e = 0.59; σ/m = 0.1 cm2/g, e = 0.38; σ/m = 1 cm2/g, e = 0.32. ",
+    "Figure 11. Ellipticity e (Eq. (<>)8) of halos fit with dPIE profiles for three different projections. The solid black histograms show e values for the five most massive CDM halos in the 50 h−1Mpc simulation, the cyan histogram shows the same halos in the SIDM1 simulation, and the green hatched histogram is for SIDM0.1. The dark blue points with uncertainties show the best-fit ellipticities and their 1-σ uncertainties from dPIE modeling of the five LoCuSS clusters with σ0 and rcore similar to those of the simulated clusters ((<>)Richard et al. (<>)2010). ",
+    "σ/m = 0.1 cm2/g. These sizes are similar to the effective radii of the brightest cluster galaxies (BCGs) at the centers of halos. There are several implications of this fact. First, it means that stellar kinematics of the BGCs will be important for probing the dark-matter halo on scales for which scattering matters. Strong lensing is less sensitive to both the density profile and halo shapes at such small scales (see, e.g., Fig. 3 in (<>)Newman et al. ((<>)2011)). Second, it means that any inferences on the dark-matter halo on such scales depends on careful and accurate modeling of the BGCs in the data analysis. Third, we would have to model the behavior of SIDM in the presence of a significant baryon-generated gravitational potential, and to explore the coevolution of dark-matter halos and BGCs. In particular, simulations of isolated disky galaxies indicate that the presence of baryons tends to make the dark-matter distribution more spherical, although it is not clear how much the dark-matter distribution changes if the central galaxy is elliptical instead ((<>)Debattista (<>)et al. (<>)2008). We note that while these issues also have implications for SIDM constraints based on radial density profiles or central densities, they may be more serious for the shape-based constraints because the shapes of σ/m = 0.1 cm2/g are already so similar to CDM halos for small radii even in the absence of baryons. "
+  ],
+  "5 CONCLUSIONS ": [
+    "The takeaway message of this work is that mapping observations to constraints on the self-interaction cross section of dark matter is significantly more subtle than previously assumed, and as such, constraints based on halo shapes are, at present, one to two orders of magnitude weaker than previously claimed. ",
+    "There are three primary reasons that contribute to this conclusion. First, the observational probes (gravitational lensing and X-ray surface brightness) of halo shapes are actually probes of some moment of the mass distribution. For lensing, the observational probes are also sensitive to all material along the line of sight. While SIDM makes the three-dimensional density distribution significantly rounder within some inner radius r, the surface density will in general not be spherically symmetric at a projected radius R = r. The surface densities are affected by material well outside the core set by scatterings where material is still quite triaxial (Fig. (<>)3). Previous constraints were made under the assumption that the observations tracked the three-dimensional halo shape for fixed projected radius. This is a less troublesome assumption for X-ray isophotes, since it is weighted by the square of the gas distribution, and hence sensitive to the central regions. The shapes measured should be related most closely to the shapes of the enclosed mass profile. So, to probe cross-sections as small as σ/m = 0.1 cm2/g, one needs to get down to O(10 kpc) from the center of the halos. The contribution of stars in this region makes it difficult to robustly estimate the shape of the dark matter profile and it also makes it difficult to get a large ensemble of galaxies for this study. ",
+    "Second, there is a fair bit of scatter added by assembly history to the observed shapes and the scatter is large enough that it precludes using a small number of objects to set constraints on SIDM cross sections. Finally, although we find that the three-dimensional shape of halos begins to become more spherical than CDM at radii where the local interaction rate is fairly low, Γ(r) ≈ 0.1 H0, there is a fair amount of triaxiality even when Γ(r) ≈ H0, a fact that was not appreciated in earlier studies (e.g., (<>)Miralda-Escude´ (<>)2002; (<>)Feng, Kaplinghat & Yu (<>)2010) ",
+    "We find that the convergence map of MS 2137-23 (Mvir ∼ 1015M) allows a velocity-independent SIDM cross section of ",
+    "σ/m = 1 cm2/g. The X-ray isophotes of NGC 720 (Mvir ∼ 1013M) likely rule out σ/m = 1 cm2/g, but are consistent with σ/m = 0.1 cm2/g at radii where we can resolve shapes in our simulations. Based on a preliminary comparison to lensing models of LoCuSS clusters, we conclude that σ/m = 0.1 cm2/g is as consistent with observations as CDM but that σ/m = 1 cm2/g is likely too large to be consistent with the observed shapes of those clusters. ",
+    "Cross sections in this range are very interesting. In Rocha et al. (2012), we show that a cross section in the neighborhood of σ/m = 0.1 cm2/g could solve the “Too Big to Fail” problem for the Milky Way dwarf spheroidals ((<>)Boylan-Kolchin, Bullock & (<>)Kaplinghat (<>)2012), the core-cusp problem in LSB galaxies ((<>)Kuzio (<>)de Naray et al. (<>)2010; (<>)de Blok (<>)2010), as well as the shallow density profiles of the galaxy clusters in (<>)Sand et al. ((<>)2008); (<>)Newman et al. ((<>)2009), and (<>)Newman et al. ((<>)2011) while not undershooting their central densities or overshooting the core sizes. Cross sections in this range are also consistent with other density-profile-based and subhalo-based constraints ((<>)Yoshida et al. (<>)2000b; (<>)Gnedin & Ostriker (<>)2001). ",
+    "Since the current set of observations appear to be consistent with a SIDM cross section of σ/m = 0.1 cm2/g, there are two relevant questions for shape-based SIDM constraints. Will shape-based constraints be competitive with other types of SIDM constraints? And what will it take to get down to σ/m ∼ 0.1 cm2/g with shapes? ",
+    "Upon closer inspection, our view is that constraints using existing data could be pushed below σ/m = 1 cm2/g, but it is not yet clear that we can get to σ/m ∼ 0.1 cm2/g. While X-ray isophotes of the elliptical galaxy NGC 720 are consistent with σ/m = 0.1 cm2/g, there are some differences and a larger ensemble of elliptical galaxies may be able to test that. There are a number of other elliptical galaxies for which high-resolution X-ray data exist (e.g., (<>)Humphrey et al. (<>)2006), but they lack the detailed shape measurements of NGC 720. So better constraints could result from X-ray shape analysis for these galaxies. For clusters, based on our quick pass through the LoCuSS results, lensing-based shape constraints on SIDM could also extend well below σ/m = 1 cm2/g if simulations are performed of a statistically significant number of massive galaxy clusters. However, in studies of both galaxies and clusters, it is likely that the measured densities in the inner regions would be a better way to test for signatures of self-interacting dark matter. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "AHGP is supported by a Gary McCue Fellowship through the Center for Cosmology at UC Irvine, NASA Grant No. NNX09AD09G and NSF grant 0855462. MR was supported by a CONACYT doctoral Fellowship and NASA grant NNX09AG01G. JSB was partially supported by the Miller Institute for Basic Research in Science during a Visiting Miller Professorship in the Department of Astronomy at the University of California Berkeley. This research was supported in part by the Perimeter Institute of Theoretical Physics during a visit by MK. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. This research was also supported in part by the National Science Foundation under Grant No. NSF PHY11-25915 during a visit by AHGP to the Kavli Institute for ",
+    "Theoretical Physics. AHGP thanks Michael Boylan-Kolchin for the use of his three-dimensional shape code. "
+  ]
+}

jsons_folder/2013MNRAS.430.2844C.json

@@ -0,0 +1,121 @@
+{
+  "ABSTRACT ": [
+    "We investigate the extent to which cosmic size magnification may be used to complement cosmic shear in weak gravitational lensing surveys, with a view to obtaining high-precision estimates of cosmological parameters. Using simulated galaxy images, we find that unbiased estimation of the convergence field is possible using galaxies with angular sizes larger than the Point-Spread Function (PSF) and signal-to-noise ratio in excess of 10. The statistical power is similar to, but not quite as good as, cosmic shear, and it is subject to di erent systematic e ects. Application to ground-based data will be challenging, with relatively large empirical corrections required to account for the fact that many galaxies are smaller than the PSF, but for space-based data with 0.1-0.2 arcsecond resolution, the size distribution of galaxies brighter than i ≃ 24 is almost ideal for accurate estimation of cosmic size magnification. ",
+    "Key words: data analysis -weak lensing-size magnification "
+  ],
+  "1 INTRODUCTION ": [
+    "General relativity predicts that the path of light from a distant galaxy is distorted by the gravitational potential fluctuations along the line of sight. This modification of the light paths is called gravitational lensing and is a powerful tool for probing the distribution of mass in the Universe. The variation of the light path depends on the position in the sky of the emitting object, the distance from the emitting object to the observer and on the potential along the light path. As the Universe is in permanent evolution photons emitted at an earlier epoch will be deflected from those emitted later, due principally to the longer path length (for some reviews see (<>)Schneider et al. (<>)1992; (<>)Narayan & Bartelmann (<>)1996; (<>)Mellier (<>)1999; (<>)Munshi et al. (<>)2008). Combining this depth information with angular information on the gravitational lensing distortion, allows for an unbiased reconstruction of the three-dimensional distribution of matter. In addition, statistical analysis to infer cosmological parameters can be made from the dependence of observables on the distance-redshift relation and growth of density perturbations with redshift. Dark energy and modifications to Einstein gravity also act to ",
+    "modify the lensing e ect by changing the distance-redshift relation in addition to the growth of density perturbations ((<>)Huterer (<>)2002; (<>)Munshi & Wang (<>)2003). Lensing e ects are therefore a particularly valuable source of information for three of the important open issues in modern cosmology, namely the distribution of dark matter, the properties of dark energy and the nature of gravity. ",
+    "Observationally there are three main e ects on the background sources: changes in the ellipticity, magnification of the flux, and magnification of the size, the last two being directly related due to the conservation of the surface brightness in gravitational lensing. For large densities of matter the e ects are all very strong, and multiple images of the background galaxies can be produced with large distortion. The studies of this distortion have led to local reconstructions of the distribution of matter (see for example (<>)Tyson et al. (<>)1984; (<>)Fort et al. (<>)1988; (<>)Tyson et al. (<>)1990; (<>)Kaiser & Squires (<>)1993; (<>)Mellier et al. (<>)1993). When the potential fluctuations and their derivatives are small, the mapping from the source position to the image position on the sky is the identity matrix with corrections which are ≪1. This weak-lensing regime does not allow significant information to be gained from individual sources, but the distortions may be observed statistically using a large sample. ",
+    "In weak lensing, the most studied e ect is the modification to the galaxy shape, a measure of the shear. The ",
+    "shape distortion has the main advantage that the intrinsic distribution of galaxy ellipticities is expected to be random, according to the cosmological principle, and therefore the average complex ellipticity is zero. Weak lensing e ects using galaxy ellipticities is a well-developed field and has been detected by several groups using different surveys and di erent methods, see for example (<>)Wittman et al. ((<>)2000); (<>)Semboloni et al. ((<>)2006); (<>)Jarvis et al. ((<>)2006); (<>)Benjamin et al. ((<>)2007); (<>)Schrabback et al. ((<>)2010). In addition important e orts have been made to include and test many possible systematic e ects on shape measurement (including the point spread function [PSF], instrumental noise, pixelization for example), and there are several algorithms that can measure shapes with varying degrees of accuracy including KSB ((<>)Kaiser et al. (<>)1995), KSB+ ((<>)Hoekstra et al. (<>)1998) and its variants ((<>)Rhodes et al. (<>)2000; (<>)Kaiser (<>)2000) and shapelets ((<>)Bernstein & Jarvis (<>)2002; (<>)Refregier & Bacon (<>)2003; (<>)Kuijken (<>)2006) amongst others. A novel Bayesian model fitting approach lensfit was presented in (<>)Miller et al. ((<>)2007); (<>)Kitching et al. ((<>)2010). In order to test, in a blind way, the ability of methods to measure the shapes of galaxies a series of simulations have been created: STEP1, STEP2, GREAT08 and GREAT10, where several methods have been tested and compared systematically. An explanation of the methods and their performance are summarised in (<>)Heymans et al. ((<>)2006); (<>)Massey et al. ((<>)2007); (<>)Bridle et al. ((<>)2010); (<>)Kitching et al. ((<>)2012) respectively. In addition to altering the shapes of galaxies, weak lensing induces a flux magnification e ect, which varies the number of galaxies above a flux threshold, and is usually quantified using the number counts (see for example (<>)Broadhurst et al. (<>)1995; (<>)Hildebrandt et al. (<>)2009, (<>)2011); the number of observed galaxies above a given flux may increase or decrease due to lensing by the foreground galaxies increasing fluxes but simultaneously increasing the solid angle covered by the images. We do not study this further in the paper but instead focus on size magnification. ",
+    "In contrast to galaxy ellipticity measurement, the size information has not been explored in detail, possibly because the complicating e ects of the PSF and pixellisation were thought to be too challenging. However, there are two reasons for revisiting size magnification as a potential tool for cosmology: one is that accurate shear estimation is itself very challenging, and size could add useful complementary information; the second is that methods devised for ellipticity estimation must deal with the PSF and pixellisation, and as a byproduct provide a size estimate, or a full posterior probability distribution for estimated size, which is currently ignored or marginalised over. ",
+    "2007",
+    "In terms of signal-to-noise (S/N) of shape distortions vs magnification estimation, the relative strengths of the methods depend on the distributions of ellipticity and size. The former has an r.m.s. of around 0.3-0.4 ((<>)Leauthaud et al. ); for bright galaxies (Mr<−20), the Sloan Digital Sky Survey (SDSS) found that the size distribution is approximately log-normal with σln R∼0.3, and for fainter galaxies σ(ln R) ∼0.5), where Ris the Petrosian half-light radius ((<>)Shen et al. (<>)2003); for deeper space data the dispersion is also around 0.3 ((<>)Simard et al. (<>)2002). Thus one might expect a slightly smaller S/N for lensing measurements based on size rather than ellipticity, but not markedly so. (<>)Bertin & Lombardi ((<>)2006) proposed a method based ",
+    "on the fundamental plane relation ((<>)Dressler et al. (<>)1987; (<>)Djorgovski & Davis (<>)1987) to reduce the observable size variance. (<>)Hu & Graves ((<>)2011) applied a similar method to measure galaxy magnification using 55,000 galaxies of the SDSS catalogue, and find consistency with shear using the same sample. Also a detection with COSMOS HST survey using a revised version of the KSB method is presented in (<>)Schmidt et al. ((<>)2012), showing reasonable consistency with shear. ",
+    "Here we revisit size magnification measurement, and will show that to use size-magnification we require i) a wide area survey that enables observations of a suÿciently large sample of galaxies, this is required to overcome the intrinsic scatter, and ii) a consistently small PSF that does not destroy the size information of the observed galaxies. Both of these requirements can be met with a wide-area space-based survey, although some science may be possible from the ground. Euclid1 (<>)((<>)Laureijs et al. (<>)2011) should meet these requirements (large samples will be available, and the PSF size is smaller than typical galaxies), so the size information could be considered as a complementary cosmological probe to weak lensing ellipticity measurements. One advantage of using the size information is that the magnification and distortion have di erent radial dependences on the spatial distribution of matter, which may be very useful to lift the so-called mass-sheet degeneracy ((<>)Bartelmann et al. (<>)1996; (<>)Fort et al. (<>)1997; (<>)Taylor et al. (<>)1998; (<>)Broadhurst et al. (<>)2005; (<>)Umetsu et al. (<>)2011; (<>)Vallinotto et al. (<>)2011), that occurs due to the reduced shear (or the measured ellipticities) being invariant under a transformation of the distortion matrix by a scalar multiple. ",
+    "Besides the degeneracy lifting, another advantage of using magnification is that combining the size magnification information with the shear will reduce uncertainties on the reconstruction of the distribution of matter ((<>)Jain (<>)2002; (<>)Vallinotto et al. (<>)2011; (<>)Sonnenfeld et al. (<>)2011). ",
+    "On the measurement of the size, all of the shear estimation methods referred to above already estimate the size of galaxies when calculating the ellipticities, so we expect to measure this additional information for free, given an accurate ellipticity measurement. However, the accuracy of size information should not be taken for granted: it is important to know the uncertainties in size measurement, and how they propagate to a convergence field estimation. It is this question of how accurately one can measure the sizes of galaxies, that this paper addresses. (<>)Amara & R´efr´egier ((<>)2007); (<>)Kitching et al. ((<>)2008) have shown that to obtain an accurate determination of cosmological parameters, such as the equation of state of dark energy, the systematic errors in the measured ellipticities should be . 0.2%, and we would expect similar requirements for size. Although a full study of the convergence bias at this level needs to be done, the main goal of this first paper is to investigate whether unbiased measurement of size is feasible at all, and to come some basic conclusions on required image sizes and signal-to-noise. ",
+    "The paper is organised as follows. First, in Section 2 we will present the weak lensing quantities that are used throughout this paper, then a definition of the estimator, ",
+    "and a brief comment on the method and the characteristics of the simulated images. In Section 3 the analysis and results are explained and finally we will summarise the conclusions in Section 4. "
+  ],
+  "2 METHOD ": [
+    "A good algorithm for weak lensing analysis must be able to take into account the distortion introduced by the PSF, pixelization e ects and pixel noise. Another requirement is that it should be computationally fast because the statistical analysis will be made on large samples. This means that algorithm development is challenging because of the dissonant requirements of both increased accuracy and increased speed as the required systematic level decreases. Several methods have been proposed and applied to weak lensing surveys, and are described in the challenge reports of STEP, GREAT08 and GREAT10 ((<>)Heymans et al. (<>)2006; (<>)Bridle et al. (<>)2010; (<>)Kitching et al. (<>)2012). These blind challenges have been critical in demonstrating to what extent methods can achieve the required accuracy for upcoming surveys by creating simulations with controlled inputs against which results can be tested. Here we propose a very similar approach as the one presented in the GREAT10 challenge, we have used simulated galaxy images with di erent properties to measure the response of the size/convergence measurement under di er-ent conditions (corresponding to changes in the PSF, S/N and bulge fraction). "
+  ],
+  "2.1 Weak lensing formalism ": [
+    "The distortions induced by gravitational lensing are described by the Jacobian matrix which maps the true angular position of the image to the angular position of the source (in the absence of deflections): ",
+    "which defines the convergence field κand complex shear field γ≡γ1 + iγ2 (for more details, see e.g. (<>)Bartelmann et al. (<>)1996; (<>)Hoekstra & Jain (<>)2008; (<>)Munshi et al. (<>)2008). In terms of the convergence and the shear there are two important variables, directly related to the lensing observables. The reduced shear, ",
+    "(1) ",
+    "represents shape changes ignoring size. The magnification of the surface area µis, ",
+    "(2) ",
+    "If κ,|γ|≪1 (which we assume throughout) can be approximated by ",
+    "The power spectrum for κcan be obtained in terms of the matter power spectrum Pδ(k,w), where wis a comoving distance coordinate which plays the role of cosmic time. For a set of sources with a distribution function p(w), ",
+    "(3) ",
+    "where dwis the co-moving distance, whis the horizon distance. mand H0 are the present matter density parameter and Hubble parameter. Note that eq. (<>)1 and (<>)2 are always valid while eq. (<>)3 is only meaningful for cosmic shear. ",
+    "In the weak lensing limit, the power spectrum of the magnification fluctuations (µ−1) is 4 times Pk(l), therefore, in principle, cosmological constraints could be made independently of the shear ((<>)Jain (<>)2002; (<>)Barber & Taylor (<>)2003), however the signal-to-noise ratio for the measured elliptici-ties is in general larger, hence the shear may carry more statistical weight. Even so a complementary analysis of shear and magnification measurements will necessarily provide tighter constraints on cosmological parameters than a shear analysis alone. In particular, in (<>)van Waerbeke ((<>)2010) it is shown that the constraints on σ8 and mcan be improved up to ∼40%, similarly combining size-magnification, galaxy densities and shear, the improvement on the precision of halo mass estimates can be ∼40%−50% ((<>)Rozo & Schmidt (<>)2010). "
+  ],
+  "2.2 Estimator ": [
+    "In this paper we will work with the semi-major axis of the images, denoted by s, and the semi-major axis of the un-lensed source, ss. Their ratio is given by where is computed in the principal axis frame. At linear therefore then order in the weak lensing regime their ratio is The contribution of shear is a zero-mean noise term which is small in comparison to the e ects of the intrinsic size distribution, and will be ignored. On the other hand, the magnification is related to the convergence, to first order, κ∼sss −1. We can construct an estimator for κin the weak value is not modified by lensing, and replacing ssby its expectation value: 1lensing limit by assuming that, since the mean size ",
+    "(4) ",
+    "From the definition of the estimator, and the width of the sdistribution, an estimate of κfrom a single galaxy will be very noisy, with smaller galaxies than the mean always giving a negative κˆ, while larger galaxies will produce positive κˆ. What is important is to test if our estimator is unbiased over a population to a suÿcient degree to be useful for real data. "
+  ],
+  "2.3 lensfit ": [
+    "Throughout we use lensfit ((<>)Miller et al. (<>)2007; (<>)Kitching et al. (<>)2008, Miller et al., 2012) to estimate the galaxy size; we use this because: 1) it has been shown that lensfit performs well on ellipticity measurement; 2) it is a model fitting code which also measures the sizes of galaxies; 3) it allows for the consistent investigation of the intrinsic distribution of galaxy sizes through the inclusion of a prior on size, and 4) it includes the e ects of PSF and pixellisation. lensfit was proposed in (<>)Miller et al. ((<>)2007) and has been proved to be a successful tool for galaxy ellipticity shape measurements ((<>)Kitching et al. (<>)2008). Although model-fitting is the optimal approach for this type of problem if the model used is an accurate representation of the data, the main disadvantage is ",
+    "that is usually computationally demanding to explore a large parameter space. lensfit solves this problem by analytically marginalizing over some parameters that are not of interest for weak lensing ellipticity measurements, such as position, surface brightness and bulge fraction. The size reported by lensfit is also marginalised over the galaxy ellipticity. "
+  ],
+  "2.3.1 Sensitivity correction ": [
+    "In the Bayesian formalism the expected value for the size of R an individual galaxy can be written as s= sp(s|sd)ds, where sdis the data and sstands for the fitted model parameter for the size explained in Sec. (<>)2.4. In terms of the prior P(s) and the likelihood L(sd|s) the expression is ",
+    "(5) ",
+    "Individual galaxy size estimates allow errors to be assigned to each galaxy, or the full posterior can be used and the information propagated to the κsignal. (<>)Miller et al. ((<>)2007) introduced the shear sensitivity, a factor that corrects for the fact that the code measures ellipticities but that shear (a statistical change in ellipticity) is the quantity of interest. A similar correction is required for size measurement, whereby we measure the size but it is the convergence that is the quantity of interest; this correction is needed because for a single galaxy the prior information for the convergence is not known, and we assume it is zero. With a Bayesian method we can estimate the magnitude of this e ect for each galaxy, a further reason to use a Bayesian model fitting code in these investigations. Consider the Bayesian estimate of the size of galaxy iand write its dependence on κas a Taylor expansion: ",
+    "(6) ",
+    "In the simple case where the likelihood L(sd|s) (for simplicity, hereafter L(s) = L(sd|s)) is described by a Gaussian distribution with variance b2 , with an expectation value s, and a prior P(s) that also follows a Gaussian distribution centred on s¯ with variance a2 , the posterior probability will follow a Gaussian distribution with expectation value: ",
+    "and variance ",
+    "These equations illustrate that the posterior is driven towards the prior in the low S/N limit (b→∞), and thus requires correction. Di erentiating the expression sd= ss(1 + κ) + σs, with σsbeing the systematic noise, we find that the κsensitivity correction is: ",
+    "(7) ",
+    "substituting into eq. (<>)6 ",
+    "we find the estimator for κwill be the same as in eq. (<>)4, ",
+    "corrected by the sensitivity factor: ",
+    "(8) ",
+    "In this work we have used this approximation for simplicity but in general a normal distribution should not be assumed. A more general estimation of the κcorrection can be done in the same way as with the shear and can be evaluated numerically, without the need of using external simulations. ",
+    "To calculate the sensitivity correction in the general case we consider the response of the posterior to a small κ, by adding the convergence contribution in the likelihood, L(s−ss) →L(s−ss−κss) and expand it as a Taylor series: ",
+    "We then substitute into eq. (<>)5 and di erentiate to obtain the analytic expression for the κsensitivity (for more details of this applied to ellipticity measurement see (<>)Miller et al. (<>)2007; (<>)Kitching et al. (<>)2008) ",
+    "(9) ",
+    "If the prior and likelihood are described by a normal distribution, this expression can be analytically computed and the sensitivity correction is the same as before. A similar empirically motivated correction on the estimator expression was used in eq.5 of (<>)Schmidt et al. ((<>)2012), where the factor is computed with simulations. "
+  ],
+  "2.4 Simulations ": [
+    "In order to test the estimation of sizes with lensfit we have generated the same type of simulations used in the GREAT10 challenge ((<>)Kitching et al. (<>)2010, (<>)2012), but with non-zero κ. Multiple images were generated, each containing 10,000 simulated galaxies in a grid of 100x100 postage stamps of 48x48 pixels; each postage stamp contains one galaxy. ",
+    "Each galaxy is composed of a bulge and a disk, each modeled with S´ersic light profiles: ",
+    "(10) ",
+    "where I0 is the intensity at the e ective radius rdthat encloses half of the total light and K= 2n−0.331. The disks were modelled as galaxies with an exponential light profile (n= 1), and the bulges with a de Vaucouleurs profile (n= 4). Ellipticities for bulge and disk were drawn from a Gaussian distribution centred on zero with dispersion σ= 0.3. Both components had distributions centred at the middle of the postage stamp with a Gaussian distribution of σ= 0.5 pixels. The galaxy image was then created adding both components. The S/N was fixed for all galaxies of the image and implemented by calculating the noise-free model flux by integrating over the galaxy model, then adding a constant Gaussian noise with a variance of unity and rescaling the galaxy model to yield the correct signal-to-noise, as in (<>)Kitching et al. ((<>)2012). Finally the PSF was modelled with a Mo at profile with β= 3, with FWHM fixed for all galaxies on the image, with di erent ellipticities drawn from a uniform distribution, with ranges given in Table (<>)1. ",
+    "The di erent types of image were generated to study the e ects of the bulge fraction (fraction of the total flux concentrated in the bulge), the S/N and the PSF separately. In summary, the main characteristics of the considered sets are: ",
+    "To characterize the size of the galaxy the semi-major axis is used, related to the half-light disk radius where qis the semi-axis ratio. We have drawn rdfrom a Gaussian distribution with expected value of 7 pixels and dispersion of 1.2 pixels, to keep disk sizes of at least 2 pixels and not larger than the postage-stamp. The galaxy sizes explored here have a somewhat smaller range (σ(ln R) ∼0.18) than found by (<>)Shen et al. ((<>)2003) with the SDSS catalogue, where in terms of pixels the mean value of the full sample is around 5 with σ(ln R) ∼0.3 (see Fig.1 of (<>)Shen et al. (<>)2003). Therefore the sensitivity corrections are consequently larger than would be needed for real data. Besides a wider distribution of galaxies, the important change from the original images for the GREAT10 challenge is the addition of a non-zero κ-field that creates a size-magnification e ect (in GREAT10 only a shear field was used to distort the intrinsic galaxy images). A Gaussian convergence field with a simple power-law power spectrum in Fourier space Pκ(ℓ) ∼10−5ℓ−1.1 has been applied to each image. The power-law is a good approximation to the theoretical power spectrum over the scales 10 . ℓ. 10000 (see i.e. (<>)Schneider (<>)2005).The size of the κ-field is and θimageis set to 10 degrees, such that the range in ℓwe used to generate the power was ℓ= [36,3600] where the upper bound is given by the grid separation cut-o . In real space this translates to a maximum |κ|of around 2%, although we investigate larger |κ|in Section (<>)3.4. The κ-field is generated on the 100x100 grid, each point representing a postage stamp, and is applied to the galaxy at the same position (s= ss(1 + κ)), neglecting the contribution of the shear. The pixel angular size is not fixed, and can be scaled to any experimental set up. "
+  ],
+  "3 RESULTS ": [
+    "Before trying to estimate the convergence field of our most realistic image, we have tested the dependence on di er-ent aspects separately: S/N, PSF size and bulge fraction. We expect these to be the observable e ects that have the largest impact on the ability to measure the size of galaxies. Lower S/N will cause size estimates to become more noisy and possibly biased (in a similar way as for ellipticity, see (<>)Melchior & Viola (<>)2012); a larger PSF size will act to remove information on galaxy size from the image and a change in galaxy type or bulge fraction may cause biases because now two characteristic sizes are present in the images (bulge and disk lengths). In order to study carefully the sensitivity of ",
+    "our estimator to systematic noise, PSF or galaxy properties, we started from the simplest case and added increasing levels of complexity. The number of galaxies used for the analysis is 200,000 for the first three sets and we increased the number to 500,000 for the last test to give smaller error bars. ",
+    "We compare the estimated κˆ computed as in eq. (<>)4 with the input field κ, and fit a straight line to the relationship to estimate a multiplicative bias mand an additive bias c: ",
+    "(11) ",
+    "after applying the sensitivity correction (section (<>)2.3.1). We bin the data2 (<>)and a linear fit is done to compute mand c. This process is shown in Fig. (<>)1. The error bars for the regression coeÿcients are given by its standard deviation, assuming that the errors are normally distributed. The regression coeÿcients and its errors are computed using the function polyfit of matlab software. ",
+    "We now discuss each of the categories in turn. "
+  ],
+  "3.1 Signal-to-noise ": [
+    "As a first approach to the problem, disk-only galaxies with a negligible PSF (FHWM= 0.01 pixels) and zero ellipticity were generated to test the dependence of the bias on S/N alone, given otherwise perfect data. In Fig. (<>)2 we can see that as we increase the S/N the accuracy of the size estimation grows, as expected. In Fig. (<>)3 we show the estimation of the convergence field, modified by the sensitivity correction. There is a clear correlation between the inputs and the outputs, and the slope is close to unity for all S/N explored. In Fig. (<>)4 the estimates for mand care shown, with and without the sensitivity correction. In this case the correction does not alter the results much except at low S/N, because the sizes are less accurately estimated. In this paper the factor a2/(a2 + b2) is estimated by the inverse of the slope of the size estimation fitting (see Fig. (<>)2). Using 200,000 galaxies for this test, the values found for mand care consistent with zero, typically m≃0.02 ±0.05, and c≃(5 ±5) ×10−4 . "
+  ],
+  "3.2 PSF e ect ": [
+    "To study the uncertainties on the size estimation due to the PSF size, we generated images with di erent FWHM PSF values, with an intermediate signal to noise (S/N=20), maintaining the same properties as before, except that we considered here a Gaussian distribution of ellipticities with mean value of e= 0 and σe= 0.3 (per component). The size estimates are good for small PSFs, but become progressively more biased as the PSF size increases beyond the disk scale length (see Fig. (<>)5). A PSF with a FWHM larger or similar to the size of the disk, tends to make the galaxy look larger, and the estimator for κbecomes biased. This e ect can be seen in the slope and intercept of κˆ vs κplot (Fig. (<>)6). Fig. (<>)7 shows the variation of the parameters mand cwith the ratio between the scale-length of the PSF and the galaxy (ratio=rd/PSFFWHM). ",
+    "Table 1. Major characteristics of the di erent sets used in this analysis. In bold are marked the variables explored in each set and the range of variation. In Set 4, PSF ellipticities are drawn from a uniform distribution in the range specified. Note that ricorresponds to the half-light radius. Last column is the galaxy ellipticity and is the same for both components, bulge and disk. ",
+    "Figure 1. Sequence of steps to obtain m and c values. First panel shows the lensfit output size compared to the input size, in the second panel the estimated  compared to the input convergence at each galaxy, and in the third panel is shown the same plot using bins. Slope and intercept values of the fitting are shown in each plot (throughout, we fit generically y = bx + c, with b = m + 1 and c = c of eq. (<>)11). This is for galaxies of Set 1 with signal-to-noise 40. ",
+    "Figure 2. Comparison of the estimated sizes by lensfit with the input galaxy size for di erent S/N in the range [10,40]. Disk-only circular galaxies with a negligible PSF e ect are considered (Set 1). Slope and intercept of the fitting are shown (b and c, respectively). Note that the input size is the lensed one. ",
+    "We find no evidence for an additive bias, but we do find a multiplicative bias for large PSFs. With a wide size distribution, some of the smaller galaxies are convolved with a PSF larger than their size, and this could produce an overall bias in κ, but if the number of those galaxies is not very large, the e ect on the global estimation of the convergence field will be correspondingly small. Similar biases exist with shear measurement for large PSFs, but the biases are larger here. For a space-based experiment, with a relatively bright ",
+    "Figure 3. Comparison of the binned estimated convergence and the input value for Set 1 with di erent S/N in the range [10,40]. Slope and intercept of the fitting are shown (b and c, respectively). For errors, see text. ",
+    "cut at i∼24.5, such as planned for Euclid, the limitation on PSF size will not be dominant because the median galaxy size is 0.24 arcsec ((<>)Simard et al. (<>)2002; (<>)Miller et al. (<>)2012), larger than the PSF FWHM of 0.18 arcsec. For ground-based surveys, such as CFHTLenS and future experiments the situation is not so clear, the measurement will be more challenging, and large empirical bias corrections of the order of m≃−0.5 will be needed (see the first point of Fig. (<>)7). ",
+    "Figure 4. m and c values computed with 200,000 galaxies of Set 1. Triangles are for the values obtained with the sensitivity correction and squares without it. ",
+    "Figure 5. Sizes estimates vs input sizes for four di erent PSF scale-lengths between 0.1 and 7 pixels. Galaxies are disks with S/N=20 and mean size 7 pixels. Slope and intercept of the fitting are shown (b and c, respectively). ",
+    "Figure 6.  estimates vs input values for four di erent PSF scale-lengths. Galaxies are disks with S/N=20 and mean size 7 pixels. Dashed line is out= inand the solid line is the least squares fit, with slope and intercept shown in the plots. Note that b=m+1. ",
+    "Figure 7. m and c values computed with 200,000 galaxies of Set 2. Triangles represent the values obtained with the sensitivity correction and squares without it. "
+  ],
+  "3.3 Bulge fraction ": [
+    "In this test we generated galaxy images with bulges with different fractions of the total flux, to test the response to the galaxy type. In Fig. (<>)8 we show that galaxy size estimates for bulge fractions of 0.2 are much better than for galaxies with bulge fractions of 0.95. This is because for bulge-dominated models the central part of the galaxy becomes under-sampled due to a limiting pixel scale. The poor estimation of sizes is reflected in the κestimation (bottom panels of Fig. (<>)8). The parameters mand cfor this set are shown in Fig. (<>)9, where we can see that for bulge fraction greater than 0.8, the results are clearly biased with m= −0.25. For all bulge fractions the error bars are around 10%. Although for bulge-only galaxies, the κestimates are poor most of the galaxies used for weak lensing experiments have bulge fractions lower than 0.5 ((<>)Schade et al. (<>)1996), so that in fact the population of useful lensing galaxies is likely to be enough to do a successful analysis. ",
+    "Figure 8. Top panels: Sizes estimates vs input sizes for di erent bulge fractions in the range [0.2,0.95]. Bulge+Disk galaxies with di erent ellipticities are used, with S/N=20 and negligible e ect of the PSF (Set3). Slope and intercept of the fitting are shown (b and c, respectively). Bottom panels: Bulge+Disk elliptical galaxies with S/N of 20 and negligible e ect of the PSF (Set 3). Dashed line is out= inand the solid line is the fit of the output values. Note that b=m+1 of eq. (<>)11. ",
+    "Figure 9. m and c values computed with 200,000 galaxies of Set 3. Values obtained with the sensitivity correction are marked by triangles and by squares are without the correction. "
+  ],
+  "3.4 Most Realistic Set ": [
+    "The last set includes realistic values for all the e ects we investigate. We have generated galaxies with elliptical isophotes with a bulge fraction of 0.5 convolved with an anisotropic PSF with FWHM of 4.5 pixels (1.5 times smaller than the characteristic scale-length of the disk), and again we investigate the dependence on S/N. This is also a challenging test for lensfit, the current version (c. 2012) of which uses a simplified parameter set where the bulge scale length is assumed to be half the disk scale length. Here, we include a dispersion in the bulge scale length of 0.6 pixels around a mean value of 3.5 pixels. The analysis was done with 500,000 galaxies, to keep the error bars smaller than 10%. As expected, the size estimation for this set is poorer than in set 1; however, the errors on κˆ remain similar thanks to the sensitivity correction (see Fig. (<>)10). While the theoretical κin the ",
+    "studied range of ℓhas a maximum amplitude of ∼2%, nonlinear density evolution increases its contribution on smaller scales (see for example Fig.17 of (<>)Bartelmann et al. (<>)1996). For this set, the analysis was performed with higher values of κto confirm that the method is valid for larger κ. A comparison of the original range with a larger range (|κ|. 0.05) is shown in Fig. (<>)10, where no significant di erences are apparent. Fig. (<>)11 shows the values of mand cfor this set, with and without the sensitivity correction. If we compare it with the previous plots we can see that as the galaxy population becomes more realistic, including several e ects, the importance of the correction increases. Results for this set are shown in Fig. (<>)11, showing unbiased results except for S/N=10, which has m= −0.19 ±0.1. For the higher S/N points, we find |m|<0.06 with errorbars of ±0.09. "
+  ],
+  "4 CONCLUSIONS AND DISCUSSIONS ": [
+    "In this paper we present the first systematic investigation of the performance of a weak lensing shape measurement method’s ability to estimate the magnification e ect through an estimate of observed galaxy sizes. We performed this test by creating a suite of simulations, with known input values, and by using the most advanced shape measurement available at the current time, lensfit. ",
+    "A full study of the magnification e ect using sizes was performed testing the dependence on S/N, PSF size and type of galaxy. The requirements on biases on shear (or equivalently convergence) for Euclid such that systematics do not dominate the very small statistical errors in cosmological parameters are stringent (see Massey et al., 2012 and Cropper et al., 2012). A much larger study will be required to determine whether these requirements can be met for size, but we find in this study no evidence for additive size biases at all, and no evidence for multiplicative bias provided that 1) the PSF is small enough (<galaxy scale-length/1.5), 2) the S/N high enough (> 15), and 3) the bulge not too dominant (bulge/disk ratio <= 4). ",
+    "Besides instrumental and environmental issues, there can be astrophysical contaminants associated with weak lensing. In the case of shape distortion, the first assumption that galaxy pairs have no ellipticity correlation is not entirely accurate. There are intrinsic alignments of nearby galaxies due to the alignment of angular momentum produced by tidal shear correlations (II correlations, see for detections (<>)Brown et al. ((<>)2002); (<>)Heymans et al. ((<>)2004); (<>)Mandelbaum et al. ((<>)2011); (<>)Joachimi et al. ((<>)2011, (<>)2012), and for theory (<>)Heavens et al. ((<>)2000); (<>)Catelan & Porciani ((<>)2001); (<>)Crittenden et al. ((<>)2001); (<>)Heymans & Heavens ((<>)2003)). In addition there can be correlations between density fields and ellipticities (GI correlations (<>)Hirata & Seljak (<>)2004; (<>)Mandelbaum et al. (<>)2006). These intrinsic correlations have been studied in detail and it is not trivial to account for or remove them when quantifying the weak lensing signal. ",
+    "Figure 10. ˆ estimates compared to the true  values for set 4. Dashed line is for in= outand solid line is the least squares fit, with regression coeÿcients shown in the plot (ˆ = b + c, where b = m + 1). Left four plots are for a maximum value of input  of ∼2% and right set of plots for |in|. 0.05. ",
+    "The intrinsic correlation of sizes and its dependence on the environment, are still open issues. In fact, the correlation of sizes and density field, is known to play an important role in discriminating between models of size evolution; recent work finds a significant correlation between sizes and the density field using around 11,000 galaxies drawn from the joint DEEP2/DEEP3 data-set ((<>)Cooper et al. (<>)2012; (<>)Papovich et al. (<>)2012), while earlier studies with smaller samples have been in disagreement. Using 5,000 galaxies of STAGES data-set, (<>)Maltby et al. ((<>)2010) find a possible anti-correlation between the density field and size for intermediate/low-mass spiral galaxies. Clustered galaxies seem to be 15% smaller than the ones in the field, while they do not find any correlation for high-mass galaxies. Also for massive elliptical galaxies from ESO Distant Clusters Survey, (<>)Rettura et al. ((<>)2010) do not find any significant correlation, while using the same data set (<>)Cimatti et al. ((<>)2012) claims a similar correlation as in (<>)Cooper et al. ((<>)2012). In (<>)Park & Choi ((<>)2009) they study the correlation between sizes and separation with late and early-type galaxies from SDSS catalogue, at small and large scales. They compare the size ",
+    "Figure 11. m and c parameters for 500,000 galaxies of Set 4. Squares are raw m and c values; triangles have the sensitivity correction included. ",
+    "of the nearest neighbour with the separation between them, and find larger galaxies at smaller separations. This correlation is found for early-type galaxies if the separation between the galaxies is smaller than the merging scale, but not for larger separations. The size of late-type galaxies seems not to have a correlation with the separation in any scale. We expect that further studies with larger samples will clarify the intrinsic correlations of sizes, we note that the systematics are generated from di erent physical processes than in the case of shear and so will a ect the signal in a di erent way; we suggest this is a positive, and another reason why a joint analysis of ellipticity and sizes is interesting. ",
+    "The analysis presented here has assumed that the statistical distribution of galaxy sizes is known, whereas in practice the size distribution depends on galaxy brightness and must be determined from observation. Gravitational lensing of a galaxy with amplification Aincreases both the integrated flux and area of that galaxy by A, which has the e ect of moving galaxies along a locus of slope 0.5 in the relation between log(size) and log(flux). Thus, if the intrinsic distribution of sizes rof galaxies scales with flux Sas r∝Sβ, the apparent shift in size caused by lensing amplification Ais r′∝A0.5−β, resulting in a dilution of the signal compared with the idealised case investigated in this paper. A similar e ect occurs in galaxy number magnification, where the observed enhancement in galaxy number density N′varies as N′∝Aα−1 , if the intrinsic number density of galaxies varies as N∝S−α((<>)Broadhurst et al. (<>)1995). The value of βat faint magnitudes has recently been estimated by (<>)Miller et al. ((<>)2012), who analysed the fits to galaxies with i. 25 of (<>)Simard et al. ((<>)2002) and estimated β≃0.29. Thus we expect this e ect in a real survey to dilute the lensing magnification signal by a factor 0.42, but still allowing detection of lensing magnification. In practice, the dilution factor could be evaluated by fitting to the size-flux relation in the lensing survey. ",
+    "Lensing number magnification surveys are also a ected by the problem that varying Galactic or extragalactic extinction reduces the flux of galaxies and thus may cause a spurious signal (e.g. (<>)M´enard et al. (<>)2010). Such extinction would also a ect the size magnification of galaxies, but with a di erent sign in its e ect. Thus a combination of lensing number magnification and size magnification might be very e ective at removing the e ects of extinction from magnification analyses. ",
+    "Space-based surveys as Euclid should overcome the limitations that we have exposed here, having a large number of galaxies, with S/N >10, and importantly a PSF at least 1.5 smaller than the average disk size. The addition of the size information to the ellipticity analysis is expected to reduce the uncertainties in the estimation of weak lensing signal, and therefore improve the constraints of the distribution of matter and dark energy properties. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "We thank Catherine Heymans for interesting discussions. BC thanks Chris Duncan for useful comments on the first draft. BC thanks the Spanish Ministerio de Ciencia e Inno-vaci´on for a pre-doctoral fellowship. We acknowledge partial financial support from the Spanish Minsterio De Econom´ıa y Competitividad AYA2010-21766-C03-01 and Consolider-Ingenio 2010 CSD2010-00064 projects.TDK is supported by a Royal Society University Research Fellowship. The authors acknowledge the computer resources at the Royal Observatory Edinburgh. The author thankfully acknowledges the computer resources, technical expertise and assistance provided by the Advanced Computing & e-Science team at IFCA. "
+  ]
+}

jsons_folder/2013MNRAS.431.1866R.json

@@ -0,0 +1,223 @@
+{
+  "arXiv:1206.5302v2  [astro-ph.CO]  8 Apr 2013 ": [],
+  "ABSTRACT ": [
+    "Cosmological surveys aim to use the evolution of the abundance of galaxy clusters to accurately constrain the cosmological model. In the context of ΛCDM, we show that it is possible to achieve the required percent level accuracy in the halo mass function with gravity-only cosmological simulations, and we provide simulation start and run parameter guidelines for doing so. Some previous works have had sufficient statistical precision, but lacked robust verification of absolute accuracy. Convergence tests of the mass function with, for example, simulation start redshift can exhibit false convergence of the mass function due to counteracting errors, potentially misleading one to infer overly optimistic estimations of simulation accuracy. Percent level accuracy is possible if initial condition particle mapping uses second order Lagrangian Perturbation Theory, and if the start epoch is between 10 and 50 expansion factors before the epoch of halo formation of interest. The mass function for halos with fewer than ∼ 1000 particles is highly sensitive to simulation parameters and start redshift, implying a practical minimum mass resolution limit due to mass discreteness. The narrow range in converged start redshift suggests that it is not presently possible for a single simulation to capture accurately the cluster mass function while also starting early enough to model accurately the numbers of reionisation era galaxies, whose baryon feedback processes may affect later cluster properties. Ultimately, to fully exploit current and future cosmological surveys will require accurate modeling of baryon physics and observable properties, a formidable challenge for which accurate gravity-only simulations are just an initial step. ",
+    "Key words: galaxies: halos – methods: N-body simulations – cosmology: theory – cosmology:dark matter "
+  ],
+  "1 INTRODUCTION ": [
+    "In the vacuum energy dominated cold dark matter cosmological model (hereafter ΛCDM, (<>)Komatsu et al. (<>)2011), large-scale structures form through the amplification of small density fluctuations via gravitational instability. At early times this amplification can be followed using linear perturbation theory of the general relativistic equations of motion for the field. At late times, owing to the nonlinearities in the equations, and after shell-crossing, the dynamics may only be accurately followed using numerical simulations. Overdense regions of the density field, whose dynamics have broken away from the evolution of the background space-time and have reached some state of virial equilibrium are commonly referred to as dark matter halos. ",
+    "The growth rate of large-scale structures is directly sensitive to the expansion rate of the Universe, and hence ",
+    "the cosmological parameters. One can show theoretically, through the excursion set formalism ((<>)Press & Schechter (<>)1974; (<>)Bond et al. (<>)1991; (<>)Sheth & Tormen (<>)1999), that the number of halos is also sensitive to cosmological parameters, and importantly for future surveys, the presence of “dark energy” ((<>)Wang & Steinhardt (<>)1998; (<>)Haiman et al. (<>)2001; (<>)Lima (<>)& Hu (<>)2004; (<>)Marian & Bernstein (<>)2006; (<>)Cunha et al. (<>)2010; (<>)Courtin et al. (<>)2011). This forecast cosmological sensitivity has recently been verified through direct testing with N-body simulations ((<>)Smith & Marian (<>)2011). ",
+    "The amount of cosmological information that can be extracted from cluster number counts is limited by our ability to detect signal-to-noise peaks in our observational survey – i.e. associate galaxies to groups, identify groups relative to an X-ray background noise level, etc. The lower that one can push the minimum detectable mass, the more cosmological information can be extracted from the survey. This comes under the proviso that one can accurately calibrate the true– observable mass relationship ((<>)Lima & Hu (<>)2005; (<>)Marian et al. ",
+    "(<>)2009; (<>)Rozo et al. (<>)2009; (<>)Mandelbaum et al. (<>)2010; (<>)Oguri & (<>)Takada (<>)2011; (<>)Angulo et al. (<>)2012). The numbers of rare halos are also sensitive to the level of non-Gaussianity in the primordial density field due to its effect upon the tail of extreme density fluctuations ((<>)Matarrese et al. (<>)2000; (<>)Marian (<>)et al. (<>)2011). Cluster counts are also sensitive to the total neutrino mass ((<>)Wang et al. (<>)2005; (<>)Carbone et al. (<>)2012; (<>)Shi-(<>)mon et al. (<>)2012, e.g. ) Thus, surveys that promise to accurately measure the evolution of the abundance of groups and clusters, also have the potential to help probe fundamental physics. Accurate theoretical predictions for the cluster mass function and its dependence on cosmology, are therefore essential to fully exploit next generation cluster surveys. ",
+    "Current cosmological constraints from clusters come from: (<>)Vikhlinin et al. ((<>)2009); (<>)Vanderlinde et al. ((<>)2010); (<>)Rozo (<>)et al. ((<>)2010); (<>)Sehgal et al. ((<>)2011); (<>)Allen et al. ((<>)2011); (<>)Planck (<>)Collaboration ((<>)2011). Over the next decade there will be a number of large surveys that will aim to strongly constrain the cosmological model through the abundance of clusters: in the X-ray there will be eROSITA ((<>)Pillepich et al. (<>)2012), with the Sunyaev-Zel’Dovich method there will be Planck, in the optical using the weak lensing method there will be DES, Euclid ((<>)Laureijs et al. (<>)2011) and LSST. Several authors have estimated the requirements on the theoretical accuracy of the halo mass function to achieve the statistically limited constraints on cosmological parameters. (<>)Wu et al. ((<>)2010) point out that, in order to constrain time evolving dark energy models for DES, the theoretical mass function must be known with an accuracy  0.5%. ",
+    "In this paper we address the question: What are the correct numerical parameters needed to achieve percent level accuracy in the mass function in a cosmological simulation? Large simulation volumes (whether by a single simulation or by multiple realizations) are able to reduce statistical uncertainties due to finite halo numbers. However, large absolute volumes are needed to reduce systematic and statistical errors associated with poor sampling of large-scale density modes (e.g. (<>)Barkana & Loeb (<>)2004; (<>)Bagla & Ray (<>)2005; (<>)Power (<>)& Knebe (<>)2006; (<>)Reed et al. (<>)2007; (<>)Crocce et al. (<>)2010; (<>)Smith & (<>)Marian (<>)2011). Over the past decade, impressive statistical precision in the halo mass function has been achieved using suites of cosmological simulations ((<>)Jenkins et al. (<>)2001; (<>)War-(<>)ren et al. (<>)2006; (<>)Reed et al. (<>)2007; (<>)Tinker et al. (<>)2008; (<>)Crocce (<>)et al. (<>)2010; (<>)Iliev et al. (<>)2012; (<>)Bhattacharya et al. (<>)2011; (<>)Smith (<>)& Marian (<>)2011; (<>)Angulo et al. (<>)2012; (<>)Alimi et al. (<>)2012; (<>)Wat-(<>)son et al. (<>)2012, and others). However, statistical precision does not imply accuracy, even when considering gravity-only simulations. Sources of systematic error include finite simulation volume, force resolution, mass resolution and discreteness effects, time-stepping, halo finding, initial condition particle mapping, and start redshift. Recent progress includes (<>)Crocce et al. ((<>)2010) and (<>)Bhattacharya et al. ((<>)2011), who each address many of the systematic uncertainties and determine a halo mass function with an estimated accuracy of ∼ 2% from a suite of large gravity-only cosmological boxes, though their results differ by significantly more than this for halos larger than ∼ 1015h−1M. Moreover, neither approach has taken into account the full covariance matrix ",
+    "of mass function estimates when deriving best fit parameters ((<>)Smith & Marian (<>)2011). ",
+    "As a first step on the path toward producing an accurate mass function in the observational plane, we limit ourselves to demonstrating how percent level accuracy in gravity-only (i.e. collisionless) simulations (wherein baryons are present but interact only via gravity) can be accomplished. We show how to set up initial conditions so that percent level accuracy can be achieved. We also isolate and test the run parameters that control force resolution (force softening and tree opening angle) and time-step size, allowing us to determine the required values to achieve percent level convergence. Finally, we ask: how many particles do we need to sample the halo mass distribution, in order to obtain a mass function accurate to better than  1%. ",
+    "The paper breaks down as follows: in §(<>)2 we discuss setting up the initial conditions for the structure formation simulations and the parameters used to run the N-body codes. In §(<>)3 we describe the suite of N-body simulations performed and halo identification. In §(<>)4 we present the results for the halo mass function and its convergence with simulation parameters. In §(<>)5 we explore the variation of the halo mass function with the method for generating the initial conditions. We also make a comparison between the results obtained from two well known N-body codes. In §(<>)6 we explore the convergence of the matter power spectrum and the 1-point probability density function of matter fluctuations. In §(<>)7 we discuss the remaining challenges of obtaining better than 1% accurate mass functions from structure formation simulations. In §(<>)8 we summarize our findings and draw up a set of guidelines for obtaining accurate gravity-only mass functions. "
+  ],
+  "2 SIMULATING STRUCTURE FORMATION ": [],
+  "2.1 initial conditions ": [
+    "In order to set up a simulation, we must first select the cosmological model and the probability distribution of the primordial density perturbations. In this study we shall work within the context of the ΛCDM paradigm and assume that the initial density modes are described by a Gaussian random field. The statistics of the field are thus fully speci-fied by the power spectrum. Hence, a particular realization of the density field in Fourier space may be obtained by drawing a set of uniform random phases and assigning amplitudes drawn from the Rayleigh distribution ((<>)Efstathiou (<>)et al. (<>)1985), or through the convolution of white noise with a filter that is related to the power spectrum ((<>)Bertschinger (<>)2001). ",
+    "A given density field must then be converted into a particle distribution, and several techniques for doing this have been discussed in the literature (e.g. (<>)Efstathiou et al. (<>)1985; (<>)Scoccimarro (<>)1998; (<>)Bertschinger (<>)1999, (<>)2001; (<>)Crocce et al. (<>)2006). The traditional approach is to place particles on a uniform lattice, and these are then displaced off the initial points q using a displacement field Ψ(q) that encodes all of the statistical properties of the density field. Hence, initial (Lagrangian) and final (Eulerian) positions, x, are related through: ",
+    "(1) ",
+    "where the coordinates x are a solution to the equation of motion: ",
+    "(2) ",
+    "where in the above dτ = dt/a(t) is conformal time, H = aH(a), and Φ is the peculiar gravitational potential. The solution for Ψ is perturbative, and each order can be found through iteration with solutions of lower order. In terms of the initial density field, and up to second order, the solutions may be written ((<>)Zel’Dovich (<>)1970; (<>)Buchert (<>)1994; (<>)Buchert (<>)et al. (<>)1994; (<>)Bouchet et al. (<>)1995; (<>)Scoccimarro (<>)1998): ",
+    "(3) ",
+    "where D1(a) and D2(a) ≈ −3D12(a)/7 are the first and second order growth factors suitable for ΛCDM. The potentials φ(1)(q) and φ(2)(q) can be found through iteratively solving the Poisson equations: ",
+    "(4) ",
+    "(5) ",
+    "where The linear solutions for Ψ, with yield the traditional Zel’Dovich approximation, which we refer to as 1LPT, and the second order solutions, with φ(2) , we refer to as 2LPT. (<>)Scoccimarro ((<>)1998) gave a detailed prescription for implementing 2LPT displacements in simulations, and we make use of a slightly modified version of the publicly available code 2LPT. (<>)Crocce et al. ((<>)2006) demonstrated that 2LPT reduces numerical “transients” to the level where an accurate representation of the halo mass function may be obtained for relatively late start times, af /ai ≈ 10, where ai and af are the initial and final expansion factors. ",
+    "As can be seen from Eq. ((<>)3), in the limit of asymptotically high initial redshift 1LPT and 2LPT become equivalent since D2(ai)/D2(af )  D1(ai)/D1(af ). This has led some to speculate that, provided one takes the initial start redshift to be sufficiently high, then it should not matter whether one uses 1LPT or 2LPT. This issue will be investigated in detail in §(<>)5. ",
+    "Several earlier studies have explored the importance of 1LPT versus 2LPT initial conditions: (<>)Knebe et al. ((<>)2009) used Gadget-2 to show that start redshift and 2LPT versus 1LPT had little effect on internal halo properties, specifi-cally testing halo concentration, spin parameter, tri-axiality. They also found little dependence on halo mass or the halo mass function. However, their results may understate any numerical issues because they focused on smaller halos of 1010–1013h−1M where the mass function is not very steep, and their statistics were limited due to using low-resolution N = 2563 particles. A more recent study by (<>)Jenkins ((<>)2010), has shown that there is a definite, although weak, dependence of the subhalo mass function inside Milky-Way mass halos on the choice of the initial conditions. ",
+    "One last issue, concerning the generation of initial Gaussian random density fields, is that some researches have ",
+    "http://cosmo.nyu.edu/roman/2LPT ",
+    "advocated the use of the “Hann filter” ((<>)Bertschinger (<>)2001). This is an anti-aliasing filter ((<>)Press et al. (<>)1992), and corresponds to setting the Fourier density modes that are outside the Nyquist sphere of the simulation, kNy = πN1/3/L, to vanish by multiplying the transfer function by W (k) = cos(πk/2kNy) for k < kNy and 0 for k > kNy. The purpose of this is to mitigate some of the anisotropies in the forces due to the cubical lattice. In §(<>)5 we shall also investigate how the presence of such filtering impacts our goal of an accurate mass function. ",
+    "Note that for some of the simulations where we test for parameter convergence, we will also make use of a modified version of Grafic-2 ((<>)Bertschinger (<>)2001). These two initial condition codes were verified to show identical convergence trends with start redshift. "
+  ],
+  "2.2 N-body codes ": [
+    "Once we have obtained an initial condition, we then need to integrate the equations of motion, Eq. ((<>)2). In this study we shall make use of two standard N-body techniques: PKDGRAV V2.2.12 and Gadget-2. ",
+    "PKDGRAV is our primary simulation code for this study, an early version of which is described in (<>)Stadel ((<>)2001). The version of the code we use has been MPI parallelized, and uses the hierarchical tree data structure to organize the individual simulation particles. The gravitational force on each particle is calculated using a multipole expansion with Ewald summation to replicate the simulation cube as an approximation of an infinite periodic universe. The peculiar potential around any given particle is obtained from an hex-adecapole expansion of the forces. PKDGRAV uses a variable time step criterion that is synchronized for global time-steps. Particle orbits are integrated with the symplectic leapfrog integrator. ",
+    "Gadget-2 is a tree-particle-mesh (Tree-PM) code, and full details of which may be found in (<>)Springel ((<>)2005). The main difference with PKDGRAV is that on large scales it uses Fourier based methods to solve for the forces and only uses the tree algorithm to solve for forces on small scales. The solution for the potential is then obtained through an interpolation of the PM and tree forces over the force matching region, and typically this is ∼ 4 − 5 mesh cells. ",
+    "In §(<>)5 we investigate the mass functions from these different codes and explore the convergence properties with different 1LPT and 2LPT start redshifts. Additionally, we aim to determine the typical values for “generic” run parameters that are required for percent level convergence. In what follows we shall describe parameters that are mainly specific to PKDGRAV, but will make reference as to how they apply to Gadget-2 or other codes. Gadget-2 parameters are tested further in (<>)Smith et al. ((<>)2012). The run parameters that we focus on are: ",
+    "Tree opening angle Θ: The tree opening angle controls the accuracy of medium and long range forces. It does this by setting the minimum distance between a given particle and tree node below which the tree node will be “opened”. ",
+    "Thus the force calculations for a given particle will include contributions from entire nodes and or individual particles. A discussion of how Θ relates to other tree types can be found in (<>)Stadel ((<>)2001). ",
+    "Softening : In order to avoid excessively large accelerations and hence excessively short time-steps, the small-scale gravitational interactions must be “softened”. This makes sense for simulations of collisonless systems like CDM, where the particles represent large coarse grained elements of the microscopic phase space. PKDGRAV and Gadget-2 both use a softened kernel: gravitational forces approach zero for spatially coinciding particles, and become Newtonian at 2 for PKDGRAV and 2.8 for Gadget-2. PKDGRAV uses the K3 softening kernal of (<>)Dehnen ((<>)2001) while Gadget-2 uses a spline kernel. The force softening leads to a minimum resolved spatial scale. Throughout, we make use of constant comoving softening. ",
+    "Time-step η: Each particle is on an adaptive time-step with length proportional to the time-step parameter η. The actual time-step length for each particle is based on the magnitude of its current acceleration |a|, the softening length , and the time-step parameter η, in accordance with the relation: ",
+    "(6) ",
+    "This technique allows significant computational savings in cosmological simulations when only a small fraction of particles are in dense regions requiring the shortest time-steps. ",
+    "In summary, we shall investigate how the halo mass function varies with: the initial start redshift; with 1LPT or 2LPT initial conditions; with Nyquist filtering; we shall explore results for two simulation codes; and how variations in Θ, , η affect our results. Besides these, we shall also explore finite volume effects and mass resolution. "
+  ],
+  "3 SIMULATIONS ": [],
+  "3.1 Simulation suite ": [
+    "We have generated a suite of N-body simulations that are designed to explore the accuracy with which we may estimate the halo mass function and its dependence on how we simulate the dark matter (as discussed in §(<>)2). All of the simulations that we have performed evolve N = 10243 equal mass dark matter particles. We consider periodic cubes of size L = 17.625 h−1Mpc evolved to z = 10, and cubes of size L = 2048 h−1Mpc evolved to z = 0. The relative box sizes were chosen so that halos corresponding to ∼ 3σ fluctuations in the density field are sampled by Nh ∼ 1000 particles at the final output. This corresponds to M ∼ 3.8 × 108h−1M for the small boxes at z = 10, and M ∼ 6.1 × 1014h−1M at z = 0 for the larger boxes. Thus, the final halos in the small box simulations are in an evolutionary state similar to the clusters in the large box simulations at z = 0. ",
+    "Although the L = 17.625 h−1Mpc box is very small, the effects of finite volume on our study are attenuated because we examine halos early, at z = 10, when the typical halo mass-scale is still much smaller than the total simulation mass. There is no need to apply a finite volume correction as in e.g. (<>)Reed et al. ((<>)2007) to these simulations because each of our convergence series utilizes identical initial conditions and particle displacements. Finite volume effects, to ",
+    "the extent that they can be accounted for with a simple linear correction technique, are thus identical within each convergence series. ",
+    "The cosmological parameters that we adopted for the small box runs were consistent with WMAP5 ((<>)Komatsu (<>)et al. (<>)2009): Ωm = 0.274, ΩΛ = 0.726, Ωb = 0.046, h = 0.705, ns = 0.96, σ8 = 0.812, where these parameters are the density parameters in matter, vacuum energy, and baryons; the dimensionless Hubble parameter; the primordial power spectral index; and the variance of the density fluctuations on scales of R = 8 h−1Mpc. The transfer function that we used to create the initial conditions was produced using the prescription of (<>)Eisenstein & Hu ((<>)1998). For the large box runs, the cosmological parameters we adopted were consistent with WMAP7 ((<>)Komatsu et al. (<>)2011): Ωm = 0.2726; ΩΛ = 0.7274, Ωb = 0.046, h = 0.704, ns = 0.963, σ8 = 0.809. The transfer function for these runs was computed using CAMB ((<>)Lewis et al. (<>)2000). Full details for the entire suite of simulations are given in Table (<>)1. "
+  ],
+  "3.2 Halo identification ": [
+    "We identify dark matter halos using the friends-of-friends (FoF) algorithm ((<>)Davis et al. (<>)1985). This links together all particles that are separated by less than the linking length b, where b is expressed in units of the mean inter-particle separation. Throughout, we use b = 0.2, and we use the particular implementation of the algorithm internal to PKDGRAV; a similar implementation is provided by the code fof. The estimated iso-density contour that the FoF recovers is δ = δρ/ρ¯ = ncb−3 − 1 ≈ 81.62 ((<>)More et al. (<>)2011). ",
+    "In the literature there is a wide range of alternate approaches to the identification of dark matter halos: e.g. the spherical over-density (SO) algorithm ((<>)Lacey & Cole (<>)1994; (<>)Tinker et al. (<>)2008); 6-D phase space algorithms ((<>)Behroozi (<>)et al. (<>)2013); and for a review of methods see (<>)Knebe et al. ((<>)2011). Rather than explore all of these different methods here, we shall work under the assumption that: an accurate FoF mass function implies an accurate mass function for all other algorithms designed to select approximately virialised objects. Anecdotal support for this is provided by (<>)McBride (<>)et al. ((<>)2011), who found similar convergence behavior with simulation set-up for the FoF (b = 0.2) and SO 200 mass functions. We shall reserve the task of establishing the veracity of this assumption for future work. ",
+    "A number of systematic errors have been noted for halos obtained with the FoF algorithm. Firstly, the recovered halo masses are systematically overestimated with respect to the “true” halo mass ((<>)Warren et al. (<>)2006; (<>)Luki´c et al. (<>)2009; (<>)Trenti et al. (<>)2010; (<>)More et al. (<>)2011). This owes to the fact that the true halo mass distribution is sampled by a fi-nite number of particles. This mass overestimation has been quantified for spherical mock halos by (<>)Luki´c et al. ((<>)2009) and more recently by (<>)More et al. ((<>)2011). Secondly, FoF halos also experience “bridging”, which may occur when two distinct halos undergo a close encounter. This systematic effect: links unvirialised systems, it acts to reduce the overall number of halos found, and it predominantly occurs for ",
+    "Table 1. Suite of cosmological simulations. Col. 1: N-body code used. Col. 2: initial condition method, note that we used the 2LPT code throughout, except where there is a -g, which denotes the use of Grafic-2; -HF denotes use of a Hann filter. Col. 3: box size. Col. 4: particle mass. Col. 5: initial condition start redshifts that have been simulated. Col. 6: final redshift. Col. 7: time-stepping parameter. Col. 8: Force softening, , in units of the mean inter-particle spacing lm. Col. 9: tree opening angle (ErrTolTheta for Gadget-2 runs). The additional Gadget-2 parameters were set to: ErrTolIntAccuracy=0.02, MaxRMSDisplacementFac=0.2, MaxSizeTimestep=0.02, MinSizeTimestep=0.000, ErrTolForceAcc=0.005, TreeDomainUpdateFrequency=0.05, PMGRID=1024. ",
+    "the highest mass objects and is stronger at higher redshifts ((<>)Luki´c et al. (<>)2009). ",
+    "(<>)Warren et al. ((<>)2006) and (<>)Bhattacharya et al. ((<>)2011) have provided empirical corrections, determined from cosmological simulations, for the systematic FoF errors. However, these empirical models are mass and redshift independent, which may make them insufficient for our goal of achieving a ∼ 1% accurate mass function. We would expect the FoF errors to include dependencies on the specific distribution of mass within halos, which depends on both mass and redshift. Nevertheless, we assert that the FoF mass overestimation should not affect our convergence tests because they are all performed at the same mass resolution. For these reasons, we use the raw FoF masses, and remark that this will affect our ability to recover an “unbiased”, FoF mass function. However, this is sufficient to our purposes of quantifying relative differences in the mass function of different simulations. "
+  ],
+  "4 MASS FUNCTION CONVERGENCE I: SIMULATION PARAMETERS ": [
+    "In this section, we show convergence of the FoF halo mass function with varying simulation run and set-up parameters. We estimate the number of halos per logarithmic mass interval, dn(M)/dlog10M, using a Gaussian kernel in log mass. ",
+    "The Gaussian kernel is convenient for diagnostics because it avoids the ‘saw-tooth’ pattern that emerges in a binned mass function as a result of the discretization of halo masses, particularly at low masses where the simulation particle mass is a significant fraction of the mass-width of a bin. The number of halos with mass Mk is estimated by the sum: ",
+    "(7) ",
+    "where fg is a Gaussian kernel (in log10M) of width h = 0.0625, chosen to minimize Poisson fluctuations without introducing systematic error to the mass function. To minimize computational cost, we truncate the kernel beyond a range of ±a = 3h. The number of halos per logarithmic mass interval per unit volume is: ",
+    "(8) ",
+    "where V is the simulation volume. The kernel mass Mk is estimated by the following: ",
+    "(9) ",
+    "analogous to using the average halo mass in a bin. Poisson errors can be estimated from the Gaussian kernel halo numbers Nh, through use of the formula ((<>)Heinrich ",
+    "(<>)2003; utilized for the halo mass function in (<>)Luki´c et al. (<>)2007): ",
+    "(10) ",
+    "In what follows, we will show results for all halos with more than 8 particles per halo. This is done for purely diagnostic purposes, since the poorly resolved halos are strongly affected by particle shot-noise errors. "
+  ],
+  "4.1 Tree opening angle Θ ": [
+    "The top panel of Figure (<>)1 presents the results from our convergence study of the tree-opening angle parameter Θ, used in the code PKDGRAV. These results are for the case of the z = 10, L = 17.625 h−1Mpc runs. The figure clearly shows that, for halos with masses M ≤ 109h−1M, the runs with Θ ≤ 0.68 are converged at the sub-percent level. For halos with masses M  109h−1M (Np  3000), the figure shows that scatter in the mass function begins to dominate our results. This implies that systematic errors at greater than the percent level cannot be ruled out for more massive halos, which may be most affected by tree-related criteria. In this case, the Θ = 0.8 run deviates modestly from the other runs. Larger values of Θ have been shown to cause significant direct force errors ((<>)Stadel (<>)2001). ",
+    "The increased scatter in the mass function for halos with M ≥ 109h−1M may seem somewhat surprising, given that all of our simulations had the same initial realization of the density field so that there is no “sample variance” between them. However, even the most accurate particle simulation is still essentially a Monte Carlo representation of a mass distribution. This means that the mass of each halo has a significant uncertainty, which can at best be equal to the square root of the number of its particles. The scatter in the mass function arises from a convolution of the true halo number counts with the scatter associated with simulating, sampling, and measuring the masses of halos (see discussion in §(<>)3.2). Hence it is non-trivial to determine the true uncertainty. Fig. (<>)1 shows the expected Poisson errors (long thin error bars), and one can see that differences between well-converged runs are at sub-Poisson levels. ",
+    "For a better estimate of the uncertainty, we create randomly subsampled 1-in-8 particle volumes from the full simulation snapshot and measure the 1 − σ scatter between the FoF mass functions of the subsampled volumes. In Fig. (<>)1, the results of this exercise are denoted by the short, thick, red error bars. This scatter tends to be an overestimate of the true uncertainty, since the scatter in the FoF mass will be larger in the randomly sampled volume due to the smaller numbers of particles per halo. For the most massive halos, this overestimation may become worse due to the increased effects of halo bridging (or unbridging), which has a large effect on halo masses and thus on the inferred mass function. Taking these issues into account, we estimate that we are sensitive to percent level systematic shifts in the FoF mass function for halos with less than ∼ 3000 particles. "
+  ],
+  "4.2 Force softening  ": [
+    "The central panel of Figure (<>)1 presents the results from our convergence study of the force softening parameter . As can ",
+    "Figure 1. Variation of the halo mass function with simulation parameters, relative to the mass function obtained from our fidu-cial simulation, as a function of FoF halo mass. All panels show the results from the L = 17.625 h−1Mpc, PKDGRAV simulations at z = 10. All runs used the same initial realization of the density field. Long thin error bars show the Poisson errors estimated from the number of halos. Short thick red error bars are estimated from the scatter of the mass functions of sub-sampled versions of the simulations. The top, middle and bottom panels show the results of variations in tree opening angle Θ, force softening , and adaptive time-step parameter η, respectively. The black dashed line in the middle panel shows the large (and assumedly undesirable) impact of application of the Hann anti-aliasing filter to the initial density field, on the halo mass function. Percent level convergence is apparent for each run parameter for halos larger than ∼ 100 particles. c 2012 RAS, MNRAS 000, (<>)1–(<>)20 ",
+    "be seen, the commonly used softening value of  = lm/20 is converged at near the percent level over all masses (lm = L/N1/3). We also see that the low-mass end of the mass function is very sensitive to the choice of . Halos with N  1000 particles appear only weakly dependent on , provided   lm/10 and within our statistical limitations. ",
+    "For the cases where   lm/10, forces do not become Newtonian until beyond the FoF linking length of lm/5. Interestingly, for these large softening lengths, we find that the halo abundances at a fixed mass are increased. One possible explanation for this effect is that the lower central densities of the heavily softened halo profiles ((<>)Moore et al. (<>)1998; (<>)Fukushige & Makino (<>)2001; (<>)Power et al. (<>)2003; (<>)Reed et al. (<>)2005; (<>)Tinker et al. (<>)2008, e.g. ) lead to higher densities near the outer edges of halos. This increased outer-shell density, implies larger FoF masses as more particles are linked to the outer layers ((<>)Bhattacharya et al. (<>)2011); (see §(<>)6.2). For the smallest halos with few particles, the virial radii and softening are of similar order. The minimum resolved halo mass thus increases as softening increases ((<>)Luki´c et al. (<>)2007, e.g. ). These issues have implications for a common running mode for cosmological simulations where computational speed-up at high redshifts is achieved by using a “physical softening”, wherein the comoving softening length is scaled by the expansion factor, with a typical maximum of fsoft max ∼ 10. Effectively, in this mode, the softening is frozen in physical coordinates at scale factor a = 1/fsoft max. Our tests suggest that allowing a comoving softening larger than lm/20 at high redshifts leads to significant numerical error for the early forming halos, which is likely to affect high density regions at late times. ",
+    "Finally, the black dashed line in the central panel of Fig. (<>)1 shows the results of applying the Hann anti-aliasing filter. Whilst it may help to correct errors due to the anisotropic lattice structure, it introduces a ∼ 30% suppression in the number of lower-mass halos relative to the un-filtered initial conditions run and relative to the expected nearly power-law behavior of the mass function predicted from theory ((<>)Bond et al. (<>)1991). Hann filtered and unfiltered runs only agree at the percent level for halos with N  3000 particles. "
+  ],
+  "4.3 Time-step size η ": [
+    "The bottom panel of Figure (<>)1 presents our study of how variations in the adaptive time stepping parameter η affects the estimated mass functions. The results demonstrate that, for halos with M  109h−1M (3000 particles), an increase in η leads to a decrease in the abundance of halos. We find that percent level convergence in the mass function can be achieved with η ≈ 0.15 for all halo masses, or η ≈ 0.2 for a 100 particle minimum mass. This value is consistent with the value of η = 0.2 found by (<>)Power et al. ((<>)2003), who examined the convergence behaviour of the density profiles of dark matter halos. This similar converged time-step size is not surprising given that low-redshift halo centers consist of some of the earliest material to be bound into halos ((<>)Die-(<>)mand et al. (<>)2005). For halos with N  1000 particles, the mass function converges with a much longer time-step corresponding to η = 0.6. ",
+    "Finally, we note that the value η = 0.2 for PKDGRAV is similar to the default size of the adaptive time stepping in ",
+    "Gadget-2: the parameter ErrTolIntAccuracy = η2/2 has a default setting of 0.025, which corresponds to η = 0.22. "
+  ],
+  "5 MASS FUNCTION CONVERGENCE II: INITIAL CONDITIONS ": [],
+  "5.1 Results: Small boxes at z=10 ": [
+    "Figure (<>)2 compares the behaviour of the 1LPT and 2LPT initial conditions, as a function of the start redshift zi, for the small-box simulations at z = 10 evolved with PKDGRAV. The top and middle panels show the ratios of the halo mass functions for different start redshifts with the halo mass function obtained from the start redshift zi = 800, for 1LPT and 2LPT, respectively. The bottom panel presents the ratio of the 1LPT and 2LPT mass functions for simulations with the same start redshift. We see that both the 1LPT and 2LPT initial conditions converge to yield the same mass function as start redshift increases. However, the convergence properties of the 1LPT runs are very slow, whereas the 2LPT runs appear to converge much faster. ",
+    "For the case of 2LPT, we notice that percent level convergence can be achieved for halos with at least ∼ 1000 particles and in simulations that have undergone af /ai  10 expansions. For 1LPT, the af /ai = 80 run (zi = 800) is barely converged down to N ∼ 1000. For halos, with N  1000 particles, even the 2LPT mass function is poorly converged with zi for all expansion factors tested. The abundances of small halos appear to diminish as start redshift is increased; this is apparent in both the 2LPT and 1LPT tests. This suggests that N ∼ 1000 particles represents a minimum halo mass for stability to zi. ",
+    "A curious coincidental feature of the 1LPT initial condition series is that small halos appear to be converged at the ∼ 2% level by zi = 200 (except for the largest masses) and nearly at the ∼ 1% level by zi = 400 (except for the smallest masses). The more accurate 2LPT start redshift series confirms that this 1LPT convergence is an illusion. With later start redshift, the increased number of halos due to more accuracy in the 1LPT initial conditions is offset by independent errors that act to decrease the number of halos, resulting in false convergence. This highlights the fact that convergence is a necessary but not sufficient condition to guarantee accuracy. Some previous studies that appeared to show good mass function convergence with early enough 1LPT initialization, such as (<>)Reed et al. ((<>)2003) and (<>)Reed (<>)et al. ((<>)2007) (Fig. A1), among others, likely also suffered from this false convergence. Our larger particle numbers and corresponding better statistical uncertainty, combined with 2LPT comparisons, allow us to make more robust conclusions. "
+  ],
+  "5.2 Results: Large boxes at z=0 ": [
+    "In order to confirm that the convergence behavior of the small box simulations at z = 10 can be applied to the cluster regime at lower redshifts, we present the results from tests run to z = 0 in the L = 2 h−1Gpc boxes. ",
+    "Figure (<>)3 shows the results from the 1LPT and 2LPT zi convergence simulations run with the code PKDGRAV. As for the case of the small-box simulations at z = 10, we see ",
+    "Figure 2. Variation in the halo mass function as a function of start redshift, for 1LPT and 2LPT initial conditions using the N-body code PKDGRAV. Top panel: results for 1LPT initial conditions. Middle panel: results for 2LPT initial conditions. Bottom panel: the ratio of the 1LPT and 2LPT mass functions approaches unity at high initial start redshifts. All panels show results of the L = 17.625 h−1Mpc box at z = 10.0. The 1LPT series displays ‘false convergence’ for ∼ 100 particle halos. Percent level convergence is met for 2LPT for or af /ai ≈ 40. ",
+    "that low-mass halos are missing with high start redshifts z  49; the z = 0 “pivot” mass-scale, below which convergence is poor, is somewhat smaller at N ∼ 300 particles. For larger halos, the 2LPT mass function is well-converged so long as curve deviates from the zi = 30 curve at just over the percent level at this mass scale, so is marginally statistically consistent at the percent level. A striking feature here is that when a high enough start redshift is used that Zel’Dovich and 2LPT initial conditions are converged, zi = 200, serious errors are present in the z = 0 mass function. A likely explanation is that with such a high zi, cosmological perturbation amplitudes becomes smaller than the effective amplitude of spurious numerical perturbations. In this zi = 200 run, spurious halos begin to form at very early times, initially dominated by 8 particle structures; visual inspection reveals that the spurious halos are aligned with the initial grid of particles. The effects of these early spurious halos lead to the over-abundance of halos at z = 0. This underscores the point that 2LPT initial condi-",
+    "tions are preferable because they allow one to start at lower redshift where numerical errors are more controllable. ",
+    "We note that pure particle mesh codes may perform better with high redshift starts because the PM technique is well-suited to following low amplitude linear perturbations. A tree code (and also a tree-PM code), however, is subject to force errors that may accumulate over time, even if they are small, because these errors are correlated with the tree structure. Tree code force errors could thus seed spurious structures that dominate over real cosmological perturbations when start redshift is very high (and initial cosmological perturbations are very low). Further, the accumulated errors would be expected to worsen if time-step length is decreased. The PM code, although it may perform better at early times, is limited in spatial resolution by the mesh size, which is typically much larger than the softening scale of a tree (or tree-PM) code, making it non-ideal for modeling the internal properties of halos. ",
+    "Figure 3. Mass functions from the simulations started with 1LPT and 2LPT initial conditions in the L = 2 h−1Gpc boxes at z = 0, relative to the simulation started at zi = 30 with 2LPT initial conditions. All simulations here were run with PKDGRAV. Percent level convergence with 2LPT is found between zi = 30 and zi = 49 runs at ∼ 1000 particles. Extremely early starts ( af /ai  100) lead to serious errors. ",
+    "Figure 4. Ratio of 1LPT mass functions with those obtained from 2LPT initial conditions as a function of the equivalent halo peak height ν. The thick solid black and thick hatched red line show results from the L = 17.625 h−1Mpc boxes at z ≥ 10, and the thin green dashed, solid black and hatched red show results from the L = 2 h−1Gpc boxes. All results here are for PKDGRAV. The ratio of 1LPT/2LPT mass functions is ‘universal’ in that it depends mainly upon af /ai and ν, independent of the specific halo mass range and redshift, and fit by the dot-dashed line. "
+  ],
+  "5.3 Transformation to universality ": [
+    "It has been noted that when halo masses are translated into equivalent ‘peak-height’, i.e., where M → ν(M, a), then the mass function takes on a ‘universal form’ ((<>)Sheth & Tor-(<>)men (<>)1999). The peak height is defined through the relation, ν = δc/σ(M, z), where δc = 1.686 is the present day linearly ",
+    "extrapolated over-density threshold for collapse in the spherical collapse model, and where σ(M, z) is the variance of matter fluctuations on mass scale M = 4πR3ρ/¯ 3. Note also that owing to the fact that σ(M, a) ∝ D(a), ν ∝ D−1(a), where D(a) is the linear theory growth factor. ",
+    "In Figure (<>)4 we present the ratio of the 1LPT with the the 2LPT mass functions for the small box at z = 10 and the big box at z = 0 as a function of ν. We see that the 1LPT mass function error appears to be relatively independent of mass and redshift for equal values of ν. This universal behavior is expected in Press-Schechter formalism wherein mean halo formation time depends only upon ν, and δc is independent of redshift. We present a fit to the ratio of the 1LPT to 2LPT mass function for our range of data 1 ∼ < ν ∼ < 5, ",
+    "(11) ",
+    "Percent level convergence between 1LPT and 2LPT initial conditions at scales relevant for the cluster mass function is not achieved until extremely early starts at af /ai ∼ 200. However, such early start redshifts lead to very small initial density perturbations, which through the relative increase of numerical errors, preclude the codes that we tested from being able to accurately follow the growth of structure. "
+  ],
+  "5.4 Comparison of PKDGRAV with Gadget-2 ": [
+    "The quest for obtaining mass function predictions accurate to within one percent requires different N-body simulation codes to provide consistent results at this level. Of course, if results disagree at  1% for any two codes, then one would need at least three independent N-body codes to break the degeneracy and so decide which results were correct. Having said that, we now compare the initial condition convergence series of simulations obtained using PKDGRAV with results obtained from the widely used N-body code Gadget-2. Note that we have made no attempt to find ‘optimal’ parameters for Gadget-2, but instead we have adopted some rather generic choices for these. The full list of simulations that we have performed with Gadget-2, including the exact choices for run parameters, are presented in Table (<>)1. ",
+    "In Figure (<>)5 we compare the 1LPT and 2LPT initial conditions as a function of zi, but this time using Gadget-2, plotted here down to the limit N = 20 particles. We find that the results exhibit almost identical behaviour to those obtained from the PKDGRAV runs. The small difference is that the suppression of the mass function at low masses with increasing start redshift, apparent in 2LPT runs for halos with fewer than N ∼ 1000 particles, is slightly milder with Gadget-2. This appears to enhance the effect of “false convergence” of the 1LPT Gadget-2 simulations. ",
+    "Figure (<>)6 shows the ratio of the mass functions obtained from Gadget-2 with those obtained from PKDGRAV. Note that we used identical initial conditions in all cases. We find that Gadget-2 systematically produces up to a 10% higher mass function for low-mass halos (N  200) than PKDGRAV. This excess abundance slightly increases with increasing start redshift. We note that the differing mass functions could be a result of differing halo structure, which could lead to systematic differences in FoF masses, and does not necessarily mean the codes are truly producing different numbers of halos. We also note that Gadget-2 appears to have several ",
+    "percent fewer halos at N ∼ 1000 particles, for the highest start redshifts. ",
+    "Figure (<>)7 compares 2LPT mass functions from Gadget-2 and PKDGRAV in the large box at z = 0. This figure shows that when the lower redshift start is used, af /ai = 30, the two codes generally agree within 2%. However, when high redshift starts are used, af /ai ∼ 200, the codes diverge from each other and from the true answer – recall Figure (<>)3 where we showed that the lower redshift start is converged in PKDGRAV runs. ",
+    "This code comparison shows that there is a weak systematic shift with start redshift between the codes. However, the convergence behavior of Gadget-2 with start redshift and of 1LPT versus 2LPT still provides useful veri-fication of the PKDGRAV initial condition tests. Ultimately, a robust comparison of absolute accuracy between codes would require that run parameters for each code are run at self-converged values. The code differences are consistent with the level of agreement found between these same codes in (<>)Heitmann et al. ((<>)2008) when considering our improved statistics and resolution. Further investigation is warranted to reveal whether the differences between the two codes is caused by inherent differences between the TreePM and the pure tree method or whether they are instead due to the use of non-ideal run parameters in Gadget-2. This is beyond the scope of this paper and we shall reserve a wider study for future work. "
+  ],
+  "6 CONVERGENCE OF OTHER PROPERTIES ": [
+    "In this section we consider the sensitivity of other dark matter statistics: to the adopted simulation parameters; to whether we employ 1LPT or 2LPT initial conditions; and to the adopted start redshift. We shall restrict our exploration to the mass power spectrum and the 1-point Probability Distribution Function (PDF) of dark matter density, as additional diagnostics for determining simulation accuracy. "
+  ],
+  "6.1 Mass power spectra ": [
+    "For a finite cubical patch of the Universe, the matter power spectrum is defined to be: ",
+    "(12) ",
+    "where Vµ is the volume of the patch and δk is the discrete Fourier series expansion of the density field. For equal mass dark matter particles, the discrete representation of the Fourier space density field can be written ((<>)Peebles (<>)1980): ",
+    "(13) ",
+    "where N is the number of particles. The matter power spectra were estimated for each simulation using the standard Fourier based methods ((<>)Smith et al. (<>)2003; (<>)Jing (<>)2005; (<>)Smith (<>)et al. (<>)2008): particles and halo centers were interpolated onto a 10243 cubical mesh, using the CIC algorithm ((<>)Hockney & (<>)Eastwood (<>)1988); the Fast Fourier Transform of the discrete mesh was computed using the FFTW libraries; the power ",
+    "in each Fourier mode was estimated and then corrected for the CIC charge assignment; these estimates were then bin averaged in spherical shells of logarithmic thickness. ",
+    "Before we proceed to the results, we note that it is not necessarily the case that a simulation that yields a  1% accurate halo mass function should also yield a  1% accurate matter power spectrum, and vice-versa. Different requirements for simulation parameters are possible because the mass range in our mass functions only involves a small fraction of the total mass in the simulation. And because, our estimates of the measured power spectra do not extend to scales as small as the virial radius of the smallest halos considered. ",
+    "6.1.1 Variation with simulation parameters ",
+    "Figure (<>)8 shows the dependence of the matter power spectrum on the simulation run parameters: (top panel) tree-opening angle Θ; (middle panel) the force softening parameter ; (bottom panel) time-step parameter η, for the N-body simulation code PKDGRAV. These results show that the estimated power spectra, on large scales (k/kfun < 10), are only weakly sensitive to variations in the choice of (Θ, , η). However, on smaller scales, the power spectra show significant deviations. For the force-softening tests, we find that for  ≤ lm/5 the spectra appear to be converged at the sub-percent level on large scales, with a ‘bump’ at k/kfun ≈ 100 and a steep drop at smaller scales. This small-scale drop in power is consistent with the puffing up of halo cores that appears to affect the mass function when softening is large. Similarly, for the case of the time-stepping parameter η, we see that for η = 0.6 there is a  1% suppression of power for k/kfun  100. This can be attributed to the large time-step not being able to follow the rapid changes in the acceleration of particle orbits in the cores of halos – and hence the failure to capture the complex orbit of particles in dense environments. This discussion is limited to PKDGRAV run parameters; a detailed study of the dependence of the power spectrum on Gadget-2 run parameters can be found in (<>)Smith et al. ((<>)2012). ",
+    "6.1.2 Variation with initial conditions: small boxes ",
+    "Figure (<>)9 shows the variation of the mass power spectra with the choice of 2LPT or 1LPT initial conditions, and with the adopted initial start redshift for the small box simulations at z = 10. The top panel of Fig. (<>)9 shows the results for the 1LPT initial conditions. We observe that the power spectra are only converged on the largest scales. On smaller scales, we find that the power increases with increasing start redshift and that the results are almost converged at the percent level only after af /ai  80 expansions. ",
+    "The middle panel of Fig. (<>)9 shows the results for the 2LPT initial conditions. Here we find that simulations that were started with zi  100 are converged for k/kfun  90. For simulations that possess lower start redshifts we find ",
+    "Note that owing to the fact that we are comparing results from the L = 17.5 h−1Mpc at z = 10 and L = 2048 h−1Mpc boxes at z = 0, we shall refer to wavenumbers in units of the fundamental frequency kfun = 2π/L. ",
+    "Figure 5. Variation in the halo mass function as a function of start redshift, for 1LPT and 2LPT initial conditions using the N-body code GADGET-2. Top panel: results for simulations started with 1LPT initial conditions. Bottom panel: results for simulations started with 2LPT initial conditions. All panels are for the L = 17.625 h−1Mpc box at z = 10.0. Convergence of GADGET-2 runs with initial conditions are very similar that found for PKDGRAV (Fig. (<>)2). ",
+    "again a suppression of power, although the effect is much reduced when compared to the equivalent 1LPT start redshift. On smaller scales, k/kfun  100, we find that the power is 1% converged for 100 ≤ zi ≤ 400 (10  af /ai  40), while the z = 800 start has up to 2% less power. ",
+    "The bottom panel of Fig. (<>)9 presents the ratio of the power spectra obtained from the 1LPT simulations with the 2LPT power spectra, for various start redshifts. We see that the convergence of the results from the 1LPT simulations with the 2LPT simulations is very slow, and that percent level convergence is only obtained for zi  800. ",
+    "Before continuing, we note that, whilst it appears that percent level convergence in the power spectra may be achieved between 1LPT and 2LPT for very high start redshifts, we have already shown in §(<>)5 that such high start redshifts are too early to produce an accurate mass function, owing to numerical noise. We are therefore cautious about such convergence. ",
+    "6.1.3 Variation with initial conditions: large boxes ",
+    "We now repeat the same set of tests as done for the previous sub-section, only this time we now consider the L = 2048 h−1Mpc simulation cubes at z = 0. ",
+    "Figure (<>)10, bottom panel, shows that the 1LPT and 2LPT initial matter power spectra, measured at z = zi, are converged at the 1% level with respect to each other for the same start redshift. However, as indicated in the top panel of Fig. (<>)10, the evolved spectra started with 1LPT are not ",
+    "converged. On the other hand, the simulations started with the 2LPT initial conditions, appear to be converged at the 1% level for af /ai ≤ 100, except perhaps at the smallest scales, even for start redshifts as low as zi ∼ 30. We note that the evolved 1LPT versus 2LPT simulations, started with zi = 200, are significantly discrepant with respect to the other results. As for the case of the mass function, we conjecture that this start redshift is too early for the code PKDGRAV to produce an accurate integration of the equations of motion. This reinforces our earlier findings that 1LPT initial conditions are inadequate for accurate simulations. ",
+    "Several earlier studies have investigated the importance of 1LPT/2LPT initial conditions on the matter power spectrum ((<>)Crocce et al. (<>)2006; (<>)Heitmann et al. (<>)2010). Our findings are broadly consistent with these studies. However, (<>)Heit-(<>)mann et al. ((<>)2010) advocated that 1LPT initial conditions started from zi = 200 would lead to better than 1% precision matter power spectra. Clearly such a statement is code and run parameter dependent, and one should be careful of increased numerical errors that may allow consistency between 1LPT and 2LPT while still resulting in inaccurate power spectra. "
+  ],
+  "6.2 1-point PDF of matter fluctuations ": [
+    "We now investigate the impact of simulation parameters and 1LPT versus 2LPT initial conditions on the 1-point PDF. At high densities, the 1-point PDF is a useful probe of the ",
+    "Figure 6. z = 10. 2LPT. Mass functions from PKDGRAV and compared with Gadget-2. Some differences are present at small scales but the relative offset is independent of start redshift, providing some confirmation of our initial condition convergence criteria. We have verified the PKDGRAV, but not the Gadget-2 run parameters for percent-level self-convergence. ",
+    "Figure 7. Mass functions from Gadget-2 compared with PKDGRAV in the L = 2 h−1Gpc box. The agreement with Gadget-2 using relatively standard run parameters is at the couple percent level with zi = 30. Extremely early starts ( af /ai  100) lead to serious errors independent of the simulation code used. ",
+    "central regions of dark matter halos, reflecting many properties of a “stacked” halo density profile (e.g. (<>)Scherrer & (<>)Bertschinger (<>)1991). There are some technical subtleties as to how one computes the 1-point PDF, since it requires an estimator for the matter density at a given point. The pro-",
+    "cedure of estimation in general requires one to smooth the particle distribution and hence the results depend up on adopted smoothing scale (see for example (<>)Watts & Taylor (<>)2001). Here we have chosen to compute the 1-point PDF with a 64 particle nearest neighbor kernel. This operates in a similar way to the SPH-kernel and constitutes an adaptive smoothing scale. ",
+    "Figure (<>)11, top panel, shows the variation of the 1-point PDF with the tree-opening angle parameter Θ. We note that the most significant changes are in the regions of highest density, though sensitivity to Θ, beyond the statistical fluc-tuations, is relatively low. Figure (<>)11, middle panel, shows the variation of the 1-point PDF with the force softening . This clearly shows that the effect of too large force softening is to damp the density distribution in the highest density inner regions of dark matter halos. This “puffs up” halos, which may explain the increased abundances of lower mass halos with increased softening length. We also note that as  = l/50 the dense regions appear to be again suppressed. This we attribute to violent two-body encounters that can evaporate halo cores. Figure (<>)11, bottom panel, shows the variation of the 1-point PDF with the time-stepping parameter η. We see that the results are well converged provided η  0.15. The suppression of the high density PDF for large η reinforces our earlier speculation, that if η is too large, then the particle orbits in the cores of halos can not be integrated sufficiently accurately, damping the densities in the inner regions of dark matter halos. ",
+    "Figure (<>)12 presents the 1-point PDF for 1LPT and 2LPT initial conditions for various start redshifts. As can be clearly ",
+    "Figure 8. Relative variation of the dark matter power spectra with the simulation run parameters for the N-body code PKDGRAV. Top panel: variation with respect to the tree-opening angle Θ. Middle panel: variation with respect to the force softening parameter . Bottom panel: variation with respect to the time-step parameter η. All panels show the L = 17.625 box at z = 10. Percent level convergence is seen for each run parameter. ",
+    "Figure 9. Relative variation of the dark matter power spectra with the initial conditions for the N-body code PKDGRAV. Top panel: variation of spectra with initial start redshift for 1LPT initial conditions. Middle panel: same as the top panel except for the case of the 2LPT initial conditions. Bottom panel: ratio of the power spectra from the 1LPT initial condition runs with respect to the 2LPT runs. All results shown are for the L = 17.625 box at z = 10. Percent level convergence is seen for 2LPT. ",
+    "Figure 10. Top panel: Ratio of the evolved z = 0 matter power spectra for runs with various initial start redshift zi. The evolved 1LPT and 2LPT power spectra from the early zi = 200 start are very similar to each other, but they lie well above the converged results of lower redshift 2LPT starts. Bottom panel: Initial ratio of the 1LPT to 2LPT matter power spectra at two selected initial start redshifts. Differences in 1LPT and 2LPT power are very small (< 1%) at zi, then grow much larger as the simulation evolves. The simulations of this figure are large box L = 2048 h−1Mpc simulations run with PKDGRAV. ",
+    "seen, the results for the 1LPT initial conditions converge very slowly with start redshift. We also note that the both the high-and low-density regions appear to be less dense for the simulations that were started with low zi. For the 2LPT simulations, convergence is reached at much lower start redshifts, roughly af /ai = 10 expansion factors of the cube (i.e. around zi ∼ 100). ",
+    "We note all of the converged parameter values, are broadly consistent with those that we identified for the mass function in §(<>)4, though variations in the PDF at the highest densities are generally larger than 1%. "
+  ],
+  "7 DISCUSSION: REMAINING CHALLENGES FOR < 1% ACCURATE MASS FUNCTIONS ": [
+    "In this section we discuss the remaining challenges that we will have to face in order to approach better than 1% accurate dark matter halo mass functions. "
+  ],
+  "7.1 Mass resolution ": [
+    "In the suite of tests above, we have seen indirect evidence that halos with fewer than N ∼ 1000 particles, are unlikely to be useful for deriving high accuracy estimates of the mass function. This suggests that there is a critical mass resolution, below which systematic numerical errors are difficult to control. Interestingly, this resolution is somewhat worse than the N ∼ 300 particle resolution limit expected for a pure particle-mesh (PM) code with mesh spacing equal to the initial inter-particle separation ((<>)Luki´c et al. (<>)2007). It is however still better than the more conservative value of N ∼ 2000 particles proposed by (<>)Bhattacharya et al. ((<>)2011). ",
+    "Figure 11. Variation of the 1-point PDF of dark matter density fluctuations with the simulation parameters: Top panel, tree-opening angle Θ; Middle panel, force softening ; and Bottom panel, time-stepping parameter η. All results here were obtained from the small L = 17.625 h−1Mpc simulations at z = 10 using the tree-code PKDGRAV. Sensitivity to numerical parameters is greatest at the highest densities. ",
+    "Figure 12. Variation of the 1-point PDF of dark matter density fluctuations with respect to the choice of either 1LPT or 2LPT initial conditions for various start redshifts. Top panel: results for the simulations started with 1LPT initial conditions. Bottom panel: shows the same but for the case of 2LPT initial conditions. These results were obtained from the small L = 17.625 h−1Mpc simulations at z = 10 using the tree-code PKDGRAV. ",
+    "Additional support for our claim, comes from the work of (<>)Trenti et al. ((<>)2010), who show through mass-resolution tests, that on a halo-by-halo basis, halo masses with N  1000 particles are systematically too low. Our statistical limitations mean we can not rule out the possibility that halos resolved with more N  3000 particles might be accurate over a larger range in af /ai than what we find for smaller halos. In a subsequent paper, we will examine directly the mass resolution convergence. ",
+    "If the critical resolution limit of N ∼ 1000 particles for accurate halo statistics is upheld, then this suggests that the tree code technique may not have much advantage over the PM code technique in recovering an accurate gravity-only mass function. Of course the higher force resolution for tree codes enables better modelling of higher density regions. "
+  ],
+  "7.2 Statistical precision ": [
+    "The full-sky volume out to z = 2 is Vµ  200 h−3 Gpc3 . This sets the requirement on the minimum simulation volume needed to replicate the survey volume accessible to future cluster surveys. This would correspond to a single simulation cube with a side length of roughly L  3.67 h−1Gpc, or if one wants to replicate the full sky-light cone, then one would require a cube of length L ∼ 8 h−1Gpc. Obviously performing such a huge simulation with sufficient mass resolution to obtain N ∼ 1000 particles per halo, for all halos with masses M  1013.5h−1M would be very challenging prospect. Such total volumes may be cheaply covered by combining the results from many smaller volume simulations. However, individual simulation boxes must be large enough to avoid systematic errors due to mode-discreteness near the box-scale and due to the lack of super-box scale power (a “DC-mode” can help for multiple realization ensembles (<>)Sirko (<>)2005). ",
+    "An estimate of the minimum box size required to avoid ",
+    "Figure 13. Estimates of the relative dependence of the mass function on simulation cube length compared to the case of an infinite cube. The dependence of the mass function on L is calculated by assuming that the power on scales k < kfun = 2π/L is zero. The bottom panel is the expected Poisson error of the cumulative halo number count within a single simulation volume. Predictions were obtained using the mass function of (<>)Bhattacharya (<>)et al. ((<>)2011). ",
+    "suppressing massive halo formation can be made by computing the effect of missing power at wavelengths larger than the box on the (empirically fit) analytic form of the mass function. Figure (<>)13 (top panel) demonstrates that a simulation box of roughly L ∼ 2 h−1Gpc box should be able to capture the mass function at sub-percent level for all halos with masses M  1016h−1M at z = 0. However, in a single realization of such a volume, statistical accuracy will be much lower; Poisson errors remain larger than 1% well below 1015h−1M. One caveat is that this calculation underestimates the finite volume effects due to the discreteness of modes near the box scale (see for example (<>)Reed et al. (<>)2007; (<>)Smith & Marian (<>)2011). "
+  ],
+  "7.3 Verification of absolute accuracy ": [
+    "The task of verifying that we have actually obtained the true answer is somewhat circular, since it implies that we know already what the true answer is. On our path toward the true answer, we should consider the possibility that our simulations suffer from some level of false convergence. One obvious approach to addressing this issue will be to verify that independent simulation codes give the same results at the desired level of accuracy. However, this does not take into account the pernicious systematic errors, such as the false convergence with redshift that we observed for the 1LPT simulations. In the future, a more complete approach would provide us with a theoretical framework for objectively quantifying ‘accuracy’ and enable us to identify directions in parameter space that would allow us to approach our desired goal. ",
+    "There are a number of systematic errors that one will need to characterise in detail. One in particular is that associated with the coarse graining of phase space. Spurious perturbations related to mass discreteness may lead to the ",
+    "collapse of small structures around lattice points ((<>)Melott (<>)1990; (<>)Joyce & Marcos (<>)2007b; (<>)Joyce et al. (<>)2009). This effect is well-known for Warm Dark Matter simulations ((<>)Wang & (<>)White (<>)2007; (<>)Schneider et al. (<>)2012), and it therefore must also be present in CDM simulations. Other effects relating to mass discreteness in particle codes have been discussed by a number of authors (e.g. (<>)Splinter et al. (<>)1998; (<>)Joyce & (<>)Marcos (<>)2007a; (<>)Romeo et al. (<>)2008). ",
+    "We have attempted to steer away from making direct statements regarding whether particular papers had errors and by how much because quantifying the accuracy of the works of other authors would require repeating their simulations with exactly the same codes and run parameters. A number of widely used fits in the literature used 1LPT initial conditions, many of them with a lower start redshift than expected to be required for good agreement between 1LPT and 2LPT ICs. In those cases, a systematic under-abundance of the halo mass function, especially at high masses or high redshifts is implied. ",
+    "An informative comparison can be made from the fact that the fitting formulae of multiple authors are in reasonable agreement with each other. For example, there is agreement at the 2 − 3% level between the FoF mass function fits of (<>)Crocce et al. ((<>)2010, using 2LPT ICs), (<>)Bhattacharya (<>)et al. ((<>)2011, using a mix of 2LPT and 1LPT with a high start redshift) and (<>)Angulo et al. ((<>)2012, using 2LPT), over a wide mass range. Also, there is  5% agreement between the (<>)Tinker et al. ((<>)2008, 1LPT ICs) and the recent (<>)Watson (<>)et al. ((<>)2012, 1LPT ICs with a higher start redshift) spherical over-density mass function fits. There is a caveat that such comparisons are only useful to the extent that the different studies do not suffer from the same systematic errors. ",
+    "If we consider the widely-used (<>)Tinker et al. ((<>)2008) mass function, the authors stated statistical accuracy of 5% is comparable to the systematic error, estimate from Eqn. (<>)11, that we would expect from their results due to their use of 1LPT initial conditions with af /ai ∼ 50, although this error would approach 10% at the highest masses, while being smaller at lower masses ( ∼ < 1015h−1M). They point out some dependence on start redshift between some of their simulations, and exclude from their fit those with the lowest start redshifts due to a systematic under-abundance of halos. We can thereby deduce that the systematic errors in that study due to initial conditions are generally within their quoted statistical accuracy. "
+  ],
+  "7.4 Narrow scale factor range for accuracy ": [
+    "In §(<>)5, we showed that significant errors are introduced in the halo mass function when the total expansion of the box lies outside the limits (10  af /ai  50). Of course, one would expect that the epoch of a particular halo’s formation is more important than final simulation output for assessing whether that halo, and by extension, the mass function, has been modelled accurately. A brief supporting argument is that any errors introduced to early structures are unlikely to “evolve away”, though suppression of the number of early forming halos may become less noticeable, at fixed mass, after more halos have formed at lower redshifts. The implication is that halos in any particular cosmological simulation can be modeled accurately only for a range in formation redshifts of Δ1+z ∼ 5. It is possible that this ",
+    "restriction may become less severe as the mass resolution of the simulation is increased. The logic being that more cosmological power at small scales may enable earlier start redshifts to be simulated without leading to an increase in the amount of spurious structure. And, as shown in § (<>)5, the mass function sensitivity to start redshift is smaller for halos resolved with more particles. The upper limit of the allowed start redshift range may be code dependent. For example, as we discussed in §(<>)5.2, a particle-mesh technique may allow higher start redshifts, but typically comes at the cost of worse force resolution. ",
+    "The narrow range in implied af /ai presents a challenge for simulations with very large dynamic range, wherein it would be difficult to model accurately the mass function of massive cluster halos forming at z ∼ 0, while also capturing accurate evolution of the early generations of dwarf galaxy halos forming already at z ∼ 10. Even though the fraction of mass assembled into galactic halos at such early times is small, early galaxy formation occurs preferentially in Lagrangian regions where clusters will later form. These early-forming galactic halos should be modeled accurately because their feedback processes could have have significant effects on the eventual baryon and total cluster mass content through energy injection and preheating, which could begin very early (e.g. (<>)Benson & Madau (<>)2003). "
+  ],
+  "7.5 Impact of baryons ": [
+    "We have purposely ignored the important effects of baryons on the halo mass function. Recent hydrodynamic simulations have shown the range of plausible baryon effects on total cluster halo masses to be up to  15% within the radius enclosing 500× the critical density of the universe ((<>)Stanek (<>)et al. (<>)2009). Even for “adiabatic simulations” wherein gas cooling, star formation and feedback are ignored, baryons may have up to ∼ 7% effects on the halo mass function ((<>)Cui (<>)et al. (<>)2012). ",
+    "Baryon influences thus present a serious challenge for percent level accuracy in the mass function required for planned dark energy missions. However, accurate gravity-only simulations, as we have explored in this work, are a prerequisite for future simulations with more complete baryon physics aiming to obtain percent level accuracy in the mass function or other properties. To save computational cost, cosmological constraints might rely on a combination of baryon and gravity-only simulations. For example, hydrodynamic simulations of limited cosmological volumes could be used to calibrate the effects of baryons on halos as well as to derive relations between halos and observable properties. Then, large volume gravity-only simulations might be utilized to map the dependence of halo numbers and other properties on cosmology. "
+  ],
+  "7.6 Calibrating mass–observable relationship ": [
+    "A further difficulty in using the halo mass function for cosmology is that any practical halo definition one might use, such as through the FoF or SO algorithms, typically have no direct observable counterpart. For example, the emission from X-ray clusters is determined by the (square of) the gas density distribution. One might argue that this leads to ",
+    "more spherical clusters the abundance of which may be better matched to SO halos in simulations, rather than to FoF halos (see discussion in (<>)Kravtsov & Borgani (<>)2012). Though weak lensing may help to calibrate halo masses ((<>)Marian et al. (<>)2009; (<>)Becker & Kravtsov (<>)2011; (<>)Mandelbaum et al. (<>)2010), optical, x-ray, and Sunyaev Zel’dovich cluster masses have large scatter and systematic uncertainties ((<>)Angulo et al. (<>)2012). ",
+    "Mock observations from simulations may thus be a superior means of obtaining a more accurate mass function in the observable plane, especially once baryon properties are better modeled. Ultimately, an observationally useful and accurate (cluster) mass function will involve modeling baryon physics and observable properties (or mock observations) and represents a formidable challenge for cosmology – a challenge that must be solved in order to fully exploit future and even current cluster surveys of the Universe. "
+  ],
+  "8 CONCLUSIONS AND GUIDELINES FOR ACCURATE SIMULATIONS ": [
+    "In this paper we have explored the dependence of the mass function of dark matter halos on simulation run parameters and initial conditions. Our aim has been to perform convergence tests that will illuminate the path to obtaining percent level accuracy in this statistic. This will be a requirement for future cluster surveys of the Universe that aim to help constrain the nature of dark energy or dark gravity. ",
+    "In §(<>)2 we gave a brief overview of the simulation method, paying special attention to how one sets up initial conditions, either using Zel’Dovich approximation (1LPT) or 2LPT. We described the simulation codes that we have employed PKDGRAV and Gadget-2, with the former being the main code used throughout this study. ",
+    "In §(<>)3 we described the large suite of N-body simulations that we have performed to study these problems. All simulations were run at N = 10243 and we covered two regimes: high redshift (z = 10), small scale (L = 17.625 h−1Mpc) and low redshift (z = 0) large scale (L = 2 h−1Gpc). ",
+    "In §(<>)4 we explored the dependence of the mass functions on the simulation parameters and found the following: the resultant mass functions were rather insensitive to the choice of the tree-opening angle, provided Θ < 0.7; the results for halos resolved with fewer than N ∼ 1000 particles were sensitive to the choice of force softening, with larger values tending to increase the abundance of halos in this regime; results were fairly insensitive to the size of the adaptive time-step parameter and that 1% converged results could be achieved for η  0.15. We also demonstrated that the use of anti-aliasing filters, such as the Hann filter, to set up initial conditions, can lead to ∼ 30% suppression in the abundance of halos resolved with N  1000 particles. We do not advocate the use of the Hann filter, since there is no aliasing in the initial conditions to correct. ",
+    "In §(<>)5 we performed a detailed study of the impact of the choice of initial conditions on the mass function. We found that the results from simulations that are initialized with 1LPT converge very slowly as the start redshift is increased. The effect of too low a start redshift being the suppression of the formation of high mass halos. Furthermore, for the large box simulations, we also found simulations started at very high redshifts zi  200 would fail to correctly follow the build up of structure due to the relative increase in numerical noise. Furthermore, 1LPT initial conditions exhibit “false convergence” with increasing start redshift. Simulations starting from 2LPT initial conditions proved to have very good convergence properties and for simulations that underwent 10-50 expansion factors, yielded percent level convergence in the halo mass function at the 10243 resolution of our tests. We made a direct comparison of these results obtained from integration of the initial conditions with the tree-code PKDGRAV with results from the Tree-PM code Gadget-2, and found almost identical be-haviour. However, a detailed comparison of the mass functions from the two codes revealed that Gadget-2 produced a ∼ 10% increase in the mass function for halos resolved with N  102 particles. These results extend and support the earlier findings of ((<>)Crocce et al. (<>)2006). ",
+    "In §(<>)6 we explored the convergence properties of two other statistics of the density field, namely the matter ",
+    "Table 2. Approximate run and initial condition parameters that permit percent-level simulation convergence in the halo mass function extracted from gravity-only simulations. 2LPT initial conditions are required. Run parameters Θ, , and η are the tree-opening angle, force softening, time-stepping parameter. ηG denotes the Gadget-2 time-step parameter ErrTolIntAccuracy = η2/2. af /ai is the ratio of initial to final scale factor at which halo properties are to be considered. L is an estimate of the minimum box length needed to avoid systematic errors in the mass function while Vµ is the comoving volume of the universe accessible to future cluster surveys. ",
+    "power spectrum and the 1-point probability density function (PDF) of matter fluctuations. We found that the simulation parameters that produced  1% convergence in the mass function would also lead to good convergence behaviour in these statistics. In addition, too high a start redshift for either 1LPT or 2LPT initial conditions would lead to systematic errors. On the other hand, the results from the simulations run with 2LPT initial conditions demonstrated excellent convergence behaviour. ",
+    "In summary, Table (<>)2 presents a general recipe for the parameters needed for percent accuracy of the mass function within a gravity-only simulation using a tree code. Except for the tree opening-angle Θ, which has some dependence on the specific tree used, all the other run parameters can be applicable to other tree codes. This list shows required values but is not complete. In future work, one would expect this table to be extended to include the following: if PM forces are used for large scale force computation, then parameters controlling their accuracy, such as the size of the PM grid should be included; multipole expansions are used to compute the tree forces, and different codes use different orders: which order is sufficiently accurate for our purposes? Also, there should be some entry associated with the parameters that control the halo finder (halo definition). ",
+    "Ultimately, inferring cosmological parameters from the cluster mass function will require a number of other issues to be solved relating to baryons and observable properties. Among the difficulties that baryons pose is the gravitational coupling of baryon processes to dark matter ((<>)Somogyi & (<>)Smith (<>)2010; (<>)van Daalen et al. (<>)2011). Inferring observable properties from the simulations for comparison via mass-observable relations or by direct mock catalogs is a further complexity. Thus, percent level accuracy in numerical simulations represents a formidable challenge, but one that we must meet if future surveys of the Universe are to live up to their potential. "
+  ],
+  "9 ACKNOWLEDGMENTS ": [
+    "We thank the anonymous referee for helpful suggestions that have improved this work. We thank Martin Crocce, Cameron McBride, Roman Scoccimarro, and Romain Teyssier for helpful discussions. We also thank Salman Habib, Katrin Heitmann, and Zarijah Luki´c for early discussions that in-fluenced this work. We thank Roman Scoccimarro for making 2LPT public; Volker Springel for making GADGET-2 public, and for providing his B-FoF halo finder; and Ed Bertschinger for making GRAFIC-2 public. The simulations were performed on Rosa at the Swiss National Supercomputing Cen-",
+    "ter (CSCS), and the zbox3 and Schr¨odinger supercomputers at the University of Zurich. RES acknowledges support from a Marie Curie Reintegration Grant and the Alexander von Humboldt Foundation. "
+  ]
+}

jsons_folder/2013MNRAS.431.3349H.json

@@ -0,0 +1,172 @@
+{
+  "Joachim Harnois-Deraps´ 1,2 ⋆and Ue-Li Pen1 †": [
+    "(<http://arxiv.org/abs/1211.6213v2>)arXiv:1211.6213v2  [astro-ph.CO]  5 Mar 2013 "
+  ],
+  "ABSTRACT ": [
+    "Estimating the uncertainty on the matter power spectrum internally (i.e. directly from the data) is made challenging by the simple fact that galaxy surveys o er at most a few independent samples. In addition, surveys have non-trivial geometries, which make the interpretation of the observations even trickier, but the uncertainty can nevertheless be worked out within the Gaussian approximation. With the recent realization that Gaussian treatments of the power spectrum lead to biased error bars about the dilation of the baryonic acoustic oscillation scale, e orts are being directed towards developing non-Gaussian analyses, mainly from N-body simulations so far. Unfortunately, there is currently no way to tell how the non-Gaussian features observed in the simulations compare to those of the real Universe, and it is generally hard to tell at what level of accuracy the N-body simulations can model complicated nonlinear e ects such as mode coupling and galaxy bias. We propose in this paper a novel method that aims at measuring non-Gaussian error bars on the matter power spectrum directly from galaxy survey data. We utilize known symmetries of the 4-point function, Wiener •ltering and principal component analysis to estimate the full covariance matrix from only four independent •elds with minimal prior assumptions. We assess the quality of the estimated covariance matrix with a measurement of the Fisher information content in the amplitude of the power spectrum. With the noise •ltering techniques and only four •elds, we are able to recover the results obtained from a large N = 200 sample to within 20 per cent, for k 6 1.0hMpc−1 . We further provide error bars on Fisher information and on the best-•tting parameters, and identify which parts of the non-Gaussian features are the hardest to extract. Finally, we provide a prescription to extract a noise-•ltered, non-Gaussian, covariance matrix from a handful of •elds in the presence of a survey selection function. ",
+    "Key words: Large scale structure of Universe • Dark matter • Distance Scale • Cosmology : Observations • Methods: data analysis "
+  ],
+  "1 INTRODUCTION ": [
+    "The matter power spectrum contains a wealth of information about a number of cosmological parameters, and measuring its amplitude with per cent level precision has become one of the main task of modern cosmology ((<>)York et al. (<>)2000; (<>)Colless et al. (<>)2003; (<>)Schlegel & others. (<>)2007; (<>)Drinkwater et al. (<>)2010; (<>)LSST Dark Energy Science Collaboration (<>)2012; (<>)Ben´•tez et al. (<>)2009, Pan-STARRS1 (<>), DES2(<>)). Cosmologists are especially interested in the detection of the Baryonic Acoustic Oscillation (BAO) scale, which allows to measure the evolution of the dark energy equation of state w(z) ((<>)Eisenstein et al. (<>)2005; (<>)Hutsi¨ (<>)2006; (<>)Tegmark et al. (<>)2006; (<>)Percival et al. (<>)2007; (<>)Blake et al. (<>)2011; (<>)Anderson et al. (<>)2012). ",
+    "Estimating the mean power spectrum from a galaxy survey is a challenging task, as one needs to incorporate the survey mask, model the redshift distortions, estimate the galaxy bias, etc. For this purpose, many data analyses follow the prescriptions of (<>)Feldman et al. ((<>)1994) (FKP) or the Pseudo Karhunen-Lo`eve ((<>)Vogeley & Szalay (<>)1996)(PKL hereafter), which provide unbiased estimates of the underlying power spectrum, as long as the observe •eld is Gaussian in nature. When these methods are applied on a non-Gaussian •eld, however, the power spectrum estimator is no longer optimal, and the error about it is biased ((<>)Tegmark et al. (<>)2006). ",
+    "As •rst discussed in (<>)Meiksin & White ((<>)1999) and (<>)Rimes & Hamilton ((<>)2005), Non-Gaussian e ects on power spectrum measurements can be quite large; for instance, the Fisher information content in the matter power spectrum saturates in the trans-linear regime, which causes the number of degrees of freedom to deviate from the Gaussian prediction by up to three orders of magnitude. The obvious questions to ask, then, are •How do non-Gaussian features propagate on to physical parameters, like ",
+    "the BAO scale, redshift space distortions, neutrino masses, etc.?• and •How large is this bias in actual data analyses, as opposed to simulations?• As a partial answer to the •rst question, it was shown from a large ensemble of N-body simulations that the Gaussian estimator, acting on non-Gaussian •elds, produces error bars on the BAO dilation scale ((<>)Padmanabhan & White (<>)2008) that di er from full Gaussian case by up to 15 per cent ((<>)Ngan et al. (<>)2012). ",
+    "The •rst paper of this series, (<>)Harnois-D´eraps & Pen ((<>)2012) (hereafter HDP1) addresses the second issue, and measure how large is the bias in the presence of a selection function. Starting with the 2dFGRS survey selection function as a study case, and mod-elling the non-Gaussian features from 200 N-body simulations, it was found that the di erence between Gaussian and non-Gaussian error bars on the power spectrum is enhanced by the presence of a non-trivial survey geometry3 (<>). The 15 per cent bias observed by (<>)Ngan et al. ((<>)2012) is, in that sense, a lower bound on the actual bias that exists in current treatments of the data. ",
+    "At this point, one could object that the sizes of the biases we are discussing here are very small, and that analyses with error bars robust to with 20 per cent are still in excellent shape and rather robust. However, the story reads di erently in the context of dark energy, where the •nal goal of the global international e ort is to minimize the error bars about w(z) by performing a succession of experiments with increasing accuracy and resolution. In the end, a 20 per cent bias on the BAO scale has a quite large impact on the dark energy ••gure-of-merit•, and removing this e ect is the main goal of this series of paper. ",
+    "Generally, the onset of non-Gaussianities can be understood from asymmetries that develops in the matter •elds subjected to gravitation, starting at the smallest scales and working their way up to larger scales ((<>)Bernardeau et al. (<>)2002). In Fourier space, Gaussian •elds can be completely described by their power spectrum, whereas non-Gaussian •elds also store information in higher moments. For instance, the non-linear dynamics that describe the scales with k >0.5hMpc−1 tend to couple the Fourier modes of the power spectrum, which e ectively correlates the measurements. This correlation was indeed found from very large samples of N-body simulations ((<>)Takahashi et al. (<>)2009), and act as to lower the number of degrees of freedom in a power spectrum measurement. ",
+    "One approach that was thought to minimizes these complications consists in excluding most of the non-linear scales, as proposed in (<>)Seo & Eisenstein ((<>)2003). However, this cuts out some of the BAO wiggles, thereby reducing our accuracy on the measured BAO scale. In addition, it is plausible that non-Gaussian features due to the non-linear dynamics, mask, and using simple Gaussian estimators on non-linear “elds interact such as to impact scales as large as k ∼0.2hMpc, as hinted by HDP1. Optimal analyses must therefore probe the signal that resides in the trans-linear and nonlinear scales, and construct the power spectrum estimators based on known non-Gaussian properties of the measured “elds. ",
+    "Characterization of the non-Gaussian features in the uncertainty about the matter power spectrum was recently attempted in HDP1, in which deviations from Gaussian calculations were parameterized by simple •tting functions, whose best •tting parameters were found from sampling 200 simulations of dark matter ",
+    "particles. This was a •rst step in closing the gap that exists between data analyses and simulations, but is incomplete in many aspects. First, it does not address the questions of cosmology and redshift dependence, halo bias nor of shot noise, which surely affect the best-•tting parameters, and completely overlooks the fact that observations are performed in redshift space. All these effects are crucial to understand in order to develop a self-consistent prescription with which we can perform non-Gaussian analyses in data. Second, and perhaps more importantly, this approach assumes that the non-Gaussian features observed in N-body simulations are unbiased representations of those that exist in our Universe. Such a correspondence is assumed in any external error analyses, which involve mock catalogues typically constructed either from N-body simulations or from semi-analytical techniques such as Log-Normal transforms ((<>)Coles & Jones (<>)1991) or PThalos ((<>)Scoccimarro & Sheth (<>)2002). In that aspect, the FKP and PKL prescriptions are advantageous since they provide internal estimates of the error bars, hence avoid this issue completely. ",
+    "In this second paper (HDP2 hereafter), we set out to determine how well can we possibly measure these non-Gaussian features internally from a galaxy survey, including simple cases of survey masks, with minimal prior assumption. In that way, we are avoiding the complications caused by the cosmology and redshift dependence of the non-Gaussian features, and that of using incorrect non-Gaussian modelling of the •elds. In many aspects, this question boils down to the problem of estimating error bars using a small number of measurements, with minimal external assumptions. In such low statistics environment, it has been shown that the shrinkage estimation method ((<>)Pope & Szapudi (<>)2008) can minimize the variance between a measured covariance matrix and a target, or reference matrix. Also important to mention is the attempt by (<>)Hamilton et al. ((<>)2006) to improve the numerical convergence of small samples by bootstrap resampling and re-weighting sub-volumes of each realizations, an approach that was unfortunately mined down by the e ect of beat coupling ((<>)Rimes & Hamilton (<>)2006). ",
+    "With the parameterization proposed in HDP1, our approach has the advantage to provide physical insights on the non-Gaussian dynamics. In addition, it turns out that the basic symmetries of the four-point function of the density •eld found in HDP1 allow us to increase the number of internal independent subsamples by a large amount, with only a few quanti•able and generic Bayesian priors. In particular, it was shown that the contributions to the power spectrum covariance matrix consist of two parts: the Gaussian zero-lag part, plus a broad, smooth, non-local, non-Gaussian component. In this picture, both the Gaussian and non-Gaussian contributions can be accurately estimated even within a single density •eld, because many independent con•gurations contribute. However, any attempt to estimate them simultaneously, i.e. without di erentiating their distinct singular nature, results in large sample variance. ",
+    "This paper takes advantage of this reduced variance to optimize the measurement of the covariance matrix from only four N-body realizations. In such low statistics, the noise becomes dominant over a large dynamical range, hence we propose and compare a number of noise reduction techniques. In order to gain physical insights, we pay special attention to provide error bars on each of the non-Gaussian parameters and therefore track down the dominant source of noise in non-Gaussian •elds. To quantify the accuracy of the method, we compare and calibrate our results with a larger sample of 200 N-body realizations, and use the Fisher information about the power spectrum amplitude as a metric of the performance of each noise reduction techniques. ",
+    "The issue of accuracy is entangled with a major aspect common to most non-Gaussian analyses: they require a measurement of the full power spectrum covariance matrix, which is noisy by nature. For instance, an accurate measurement of N2 matrix elements generally requires much more then N realizations; it is arguable that N2 independent measurements could be enough, but this statement generally depends on the •nal measurement to be carried and on the required level of accuracy that is sought. Early numerical calculations were performed on 400 realizations ((<>)Rimes & Hamilton (<>)2005), while (<>)Takahashi et al. ((<>)2009) have performed as many as 5000 full N-body simulations. (<>)Ngan et al. ((<>)2012) have opted for fewer realizations, but complemented the measurements with noise reduction techniques, basically a principal component decomposition (see (<>)Norberg et al. (<>)2009, for another example). In any case, it is often unclear how many simulations are required to reach convergence; in this paper, we deploy strategies such as bootstrap re-sampling to assess the degree of precision of our measurements. ",
+    "We •rst review in section (<>)2 the formalism and the theoretical background relevant for the estimations of the matter power spectrum and its covariance matrix, with special emphases on the dual nature and symmetries of the four point function, and on the dominant source of noise in our non-Gaussian parameterization. We then explain how to improve the measurement of C(k,k′) in section (<>)3 with three noise-reduction techniques, and compare the results with a straightforward bootstrap resampling. In section (<>)4 we measure the Fisher information of the noise “ltered covariance matrices, and compare our results against the large sample. Finally, we describe in section (<>)5 a recipe to extract the non-Gaussian features of the power spectrum covariance in the presence of a survey selection function, in a low statistics environment, thus completely merging the techniques developed here with those of HDP1. This takes us signi“cantly closer to a stage where we can perform non-Gaussian analyses of actual data. Conclusions and discussions are presented in the last section. "
+  ],
+  "2 ESTIMATION OF C(K,K′): NON-GAUSSIAN PARAMETERIZATION ": [],
+  "2.1 Power spectrum estimator ": [
+    "In the ideal situation that exists only in N-body simulations • periodic boundary conditions and no survey selection function e ect … the matter power spectrum P(k) can be obtained in an unbiased way from Fourier transforms of the density contrast. The latter is de“ned as δ(x) ≡ρ(x)/ρ¯ −1, where ρ(x) is the density “eld and ρ¯ its mean. Namely, ",
+    "(1) ",
+    "The Dirac delta function enforces the two scales to be identical, and the bracket corresponds to a volume (or ensemble) average. We refer the reader to HDP1 for details on our simulation suite, and brie•y mention here that each of the N = 200 realization is obtained by evolving 2563 particles with CUBEP3M ((<>)Harnois-D´eraps et al. (<>)2012) down to a redshift of z = 0.5, with cosmological parameters consistent with the WMAP+BAO+SN •ve years data release ((<>)Komatsu et al. (<>)2009). Simulated dark matter particles are assigned onto a grid following a •cloud in cell• interpolation scheme ((<>)Hockney & Eastwood (<>)1981), which is deconvolved in the power spectrum estimation. The isotropic power spectrum P(k) is •nally obtained by taking the average over the solid angle. Observations depart from this ideal environment: they must ",
+    "Figure 1. (top:) Dimensionless power spectrum at z = 0.5, estimated from our template of 200 N-body simulations (thin line) and from our 4 •measurements• (thick line). The error bars are the sample standard deviation. Throughout this paper, we represent the N = 4 and N = 200 samples with thick and thin solid lines respectively, unless otherwise mentioned in the legend or the caption. (bottom:) Fractional error with respect to the nonlinear predictions of HALOFIT ((<>)Smith et al. (<>)2003). ",
+    "incorporate a survey selection function and zero pad the boundary of the survey when constructing the power spectrum estimator, plus the galaxy positions are obtained in redshift space. We shall return to this framework in section (<>)5, but for now, let focus our attention on simulation results. To quantify the accuracy of our measurements of P(k) and its covariance matrix in the context of low statistics, we construct a small sample by randomly selecting N = 4 realizations among the 200; we hereafter refer to these two samples as the N = 200 and the N = 4 samples. Fig. (<>)1 shows the power spectrum as measured in these two samples, with a comparison to the non-linear predictions of HALOFIT ((<>)Smith et al. (<>)2003). We present the results in the dimensionless form, de“ned as 2(k) = k3 P(k)/(2π2) in order to expose the scales that are in the trans-linear regime (loosely de“ned as the scales where 0.1 <2(k) <1.0) and those in the non-linear regime (with 2(k) >1.0). ",
+    "The simulations show a ∼5 per cent positive bias compared to the predictions, a known systematic e ect of the N-body code that happens when the simulator is started at very early redshifts. Starting later would remove this bias, but the covariance matrix, which is the focus of the current paper, becomes less accurate. This is an unfortunate trade-o that will be avoided in future production runs with the advent of an initial condition generator based on second order perturbation theory. The plotted error bars are smaller in the N = 4 sample, a clear example of bias on the error bars: the estimate on the variance is poorly determined, as expected from such low statistics, and the error on the N = 4 error bar is quite large. The mean P(k) measured in the two samples, however, agree at the few per cent level. Following HDP1, we extract from this “gure the regime of con“dence, inside of which the simulated structures are well resolved, and exclude any information coming from k-modes beyond; in this case, scale with k >2.34hMpc−1 are cut out. "
+  ],
+  "2.2 Covariance matrix estimator ": [
+    "The complete description of the uncertainty about P(k) is contained in a covariance matrix, de•ned as : ",
+    "(2) ",
+    "where P(k) refers to the ”uctuations of the power spectrum about the mean. If one has access to a large number of realizations, this matrix can be computed straightforwardly, and convergence can be assessed with bootstrap resampling of the realizations. In actual surveys, however, only a handful of sky patches are observed, and a full covariance matrix extracted from these is expected to be singular. ",
+    "To illustrate this, we present in the top panels of Fig. (<>)2 the covariance matrices, normalized to unity on the diagonal, estimated from the N = 200 and N = 4 samples. While the former is overall smooth, we see that the latter is, in comparison, very noisy, especially in the large scales (low-k) regions. This is not surprising since these large scales are measured from very few Fourier modes, hence intrinsically have a much larger sample variance. It is clear why performing non-Gaussian analyses from the data is a challenging task: the covariance matrix is singular, plus the error bar about each element is large. This is nevertheless what we attempt to do in this paper, and in order to overcome the singular nature of the matrix, we need to approach the measurement from a slightly di erent angle. ",
+    "It was shown in HDP1 that there is an alternative way to estimate this matrix, which “rst requires a measurement of C(k,k ′,θ), where θis the angle between the pair of Fourier modes (k,k′). We summarize here the properties of C(k,k ′,θ), and refer the reader to HDP1 for more details: ",
+    "As discussed in section 5.3 and in the Appendix of HDP1, C(k,k ′) can be obtained from an integration over the angular dependence of C(k,k ′,θ): ",
+    "where G is the “rst term of the second line, and NG is the remaining two terms. In the above expressions, C(k,k ′,µ= 1) is the zero-lag point, with µ= cosθ. The second line is simply in the above equation obtained by turning the integral into a sum, and splitting apart the contribution from the zero-lag term in the case where k ′= k. For instance, in the case where k ′, k, only the third term contributes ",
+    "Figure 3. Comparison of the Gaussian term with the analytical expression. The top panel shows the ratio for the N = 200 sample, i.e. G200(k)/Cg (k), while the bottom panel shows the N = 4 ratio. In both cases, error bars are from bootstrap resampling. As explained in the text, the bias at low-k comes from from poor estimates of dµin the linear regime. ",
+    "to NG, which now includes the θ= 0 point4 (<>). When comparing [Eq. (<>)2] and [Eq. (<>)3] numerically, slightly di erent residual noise create per cent level di erences, at least in the trans-linear and non-linear regimes5 (<>). "
+  ],
+  "2.3 k = k ′case ": [
+    "The break down of the covariance matrix proposed in [Eq. (<>)3] opens up the possibility to explore which of the two terms is the easiest to measure, which is noisier, and eventually organize the measurement such as to take full advantage of these properties. The “rst term on the right hand side, G(k,k ′), corresponds at the few per cent level … at least in the trans-linear and non-linear regimes … to the Gaussian contribution Cg(k) = 2P2(k)/N(k), where N(k) is the number of Fourier modes in the k-shell. This comparison is shown in Fig. (<>)3, where the error bars are estimated from bootstrap resam-pling. In the N = 200 case, we randomly pick 200 realizations 500 times, and calculate the standard deviation across the measurements. In the N = 4 case, we randomly select 4 realizations 500 times, always from the N = 200 sample. In the low-k regime, the simulations seem to underestimate the Gaussian predictions by up to 40 per cent. This is not too surprising since the discretization effect is large there, and the angle between grid cell, dµ, are less accurate. However, it appears that a substitution G(k,k ′) →Cg would improve the results by correcting for this low-k bias. ",
+    "G + NG break down allows for more sophisticated error estimates (see section (<>)3). ",
+    "An important observation is that the shape of the ratio is similar for both the large and small samples, which leads us to the conclusions that 1-departures from Gaussianities are clearly seen even in only four “elds, and 2-both samples can be parameterized the same way. Following HDP1, we express the diagonal part of NG(k,k′) and C(k,k′) as6(<>): ",
+    "(4) ",
+    "In this parameterization, k0 informs us about the scale at which non-Gaussian departure become important, and αis related to the strength of the departure as we progress deeper in the non-linear regime. The best-“tting parameters are presented in Table (<>)1. As seen from Fig. (<>)4, this simple power law form seems to model the ratio up to k ∼1.0hMpc−1 , beyond which the signal drops under the “t. Without a thorough check with higher resolution simulations, it is not clear whether this shortfall is a physical or a resolution e ect. In the former case, we could modify the “tting formula to include the ”attening observed at k ∼1.0hMpc−1 , but this would require extra parameters, the number of which we are trying to minimize. We thus opt for the simple, conservative approach that consists in tightening our con“dence region and exclude modes with k >1.0hMpc−1 , even though the simulations resolve smaller scales. ",
+    "The two sets of parameters are consistent within 1σ, which means that the N = 4 sample has enough information to extract the pair (α, k0), and therefore attempt non-Gaussian estimates of C(k,k′). The fractional error on both parameters is of the order of a few per cent in the large sample, and about 20-50 per cent in the small sample. A second important observation is that the fractional error about αis about twice smaller than that of k0, which means that αis the easiest non-Gaussian parameter to extract. ",
+    "We are now in a position to ask which of G(k,k′) or NG(k,k′) has the largest contribution to the error on C(k,k). We present in the bottom panel of Fig. (<>)4 the fractional error √on both terms, in both samples. We scale the bootstrap error by N to show the sampling error on individual measurements, and observe that in both cases, the non-Gaussian term dominates the error budget by more than an order of magnitude. "
+  ],
+  "2.4 k , k′case ": [
+    "We now turn our attention to the o -diagonal part of the covariance matrix, whose sole contribution comes from the non-Gaussian term. For this reason, and because there are many more elements to measure from the same data (N2 vs. N), it is expected to be much noisier that the diagonal part. ",
+    "It is exactly this noise that makes C(k,k′) singular, but luckily we can “lter out a large part of it from a principal component analysis based on the Eigenvector decomposition√of the cross-correlation coeÿcient matrix r(k,k′) ≡C(k,k′)/C(k,k)C(k′,k′). As discussed in (<>)Ngan et al. ((<>)2012), this method improves the accuracy of both the covariance matrix and of its inverse. HDP1 further provides a “tting function for the Eigenvector, and we explore here ",
+    "Figure 4. (top:) Ratio between the diagonal Ł of the covariance  matrix and the Gaussian analytical expression, i.e G(k) + NG(k,k) /Cg(k) in the N = 200 sample. The measurements from [Eq. (<>)3] are represented with the thin line, the thick solid line is from the “t, the dashed line is obtained from [Eq. (<>)2], and the horizontal dotted line is the linear Gaussian prediction. The error bars are from bootstrap resampling. (middle:) Same as top panel, but for the N = 4 sample. This “gure indicates that the con“dence region for our choice of parameterization of the non-Gaussian features stops at √k = 1.0hMpc−1 . (bottom:) Fractional error on G and NG, scaled by N for comparison purposes. The thin and thick lines correspond to the N = 200 and N = 4 sample respectively, and the calculations are from bootstrap resampling. It is obvious from this “gure that the Gaussian term is much easier to measure than NG. ",
+    "how well the best-•tting parameters can be found in a low statistics environment. ",
+    "This decomposition is an iterative process that factorizes the cross-correlation coeÿcient matrix into a purely diagonal component and a smooth symmetric o -diagonal part. The latter is further Eigen-decomposed, and we keep only the Eigenvector U(k) that corresponds to the largest Eigenvalue λ. In that case, it is convenient directly. Since the diagonal elements are unity by construction, the exact expression is This effectively puts a prior on the shape of the covariance matrix, since any part of the signal that does not “t this shape is considered as noise and excluded. As shown in HDP1, this decomposition is accurate at the few per cent level in the dynamical range of interest, for the N = 200 sample. We present in the top panel of Fig. (<>)5 the Eigenvector extracted from both samples, against a “tting function of the form7(<>): ",
+    "(5) ",
+    "In this parameterization, A represents the overall strength of the non-Gaussian features, while k1 is related to the scale where cross-correlation becomes signi•cant in our measurement. If A = 0, then ",
+    "Table 1. Best-•tting parameters of the diagonal component of the covariance matrix, parameterized as and for ",
+    "the principal Eigenvector, parameterized as The error bars are obtained from bootstrap resampling and re•tting the measurements. The Wiener •lter and T-rotation techniques are described in sections (<>)3.1 and (<>)3.2 respectively. The parameters (α, k0 ) do not apply to the T-rotation, which acts only on the Eigenvector. ",
+    "we recover r(k,k′) = δkk′, which corresponds to no mode cross-correlation. The best “tting parameters are shown in Table (<>)1. We observe that the error bar on A is at the few per cent level, and that the measurements in both samples are both very close to unity. On the other hand, k1 is much harder to constrain: in the N = 200 sample, the fractional error bar is about 30 per cent, and in the N = 4, the error bar is three times larger than its mean. In other words, k1 is consistent with zero within 1σin the small sample, which corresponds to a constant Eigenvector. The non-Gaussian noise is thus mostly concentrated here, and improving the measurement on k1 is one of the main tasks of this paper. ",
+    "If we model the N = 4 covariance matrix with this •t to the Eigenvector, the matrix is no longer singular, as shown in the bottom left panel of Fig. (<>)2. It does exhibit a stronger correlation at the largest scales, compared to the matrix estimated from the large sample; this di erence roots in the fact that the N = 4 Eigenvector remains high at the largest scales, whereas the N = 200 vector drops. There is thus an overestimate of the amount of correlation between the largest scales, which biases the uncertainty estimate on the high side. In any case, these large scales are given such a low weight in the calculation of Fisher information • they contain a small number of independent Fourier modes • that their contribution to the Fisher information is tiny, as will become clear in section (<>)4. The bottom left panel of Fig. (<>)2 also shows that we do recover the region where the cross-correlation coeÿcient is 60-70 per cent, also seen in the top left panel of the •gure. It is thus a signi•cant step forward in the accuracy of the error estimate compared to the Gaussian approach. ",
+    "We show in sections (<>)3.1 and (<>)3.2 that noise •ltering techniques are able to reduce this bias down to a minor e ect, even when working exclusively with the same four “elds. To contrast the pipeline presented in this section (of the form [N = 4 →PCA →“t ]) to those presented in future sections, we hereafter refer to this approach as the N = 4 naive way. "
+  ],
+  "3 OPTIMAL ESTIMATION OF C(K,K′): BEYOND BOOTSTRAP ": [
+    "In the calculations of section (<>)2, we show that even in low statistics, we can extract four non-Gaussian parameters with the help of noise •ltering techniques that assume a minimal number of priors on the non-Gaussian features. As mentioned therein, all the error bars are obtained from bootstrap resampling, which is generally thought to be a faithful representation of the underlying variance only in the large sample limit. How, then, can we trust the signi•cance of our results in the N = 4 sample, which emulates an actual galaxy sur-",
+    "vey? More importantly, can we do better than bootstrap? In this section, we expose new procedures that optimize the estimate of both the mean and the error on C(k,k′), and we quantify the improvements on all four non-Gaussian parameters (α, A, k0 and k1). "
+  ],
+  "3.1 Wiener •ltering ": [
+    "Let us recall that in the bootstrap estimate of the error on C(k,k′), we resample the measured C(k,k′,θ), integrate over the angle θand add up the uncertainty from di erent angles … including the zero-lag point … in quadrature. We propose here a di erent approach, based on our knowledge that C(k,k′,θ) is larger for smaller angles. At the same time, we take advantage of the fact that the noise on G(k) is much smaller than that on NG(k,k′). Since the mean and error should be given more weight in regions where the signal is cleaner, we replace the quadrature by a noise-weighted sum in the angular integration of C(k,k′,θ). This replacement reduces the error on NG by an order of magnitude or so, depending on the scale (see Appendix (<>)A for details). ",
+    "At this stage, we now have accurate estimates of the error on the covariance C(k,k′) in the N = 4 sample, as well as accurate measurements of the signal and noise of the underlying covariance matrix from the N = 200 sample, which we treat as a template. The technique we describe here is a Wiener “ltering approach that uses known noise properties of the system in order to extract a signal that is closer to the template. The error on G(k) is obtained from bootstrap resampling the zero-lag point, while the error on NG(k,k′) comes from the noise-weighted approach mentioned above and discussed in Appendix (<>)A. We “rst apply the “lter on both quantities separately, and then combine the results afterward. Namely, we de“ne our Wiener “lters as ",
+    "(6) ",
+    "with ",
+    "(7) ",
+    "and ",
+    "(8) ",
+    "Note that the errors that appear in the above two expressions correspond to the estimates from the N = 200 and N = 4 samples on G and NG respectively. ",
+    "We present in Fig. (<>)6 the Wiener •ltered variance on P(k), compared to the N = 200 and N = 4 samples. We observe in the range ",
+    "Figure 5. Main Eigenvector extracted from the di erent estimates of the cross-correlation coeÿcient matrix. As explained in the text, the Eigenvalue is absorbed in the vector to simplify the comparison. (top:) The thin solid line (with error bars) and the thick solid line (with grey shades) represent the N = 200 and N = 4 measurements respectively. Since no other noise reduction technique are applied to extract these vectors, we refer to this N = 4 estimate as the •naive• estimate. The error bars are from bootstrap, and the •ts to these curves are provided with the parameters of Table (<>)1 and represented by the dot-dashed lines. (bottom:) Ratio between the main Eigenvector extracted from three noise reduction techniques, and that of the N = 200 sample ( shown in the upper panel). The G(k) →2P2(k)/N(k) substitution is described in section (<>)2.3, while the Wiener “lter and T-rotation approaches are described in sections (<>)3.1 and (<>)3.2 respectively. Except for the “rst bin, the T-rotation technique recovers the N = 200 Eigenvector to within 20 per cent for k <0.2hMpc−1; all techniques achieve per cent level precision for smaller scales, due to the higher number of modes per k-shell. ",
+    "0.3 <k <2.0hMpc−1 that the “lter decreases the size of the ”uctuations about the N = 200 sample, compared to the original N = 4 sample. For larger scales, it is not clear that the e ect of the “lter represents a gain in accuracy: while the variance on the fundamental mode is 3 times closer to the templates measurement, the variance about the second largest mode does 3 times worst, while the change in others large modes seems to have no gain. However, we recall that very little weight is given to these low-k modes in the calculation of the Fisher information about the dark matter power spectrum. Hence slightly degrading the accuracy of the variance about the two largest modes is a mild cost if we can improve the range that ultimately matters, i.e. 0.1 <k <1.0hMpc−1 . In addition, our parameterization of the non-Gaussian features assign a smaller weight to the large scales, which are smoothly forced towards the analytical Gaussian predictions. ",
+    "There is a positive bias of about 15 per cent and up that appears for k >1.0hMpc−1 , both in the original N = 4 sample and in the Wiener “ltered product. The bias in the un“ltered “elds is simply a statistical ”uctuation, since we know it does converge to the large sample by increasing the number of “elds. It does, however, propagate in a rather complicated way through the Wiener “lter, causing a sharp increase at k >1.0hMpc−1 . Because the details of how and why this happens are rather unclear, we decided to exclude this region from the analysis, based on suspicion of systematics. The full Wiener “ltered cross-correlation matrix is presented in the bottom right panel of Fig. (<>)2 and shows that some of the noise has been “ltered out: the regime k >0.5hMpc−1 is smoother than the original N = 4 measurement, and except for the largest two modes, the matrix is brought closer to the N = 200 sample. ",
+    "The next steps consist in computing the new Eigenvector U(k) ",
+    "Figure 6. Comparison between the variance about P(k) with and without the Wiener •ltering technique. Results are expressed as the fractional error with respect to the N = 200 sample, acting as a signal template in our •lter. This plot shows that Wiener •ltering can reduce the noise on the diagonal elements, as seen by the smaller •uctuations about the N = 200 sample. ",
+    "constructed with CWF and to •nd the new best-•tting parameters (α, k0, A, k1). The bottom panel of Fig. (<>)5 presents U(k) and shows that most of the bene“ts are seen for 0.08 <k <0.2hMpc−1 , which is the range we targeted to start with, and the best-“tting parameters are tabulated in Table (<>)1. Overall, the improvement provided by the Wiener “lter is still hard to gauge by eye from Fig. (<>)2, because the Eigenvector is still very noisy. This is to be expected: the method is mostly eÿcient on the diagonal part, where we can take advantage of the low noise level of the Gaussian term. "
+  ],
+  "3.2 Noise-weighted Eigenvector decomposition ": [
+    "In this section, we describe a last noise •ltering technique that utilizes known properties of the noise about the Eigenvectors and their Eigenvalues to improve the way we perform the principal component decomposition in the N = 4 sample. It is a general strategy that could be combined with others techniques described in the preceding sections, however, for the sake of clarity, we only present here the standalone e ect. ",
+    "In the Eigen-decomposition, not all Eigenvalues are measured with the same precision. For instance, most of the covariance matrix can be described by the •rst Eigenvector U(k), hence we expect the signal-to-noise ratio about its associated Eigenvalue to be the largest. Considering again the N = 200 sample as our template of the underlying covariance, the error on each λcan be obtained by bootstrap resampling the 200 realizations. We present this measurement in Fig. (<>)7, where we observe that the “rst Eigenvalue is more than an order of magnitude larger than the others, which are also noisier. ",
+    "Since general Eigenvector decompositions are independent of rotations, our strategy is to rotate the N = 4 cross-correlation matrix into a state T where it is brought closer to the template, then apply a signal-to-noise weight before the Eigenvector decomposition. More precisely, we apply the following algorithm, which we refer to as ",
+    "the •T-rotation• method (for rotation into T-space) in the rest of this paper: ",
+    "The rotation in step (i) is de•ned as: "
+  ],
+  "R = T−1ρT ": [
+    "(9) ",
+    "and, by construction, reduces to the diagonal Eigenvalues matrix in the case where ρis the template cross-correlation coeÿcient matrix. The weighting in step (ii) is performed in two parts8(<>): 1-we p scale each matrix element Ri j by 1/λiλj, and 2-we weight the result by the signal to noise ratio of each λ. Combining, we de“ne9(<>): ",
+    "(10) ",
+    "As seen in Fig. (<>)7, the Eigenvalues drop rapidly, and we expect only the “rst few to contribute to the “nal result. In fact, our results present very small variations if we keep anywhere between two and six Eigenvalues and exclude the others. Since it was shown in HDP1 that in some occasions, we need up to four Eigenvectors to describe the observed C(k,k′) matrix, we choose to keep four Eigenvalues as well, and cut out the contributions from λi>4. ",
+    "In step (iii) the resulting matrix D is decomposed into Eigenvectors S: ",
+    "(11) ",
+    "Then, in step (iv), these Eigenvectors are weighted back by absorbing the weights directly: ",
+    "(12) ",
+    "The result is •nally rotated back into the original space: ",
+    "(13) ",
+    "If no cut is applied on the Eigenvalues, this operation essentially does nothing to the matrix, as the equivalence between ρ\u001f and ρis exact: every rotation and weights that are applied are removed, and we get U(k) ≡T\u001f1(k). However, the cut, combined with the rotation and weighting, acts as to improve the measurement of the Eigenvector. Physically, this is enforcing on the measured matrix a set of priors, corresponding to the Eigenvectors of the template, with a strength that is weighted by the known precision about the underlying Eigenvalue. For a Gaussian covariance matrix normalized to 1 on the diagonal, all frames are equivalent, and any rotation from any prior has no impact on the accuracy. When the covariance is not diagonal, however, some frames are better than others, and the Eigenframe is among the best, as long as the simulation Eigenframe is similar to that of the actual data. If these frames were unrelated, this T-rotation would generally be neutral. ",
+    "Figure 7. Signal and noise of the Eigenvalues measured from the N = 200 sample. The error bars are obtained from bootstrap resampling the power spectrum measurements. Only the four largest Eigenvalues are kept in the analyses. ",
+    "We present in the bottom panel of Fig. (<>)5 the e ect of this T-rotation on the original N = 4 Eigenvector. We observe that it traces remarkably well the N = 200 vector, to within 20 per cent even at the low k-modes, and outperforms the other techniques presented in this paper in its extraction of U(k). The best •tting parameters corresponding to T˜1(k) are summarized in Table (<>)1. We discuss in section (<>)5 how, in practice, one can us these techniques in a real survey. "
+  ],
+  "4 IMPACT ON FISHER INFORMATION ": [
+    "In analyses based on measurements of P(k), the uncertainty typically propagates to cosmological parameters within the formalism of Fisher matrices ((<>)Tegmark (<>)1997). The Fisher information content in the amplitude of the power spectrum, de•ned as ",
+    "(14) ",
+    "e ectively counts the number density of degrees of freedom in a power spectrum measurement. In the above expression, Cnorm is simply given by C(k,k′)/[P(k)P(k′)]. The Gaussian case is the simplest, since the covariance is given by where N(k) is the number of cells in the k-shell. We recall that the factor of two comes in because the symmetry, which reduces ",
+    "We see how I(k) is an important intermediate step to the full Fisher matrix calculation, as it tells whether we can expect an improvement on the Fisher information from a given increase in survey resolution. It was •rst shown by (<>)Rimes & Hamilton ((<>)2005) that the number of degrees of freedom increases in the linear regime, following closely the Gaussian prescription, but then reaches a trans-linear plateau, followed by a second increase at even smaller scales. This plateau was later interpreted as a transition between ",
+    "the two-haloes and the one-halo term ((<>)Neyrinck et al. (<>)2006), and corresponds to a regime where the new information is degenerate with that of larger scales. By comparison, the Gaussian estimator predicts ten times more degrees of freedom by k ∼0.3hMpc−1 . ",
+    "What stops the data analyses from performing fully non-Gaussian uncertainty calculations is that the Fisher information requires an accurate measurement of the inverse of a covariance matrix similar to that seen in Fig. (<>)2, which is singular. With the noise reduction techniques described in this paper, however, the covariance matrix is no longer singular, such that the inversion is •nally possible. To recapitulate, these techniques are: ",
+    "The •Naive N = 4 way• : straight Eigenvector decomposition ",
+    "In this section, we assume that there are no survey selection function e ects, and that the universe is periodic. We discuss more realistic cases in section (<>)5. ",
+    "We present in the top panel of Fig. (<>)8 the Fisher information content for each technique, compared to that of the template and the analytical Gaussian calculation. We also show the results for the N = 200 sample after the Eigen-decomposition, which is our best estimator of the underlying information ((<>)Ngan et al. (<>)2012). The agreement between this and the original information content in the N = 200 sample is at the few per cent level for k <1.0hMpc−1 anyway. We do not show the results from the N = 4 sample, nor that after the Eigenvector decomposed only, as the curve quickly diverges. It actually is the “tting procedure, summarized in Table (<>)1, that clean up enough noise to make the inversion possible. In all these calculations, the error bars are obtained from bootstrap re-sampling. The bottom panel represents the fractional error between the di erent curves and our best estimator. ",
+    "As •rst found by (<>)Rimes & Hamilton ((<>)2005), the deviation from Gaussian calculations reaches an order of magnitude by k ∼0.3h/Mpc, and increases even more at smaller scales. With the “t to the Eigenvector (technique (i) in the list above mentioned), we are able to recover a Fisher information content much closer to the template; it underestimates the template by less than 20 per cent for k <0.3hMpc−1 , and then overestimates the template by less than 60 per cent away for 0.3 <k <1.0hMpc−1 . The “t to the analytical substitution of G(k) (technique (ii)) has even better performances, with maximum deviations of 20 per cent over the whole range. The “t to the Wiener “lter (iii) is not as performant, but still improves over the naive N = 4 way, with the maximal deviation reduced to less than 45 per cent. Finally, the “t to the T-rotated (iv) Eigenvectors also performs well, with deviations by less than 20 per cent. Most of the residual deviations can be traced back to the fact that in the linear regime, the covariance matrix exhibited a large noise that we could not completely remove. This extra correlation translates into a loss of degrees of freedom in the linear regime, a cumulative e ect that biases the Fisher information content on the low side. Better noise reduction techniques that focus in the large scales cleaning could outperform the current information measurement. In any case, this represents a signi“cant step forward for non-Gaussian data analyses since estimates of I(k) can be made accurate to within 20 per cent over the whole BAO range, even from only four “elds, with minimal prior assumptions. ",
+    "Figure 8. (top:) Fisher information extracted from various noise •ltering techniques, compared to Gaussian calculations. Results from the original N = 200 sample are shown by the thin solid line, with error bars plotted as grey shades; calculations from the main Eigenvector of the N = 200 matrix are shown by the dashed line, with error bars; results from •tting directly the main Eigenvector of the N = 4 sample (see section (<>)2.4) are shown by the thick solid line; the e ect of replacing G(k) →2P(k)/N(k) (+ “t) is shown by the thick dashed line (see section (<>)2.3); the e ect of Wiener “ltering the covariance matrix (+ “t) is shown by the crosses (see section (<>)3.1); “nally, the noise-weighted T-rotation calculations (+ “t) are shown by the open circles (see section (<>)3.2). (bottom:) Fractional error between each of the top panel curves and the measurements from the main N = 200 Eigenvector. "
+  ],
+  "5 IN THE PRESENCE OF A SURVEY SELECTION FUNCTION ": [
+    "The results from section (<>)4 demonstrate that it is possible to extract a non-Gaussian covariance matrix internally, from a handful of observation patches, and that with noise •ltering techniques, we can recover, to within 20 per cent, the Fisher information content in the amplitude of the power spectrum of (our best estimate of) the underlying •eld. The catch is that these are derived from an idealized ",
+    "environment that exist only in N-body simulations, and the objective of this section is to understand how, in practice, can we apply the techniques in actual data analyses. 10 (<>)We explore a few simple cases that illustrates how the noise reduction techniques can be ap-",
+    "plied, and how the non-Gaussian parameters can be extracted in the presence of a survey selection function W(x). "
+  ],
+  "5.1 Assuming deconvolution of W(k) ": [
+    "The •rst case we consider is the simplest realistic scenario one can think of, in which the observation patches are well separated, and for each of these the survey selection functions can be successfully deconvolved from the underlying •elds. For simplicity, we also assume that each patch is assigned onto a cubical grid with constant volume, resolution and redshift, such that the observations combine essentially the same way as the N = 4 sample presented in this paper. Once the grid is chosen, one then needs to produce a large sample of realizations from N-body simulations, with the same volume, redshift and accuracy, and construct the equivalent of our N = 200 sample. ",
+    "ance matrix Cobs(k,k′) is related to the underlying one via a six-dimensional convolution: ",
+    "(16) ",
+    "In HDP1, C(k,k′) is calculated purely from N-body simulations, therefore it is known a priori; only P(k) and W(x) are extracted from the survey. It is in that sense that the technique of HDP1 provides an external estimate of the error. What needs to be done in internal estimates is to walk these steps backward: given a selection function and a noisy covariance matrix, how can we extract the non-Gaussian parameters of Table (<>)1? Ideally, we would like to deconvolve this matrix from the selection function, but the high dimensionality of the integral in [Eq. (<>)16] makes the brute force approach numerically not realistic. ",
+    "There is a solution, however, which exploits the fact that many of the terms involved in the forward convolution are linear. It is thus possible to perform a least square •t for some of the non-Gaussian parameters, knowing Cobs and W(x). We start by casting the underlying non-Gaussian covariance matrix into its parameterized form, which expresses each of its Legendre multipole matrices C ℓi j into a diagonal and a set of Eigenvectors (see [Eq. 51-54] and Tables 1 and 2 of HDP111(<>)). We recall that only the ℓ= 0,2,4 multipoles contain a signi“cant departure from the Gaussian prescription; the complete matrix depends on 6 parameters to characterize the diagonal components, plus 30 others to characterize the Eigenvectors. In principle, these 36 parameters could be found all at once by a direct least square “t approach. However, some of them have more importance than other, and, as seen in this paper, some of them are easier to measure, therefore we should focus our attention on them “rst. In particular, it was shown in “gure 22 of HDP1 that most of the non-Gaussian deviations come from C0, hence we start by solving only for its associated parameters. ",
+    "To simplify the picture even more, we decompose the problem one step further and focus exclusively on the diagonal component. In this case, we get, with the notation of the current paper: ",
+    "(17) ",
+    "The tilde symbol serves to remind us that this is not the complete ℓ= 0 multipole but only its diagonal. The term with the δµ1 is the Gaussian contribution, and yields to ([Eq. 56] of HDP1): ",
+    "(18) "
+  ],
+  "5.2 Assuming no deconvolution of W(k) ": [
+    "The second case is a scenario in which the observation mask was not deconvolved from the underlying •eld. This set up introduces many extra challenges, as the mask tends to enhance the non-Gaussian features, hence, for simplicity, we assume that there is a unique selection function W(k) that covers all the patches in which the power spectra are measured. Let us •rst recall that in presence of a selection function, the observed power spectrum of a patch •i• is related to the underlying one via a convolution with the Fourier transform of the mask, namely: ",
+    "For the second term, the δkk′allows us to get rid of one of the radial integral in [Eq. (<>)16], and the remaining part is isotropic, therefore the angular integrals only a ect the selection functions. These integrals can be precomputed as the X(k,k′′) function in [Eq. 57] of HDP1, with w(θ′′,φ′′) = 1, and we get ",
+    "(19) ",
+    "where the angle brackets refer to an average over the angular dependence. At the end of this calculation, we obtain, for each (k,k′) ",
+    "The •rst paper of this series describes a general extension to the FKP calculation in which the underlying covariance matrix C(k,k′) is non-Gaussian. Speci“cally, the observed covari-",
+    "pair, a value for αand β, and all that is left is to “nd the parameter values that minimize the variance. ",
+    "The next step is to include the o -diagonal terms of the ℓ= 0 multipole, in which case the full C0 is modelled. The underlying covariance matrix is now parameterized as ",
+    "We emulate a typical observation with a subset of only N = 4 N-body simulations, and validate our results against a larger N = 200 sample. The estimate of C(k,k′) obtained with such low statistics is very noisy by nature, and we develop a series of independent techniques that improve the signal extraction: ",
+    "where ",
+    "and ",
+    "(21) ",
+    "There are two new best-•tting parameters that need to be found from H0, namely A and k1, and we can use our previous results on αand k0 as initial values in our parameter search. Since the X functions only depend on W(k), we can still solve these N2 equations with a non-linear least square “t algorithm and extract these four parameters. ",
+    "Including higher multipoles can be done with the same strategy, i.e. progressively •nding new parameters from least square •ts, using the precedent results as priors for the higher dimensional search. One should keep in mind that the convolution with C2 and C4 becomes much more involved, since the number of distinct X functions increases rapidly, as seen in Table 4 of HDP1. In the end, all of the 36 parameters can be extracted out of N2 matrix elements, in which case we have fully characterized the non-Gaussian properties of the covariance matrix from the data only. ",
+    "The matrix obtained this way is expected to have very little noise, as this procedure invokes the •tting functions, which smooth out the •uctuations. In principle, assuming that the operation was loss-less, the recovered covariance matrix would be completely equivalent to the naive N = 4 way, had the selection function been deconvolved •rst. It could be possible to improve the estimate even further by attempting the T-rotation on the output, as explained is section (<>)5.1, but since we do not have access to the underlying density •elds, the Wiener •lter technique is not available in this scenario. "
+  ],
+  "6 DISCUSSION ": [
+    "With the recent realization that the Gaussian estimator of error bars on the BAO scale is biased by at least 15 per cent ((<>)Ngan et al. (<>)2012; (<>)Harnois-D´eraps & Pen (<>)2012), e orts must be placed towards incorporating non-Gaussian features about the matter power spectrum in data analyses pipeline. This implies that one needs to estimate accurately the full non-Gaussian covariance matrix C(k,k′) and, even more challenging, its inverse. The strategy of this series of paper is to address this bias issue, via an extension of the FKP formalism that allows for departure from Gaussian statistics in the estimate of C(k,k′). The goal of this paper is to develop a method to extract directly from the data the parameters that describe the non-Gaussian features. This way, the method is free of the biases that a ect external non-Gaussian error estimates (wrong cosmology, incorrect modelling of the non-Gaussian features, etc.). ",
+    "(iii) We optimize the uncertainty on the smooth non-Gaussian component from a noise-weighted sum over the di erent angular contributions, and apply a Wiener •lter on the resulting covariance matrix, ",
+    "These techniques are exploiting known properties about the noise, and assume a minimal number of priors about the signal. We quantify their performances by comparing their estimate of the Fisher information content in the matter power spectrum to that of the large N = 200 sample. We “nd that in some cases, we can recover the signal within less then 20 per cent for k <1.0hMpc−1 . We also provide error bars about the Fisher information whenever possible. By comparison, the Gaussian approximation deviates by more than two orders of magnitude at that scale. ",
+    "We “nd that the diagonal component of NG(k,k′) is well mod-elled by a simple power law, and that in the N = 4 sample, the slope αand the amplitude k0 can be measured with a signal-to-noise ratio of 4.2 and 2.2 respectively. The o -diagonal elements of NG(k,k′) are parameterized by “tting the principal Eigenvector of the cross-correlation coeÿcient matrix with two other parameters: an amplitude A, which has a signal-to-noise ratio of 32.1, and a turnaround scale k1, which is measured with a ratio of 0.30 and is thus the hardest parameter to extract. Even in the large N = 200 sample, k1 is measured with a ratio of 3.1, which is “ve to ten times smaller than the other parameters. This help us to better understand the parts of the non-Gaussian signals that are the noisiest, such that we can focus our e orts accordingly. ",
+    "We then propose a strategy to extract these parameters directly from surveys, in the presence of a selection function. We explore two simple cases, in which a handle of observation patches of equal size, resolution and redshift are combined, with and without a deconvolution of the survey selection function. The •rst case is the easiest to solve, since the deconvolved density •elds are in many respect similar to the simulated N = 4 sample that is described in this paper. We show that it is possible to apply all of the four noise •ltering techniques described above to optimize the estimate of the underlying covariance matrix. ",
+    "In the second case, we explore what happens when deconvolution is not possible. We propose a strategy to solve for the non-Gaussian parameters with a least square •t method, knowing Cobs(k,k′) and W(k). The approach is iterative in the sense that it “rst focuses on the parameters that contribute the most to the non-Gaussian features, then source the results as priors into more complete searches. ",
+    "The main missing ingredient from our non-Gaussian parameterization is the inclusion of redshift space distortions, which will be the focus of the next paper of this series. To give overview of the ",
+    "challenge that faces us, the approach is to expand the redshift space power spectrum into a Legendre series, and to compute the covariance matrix term by term, again in a low statistics environment. Namely, we start with P(k,µ) = P0(k)+P2(k)P2 (µ)+P4(k)P4(µ)+...where Pi(k) are the multipoles and Pℓ(µ) the Legendre polynomials, and compute the nine terms in C(k,µ,k′,µ′) = P0(k)P0(k′)+ P0(k)P2(k′)P2(µ) +...We see here why a complete analysis needs to include the auto-and cross-correlations between each of these three multipoles, even without a survey selection function. ",
+    "As mentioned in the introduction, many other challenges in our quest for optimal and unbiased non-Gaussian error bars are not resolved yet. For instance, many results, including all of the •tting functions from HDP1, were obtained from simulated particles, whereas actual observations are performed from galaxies. It is thus important to repeat the analysis with simulated haloes, in order to understand any di erences that might exist in the non-Gaussian properties of the two matter tracers. In addition, simulations in both HDP1 and in the current paper were performed under a speci•c cosmology, and only the z = 0.5 particle dump was analyzed. Although we expect higher lower redshift and higher m cosmologies to show stronger departures form Gaussianities • clustering is stronger • we do not know how exactly this impact each of the non-Gaussian parameters. ",
+    "To summarize, we have developed techniques that allow for measurements of non-Gaussian features in the power spectrum uncertainty for galaxy surveys. We separate the contributions to the total correlation matrix into two kinds: diagonal and o -diagonal. The o -diagonal is accurately captured in a small number of Eigen-modes, and we have used the Eigenframes of the N-body simulations to optimize the measurements of these o -diagonal non-Gaussian features. We show that the rotation into this space allows for an eÿcient identi•cation of non-Gaussian features from only four survey •elds. The method is completely general, and with a large enough sample, we always reproduce the full power spectrum covariance matrix. We •nally describe a strategy to perform such measurements in the presence of survey selection functions. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "The authors would like to thank Chris Blake for reading the manuscript and providing helpful comments concerning the connections with analyses of galaxy surveys. UP also acknowledges the •nancial support provided by the NSERC of Canada. The simulations and computations were performed on the Sunnyvale cluster at CITA. "
+  ]
+}

jsons_folder/2013MNRAS.431.3678R.json

@@ -0,0 +1,123 @@
+{
+  "ABSTRACT ": [
+    "Studies of the peculiar velocity bulk flow based on di erent tools and datasets have been consistent so far in their estimation of the direction of the flow, which also happens to lie in close proximity to several features identified in the cosmic microwave background, providing motivation to use new compilations of type-Ia supernovae measurements to pinpoint it with better accuracy and up to higher redshift. Unfortunately, the peculiar velocity field estimated from the most recent Union2.1 compilation su ers from large individual errors, poor sky coverage and low redshift-volume density. We show that as a result, any naive attempt to calculate the best-fit bulk flow and its significance will be severely biased. Instead, we introduce an iterative method which calculates the amplitude and the scatter of the direction of the best-fit bulk flow as deviants are successively removed and take into account the sparsity of the data when estimating the significance of the result. Using 200 supernovae up to a redshift of z=0.2, we find that while the amplitude of the bulk flow is marginally consistent with the value expected in a CDM universe given the large bias, the scatter of the direction is significantly low (at & 99.5% C.L.) when compared to random simulations, supporting the quest for a cosmological origin. ",
+    "Key words: peculiar velocities – bulk flow – supernovae: type-Ia "
+  ],
+  "1 INTRODUCTION ": [
+    "In the last couple of decades a considerable e ort has been devoted to the analysis of the peculiar velocity field in search for an overall bulk flow (BF) on ever increasing scales, lately reaching as high as ∼100 Mpc/h using galaxy surveys [(<>)1– (<>)16] and type-Ia supernovae (SNe) [(<>)17–(<>)23] and even an order of magnitude higher, based on measurements of the kinetic Sunyaev-Zeldovich e ect in the cosmic microwave background (CMB) [(<>)24–(<>)29]. While there have been conflicting claims regarding the amplitude of the dipole moment of this field and its tension with the expected value in a CDM universe, the vast majority of these surveys have been consistent in their findings for the direction of the dipole 1 (<>). ",
+    "Meanwhile, several features in the CMB temperature ",
+    "maps from the COBE DMR [(<>)31] and WMAP [(<>)32] experiments have been identified in roughly the same region of the sky, from the dipole moment [(<>)33] to several reported anomalies, including the alignment between the quadrupole and octupole [(<>)34, (<>)35], mirror parity [(<>)36–(<>)38] and giant rings [(<>)39]. This coincidence provides further motivation to search for a unified cosmological explanation [(<>)40]. ",
+    "Over the years a number of cosmological scenarios have been suggested as possible sources for a peculiar velocity BF, such as a great attractor [(<>)1, (<>)2], a super-horizon tilt [(<>)41], over-dense regions resulting from bubble collisions [(<>)42] or induced by cosmic defects 2 (<>)[(<>)43, (<>)44], etc. In an attempt to test these hypotheses and distinguish between them, any knowledge regarding the redshift dependence of the BF can be a crucial discriminator. ",
+    "Type-Ia SNe, whose simple scaling relations provide empirical distance measurements and which have been detected up to redshifts z & 1, provide a unique tool to estimate the peculiar velocity BF and study its direction and redshift extent. However, this approach also contains certain caveats. First, datasets from typical type-Ia SNe surveys are orders of magnitude smaller than those from galaxy surveys and their sky coverage and redshift-volume density are extremely poor. Secondly, di erent SNe compilations often use di er-ent light-curve fitters, involving di erent nuisance parameters. Currently, the most promising candidate for a large scale BF search is the Union2.1 compilation [(<>)45] (see also [(<>)46, (<>)47]), comprising of 19 di erent surveys which are all analyzed with a single light-curve fitter (SALT2 [(<>)48]) ",
+    "The purpose of this work is to investigate the peculiar velocity field extracted from the Union2.1 data and given its limitations determine which conclusions can be reliably made as to the BF in the inferred radial peculiar velocity field, placing an emphasis on its direction and redshift extent. Accounting for the substantial bias due to the sparsity of the data and using a dedicated algorithm to iteratively remove outlying data points from the analysis, we test the amplitude and the scatter of the direction of the BF and estimate the significance of the results using Monte Carlo simulations. ",
+    "The paper is organized as follows. In Section 2 we describe the initial filtering of the data and the method for extracting the individual radial components of the peculiar velocities, as well as how we generate random simulations of data with the same spatial distribution. In Section 3 we address the inevitable bias due to sparsity in both the amplitude and direction in naive best-fit methods used to detect an overall BF. We introduce our method in Section 4 and define a score which measures the scatter of the best-fit direction in successive iterations. We demonstrate that this score is e ective in identifying simulated datasets with an artificially inserted BF and discuss how the significance of its findings can be estimated. In Section 5 we consider both the full dataset and the application of the scatter-based iterative method to the data and present the results. We conclude in Section 6. "
+  ],
+  "2 PRELIMINARIES ": [],
+  "2.1 Data filtering ": [
+    "We use the recent type-Ia SNe compilation Union2.1 [(<>)45], which contains 580 filtered SNe at redshifts 0.015 < z < 1.4. This compilation is drawn from 19 datasets, all uniformly analyzed with a single light-curve fitter (SALT2 [(<>)48]), and analyzed in the CMB-frame. At high redshifts, the spatial distribution of this dataset grows increasingly sparse, the individual errors become large and some of the induced radial peculiar velocities, calculated as described below, take on unreasonable values (such as > 0.5c). In order to avoid these pathologies while still retaining the ability to examine the behavior at distances larger than those accessible with galaxy surveys (. 100 Mpc/h), we apply an initial cuto in redshift and remove all points with z > 0.2 (corresponding to . 550 Mpc/h) from our dataset. ",
+    "In Fig. (<>)1 we plot the spatial distribution of the Union2.1 ",
+    "Figure 1. The spatial scatter of all SNe in the Union2.1 compilation. The red triangles indicate SNe with z > 0.2 that are filtered out before any analysis is performed. ",
+    "dataset with the remaining 200 SNe marked in blue. It is apparent that even outside the galactic plane the sky coverage is quite poor and the three-dimensional distribution of the remaining data is significantly sparse and inhomogeneous. The implications of this will be discussed in the next section. "
+  ],
+  "2.2 Peculiar velocities and best-fit bulk flow ": [
+    "The Union2.1 dataset specifies for each SN its measured redshift z, the inferred distance modulus µobs and the error µobs. The relation between the cosmological (“true”) redshift z¯ and the distance modulus is given by ",
+    "(1) ",
+    "where dL is the luminosity distance, which in a flat universe with matter density M , a cosmological constant  and a current Hubble parameter H0, is ",
+    "(2) ",
+    "Due to the peculiar velocity, both the observed redshift and distance modulus (through the luminosity distance) will differ from their true cosmological values [(<>)49]. To first order in v·nˆ, where nˆ is the direction pointing to a SN with peculiar velocity v, we get ",
+    "(3) ",
+    "In order to extract the radial peculiar velocity vr of the SNe in our dataset, we follow the first order expansion in [(<>)20, (<>)49] ",
+    "(4) ",
+    "where H(z) is the Hubble parameter at redshift z, and dA(z) = dL(z)/(1 + z)2 is the observed angular diameter distance to the SN. ",
+    "We then find the best-fit BF velocity vBF in our set of N SNe, each with a radial velocity amplitude vri in a direction nˆi, by minimizing ",
+    "(5) ",
+    "with respect to the direction and amplitude of vBF, where ",
+    "vri are the individual errors obtained from the measurement errors in the distance moduli µobs i using Eq. ((<>)4). "
+  ],
+  "2.3 Monte Carlo simulations ": [
+    "Our Monte Carlo simulations consist of random permutations of the sky locations of the SNe in our dataset, after removing the initial BF velocity vBFinit from the entire set by subtracting its corresponding component from the individual velocities ",
+    "(6) ",
+    "The new dataset will have the same spatial distribution and its own initial random BF with a typical vrms amplitude. In order to simulate a random realization with a specifically chosen cosmological BF (up to statistical noise), for the purposes of testing our method, we simply add the chosen non-random BF contribution to the individual velocities after the permutation. ",
+    "For the analysis in this paper we use 16, 000 random realizations (spatial permutations) of the Union2.1 data with no artificially inserted BF in order to test against the null hypothesis. To examine the detection capabilities of our method, we use 6, 000 di erent random realizations for each inserted BF amplitude in the range |vBF|= {50, 100 . . . 450 km/s}, all in the direction (l, b) = (295◦, 5◦), which is the direction of the best-fit BF on the full dataset (for the purposes of estimating the significance of our results, we have verified that this specific choice of direction has no e ect). "
+  ],
+  "3 SPARSITY BIAS ": [
+    "As mentioned above, the spatial distribution of the SNe dataset is inhomogeneous and sparse across the sky and in redshift depth. As a consequence, any search for an overall BF will be severely biased. Such a bias must be taken into account when evaluating the significance of a measured best-fit BF vs. the expectation from a CDM universe. We now examine this bias separately in terms of the direction and amplitude of the BF. In the first subsection we show that the sparsity of our dataset causes a preference for a flow in directions within the galactic plane. In the second subsection we show that the root-mean-square (rms) velocity typically used under the CDM hypothesis is inappropriate for a significance estimation of the BF amplitude in a sparse dataset such as ours. "
+  ],
+  "3.1 Bulk flow - direction ": [
+    "In a dense homogeneous dataset (which has no preferred direction), if we perform many random mixings of the sky locations of the SNe, the best-fit BF direction will be distributed uniformly over the 4ˇ area of the sky. In a histogram of the measured directions, inside a circle of radius around any sky coordinate we expect to find a fraction ",
+    "(7) ",
+    "of the results. ",
+    "To demonstrate the bias induced by the sparsity of our dataset, we plot in Fig. (<>)2 the ratios between the measured ",
+    "fraction and its expected value fmeas./f for a uniformly distributed set (Left) as well as for our dataset (Right), using = 20◦. We see that the result for our dataset is far from isotropic. Its spatial distribution, regardless of the observed magnitudes, is biased towards a specific portion of the sky, namely the region surrounding the galactic plane. "
+  ],
+  "3.2 Bulk flow - amplitude ": [
+    "Another implication of the sparsity in the data is that the random component of the BF does not follow the expected CDM behavior. We must therefore quantify the di erence between the expected CDM rms velocity and the rms velocity we expect when dealing with a sparse dataset such as Union2.1. "
+  ],
+  "3.2.1 Velocity rms in CDM ": [
+    "In CDM, the expected value for the BF amplitude is zero v= 0 while its variance satisfies [(<>)3] ",
+    "(8) ",
+    "where f = m 0.55 is the dimensionless linear growth rate, P(k) is the matter power spectrum, W (kR) is the Fourier transform of a window function with characteristic scale R and the angle brackets ..denote an ensemble average. Since CDM is isotropic, this means that for each primary direction i ∈{x, y, z}in a Cartesian coordinate system the BF amplitude may be described using a normal distribution ",
+    "(9) ",
+    "To estimate the significance of a non-vanishing BF measured in a given survey, a common approach is to tweak the frame of reference so that the BF points exactly in one of the primary directions, e.g. eˆy,√and compare the “single component” measured BF to ˙/ 3. However, this ignores the fact that the BF amplitude in the other two directions vanishes due to this particular choice of frame and would lead to an overestimated significance of the BF amplitude. ",
+    "(10) ",
+    "That is, it follows an “unnormalized” ˜ distribution with 3 degrees of freedom (a Maxwell-Boltzmann distribution) [(<>)50]. Eq. ((<>)10) represents the probability density function (PDF) of the BF amplitude inside some volume, that is modulated by the same window function as in Eq. ((<>)8), in an unbiased way. "
+  ],
+  "3.2.2 Velocity rms in Union2.1 ": [
+    "In order for the right-hand side of Eq. ((<>)10) to describe the observed BF |v obs|appropriately, one needs to measure the peculiar velocity in many spatial locations, so that the typical separation between any two nearest neighbors that were measured will be much smaller than the coherence scale. This is clearly not satisfied for the sparse Union2.1 dataset. Therefore we should replace the window function with a sum ",
+    "Figure 2. Left: The ratio between the measured and expected fractions fmeas./f of 16, 000 randomly picked directions (simulating the homogeneous case) that point within = 20◦from each coordinate. Right: The same ratio inferred from 16, 000 random permutations of the locations of SNe of Union2.1 dataset, where the preference for the galactic plane is clearly seen. ",
+    "of N delta functions, each centered on the location Ri of a single SN ",
+    "(11) ",
+    "However, since in Fourier space ",
+    "(12) ",
+    "the new window function term will consist of ∼N2 interference terms that are no longer spherically symmetric. Therefore using Eq. ((<>)11) to evaluate the sparse-case equivalent of Eq. ((<>)10) is unfeasible. Instead we use the amplitudes of the best-fit BF of 16, 000 random spatial permutations of our dataset, as described in §(<>)2.3, as an approximation of the PDF for the BF amplitude inside a sphere of radius z = 0.2. The di erence between this approximation and the isotropic CDM scenario will be encoded in a best-fit ˙fit (instead of ˙) which describes the observed distribution ",
+    "(13) ",
+    "In Fig. (<>)3 we plot the approximated PDF for the BF amplitude and the corresponding best-fit ˜3 distribution according to Eq. ((<>)13). We find ",
+    "(14) ",
+    "as opposed to ˙ = 43 km/s calculated directly from Eq. ((<>)8) for a top-hat window function of size R = 550 Mpc/h. We see from Fig. (<>)3 that a naive estimation of the significance of a measured BF amplitude in a sparse survey would be highly overestimated. "
+  ],
+  "4 SCATTER-BASED METHOD ": [
+    "We present a method based on an iterative process of repeatedly fitting a BF to the peculiar velocity field after the removal of the datapoint with the highest deviation from the previous fit. If there is a significant BF in the full dataset, the compactness of the scatter in the directions identified for the best-fit BF in each iteration can be used as an eÿ-cient estimator of the significance of the original flow. The stronger the flow in the full dataset, the smaller the scatter we will measure in the iterations. ",
+    "Figure 3. The normalized PDF for the amplitude of the BF for CDM inside a sphere of radius 550 Mpc/h, calculated according to Eqs. ((<>)9)-((<>)10) (black) as well as for random realizations given the sparsity√of the Union2.1 data (blue). The red line is the best fit ˜3( 3x/˙fit) according to 16, 000 random permutations of the locations of our dataset, as described in §(<>)3.2. The goodness of fit is R2 = 0.9945. "
+  ],
+  "4.1 Iterative algorithm ": [
+    "Heuristically, the algorithm can be sketched as follows ",
+    "After calculating the best-fit BF of the complete set according to Eq. ((<>)5), we examine the residual velocities of the di erent SNe in order to identify the one with the strongest deviation from the bulk. In each iteration, we find the best-fit vBF iter and then identify the point i with the largest contribution ",
+    "(15) ",
+    "and remove it from the dataset before the next iteration. By iteratively removing these deviants, we can also verify that ",
+    "Figure 4. Illustration of the scatter of the best-fit BF direction in each iteration for a random realization with no inserted flow (blue) and for various sets with artificially inserted BF amplitudes, all in the direction (l, b) = (295◦, 5◦). The total number of iterations shown here is 191, after which only 10 SNe were left in the dataset. The score for each realization is shown in the appropriate color, normalized by the score of the real data. ",
+    "our results are not dominated by a small subset of the data with some common characteristic such as low redshift or a specific location on the sky. "
+  ],
+  "4.2 Scatter score ": [
+    "To measure the scatter, we assign a scatter score to the data, defined by ",
+    "(16) ",
+    "which is a cumulative sum of the consecutive and total shifts, i.e. the sum of the distances from the direction of the best-fit BF in the current iteration nˆj to the one in the last iteration nˆj−1 and to that of the first iteration nˆ1. This measures both the tightness and the extent of the scatter of the measured directions throughout the iterative process. ",
+    "In Fig. (<>)4 we demonstrate the results for the scatter score S by plotting the directions of the best-fit BF at each iteration for a random realization with just a random BF and with increasing artificially-added BF amplitudes in the direction (l, b) = (295◦, 5◦), which is the direction of the best-fit BF of our dataset (this choice of inserted direction allows a straightforward comparison with the data and accounts for a possible bias, as mentioned in §(<>)3.1, but we have verified that it has no e ect on our significance estimation). The results are consistent with the expected behavior: as the inserted BF amplitude is increased, the scatter becomes smaller and converges to a region closer to the inserted BF direction. "
+  ],
+  "4.3 Significance estimation ": [
+    "We compare Sdata with the mean value S evaluated using 6, 000 random simulations for each inserted BF amplitude |vBF|and infer the significance of the data in terms of the probability that a random CDM realization will get a lower score than the data ",
+    "(17) ",
+    "where P(|v|)d|v|is the probability that a CDM realization of the data will have a BF of amplitude between |v|and |v|+ d|v|given the sparsity of the data according to §(<>)3.2, and P(S < Sdata ||v|) is the conditional probability that a random simulation will result in S < Sdata given a BF amplitude |v|. "
+  ],
+  "5 RESULTS ": [],
+  "5.1 Full dataset ": [
+    "Before applying our scatter-based method described in the last section, we note that using a naive best-fit, the overall BF in our dataset has an amplitude |vBF|= 260 km/s and points in the direction (l, b) = (295◦, 5◦), which is in agree-ment with results reported elsewhere [(<>)5–(<>)7, (<>)9, (<>)10, (<>)17, (<>)19– (<>)23, (<>)26, (<>)27, (<>)29]. This direction lies in proximity to features in the CMB (most of all to the giant rings reported in [(<>)39]), but is also close to the galactic plane, as might have been expected given the sparsity bias shown in Fig. (<>)2. In addition, referring back to Fig. (<>)3 we see that when comparing with the expected rms amplitude in a finite-size survey with the same spatial distribution, this amplitude, although high, is consistent with CDM at the 95% C.L. (naively using the unbiased CDM expectation, one might have assigned a much larger significance to this result). ",
+    "Thus, using the full dataset, we conclude that no claim can be made as to the existence of a cosmological BF in the Union2.1 type-Ia SNe data up to redshift z = 0.2 given the significant bias induced by the poor sky coverage and redshift-volume density of this dataset. "
+  ],
+  "5.2 Sifting iteratively through the data ": [
+    "The scatter of the best-fit BF direction measured in the iterative process described in §(<>)4 is plotted in the left panel of Fig. (<>)5. In the right panel we plot the luminosity distance to the excluded SN as a function of the iteration number, and demonstrate that our results are not dominated by a subset of nearby SNe (SNe at distances & 500 Mpc/h remain in the dataset until the final iterations). Comparing Figs. (<>)4 (Left) and (<>)5 (Left) we see that the scatter of the data is much smaller than that of the realizations with |vBF|≤300 km/s, and is comparable in size to a |vBF|& 450 km/s realization. ",
+    "This is also shown quantitatively in Fig. (<>)6 (Left), where we plot the significance of the compactness of the scatter with respect to CDM, as described by Eq. ((<>)17), as a function of the total number of iterations Niter. For Niter = 110 (chosen arbitrarily), we show in Fig. (<>)6 (Right) a few percentiles of the results of the normalized score evaluated for random realizations of the data according to ((<>)17), along with the data result. We see that the score for our dataset is outside the 95% C.L. for any initial (i.e. for the whole dataset) BF amplitude smaller than 300 km/sec. ",
+    "Integrating over all possible initial BF amplitudes, we see that Sdata is surprisingly low with respect to the expectation from a CDM universe: the overall probability that a single CDM realization would get a score that is as low as the score of the real data is < 0.5% for any Niter > 30, and gets as low as 0.1% for some choices of Niter. Thus we conclude that the scatter of the best fit BF direction is significantly low, at a & 99.5% C.L. ",
+    "Figure 5. Left: The scatter of the best-fit BF in the Union2.1 dataset at redshifts z < 0.2. The black stars mark the best-fit BF direction of each iteration until only 10 SNe are left in the dataset. The plus signs indicate the spatial coordinate of the SN that is excluded at each iteration and are coloured as a function of the iteration number (blue -excluded first, red -excluded last). Right: The distance to the excluded SN in each iteration as a function of the iteration number. The dashed line marks the distance to the farthest SN remaining in the dataset at each iteration. ",
+    "Figure 6. Left: The significance of the compactness of the scatter with respect to CDM, as described by Eq. ((<>)17), as a function of the total number of iterations Niter, Right: A few percentiles of the results of the normalized score evaluated for random realizations of the data according to ((<>)17), along with the data result, for Niter =110. "
+  ],
+  "6 CONCLUSIONS ": [
+    "The goal of this work was to use the most recent compilation of type-Ia SNe measurements in order to test the claims of a peculiar velocity BF in di erent studies. After truncating the Union2.1 catalogue at redshift z = 0.2 and extracting the radial peculiar velocity field, we showed that a naive attempt to measure a best-fit BF in this field ignores a significant bias due to its sparse spatial distribution and renders inconclusive results for the amplitude and direction of the best-fit flow. This sparsity bias was discussed in detail above along with the diÿculty in determining the correct CDM prediction with which any result should be compared. We presented a prescription for estimating this value in a finite survey of given redshift extent and spatial distribution, and concluded that the BF amplitude measured in the Union2.1 data up to redshift z = 2 is consistent with the 95% C.L. limits. ",
+    "Given the consistency in the reports from a wide spectrum of analyses regarding the direction of the measured BF and the alignment between the reported values and certain CMB features, we focused on the direction and introduced a method which measures the scatter in the best-fit BF direction as outlying points are removed in iterations. We were careful to use realistic expectations for a BF amplitude in a sparse dataset and used Monte Carlo simulations with similar sparsity to estimate the significance of our findings. Our results suggest that the Union2.1 data up to redshift z = 0.2 contains an anomalous BF at a 99.5% C.L. compared to random simulations with the same sparsity as the data. ",
+    "In the future, as more data is collected, the method used in this work will become more and more robust and enable the measurement of the BF in consecutive redshift bins to yield a better analysis of the redshift dependence of the measured result. In addition, it might be possible to focus on measurements from a single survey and thus reduce ",
+    "the errors stemming from combining several surveys with di erent characteristics. ",
+    "If the reports of a BF which is inconsistent with CDM are verified by future observations, it shall serve as a promising lead for theoretical research exploring areas beyond the concordance cosmological model. The full potential of type-Ia SNe data to settle this issue is yet to be realized. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "BR thanks A. Nusser and D. Poznanski for useful discussions. We also thank A. Nusser for comments on the first version of this work. EDK was supported by the National Science Foundation under Grant Number PHY-0969020 and by the Texas Cosmology Center. "
+  ]
+}

jsons_folder/2013MNRAS.432.1989S.json

@@ -0,0 +1,217 @@
+{
+  "ABSTRACT ": [
+    "We simulate the evolution of a 109 M dark matter halo in a cosmological setting with an adaptive-mesh refinement code as an analogue to local low luminosity dwarf irregular and dwarf spheroidal galaxies. The primary goal of our study is to investigate the roles of reionization and supernova feedback in determining the star formation histories of low mass dwarf galaxies. We include a wide range of physical effects, including metal cooling, molecular hydrogen formation and cooling, photoion-ization and photodissociation from a metagalactic (but not local) background, a simple prescription for self-shielding, star formation, and a simple model for supernova driven energetic feedback. To better understand the impact of each physical effect, we carry out simulations excluding each major effect in turn. We find that reionization is primarily responsible for expelling most of the gas in our simulations, but that supernova feedback is required to disperse the dense, cold gas in the core of the halo. Moreover, we show that the timing of reionization can produce an order of magnitude difference in the final stellar mass of the system. For our full physics run with reionization at z = 9, we find a stellar mass of about 105 M at z = 0, and a mass-to-light ratio within the half-light radius of approximately 130 M/L, consistent with observed low-luminosity dwarfs. However, the resulting median stellar metallicity is 0.06 Z, considerably larger than observed systems. In addition, we find star formation is truncated between redshifts 4 and 7, at odds with the observed late time star formation in isolated dwarf systems but in agreement with Milky Way ultrafaint dwarf spheroidals. We investigate the efficacy of energetic feedback in our simple thermal-energy driven feedback scheme, and suggest that it may still suffer from excessive radiative losses, despite reaching stellar particle masses of about 100 M, and a comoving spatial resolution of 11 pc. ",
+    "Key words: galaxies: dwarf – Local Group – hydrodynamics – galaxies: star formation – dark ages, reionization, first stars – ISM: evolution "
+  ],
+  "1 INTRODUCTION ": [
+    "Dwarf galaxies are the most dark matter dominated objects in the universe, with gravitational masses a hundred or even a thousand times greater than their observed baryonic masses. They therefore appear to lie at the extreme limit of galaxy formation. Despite this, however, they exhibit re-",
+    "markable consistency in many of their properties. Milky Way dwarfs appear to have a constant central mass (within 300 pc) of 107 M over five orders of magnitude in luminosity ((<>)Strigari et al. (<>)2008) and their mean stellar metallicity tightly correlates with their luminosity over more than three orders of magnitude ((<>)Kirby et al. (<>)2011). Despite their small sizes and large mass-to-light ratios, dwarf galaxies appear to lie on many of the scaling relations seen in massive galaxies ((<>)Kormendy et al. (<>)2009; (<>)Tolstoy, Hill, & Tosi (<>)2009). Under-",
+    "standing the physics that shape dwarf galaxies is partially an effort to understand a particularly inefficient mode of galaxy formation, but it also is an effort to understand how physical processes involved in galaxy formation scale across galaxy mass to produce the observed continuous evolution in galaxy properties. ",
+    "The competition between a variety of baryonic heating and cooling mechanisms plays an important role in regulating the gas available for star formation in galaxies. Understanding galaxy formation is therefore in part about understanding how these microphysical processes work in galaxies. These processes operate in a non-linearly growing potential well while being perturbed by environmental effects such as ram pressure and by effects of secular evolution of massive baryonic structures such as disks and bars. Since dwarf galaxies in the Local Group, especially dwarf spheroidal galaxies (dSphs), are observed to have large mass-to-light ratios and old stellar populations, it is likely that their evolution has been heavily influenced by heating processes that suppressed later star formation. In addition, the number of dwarf galaxies observed around the Milky Way is several orders of magnitude less than the predicted number of dark matter subhaloes found in cosmological N-body simulations ((<>)Klypin et al. (<>)1999; (<>)Moore et al. (<>)1999). This ’missing satellite’ discrepancy had been somewhat alleviated by the discovery of many ‘ultrafaint’ dSphs (e.g. (<>)Willman et al. (<>)2005) and by hydrodynamical simulations of dwarf satellite systems that have shown baryonic processes can suppress star formation ((<>)Okamoto et al. (<>)2010; (<>)Wadepuhl & Springel (<>)2011). Several heating processes are at play in dwarf evolution, including the metagalactic UV background during the epoch of reionization ((<>)Bullock, Kravtsov, & Weinberg (<>)2000; (<>)Gnedin & Kravtsov (<>)2006), supernova feedback ((<>)Governato (<>)et al. (<>)2010; (<>)Sawala et al. (<>)2010) as well as local UV heating and winds from young stars. ",
+    "While these heating processes act in the evolution of galaxies of all sizes, dwarf galaxies provide an attractive laboratory for their study since their small sizes allow simulators the ability to reach higher resolutions. High resolution is important for resolving the dense gas from which stars form and for retaining the energy in hot gas, and is therefore key to constraining the star-formation rate. High spatial resolution (of order 1 pc) is especially important in limiting diffusion from cold, high-density gas into hot, rarefied gas produced by supernova explosions (e.g, (<>)de Avillez & Mac (<>)Low (<>)2002; (<>)Joung & Mac Low (<>)2006). Without resolution on this scale, feedback energy is rapidly radiated (e.g. (<>)Katz, (<>)Hernquist, & Weinberg (<>)1992). Simulations of galaxy formation often compensate for this behavior by imposing feedback driven winds or by enhancing the impact of feedback heating by either distributing energy to diffuse gas phases (e.g. (<>)Springel & Hernquist (<>)2003; (<>)Scannapieco et al. (<>)2006) or turning off cooling for a time ((<>)Stinson et al. (<>)2006; (<>)Gov-(<>)ernato et al. (<>)2010). These different approaches to modeling feedback can produce different star formation histories and galaxy properties even when keeping the total amount of supernova energy the same between different model implementations ((<>)Schaye et al. (<>)2010; (<>)Sales et al. (<>)2010). We understand a great deal about the structure of supernova remnants from observations of nearby resolved examples (e.g. (<>)Badenes (<>)2010), and it is possible to model the impact of supernovae in idealized simulations of the ISM (e.g, (<>)de Avillez ",
+    "(<>)2000; (<>)Joung & Mac Low (<>)2006), but how these processes depend on, and interact with, global galaxy properties to produce global behavior such as galactic winds remains an open question. ",
+    "Heating mechanisms appear to be very important in dwarfs, but understanding the cooling mechanisms that balance them is also crucial. Many of the heating processes we have outlined are a consequence of stellar evolution and are therefore correlated with the star formation rate. In low mass haloes with very low metallicities, the effect of molecular line cooling from H2 may be an important factor in determining the star formation rate. Cosmological galaxy simulations often assume an equilibrium cooling curve for low metallicity gas, but non-equilibrium effects may also be important ((<>)Abel, Bryan, & Norman (<>)2002; (<>)Glover & Clark (<>)2012). ",
+    "As we have discussed, reproducing the proper phase distribution of gas in the interstellar medium is quite dif-ficult, however, modeling star formation from this medium through the creation of aggregate star particles is also quite uncertain. We see stars forming from dense molecular clouds in our own galaxy and (<>)Kennicutt ((<>)1998) has demonstrated that the star formation rate of galaxies correlates strongly with the gas surface density. Despite this observed relation, the gas density threshold for star formation is often an adjustable parameter in cosmological galaxy simulations in part because of resolution limitations, and indeed, adjusting the star formation threshold at fixed resolution can produce very different galaxy properties (see (<>)Guedes et al. (<>)2011). Modeling star formation from particular gas phases may also produce different behavior; (<>)Kuhlen et al. ((<>)2012) have shown that modeling star formation as dependent on the molecular gas fraction suppresses the star formation rate in low mass galaxies at high redshift. However, (<>)Glover & Clark ((<>)2012) have argued that simply the gas density determines the star formation rate and the molecular gas fraction plays little direct role. Since many of the other uncertain subgrid processes that we have discussed (i.e. feedback) are dependent on the star formation rate, uncertainties in modeling star formation have the potential to compound themselves in a galaxy model, and in low mass dwarf galaxies where star formation and its quenching can balance so precariously, these issues may be especially important. ",
+    "For this study, we have deliberately chosen simple and widely used prescriptions to model subgrid baryonic effects such as supernova feedback and reionization. Our goal is to test these model prescriptions at high resolution by carefully comparing our simulation results to observations. We believe that the specific ways in which our simulations succeed or fail to reproduce observations can tell us much about the ability of these model prescriptions to capture the relevant baryonic physics properly. ",
+    "We will also attempt to better understand the factors that control the gas content, star formation rate, and stellar mass for Local Group dwarf analogues. We are particularly interested in probing the relative impacts of supernova feedback and reionization on the evolution of these low-mass systems. We will attempt to do this by better understanding the detailed evolution of the gas phase distribution within a cosmological context. The simplicity of our model assumptions for subgrid baryonic physics will hopefully provide clarity in ",
+    "interpreting the implications of our results for the evolution of real systems. ",
+    "To these ends, we have conducted a series of high resolution cosmological, hydrodynamical simulations of a single dwarf halo with prescriptions for H2 and metal line cooling; star formation and supernova feedback; and a global UV background that ionizes neutral gas and dissociates molecules. We target a dark halo mass of 109 M, at the low-mass end of the range in dwarf galaxy halo masses. Modeling of the dynamics of Local Group dwarfs suggests they reside in dark matter haloes of approximately this mass or smaller (e.g (<>)Tollerud et al. (<>)2011). ",
+    "We describe our simulation methods and physical prescriptions in Section (<>)2 and present the results of our canonical simulations in section (<>)3.1. We have also conducted simulations where we have adjusted some of the physical prescriptions implementing supernova feedback and reionization to gauge their effect in our model. We present the results of these alternate physics runs in Section (<>)3.2. We discuss the results of our simulations and compare our results to observations and other simulations in Section (<>)4, and summarize our conclusions in Section (<>)5. "
+  ],
+  "2 METHODS ": [
+    "We conducted our simulations with the structured adaptive mesh refinement (AMR) hydrodynamics code Enzo ((<>)Bryan (<>)1999; (<>)Norman & Bryan (<>)1999; (<>)O’Shea et al. (<>)2004). Enzo uses an Eulerian method for solving the hydrodynamics equations on a Cartesian grid. We chose a grid-based method because of its ability to resolve interfaces in multiphase gas ((<>)Slyz et al. (<>)2005; (<>)Agertz et al. (<>)2007; (<>)Tasker et al. (<>)2008). We used the ZEUS hydro solver in Enzo which uses a simple and robust second-order finite difference method ((<>)van Leer (<>)1977; (<>)Stone & Norman (<>)1992). Dark matter and stars are represented by particles, and the gravitational interactions are computed by solving the potential on the mesh ((<>)O’Shea (<>)et al. (<>)2004). Our model also solves non-equilibrium evolution rate equations for e− , H, H+ , He, He+ , He++ , H− , H2, and H2+ , as well as cooling from these species ((<>)Anninos et al. (<>)1997; (<>)Abel et al. (<>)1997). In addition, we include metal line cooling, photoionizing and photodissociating backgrounds, star formation and thermal feedback, and self-shielding by neutral and molecular gas, which are all described in more detail below. Our version of the code is publicly available in the auto-inits branch of the online Enzo repository 1 (<>)as changeset 15651fe320ff. "
+  ],
+  "2.1 Initial conditions ": [
+    "We generated cosmological initial conditions with Enzo’s initial conditions generator inits. We used the best fit cosmological parameters from the WMAP5 data release (Ωm = 0.274, Ωb = 0.0456, ΩΛ = 0.726 and h = 0.705) ((<>)Hinshaw (<>)et al. (<>)2009). We begin our simulations at redshift z = 99 when perturbations in the universe still grow linearly. Our cosmological box is 4 comoving Mpc h−1 on a side and is divided into 1283 cells on the root grid. We note that our ",
+    "box size is too small to accurately sample large scale modes, and the largest mode in the box becomes non-linear at low redshift. This will affect the statistics of the haloes in our box, and will also impact accretion at late times; however, since this is an exploratory study to understand the gross evolutionary properties of a single low mass dwarf halo, we argue that this level of error is acceptable. In particular, we note that while the accretion history of our chosen halo may be biased, it is likely to fall within the wide range of possible such histories for haloes of this mass. We will redress this problem in later work. ",
+    "Our goal is to simulate a single dwarf halo at high resolution. We first selected a target halo from a simulation of our cosmological box with no refinement. We identified haloes close to our target mass of 109 M at z = 0. We found that lower mass haloes traveled a longer distance relative to their size than higher mass haloes (reflecting the fact that all haloes participate in large-scale bulk flows). We chose a halo that traveled a relatively small distance relative to its r200 radius during the simulation to minimize the area of refinement necessary in resimulations. Our chosen halo travels a distance of 0.9 comoving Mpc h−1 during the simulation. This choice was motivated by concern for computational efficiency, however, it had the result of selecting a relatively isolated halo. The closest halo with comparable mass to our target halo has a mass of 8.52×108 M and is at a distance of 338 kpc, which is approximately 14 times r200 for our halo. The most massive halo in the box is 1.43×1012 M and is 2.9 Mpc from our target halo. ",
+    "The target halo identified, we then created new, refined initial conditions based on the trajectory of our halo and its particles. We laid down a series of nested static subgrids that refine the root grid by a total of three additional levels so that in the most refined region the effective initial resolution was 10243 . The cell size within the most refined static subgrid before adaptive refinement is therefore 5.54 comov-ing kpc. One corner of the maximally refined static subgrid was defined by the target halo’s final position plus a buffer of 10 r200 radii. The opposite corner was set to contain the volume enclosing the initial positions of the halo’s particles in the coarse simulation, plus an additional buffer of 10% of the width of this enclosing volume in each direction. A buffer region of four intermediate resolution grid cells was placed around the boundaries of each successively nested static grid. The initial resolution of a cell sets the mass of the dark matter particles laid down within it, so the higher resolution cells have lower mass dark matter particles. The buffer regions are important to ensure that higher mass particles did not impact the evolution inside the highly refined region. These initial conditions set the minimum mass of dark matter particles to be 5353 M. ",
+    "To further restrict refinement to the halo of interest, we have employed a new technique that identifies dark matter particles in our refined initial conditions that end the simulation in our target halo and then requires the presence of these particles for the refinement of a given cell. We identified halo dark matter particles in our refined initial conditions by first running a dark matter only simulation to z = 0. We identified particles that ended the simulation within 3r200 radii of the halo centre and tagged them as ‘must refine particles.’ In all subsequent runs with hydrodynamics, we restrict adaptive refinement to cells that contain ",
+    "must refine particles and that are within the highest resolution initial subgrid. Cells meeting these criteria may be further refined based on their dark matter and baryon density such that additional refinement was added (by a factor of 2) whenever the dark matter mass in a cell exceeded four times the dark matter particle mass, with a similar criterion for the gas. We did not explicitly implement refinement based on the Jeans length, however, we found that with our density refinement criteria that in most dense regions we either resolved the Jeans length by four grid cells (meeting the criterion of (<>)Truelove et al. ((<>)1997) to avoid artificial fragmentation) or the density of the gas was greater than our chosen threshold density for star formation. The net result of our method is that the adaptive refinement tracks the dark matter particles and gas that ends up in the halo of interest. In our highest resolution run (Simulation R10 in Table (<>)1), we find that 99% of the dark matter particles within r200 are must refine particles at z = 0. This method resulted in a computational savings of more than a factor of 10, as compared to allowing refinement anywhere in the most refined initial grid, which is standard practice. ",
+    "In our highest resolution simulations, we allow a total of 12 levels of adaptive refinement beyond the root grid. These simulations therefore have a minimum cell length of 10.8 comoving pc. This means at high redshift (z ∼ 9) our calculations have a physical resolution of order one pc. We have also conducted simulation R43 that allows only 10 levels of adaptive refinement beyond the root grid for a minimum cell length of 43.3 comoving pc. We will discuss this simulation in Section (<>)4.3. "
+  ],
+  "2.2 Metal cooling ": [
+    "As noted earlier, we include radiative cooling from nine atomic and molecular species ((<>)Abel et al. (<>)1997; (<>)Anninos (<>)et al. (<>)1997), whose (non-equilibrium) abundances are explicitly followed. In addition, the code also tracks a mean metallicity, and additional metal heating and cooling rates are interpolated from equilibrium cooling tables, in a way similar to that described in (<>)Smith, Sigurdsson, & Abel ((<>)2008): Cloudy ((<>)Ferland et al. (<>)1998) is used to generate five-dimensional tables that give the net metal cooling and heating rates, depending on the gas metallicity, electron fraction, density, temperature and redshift. The redshift tracks the time-dependence of the metagalactic UV background (see below). The combination of heating and cooling from non-equilibrium atomic and molecular hydrogen combined with equilibrium metal lines, allows for a more accurate estimate of the cooling rates, particularly for low metallicity gas. Since we follow the abundance of H2, the cooling rates we compute for low temperature, low metallicity gas where H2 cooling dominates are particularly accurate. We do not include molecular hydrogen formation on dust grains, but by the time this pathway becomes important, metal cooling dominates over H2 cooling anyway ((<>)Glover (<>)2003). Finally, we note that we do not include molecules formed out of heavy elements, but these tend to be less important than fine-structure lines ((<>)Glover & Clark (<>)2012), particularly at low abundances. "
+  ],
+  "2.3 UV background ": [
+    "We include both photoionizing and photodissociating meta-galactic backgrounds in our model. We assume spatially uniform photoionizing rates for H I, He I and He II that vary with redshift, taken from (<>)Haardt & Madau ((<>)2001). This background includes ionization from both quasars and stars. For most of our runs we start turning on the photoioniz-ing background at z = 7 and gradually ramp it up to full strength by z = 6. The photodissociation rate of H2 is taken to be 1.13×10−8 times the flux in the Lyman-Werner bands ((<>)Abel et al. (<>)1997). We adopt the average flux in the Lyman-Werner bands from the spectra of (<>)Haardt & Madau ((<>)2011). This flux is redshift dependent and we assume it to be spatially uniform. We turn on the photodissociating background at the same time as we start the photoionizing background (without a ramp-up period, as there is no significant gas heating associated with this transition). In order to investigate the impact of the timing of the reionization epoch, we also carried out a simulation in which we turned on the UV background at an earlier redshift, z = 8.9, and ramped up the ionizing background to full strength by redshift z = 8. ",
+    "Although the UV background is spatially uniform, we apply a crude self-shielding correction. The H I ionizing flux felt by each cell is attenuated by a factor of exp(−ΔxnHIσ¯ion), where Δx is the cell size, nHI is the neutral hydrogen density, and σ¯ion is the frequency-averaged photoionization cross-section for H I. We computed the frequency-averaged photoionization cross-section as ",
+    "(1) ",
+    "where J is the flux of the ionization background, which we approximate as J ∝ νβ , and σ is the frequency dependent ionization cross-section, which is zero for frequencies less than ν0, the threshold frequency for ionization of H I, and σ ∝ A0ν−3 for frequencies greater than ν0. The parameter β is the power law slope of the ionization background which we take to be -1.57, approximately the slope of the photoion-ization background that we use. The parameter A0 is the peak ionization cross-section for H I. With these assumptions we calculate the average photoionization cross-section to be σ¯HI = Aoβ/(β − 3). ",
+    "A similar correction is made for the H I photoheat-ing rate, where we use the frequency-averaged photoheating cross-section which we compute as ",
+    "(2) ",
+    "which we find is proportional to σ¯ion by a factor of (β + 1)/(β − 2). Corrections are also made for He I and He II ionization and heating using the corresponding values of A0 for each species taken from (<>)Brown ((<>)1971) and (<>)Osterbrock & (<>)Ferland ((<>)2006). These corrections are approximate, as they assume that only gas in the local cell contributes to self-shielding, but they do suppress ionization and heating in dense regions. ",
+    "Table 1. Summary of Simulations. ",
+    "(2) the fraction of rest mass energy that star particles return to the gas, ",
+    "We also apply a simple self-shielding correction to the Lyman-Werner background as described in (<>)Shang, Bryan, & (<>)Haiman ((<>)2010); this uses the local H2 densities multiplied by the local Jeans length to determine an estimate of the column density of H2 that is shielding each cell. The simple estimate in (<>)Draine & Bertoldi ((<>)1996) is then used to compute a self-shielding correction factor. (<>)Wolcott-Green, Haiman, (<>)& Bryan ((<>)2011) have recently shown that this can result in an overestimate of the self-shielding correction for our conditions; however, given the highly uncertain level of the Lyman-Werner background, this approximation is sufficient for this work. "
+  ],
+  "2.4 Star formation and supernova feedback ": [
+    "Star particles are created during the course of a simulation following the prescription of (<>)Cen & Ostriker ((<>)1992). The implementation in Enzo is described in more detail in (<>)Tasker (<>)& Bryan ((<>)2006), but we briefly outline it here. Star particles are created in a cell if its density rises above 10 5 times the universal mean density at that redshift, if the divergence of the local velocity is negative, and if the local cooling time is less than the dynamical time (or the gas temperature is less than 10 4 K). If these requirements are met, then the star formation rate is computed according to ρ˙SFR = SFρgas/tdyn, where SF = 0.01 is the star formation efficiency (e.g. (<>)Krumholz & Tan ((<>)2007)) and tdyn = (3π/32Gρ)1/2 is the dynamical time. A star particle is then created with mass M∗ = ρ˙SFRΔtΔx 3 , where Δt is the timestep. To prevent very small star particle masses, a stochastic prescription is used such that star particles are not created until 100 M of stars are predicted to form; once that limit is reached, a star particle of 100 M is created (up to a maximum of 80% of the baryonic mass in the cell). ",
+    "Once they are created, star particles return both energy and mass to their surrounding gas, also following the prescription of (<>)Cen & Ostriker ((<>)1992). Star particles return some fraction of their rest mass energy to thermal energy in the gas. We chose this value to be 3.7 × 10−6 for most of our simulations. This corresponds to 150 M worth of stars to produce one supernova’s worth of energy (1051 ergs). This energy is continuously injected as thermal energy into the ",
+    "gas over the feedback time tf , which is a few dynamical times (i.e. ten Myr to a few tens of Myr) as detailed in (<>)Tasker & Bryan ((<>)2006). The energy and mass return fractions depend sensitively on assumptions regarding the IMF; the values adopted in this paper are in the ranges determined by other works (e.g. (<>)Jungwiert, Combes, & Palouˇs (<>)2001; (<>)Kroupa (<>)2007; (<>)Oppenheimer & Dav´e (<>)2008; (<>)Conroy & (<>)Gunn (<>)2010). Note that we do vary the fraction of rest mass energy returned in feedback in order to investigate the impact this has on our results. The particle also returns 25% of its mass to the gas. ",
+    "Our choice of a purely thermal feedback model is motivated by simple models of individual supernovae which show that the supernova driven Sedov blast wave reaches a radius of a few parsecs in dense gas before radiative cooling begins to slow it down and it radiates away energy ((<>)Chevalier (<>)1974). One might expect that in a galaxy simulation with a resolution comparable to this scale, artificial radiative losses seen in previous lower resolution studies (e.g. (<>)Katz, Hernquist, & (<>)Weinberg (<>)1992) would be small. In such a simulation this resolution would negate the need for artificial subgrid models necessary to compensate for this effect (e.g. turning off radiative cooling). Our main simulations have a spatial resolution of 10.8 comoving pc; therefore, for z  3, our simulations have a spatial resolution less than 3 pc, which is the level of resolution needed to test this hypothesis. Given the observed old stellar populations found many dSphs and their small sizes, these systems are an ideal test case for this type of model run at these resolutions. We will discuss the efficacy of this model and our assumptions in Section (<>)4.2. ",
+    "We follow a single gas metallicity field in all our simulations, so we do not follow the detailed chemical evolution of individual metal species. The metallicity field (ρZ ) is initialized to a low value at the beginning of the simulation (10−10 times the mean gas density). When star particles form, they are assigned the metal fraction ρZ /ρgas of their birth cell. Stars return 2% of their total mass to this metal-licity field over the feedback timescale tf using the same temporal functional form as used for the thermal feedback. During each time step, the ejected metal mass is added directly to the single cell in which the star particle resides. The 2% metal yield we use is a fiducial value consistent ",
+    "with previous work ((<>)Madau et al. (<>)1996). Uncertainties in individual stellar yields and the IMF make this value very difficult to constrain. Moreover, a more sophisticated chemical model could be employed that includes different types of supernovae with different injection timescales and chemical yields. We are interested in probing the broad effect of a using a purely thermal supernova model at high resolution in an AMR code and understanding the relative effects of supernovae and reionization. For these reasons we have chosen to use a simple chemical model. "
+  ],
+  "2.5 Halo tracker and data analysis ": [
+    "The problem of finding and tracking inheritance between dark matter haloes within cosmological simulations is not a trivial one. We used the halo finder hop ((<>)Eisenstein & (<>)Hut (<>)1998) to identify haloes in our simulation and a simple halo tracker to track inheritance between haloes, starting with the final target halo at z = 0 and working backwards in time to higher redshifts. For each child halo, the tracker finds parent haloes in the preceding output by identifying haloes that contain dark matter particles that end up in the child halo. Parent haloes that contribute more than 10% of the child halo’s dark matter mass or contain more than 107 M in dark matter mass are considered significant parents. The lineages of these significant parents are then tracked back to previous outputs in the same manner. ",
+    "The ability of this simple halo tracker to separate halo lineages is limited by the ability of hop to separate interacting haloes and by the cadence of simulation outputs. There were cases of interacting haloes where hop was unable to properly separate haloes and the halo tracker was therefore unable to properly separate lineages containing these haloes. In these cases, we present the potential lineages of interacting haloes as equivalent and do not attempt to distinguish between them. ",
+    "We analysed the baryon quantities of identified haloes with the simulation data analysis and visualization tool yt ((<>)Turk et al. (<>)2011). We also used yt to construct the images, phase diagrams and radial halo profiles which we present. "
+  ],
+  "3 RESULTS ": [
+    "We have run a suite of simulations of a single dark matter halo, varying the physical prescriptions outlined in Section (<>)2. Table (<>)1 summarizes the simulations discussed in this paper. Analysis is conducted on simulation outputs that are written every 108 Myr. Two of our runs, R10 and R10-earlyUV, include all of the physics we have described previously, but differ in the time at which the UV backgrounds are introduced. We call these two runs our canonical runs, and describe them in detail below. We have also run a simulation completely neglecting the UV backgrounds, simulation R10noUV. This simulation, unlike our other simulations which were run to z = 0, was run only to z = 3.1. We chose to end R10-noUV at this redshift because of the copious cold, dense gas produced. This gas made the simulation run quite slowly and by redshift 3.1, the difference in evolution was clear. Simulations R10-lowFB, R10-noFB and R10-noFB-LimCool all examine the impact of changing the strength of supernova feedback. We also tested the importance of H2 for ",
+    "Figure 1. Top: Evolution of the dark matter mass within r200 (top) and virial temperature (bottom) of progenitor haloes in simulation R10. Coloured lines indicate haloes containing star particles, while gray lines indicate haloes that remain dark. A line begins when a halo becomes massive enough to be detected by our halo finder and ends when the halo merges into a more massive halo. We note that substructure can occasionally separate far enough from its parent halo to be detected for a brief time as a separate halo, and therefore appears as short lines. In particular, two star forming progenitors have a series of close encounters during which our halo finder was unable to distinguish between them – their evolution is shown in orange. ",
+    "cooling by removing it as a coolant in simulation R10-noH2. This set of simulations gives us broad levers on the relative importance of most of the heating and cooling effects important in dwarf formation. In particular, we aim to understand the fundamental question of how the dual effects of supernova feedback and reionization shape the baryon fractions and star formation rates of dwarf galaxies. "
+  ],
+  "3.1 Canonical runs ": [
+    "In this section, we describe in detail the results of R10 and R10-earlyUV, which are the highest resolution simulations to include all of the physics outlined in Section (<>)2. R10-earlyUV differs from R10 in that the uniform UV back-",
+    "Figure 2. Evolution of baryon properties, within r200, of progenitor haloes in simulation R10 (left column) and R10-earlyUV (right column). Top row: The ratio of baryon mass to total mass. Middle row: The ratio of gas mass to total mass. Bottom row: The total stellar mass. The cumulative mass distribution of star particles that end the simulation in the final halo is shown in black. The solid line colours have the same meaning as in Figure (<>)1. The dotted lines bracket the redshift range over which the photoionization background is introduced and ramped up to full strength. ",
+    "grounds were turned on in the same way as described in Section (<>)2 but between redshifts 8 and 8.9 instead of between redshifts 6 and 7. The purpose of introducing the global UV background at different times is to explore the effect of patchy reionization. More isolated regions of the universe ",
+    "farther from major sources of ionizing photons may be affected by the ionizing background later than less isolated regions. In both R10 and R10-earlyUV, the universe is ionized by redshift six. "
+  ],
+  "3.1.1 Global properties ": [
+    "The halo we have chosen is fairly isolated at z = 0; however, like all dark matter haloes in cosmological simulations, it assembles hierarchically. Figure (<>)1 shows the evolution of the dark matter halo masses and virial temperatures (as defined in (<>)Machacek, Bryan, & Abel (<>)2001) of progenitor haloes in R10 and R10-earlyUV. We present the dark matter evolution only for haloes in R10 since the dark matter evolution is virtually identical in R10-earlyUV. At z = 9, there are 30 progenitor haloes more massive than 106 M. Two of these haloes are more massive than 107 M, and these two haloes gradually build up their mass within two groups over the course of the simulation. The two haloes merge at z = 1.8 in a merger that is about 2:1 in dark matter and nearly 1:1 in stellar mass in both R10 and R10-earlyUV. ",
+    "The evolution of a variety of baryon quantities in progenitor haloes is shown in Figures (<>)2 and (<>)3. We track gross properties of progenitor haloes in Figure (<>)2 such as the total baryon fraction, gas fraction and stellar mass and quantities associated with the densest cell in each halo in Figure (<>)3 such as its density and metallicity. The densest cell within each halo is the cell most likely to form star particles in our model. Given the low star formation rates expected of progenitor haloes and the fact that our star formation and supernova feedback models operate on a cell-by-cell basis, the properties of the cell with the maximum likelihood of star formation can be very informative. ",
+    "The evolution of the gas fraction in progenitor haloes appears to be dominated by reionization. Figure (<>)2 shows sharp declines in the gas and baryon fractions in both R10 and R10-earlyUV at their respective times of reionization. These declines are due to photo-evaporative outflows triggered by reionization ((<>)Barkana & Loeb (<>)1999; (<>)Gnedin & (<>)Kravtsov (<>)2006). We see that once the gas fraction declines during reionization, it remains suppressed for the remainder of the simulation. We see no evidence for re-accretion of gas once the main halo has been assembled at z = 1.8. ",
+    "There are also smaller, but still significant, declines in the gas fraction prior to reionization in several luminous progenitors (Figure (<>)2). These declines appear to be correlated with peaks in the star formation rate as shown in the bottom panels of Figure (<>)3. Therefore, we conclude that they are primarily due to supernova feedback. ",
+    "The gas fraction indicates how the bulk of the gas responds, but star formation depends on the presence of dense gas. The evolution of the density of the densest cell in each progenitor halo shares some characteristics with the evolution of the gas fraction, but it is not identical. The peak cell density declines after reionization, but the decline is delayed relative to the declines seen in gas fraction. This is due, in part, to self-shielding from the UV background. In R10 particularly, there appears to be an extended epoch of elevated gas density in one progenitor that does not end until z = 4 and another progenitor is able to briefly re-cool some gas, although this dissipates by z = 3.5. We see that the evolution of the peak cell density tracks the star formation rate in individual haloes, also shown in Figure (<>)3, which is unsurprising as the presence of dense gas controls star formation in our model. ",
+    "The evolution of the properties of the densest cell shown in Figure (<>)3 can be quite stochastic in nature, with sharp ",
+    "changes especially at high redshift. These changes are due to the short timescale for cell-by-cell variations in our models. Our high spatial resolution enhances the importance of mixing to the evolution of the ISM, which likely plays a role in these variations. Also at this epoch, star-formation with accompanying supernova feedback is very important. At high redshift, regions of high gas metallicity coincide with regions of recent star formation. Over time these regions of enhanced gas metallicity expand, driven by the energy of supernovae to pollute the IGM as seen in Figure (<>)4. This expansion causes the gas metallicity in the central regions where the stars are located to decline. We discuss the effec-tiveness of metal ejection in Section (<>)4.4. ",
+    "There are multiple star forming progenitor haloes in both simulations; however, R10-earlyUV has fewer, due to the earlier onset of reionization. It appears that some haloes which cooled later in R10 do not have time to cool before reionization occurs in R10-earlyUV. The bottom panels of Figure (<>)3 show both the star formation rate inferred from the stellar population in our target halo at redshift zero, and the instantaneous star formation rates in all progenitor haloes measured at each data output. The star-formation rate inferred from the stellar population at redshift zero is built up from star-formation events in multiple progenitor haloes with varying durations and intensities. ",
+    "Several star forming progenitors undergo star formation events that appear to be single bursts and have a duration of order of or less than the time between data outputs (108 Myrs). Three star forming progenitors in R10 and four star forming progenitors in R10-earlyUV are captured in a star-forming state in only a single data output. One progenitor in each of R10 and R10-earlyUV undergoes a star burst that occurs between outputs. The total mass in stars produced in this mode is small in R10, constituting less than 8% of the final stellar mass. In R10-earlyUV its contribution to the final (smaller) stellar mass is much greater, constituting over 57%. In R10-earlyUV there is essentially a single progenitor that has an extended period of star formation. "
+  ],
+  "3.1.2 A detailed look at the evolutionary stages ": [
+    "In order to get a better qualitative understanding of how our simulated dwarf galaxy evolves, we next look at the spatial properties of the halo at various times in R10. The evolution of gross halo properties presented in Figures (<>)1-(<>)3 can be tracked through the progression of projections presented in Figure (<>)4, which are centered on one of the two massive, star-forming progenitor haloes of our final halo and show its assembly at high redshift from a small group of other dwarf progenitors. We can see the spatial variations in gas density, temperature and metallicity produced by the processes of cooling, supernova feedback, reionization and self-shielding. We can also see the hierarchal build-up of both dark matter mass and stellar mass which constitute the final halo. We can break down the evolution of this halo into a number of states described by these projections and by the density-temperature phase plots for the same progenitor halo presented in Figure (<>)5. ",
+    "The first stage presented is at z = 9 and is shown in the top left panel of Figure (<>)5. We see the halo just prior to the onset of star formation. Near the virial radius the gas shock heats and creates a reservoir of gas at roughly ",
+    "Figure 3. Evolution of the peak density, metallicity and star-formation rate within progenitor haloes in R10 (left column) and R10earlyUV (right column). Top row: Evolution of the maximum density within each progenitor halo. The density threshold for star formation is shown as a dashed line. Middle row: Evolution of the metallicity of the peak density cell shown in the top row. Bottom row: The star-formation rate within the last 22 Myr for each progenitor halo is plotted with colour lines, while the star-formation rate inferred from the star particles that end the simulation in the final halo is shown in black. One halo in R10 (plotted in dark green) underwent a single star formation event that happens between outputs. Another halo in R10 (plotted in dark purple) accreted its stellar population through a major merger with a slightly less massive progenitor but did not form its own in situ stellar population before the merger. Neither halo is therefore plotted in the bottom panel. A different halo in R10-earlyUV (plotted in light green) also underwent a star formation event between outputs and is not plotted in the bottom panel. ",
+    "The dotted lines bracket the redshift range over which the photoionization background is introduced and ramped up to full strength. ",
+    "Figure 4. From top to bottom, cubic projections centered on a massive star-forming progenitor halo at z = 9.0, 7.04, 5.82, 3.48 that also show several other lower mass star-forming progenitors. The bottom row shows the final halo at z = 0. From left to right, the panels show projected gas density, temperature, metallicity, dark matter density, and stellar density. The panels presented in the first four rows have a comoving width of 150 kpc; the final row of projections at z = 0 have a width of 48 kpc, which is 2r200 for the final halo. The scale of the images in physical, non-comoving units is indicated for each redshift. At z = 9 the other massive star-forming progenitor is 14 physical kpc from the centered halo and is therefore not shown. Projections of gas density, temperature and metallicity are weighted by gas density and projections of dark matter density and stellar mass density are unweighted (see Equation 3 in (<>)Turk et al. ((<>)2011)). Note that this weighting scheme gives units of volume density for gas density and units of surface density for dark matter and stellar density. ",
+    "Figure 5. Density-temperature distributions of gas within the r200 radius for one of the massive halo progenitors at the redshifts shown. The colour of cells shows the cumulative sum of mass within the corresponding density-temperature bin. ",
+    "the virial temperature of the halo. This gas can then begin to cool via H2 cooling (e.g. (<>)Abel, Bryan, & Norman (<>)2002). Figure (<>)1 shows the evolution of the virial temperature of many progenitor haloes; prior to reionization in both the R10 and R10-earlyUV runs, all progenitor haloes have virial temperatures less than 104 K. Therefore, for primordial gas ",
+    "in these haloes, the only important coolant is molecular hydrogen; atomic line cooling is not significant. This stage is also shown in projections in the first row of Figure (<>)4. ",
+    "Eventually the gas reaches the second stage (top-right panel of Figure (<>)5; z = 7.88) where gas temperatures in the centre fall to 200 K and gas densities cross 10−21 g cm−3 , ",
+    "roughly the gas density threshold for star formation in our model at high redshift. Once gas becomes dense enough to form stars in this second stage, we see evidence of supernova-heated gas with temperatures in excess of 106 K and the picture becomes more complex. ",
+    "In the third stage (see panel labelled z = 7.04 in Figure (<>)5), gas continues to be heated by supernovae and shows evidence of pressure equilibrium at low densities and high temperatures, as shown in the phase diagram. Also, with the injection of metals, gas can now cool to temperatures below 100 K at a broad range of densities. In some cases, the gas does appear to be significantly affected by supernova feedback in this stage. Figures (<>)2 and (<>)3 show the evolution of the gas fraction and the peak gas density of many haloes. Prior to reionization there are examples of decrements in both quantities, which must be due to supernova feedback. The second row in Figure (<>)4 also shows this stage. We can see that, by this point, metals have been ejected from progenitor haloes and have significantly enriched the intra-group medium. ",
+    "After z = 7 (in the R10 run), the onset of photoioniz-ing and photodissociating backgrounds causes a dramatic change in the phase structure of gas within progenitor haloes. In this fourth stage (see panels labelled z = 6.36 and z = 5.82 in Figure (<>)5), we see nearly all of the gas heated to a temperature of about 104 K. In some haloes (including the one shown in Figures (<>)4 and (<>)5), the gas is able to remain dense or briefly recool, producing an additional wave of star formation. The third row of Figure (<>)4 shows this stage. This stage does not appear in haloes in R10-earlyUV and it ends in all progenitor haloes in R10 by z = 3.5. ",
+    "After this point, once the dense star-forming gas has been dissipated, a small amount of high-temperature gas persists within the supernova heated phase in a fifth stage (see panel labelled z = 4.97 in Figure (<>)5). However, this gas phase eventually dissipates and the small amount of remaining gas sits at a temperature slightly above 104 K. This is both the temperature of the IGM and roughly the virial temperature of the final halo. ",
+    "At low redshift (see the last two panels of Figure (<>)5), a series of dry mergers continue until the final halo is assembled. The final haloes that result in R10 and R10-earlyUV are gas poor spheroids of dark matter and star particles. R10 and R10-earlyUV differ in stellar mass by an order of magnitude: the halo in R10, which had a late onset of reionization, has a final stellar mass of 1.43 × 106 M, while the halo in R10-earlyUV, which had an earlier onset of reionization, has a final stellar mass of 1.16 × 105 M. Table (<>)2 summarizes some of the final halo properties in these simulations. "
+  ],
+  "3.2 Alternate physics runs ": [
+    "We have also conducted a number of simulations in which we have altered some aspect of our physical prescriptions in order to better understand their effect on the evolution of the final halo. We have done simulations that have changed some aspect of the cooling prescription, the supernova feedback prescription and the UV background prescription. Table (<>)1 summarizes these simulations. ",
+    "Table 2. Summary of Final Halo Properties. ",
+    "Note: The quantities presented in each row are (1) the total mass within r200, (2) the total stellar mass within r200, (3) the total gas fraction within r200, (3) r200, the radius within which the mean halo density is 200 times the critical density of the universe, (4) the radius enclosing half the stellar mass, (5) the total mass within r1/2, (6) the total mass within 300 pc, (7) the velocity dispersion of star particles within r1/2, (8) the mass-weighted median of the star particle metallicities, (9) the mass-weighted mean of the star particle metallicities, (10) the mass-weighted standard deviation of the star particle metallicities. "
+  ],
+  "3.2.1 Simulation without H2 cooling ": [
+    "We conducted a simulation without the creation of or cooling from H2. Simulation R10-noH2 has line cooling from six atomic species of hydrogen and helium as well as metal line cooling and heating from the Cloudy models of (<>)Smith, (<>)Sigurdsson, & Abel ((<>)2008). The UV backgrounds, the self-shielding by neutral gas, and the star formation and feedback models are the same as R10. This simulation produced an entirely dark halo; no star formation occurred. We found that without molecular hydrogen cooling, gas temperatures in the most massive progenitors did not fall below 500 K and densities remained below 6 × 10−24 g cm−3 . The peak in gas density occurred at z = 5.8, shortly after reionization reached full strength. Our model requires gas to be denser than 8.09 × 10−23 g cm−3 to form star particles at this redshift. With no initial star formation, there is no source for metals, which are the most important gas cooling agents for star formation. Once the photoionizing background is turned on, the halo gas is further heated and the gas becomes even more difficult to cool. The result is an entirely dark halo at z = 0. "
+  ],
+  "3.2.2 Simulations with alternate UV backgrounds ": [
+    "Our canonical simulations demonstrate that the UV background has an important effect on the evolution of the halo gas. We observe that the gas fractions of progenitor haloes drop dramatically at the redshift of full-strength reioniza-tion in both our early reionization simulation (R10-earlyUV) and our late reionization simulation (R10). We also observe gross differences in the properties of the final stellar component between these two simulations. The total stellar mass in the final halo differs by an order of magnitude between the two runs and the star-formation history is more bursty and truncated in R10-earlyUV. The median stellar metallic-ity is much lower in R10-earlyUV (0.06 Zversus 0.51 Z), a ",
+    "Figure 6. Evolution of properties for two massive progenitors in simulations R10 (black) and R10-noUV (green). R10-noUV was not run past a redshift of 3.1. The properties shown here are the halo baryon fraction within the r200 radius (top left); the halo gas fraction within the r200 radius (top right); the density of the densest cell within each halo (bottom left); and the stellar mass within the r200 radius for each halo (bottom right). The density threshold for star formation is shown as a dashed line in the bottom left panel showing the peak gas density. ",
+    "consequence of the lack of late and extended star-formation bursts. ",
+    "To further explore the effect of the UV heating on the halo’s evolution, we conducted a simulation without the pho-toionizing and photodissociating UV fields, R10-noUV. This simulation was only run to a redshift of 3.1, but interesting comparisons can still be made. Figure (<>)6 shows the evolution of a variety of gas properties for the two massive progenitors of our final halo in R10-noUV (we show only two haloes for clarity). There are some striking similarities and differences in the evolution of these haloes between R10 and R10-noUV. We see dips in the gas fractions of haloes in R10noUV, some quite dramatic, but the gas fraction is able to rebound in both massive progenitors. By z = 3.1, when we stop R10-noUV, there is an order of magnitude difference in baryon and gas fractions for both haloes between the two simulations. The baryon fraction in one halo has rebounded to its level at z = 12. ",
+    "The dense gas exhibits similar behavior. The peak gas ",
+    "density does drop considerably between redshifts of 6 and 4, but the gas is able to re-cool and condense to a level where it is able to form stars. This produces an uptick in the star formation rate and several haloes are forming stars at z = 3.1 when the simulation was ended. ",
+    "The dips seen in the gas fraction and peak gas density in R10-noUV are most likely due to the effect of supernova feedback. In the absence of UV heating, supernovae act as the main regulator of the star formation rate in this run. The degree of supernova heating scales with the star formation rate and once the rate drops, gas is able to both re-accrete onto the halo and re-cool in its centre. This produces an increase in the star formation rate. We did not run this simulation beyond z = 3.1, so it is impossible to say whether this cyclical process will continue or whether the constant bursts of star formation will produce an overall net decline in the gas fraction or peak gas density. ",
+    "These simulations indicate that the UV background plays a crucial role in regulating the gas fractions of the ",
+    "Figure 7. Evolution of properties for two massive progenitors in simulations R10 (black) and R10-lowFB (blue). The properties depicted are the same as those shown in Figure (<>)6. ",
+    "progenitor haloes. In our model, it produces a sharp drop in the gas fraction in all haloes. This drop leaves an imprint on the star formation history inferred from the final stellar population of our target halo (the solid black lines in the bottom two panels of Figure (<>)3). This imprint is particularly evident because our UV backgrounds are spatially uniform, so all progenitors are affected with the same level of flux, and all the progenitor haloes are in the mass range sensitive to the UV backgrounds. "
+  ],
+  "3.2.3 Simulations with alternate supernova feedback levels ": [
+    "We also conducted three simulations exploring the effect of changing the strength of supernova feedback in our model. In most of our simulations, including R10, star particles return 3.7 × 10−6 of their rest mass energy to thermal gas energy. In simulation R10-lowFB, we have set this fraction to be 10−6 . In simulations R10-noFB and R10-noFB-LimCool, star particles return zero thermal energy to the gas through supernovae, however, star particles do return metals to the gas in the same way as in R10 and R10-lowFB. ",
+    "Properties for the two most massive progenitor haloes ",
+    "in simulation R10-lowFB are shown in Figure (<>)7. The gas fractions for these two haloes behave in nearly the same fashion as they do in simulation R10. There appear to be smaller declines in the gas fraction prior to z = 6, which must be due to the reduced impact of supernova heating. Curiously, while the gas fraction declines in the same way and to the same levels as in R10, the peak gas density within each halo behaves differently. There are sharp declines in the peak gas density between redshifts 6 and 4, but the peak gas density is then able to rise significantly in one of the progenitors, up to the level required for star formation. ",
+    "This difference in the evolution of dense gas results in steady, low-level star formation in R10-lowFB down to low redshift, unlike in R10. The final stellar mass in R10-lowFB is 5.03 × 106 M, almost five times the stellar mass found in R10. The stellar component is also more metal rich than in R10: the log of the mean and median stellar metallicities is 0.30 and 0.10 respectively, more than 0.4 dex higher than in R10. The longer star formation history, higher stellar mass and higher stellar metallicities are due to the decreased ability of supernova feedback to destroy self-shielded clumps and drive metals from star-forming gas in this simulation. ",
+    "Figure 8. Evolution of properties for two massive progenitors in simulations R10 (black), R10-noFB (yellow) and R10-noFB-LimCool(red). The properties depicted are the same as those shown in Figure (<>)6. ",
+    "Star particles in our model impact the thermal state of the gas in two ways: first, by heating it through supernova feedback, and second, by injecting metals that act as coolants. In simulations R10-noFB and R10-noFB-LimCool we have completely eliminated thermal feedback while maintaining the metal feedback. Unsurprisingly, we see metals collecting in the centres of haloes to a much greater degree than in R10, making it unclear if changes in the no-feedback runs are due to a lack of energetic input, or an increase in the metal cooling rate. ",
+    "To differentiate between these causes, in run R10-noFB-LimCool we capped the effective metallicity used for cooling at 0.1 Z. Figure (<>)8 shows that the differences between R10noFB and R10-noFB-LimCool are minimal; therefore the differences seen between these two simulations and R10 are due to a lack of heating by supernovae, not to enhanced cooling from the collected metals. ",
+    "The gas fractions of haloes in R10-noFB and R10-noFB-LimCool decline in almost the same way as in R10 after the introduction of the UV fields. They are slightly elevated down to z ∼ 2, as compared to the gas fractions in R10, but this may be due to their higher gas fractions at z = 6 ",
+    "when the ionizing background reaches its full strength. As in R10-lowFB, the overall decline in the gas fraction does not correlate with an overall decline in the peak gas density. The peak gas density in both massive progenitors dips at z = 6, but it does not fall below the threshold density for star formation, and we see that a low level of star formation persists in both progenitors down to z = 0. "
+  ],
+  "4 DISCUSSION ": [
+    "We have explored a variety of physical effects in a series of high-resolution, hydrodynamical, cosmological simulations. Our goals were to better understand the physics that regulate star formation in a dwarf halo comparable in mass to the dwarf satellite galaxies seen in the Local Group, as well as to test current feedback models in such systems. We found that the combination of supernova feedback and reioniza-tion causes a large suppression of the star formation rates in these haloes. Reionization appears to regulate the overall gas budget within the halo. Supernova feedback seems to more directly affect the dense gas that is available for star formation. Of course, these heating sources are not strictly exclusive in their effects; supernova feedback can have a quasi-periodic effect on the gas fraction and reionization can cause a dip in the peak gas density. However, the quantities affected are typically able to recover in the absence of their primary regulator. ",
+    "The reason for this dichotomy between reionization and supernova feedback is primarily their different physical locations within the halo. The UV backgrounds we implement are uniform and are attenuated by our self-shielding prescriptions in dense gas at halo centres. At the onset of reion-ization, the ionizing background is able to produce a pressure imbalance nearly everywhere in the halo except the very cen-tre. A large fraction of gas is therefore driven out of the halo in photoevaporative winds, while the central dense gas can remain intact for some time ((<>)Alvarez, Bromm, & Shapiro (<>)2006; (<>)Gnedin & Kravtsov (<>)2006; (<>)Whalen et al. (<>)2008) ",
+    "Thermal energy from supernova feedback is only injected into the single cell containing a young star particle in our model. Since the star particles tend to form and remain centrally located in haloes throughout the simulation, the energy they inject tends to affect central dense gas. We do see evidence that supernovae in our model affect regions outside the central dense gas in the form of supernovae driven outflows which enrich the IGM with metals, as seen in Figure (<>)4 and discussed more below. It is unclear, however, to what extent our supernova feedback model accurately captures the heating of the ISM. While the simulations that we have run with little or no thermal feedback seem to indicate that our feedback prescription is key in expelling dense gas and truncating the star formation history, we will explore this issue in more detail later in this section. ",
+    "In the following sections, we will first compare our results to observed properties of low mass dwarf systems, then we will examine the effect of supernova heating in more detail, followed by discussions of spatial resolution and metal dispersal, and ending with a discussion dark matter properties and neglected physics. "
+  ],
+  "4.1 Observable properties ": [
+    "In this section we compare our models to observations of several types of low-luminosity dwarf galaxies. This comparison is important because understanding the ways in which our simulations fail to produce realistic galaxies can provide important insights into the specific ways in which our model prescriptions fail. We can consider two classes of dwarf galaxies for comparison: mass analogues and environmental analogues. Our simulated halos have stellar masses ",
+    "and velocity dispersions similar to those of dSphs found near the Milky Way. Unfortunately, their proximity to a large galaxy does not make them suitable environmental analogues; our simulated halo is 2.9 Mpc from a Milky Way sized halo. Dwarf galaxies have been observed in underdense environments, however, most of these are dIrrs that are more luminous than both the typical Milky Way dSphs and our simulated haloes ((<>)Weisz et al. (<>)2011a). A handful of dSphs are known in low-density environments (e.g. (<>)Makarov et al. (<>)2012), however while some of these systems may be relics of reionization ((<>)Monelli et al. (<>)2010), others likely underwent pericentric passages with a large host galaxy ((<>)Teyssier, (<>)Johnston & Kuhlen (<>)2012). Many of the lowest luminosity dwarfs discovered around the Milky Way have been found in the SDSS, for which the distance limit for detection has been demonstrated to be less than the Milky Way virial radius ((<>)Koposov et al. (<>)2008). It is therefore possible that similar low-luminosity dwarfs await detection at greater distances in low-density environments. ",
+    "As shown in Table (<>)2, our canonical simulations R10 and R10-earlyUV produce final halos with dynamical masses within 300 pc close to 107 M, similar to those derived for Milky Way dSphs ((<>)Strigari et al. (<>)2008). The final velocity dispersion of star particles within the radius enclosing half the stellar mass, r1/2, is roughly 8 km s−1 in both simulations, making them dynamical analogues of Milky Way dSphs as shown in Figure (<>)9. In the following subsections we discuss other observational comparisons. "
+  ],
+  "4.1.1 Total stellar mass ": [
+    "The final stellar masses produced in our simulated halo are 1.43 × 106 M in R10 and 1.16 × 105 M in R10earlyUV. Assuming a stellar mass-to-light ratio in the V band of 2 M/L for our (old) stellar population ((<>)Krui-(<>)jssen & Mieske (<>)2009), the haloes in R10 and R10-earlyUV would have V band luminosities of approximately 7.15 × 105 L and 5.8 × 104 L respectively. These estimates place the halo in R10-earlyUV at the upper luminosity end of the ultrafaint dSphs and R10 among the lower luminosity classical dSphs ((<>)Walker et al. (<>)2009b; (<>)Simon & Geha (<>)2007), as shown in Figure (<>)9. If we compare our estimated luminosities to the haloes’ total gravitational masses, these haloes have mass-to-light ratios within r1/2 (the radius enclosing half the stellar mass) of 85 M/L for R10 and 133 M/L for R10-earlyUV. The spatial extent of the final stellar component is also comparable to real systems; Figure (<>)9 shows that the half stellar mass radii for the final haloes in R10 and R10-earlyUV are similar to the half-light radii of dSphs with similar luminosities. ",
+    "In other highly resolved cosmological calculations of low-mass dwarf haloes, the total stellar mass is generally similar to what we have found. (<>)Sawala et al. ((<>)2010) found, for their highest resolution model of a similar halo mass, a simulated stellar mass of 7.35 × 106 M. Recent work by (<>)Governato et al. ((<>)2012) also probed halo masses close to 109 M, and while the stellar content is not the focus of their study, their models appear to produce only ∼ 5 × 104 M of star particles for haloes close to this mass. One of the many differences between these two studies is the time of reioniza-tion; (<>)Sawala et al. ((<>)2010) reionize the universe at z ∼ 6 and (<>)Governato et al. ((<>)2012) do so much earlier at z ∼ 9. Con-",
+    "Figure 9. Comparison between the observational properties of Local Group dSphs and the simulated properties of the final haloes produced in R10 and R10-earlyUV. All quantities are plotted against total V band luminosity. V band luminosities are estimated for our simulated haloes as described in section (<>)4.1.1. Top panel: Velocity dispersions for 28 Local Group dSphs collected by (<>)Walker et al. ((<>)2009b)3 (<>), but including the velocity dispersion for the dynamically cold component of Bootes I measured by (<>)Ko-(<>)posov et al. ((<>)2011) (open circles); and the three-dimensional velocity dispersions of star particles within the half-stellar mass radii of R10 and R10-earlyUV (solid squares). Middle panel: The half-light radii for the same sample of dSphs (open circles) and the half stellar mass radii for the final haloes in R10 and R10-earlyUV (solid squares). Bottom panel: The mean stellar metallicities for 15 Milky Way dSphs measured by (<>)Kirby et al. ((<>)2008) and (<>)Kirby (<>)et al. ((<>)2011) (open circles), the mean (solid squares) and median (solid triangles) star particle metallicities for the final haloes in R10 and R10-earlyUV. ",
+    "sidering this, the results of (<>)Sawala et al. ((<>)2010) are most analogous to our simulation R10, which has a final stellar mass of 1.43 × 106 M, and the results of (<>)Governato et al. ((<>)2012) are most analogous to simulation R10-earlyUV which has a final stellar mass of 1.16 × 105 M. In this light, these results appear to be roughly consistent with each other (and with the idea that later reionization leads to larger stellar masses), although differences in final stellar mass between analogous haloes can approach an order of magnitude. "
+  ],
+  "4.1.2 Metallicity ": [
+    "Milky Way dwarfs are observed to lie on a fairly tight luminosity-metallicity relation ((<>)Kirby et al. (<>)2011), shown in Figure (<>)9, which may extend beyond the Milky Way ((<>)Kirby, (<>)Cohen, & Bellazzini (<>)2012). Figure (<>)9 shows the metallicity-luminosity relation found for Milky Way dSphs. Star particles in R10 have a mean metallicity of 0.84 Z and a median metallicity of 0.51 Z; in R10-earlyUV they have a mean metallicity of 0.12 Z and a median metallicity of 0.06 Z. If we make the estimate that [Fe/H] ∼ log(Z/Z) (e.g. (<>)Woo, Courteau, & Dekel (<>)2008), then these values translate to mean and median [Fe/H] values of -0.076 and -0.29 dex for R10 and mean and median [Fe/H] values of -0.92 and -1.2 dex for R10-earlyUV. Our assumption that [Fe/H] ∼ log(Z/Z) is a somewhat flawed one given the short duration of star formation in our progenitor haloes, and the fact that we do not properly model contributions from SNIa. We would expect this short duration to result in elevated values of [α/Fe] for their stellar populations ((<>)Tins-(<>)ley (<>)1979). This has the potential to decrease our estimated [Fe/H] by a few fractions of a dex, but we are interested in understanding differences in [Fe/H] of a dex or more. ",
+    "Based on our estimated luminosities calculated in Section (<>)4.1.1 and according to the dSph luminosity-metallicity relation of (<>)Kirby et al. ((<>)2011), star particles in the final halo in R10 should have an average [Fe/H] of -1.76 dex (1.7×10−2 Z) and -2.09 dex (8.1 × 10−3 Z) in R10-earlyUV. Figure (<>)9 shows this discrepancy, which is over 1.5 dex for R10 and over 1 dex for R10-earlyUV. This 1-2 dex difference between observed systems and our simulations has important implications for the utility of the feedback model we use. It appears that while our adopted feedback model effectively suppresses the formation of dense gas and stars, it does not drive sufficient metal ejection from the ISM. "
+  ],
+  "4.1.3 Gas content and star formation history ": [
+    "Our simulated halo in R10 and R10-earlyUV, has a final gas fraction that is very suppressed; the total mass in gas is less than 1% of the total halo mass, well below the cosmic baryon ",
+    "Figure 10. Virial temperature versus redshift for progenitor haloes that are constituted of at least 50% final target halo dark matter particles. Haloes plotted in black contain no star particles; haloes plotted in cyan have formed star particles within the last 20 Myrs; and haloes plotted in red contain star particles, but have not formed star particles within the last 20 Myrs. ",
+    "fraction (see Table (<>)2). As we have discussed in Section (<>)3.1.2, this remaining halo gas is very diffuse and highly ionized with a temperature of a few factors of 104 K (see the z = 0 panel of Figure (<>)5) and would not be directly observable in a real system. ",
+    "Many low-luminosity dSphs in the Milky Way are very gas poor with little or no H I, but (unlike our simulated system) some of the more distant Milky Way dwarfs can be quite H I rich, for example Leo T ((<>)Ryan-Weber et al. (<>)2008). Our simulated halo is isolated and has had no interactions with the hot halo of a massive galaxy during its formation. We might, therefore, expect it to be more analogous in its gas content to the more distant Local Group dwarfs. The observed strong correlation between environment and gas content for Local Group dwarfs ((<>)Grcevich & Putman (<>)2009) suggests that their gas content may be due to environmental effects, which this study does not explore since we only simulate one environment. ",
+    "Reionization appears to be the mechanism that removes most of the gas mass in our models and the only simulation with evidence for late time gas accretion is R10-noUV, which had no UV background. From this simulation, we conclude that the lack of reaccretion of gas onto our simulated halo is due to its low virial temperature relative to the warm temperature of the IGM after reionization, a consequence of the halo’s low mass (Tvir ∝ M2/3). It does not appear that supernovae are a factor in preventing the reaccretion of gas, as the suppression of gas fractions is remarkably similar in our simulations with different levels of supernova feedback. ",
+    "Figure (<>)10 shows that at late times the main progenitor haloes and massive subhaloes in R10 all have virial temperatures well below the temperature of the IGM (a few factors of 104 K). This plot also shows that, prior to reion-ization, with a few exceptions, progenitor haloes generally need to have virial temperatures above 2000 K in order to form stars, due to the inefficiency of H2 cooling, see (<>)Tegmark ",
+    "(<>)et al. ((<>)1997). After reionization, most progenitor haloes stop forming stars. As we discussed in Section (<>)3, this suppression of star formation was due to a combination of the large scale photoevaporation of gas from progenitor haloes and the effect of supernova heating on the remaining self-shielded clumps of dense gas. The net effect is consistent with the idea that reionization introduces a filtering mass or filtering virial temperature, below which star formation is truncated (e.g. (<>)Gnedin (<>)2000). ",
+    "Observations of dwarfs in the present epoch cannot tell us the complete evolution of gas in these systems, but their star formation histories derived from color-magnitude diagrams do give us the history of dense star-forming gas. We find that our simulated star formation histories in R10 and R10-earlyUV are sharply truncated after reionization. R10 has the most extended star formation history; however, all star formation in this model ends by a redshift of 3.5. Milky Way dSphs that are closest in luminosity to R10 and R10earlyUV have a range of velocity dispersions and star formation histories. In general, the most truncated star formation histories tend to be found in systems with the lowest velocity dispersions (∼ 3 km s−1) ((<>)Brown et al. (<>)2012), although recent analysis suggests at least one system with a luminosity and velocity dispersion comparable to our simulated haloes, Canes Venatici I, has only ancient stellar populations ((<>)Okamoto et al. (<>)2012). In general, however, most of the Milky Way dwarfs contain some intermediate-age stellar population ((<>)Tolstoy, Hill, & Tosi (<>)2009) which we do not see in our simulations. "
+  ],
+  "4.1.4 Implications of observational comparisons ": [
+    "Given the difficulties in determining the correct observational comparison sample as discussed in the first paragraph of this section, what can we conclude about the discrepancies between our simulated haloes and observed Local Group dwarf systems, especially in regards to the lack of an intermediate age (i.e. 1-8 Gyr old, see (<>)Tolstoy, Hill, & Tosi ((<>)2009)) stellar population? The star-forming state of our simulation appears to be heavily dependent on the metagalactic UV background we implement and this is relatively well understood for z < 6. The lack of dense, star-forming gas in our simulations at late times implies one of four things: one, either the implementations of the metagalactic UV background or the local shielding are inadequate and a larger reservoir of gas should survive reionization in these systems; two, our supernova feedback prescription is too effective in destroying dense gas that survives reionization; three, the handful of gas rich, but low luminosity, dwarfs (such as Leo T) observed at large galactic radii have virial temperatures above that of the IGM (and above the halo we simulate) which allows them to accrete gas at late times; or four, our halo merger tree is atypical for this halo mass or is atypical for dwarfs that end up in dense environments. ",
+    "The first scenario is possible and more sophisticated methods may be used to simulate ionization and shielding, as we will discuss in Section (<>)4.6. However, self-shielding would have to be many times more effective than in our current model to significantly impact the gas fractions. The second scenario also seems unlikely, since the discrepancy in stellar metallicity between our simulations and observed systems indicates that our feedback prescription is not effec-",
+    "Figure 12. Evolution of properties for two massive progenitors in the canonical simulations R10 (black) and the lower minimum resolution simulation R43 (magenta). The properties depicted are the same as those shown in Figure (<>)6. ",
+    "one supernova’s worth of energy. Reducing tf or even eliminating it and instantaneously injecting energy into the cell would be more appropriate. Reducing tf would result in a shorter theat (eq. (<>)3), and so cooling would not be able to act before the injected feedback energy begins to operate. Similar models have been explored in high-resolution local simulations of the ISM ((<>)Joung & Mac Low (<>)2006). We found, however, that even with our high spatial resolution, injecting a supernova’s worth of energy into one resolution element instantaneously proved to be computationally challenging and we are working to develop an improved algorithm. ",
+    "In our current model implementation, energy that is able to escape the central regions with shorter cooling times will not be quickly lost since gas everywhere outside the central region has comparatively long cooling times. Indeed in Figure (<>)4 we do see evidence for supernova heated bubbles and metal pollution of the ISM and IGM. Previously in Section (<>)3, we had concluded that reionization determines the overall gas fraction of haloes and that dense gas is more directly affected by feedback. This interpretation still largely holds, however, the effect on dense gas may be more pronounced than what we have observed in our simulations. ",
+    "This would have the effect of enhancing the dominance of feedback over the UV background as the regulator of dense gas. "
+  ],
+  "4.3 Resolution effects ": [
+    "To explore the impact of spatial resolution, we examine simulation R43, which is a run with the same dark matter particle resolution and physics as R10, but with four times coarser spatial resolution. R43 has a minimum cell length of 43 co-moving parsecs. Figure (<>)12 shows the evolution of relevant quantities for the two main star forming progenitors in R43 and Table (<>)3 lists many of the final halo’s properties. The gas fractions of haloes in R43 evolve in a similar way to those in R10, with a large decline around z = 6. The declines in gas fraction prior to reionization, however, are almost nonexistent. These declines in R10 were due to supernova feedback and we see that coarser spatial resolution has decreased its effect. ",
+    "The dense gas, which we found was more directly regulated by supernova feedback, also has very different behavior. The dense gas in the two main progenitors does not rise ",
+    "Table 3. Summary of Final Halo Properties for Coarse Resolution Simulation R43. ",
+    "Note: The quantities presented in each row are the same as in Table (<>)2. ",
+    "to quite as high a peak density, but is able to survive longer because of the diminished impact of supernovae in the low resolution run. Cells in R43 encompass 64 times the volume of cells in R10; therefore when a star particle injects energy into a cell in R43, the specific heating rate is approximately 1/64th of what it is in R10. Dense gas is therefore able to survive longer. The maximum density cell within each halo peaks at a somewhat higher density in R10 because we are able to better resolve the collapse of cold clouds. ",
+    "The star formation events in R43 are of longer duration due to the enhanced survivability of dense gas. Star formation continues in the main massive progenitor down to z = 2. This produces a final halo with a greater stellar mass (6.82 × 106 M). This is somewhat counter to the expectation that increased resolution will produce more star formation (since we resolve denser gas), however this result makes sense in light of the resolution-dependent effectiveness of our supernova feedback model. ",
+    "Two other high-resolution, cosmological simulation studies track the evolution of similar mass haloes to z = 0: (<>)Sawala et al. ((<>)2010) and (<>)Governato et al. ((<>)2012). Both studies use a SPH code, so it is not possible to directly compare our resolutions in a consistent way. However, both simulations are closer in spatial resolution to our simulation R43; (<>)Sawala et al. ((<>)2010) fix their softening length in such a way that their resolution is typically less than 100 pc and (<>)Gover-(<>)nato et al. ((<>)2012) have a softening length of 64 pc for their highest resolution run. In simulations of somewhat more massive haloes (1010 M), (<>)Governato et al. ((<>)2010) found that increasing resolution was key in reducing the central angular momentum of galactic disks that form in their haloes and attribute this difference to better resolving spatially separated clouds in their higher resolution simulations, which enhanced the effect of supernova feedback as a regulator of star formation. They also found convergence in behavior between their medium resolution simulation (with a force resolution of 116 pc) and their high resolution simulation (with a force resolution of 86 pc), in contrast to the behavior of our simulations R10 and R43. Therefore, while it appears that resolution in key in simulating star formation and supernova feedback in galaxy simulations, the exact mechanisms at play and the scales on which behavior converge are dependent on the physical prescriptions and hydrodynamical methods used. ",
+    "Simulations R10 and R43 do not converge on a star-formation history or baryon fraction for our final halo, however we argue that many of the conclusions we have drawn from our higher resolution simulations hold. Clearly, reion-ization and feedback operate in the same way in both simulations, where the overall gas fraction is regulated by reion-ization and the dense gas evolution is regulated by supernova feedback. We do see an increasing effect of supernova feedback on the gas fraction with increasing resolution, so it is possible that increasing the resolution even more will have an even greater effect. The effect of reionization, however, is unchanged and still quite dominant. We may not have converged on a final stellar mass for this halo. We therefore conclude that our measures of the final stellar mass are likely to be an upper limit. "
+  ],
+  "4.4 Metal ejection ": [
+    "We find that the main mechanism for gas ejection from these low mass haloes is photo-evaporative winds due to reioniza-tion. It remains unclear, however, if this is also the mechanism for metal ejection. We see evidence for metal rich supernova heated winds in Figure (<>)4, but it also appears from Figure (<>)3 that the metallicity of dark haloes increases after reionization. ",
+    "We can answer this question by comparing simulations with and without supernova feedback and reionization: R10, one of our canonical runs that contains our complete physical model; R10-noFB-LimCool, which has no thermal supernova feedback; and R10-noUV, which has no UV background. Figures (<>)6 and (<>)8 show that these three simulations have produced varying amounts of star particles over somewhat different star formation histories, but we can nevertheless draw robust conclusions. ",
+    "Figure (<>)13 shows projections of gas metallicity of a large volume that encompasses the dwarf group at z = 3.3, which eventually forms the final dwarf halo. It clearly shows that in simulations with thermal supernova feedback, metals are ejected to much greater distances and more completely fill the volume. The simulation without thermal feedback, R10noFB-LimCool, has significantly less IGM metal pollution. This is despite the fact that the total gas fractions of haloes in R10-noFB-LimCool are quite similar to those seen in R10 (Fig. (<>)8). The gas fractions of haloes in R10-noUV are quite elevated at this redshift as compared to haloes in R10 (Fig. (<>)6). Despite this, the extent of metal pollution is relatively similar between the two runs with supernova feedback. Therefore, we conclude that supernova feedback is the primary mechanism for metal ejection in our model. ",
+    "Increased enrichment of dark haloes after reionization as shown in Figure (<>)3 is likely quite complicated and due to a combination of effects. Since supernova feedback is the mechanism for metal ejection from luminous haloes in our model, the enrichment of dark haloes depends on the proximity of dark haloes to luminous haloes and the speeds of supernova enriched winds (e.g. (<>)Cen & Bryan (<>)2001). However, the increased degree of enrichment occurs after the cessation of photoevaporative winds due to reionization. The large drop in gas fraction seen in Figure (<>)2 indicates the effect of these photoevaporative winds on halo gas. This decline happens in both R10 and R10-earlyUV just before the increase in metallicity of dark haloes. It is likely more difficult for su-",
+    "pernova driven winds to penetrate haloes undergoing strong photoevaporative winds. This issue may be an interesting topic for future study. ",
+    "As we have discussed, stellar populations of dSph galaxies are extremely metal poor and this does not appear to be simply due to their low star formation rates. (<>)Kirby, Mar-(<>)tin, & Finlator ((<>)2011) have demonstrated that dSphs in the Milky Way eject almost all of their metals. Dwarf spheroidals are also observed to be quite gas poor ((<>)Mateo (<>)1998). As we have discussed, environment most likely plays a key role in the gas content of Milky Way dwarfs. However, our simulations at least demonstrate that the main mechanism for gas expulsion need not be the same as for metal ejection. This picture is consistent with the simulations of (<>)Mac Low (<>)& Ferrara ((<>)1999) and (<>)Fragile et al. ((<>)2003), who found, using high-resolution, idealized models of dwarf galaxies, that metals were more easily ejected from galaxies than gas. ",
+    "The discrepancy in metallicity between our simulated stellar populations and observed systems described in section 4.1.2 indicates that star-forming gas in our model is too metal rich. This over-enrichment of star-forming gas may be due to insufficient ejection of metals by our supernova feedback model, despite the apparent large scale enrichment of the IGM on the scale of tens of kpc seen in Figures (<>)4 and (<>)6. We therefore cannot confidently make predictions for the density of metals in the IGM produced by dwarfs. It is certainly possible that feedback mechanisms other than supernovae may play an important role in ejecting metals, such as ionization from young stars. What our models do show, however, is that in systems where the gas fraction is determined by the cosmic UV background, an extra ingredient that preferentially affects metal rich gas is needed to eject metals. ",
+    "If supernova feedback is primarily responsible for the stellar metallicity of dSphs, then these systems are an excellent test to judge the efficacy of feedback models, given the clear constraints of observations. Several simulated models produce low metallicities for Milky Way dSph analogues using a variety of approaches, such as idealized, non-cosmological models (e.g. (<>)Revaz & Jablonka (<>)2012); cosmological models focusing on high redshift evolution ((<>)Ri-(<>)cotti & Gnedin (<>)2005; (<>)Tassis, Gnedin, & Kravtsov (<>)2012; (<>)Wise et al. (<>)2012b); coarsely resolved cosmological models of satellite systems of Milky Way type spiral galaxies ((<>)Okamoto et al. (<>)2010; (<>)Sawala, Scannapieco, & White (<>)2012); and highly resolved cosmological zoom-in simulations like our own ((<>)Sawala et al. (<>)2010). Most of these studies rely on feedback schemes that compensate for resolutions too low to capture the Sedov phase of supernovae, with the exception of (<>)Wise et al. ((<>)2012b), who have very high resolutions (1 comoving pc) in their high redshift study and find that momentum from feedback, in the form of radiation pressure, is necessary to produce low metallicities. The model most comparable to our own, which is run down to z = 0, is that of (<>)Sawala et al. ((<>)2010), who in high resolution simulations (< 100 pc) of isolated haloes similar in mass to our own, were able to produce haloes that lie on the observed luminosity-metallicity relation. It is unclear, however, how natural this result is given that the fraction of metals injected into the hot (or cold) phase can be calibrated in their subgrid model. In addition, we note that metal mixing remains a serious uncertainty in SPH ((<>)Booth et al. (<>)2012). Simulations of larger ",
+    "Figure 13. Gas density weighted projections of gas metallicity at redshift 3.31 for R10, R10-noFB and R10-noUV. All panels show projections of 150 kpc cubic volumes that encompass all the progenitor haloes at this redshift. ",
+    "cosmological volumes that contain larger haloes have also found that feedback is important in explaining the evolution of galaxy metallicity and enrichment of the IGM over cosmic time ((<>)Finlator & Dav´e (<>)2008). "
+  ],
+  "4.5 Dark matter properties ": [
+    "Dark matter haloes in cosmological N-body simulations follow a predictable density profile with a steeply-sloped cusp at the centre ((<>)Navarro, Frenk, & White (<>)1997; (<>)Navarro et (<>)al. (<>)2010). Several previous studies have found that baryon physics, particularly supernova feedback, can weaken the central dark matter cusp (e.g. (<>)Navarro, Eke, & Frenk (<>)1996; (<>)Gnedin & Zhao (<>)2002; (<>)Governato et al. (<>)2012). Several mechanisms for this transformation have been proposed, such as the response of dark matter to the sudden removal of gas from halo centres (e.g. (<>)Navarro, Eke, & Frenk (<>)1996; (<>)Gnedin & Zhao (<>)2002), and the direct transfer of energy from repeated energetic gas outflows to dark matter particles ((<>)Pontzen & Governato (<>)2012; (<>)Governato et al. (<>)2012). ",
+    "Measuring the actual dark matter density profiles of galaxies is, of course, quite challenging, but one way is to use the resolved stellar populations in dwarf spheroidal galaxies. To date, studies comparing the dynamics of dSphs to cosmological N-body simulations have been inconclusive ((<>)Boylan-(<>)Kolchin, Bullock, & Kaplinghat (<>)2012; (<>)Strigari, Frenk, & (<>)White (<>)2010; (<>)Vera-Ciro et al. (<>)2012). Density profiles with shallow or steep central slopes have been found to fit the observational data equally well ((<>)Walker et al. (<>)2009b). ",
+    "Figure (<>)14 compares the dark matter density profiles for the final halo in R10 and R10-DM, a dark matter only simulation run with the same initial conditions. We see that the dark matter density profile is almost the same between R10 and R10-DM; the halo in R10 is slightly less dense in the inner regions relative to R10-DM, indicative of a mild heating effect. We therefore conclude that the impact of baryon physics on the dark matter density was negligible for our halo. Although not shown in Figure (<>)14, both profiles are well fit by a NFW profile. The stellar density profile does not follow a NFW profile. It appears to have a central slope similar to a NFW profile but falls off more quickly beyond 300 pc. Visual inspection of the final stellar density map shown in the bottom right panel of Figure (<>)4 also shows that clumpiness and tidal features from late mergers remain, which produces a bump in the stellar density profile. ",
+    "The one other high-resolution study to examine the density profile of dark matter haloes at this halo mass scale with baryon physics is (<>)Governato et al. ((<>)2012), though using a different hydrodynamical method and stellar feedback model. They find flattened central density profiles for haloes with virial masses above 1010 M. For haloes below this threshold, they find haloes down to our halo mass of 109 M have density profiles consistent with NFW profiles, similar to our results. Haloes in their models do not appear to have consistently flattened central density profiles until the stellar mass rises above 5 × 106 M. ",
+    "As we have discussed, our supernova driven outflows may not be sufficiently energetic (as evidenced by the metal-licity distribution). It is possible that this failure results in the central density of our halo remaining cuspy, however it is also possible that the low star formation rates of our halo ",
+    "Figure 14. Dark matter density profile (solid black line), stellar mass density profile (dotted line) and gas density profile (dashed line) for the final halo at z = 0 in R10. The dark matter density profile for the final halo in R10-DM is shown in grey. ",
+    "are just insufficient to produce enough energy to have a sig-nificant impact on the density profile of our simulated halo. "
+  ],
+  "4.6 Neglected physics ": [
+    "In this section, we briefly discuss physical effects that we do not include in our model. We do not have an implementation of local UV heating from young stars, either ionizing or dissociating, in our model. This effect may have an impact on dense gas as young stars will be located within close proximity. (<>)Gnedin ((<>)2010) found that local UV heating sources dominated over the cosmic UV background for both ionizing and Lyman-Werner radiation in haloes with masses between 1010 and 1012 M at a redshift of three. We are probing haloes at much lower masses with much lower star formation rates, but it may be that UV heating from young stars can suppress star formation or make supernova feedback more effective by preheating gas. ",
+    "We do not include any effects of dust in our model. The formation of H2 on the surface of dust grains is important in gas with metallicities above approximately 10−3 Z ((<>)Glover (<>)2003). The main effect of H2 in our models is as a coolant in very metal poor gas. Since the amount of dust in gas with metallicities below 10−3 Z is too small to be important in H2 production, the lack of dust does not significantly affect cooling and therefore star formation in our models. It does mean that our models do not accurately follow the molecular gas fraction of haloes, which may be an interesting topic of future study. ",
+    "We do not model early metal-free star formation as a distinct mode of star formation. (<>)Wise et al. ((<>)2012a) presented high-resolution simulations of low mass haloes at high redshift that include the transition between Population III and Population II star formation. They found that a single Population III supernova can enrich the ISM of a halo to the level where metal line cooling dominates over molecular H2 cooling. ",
+    "We model supernovae as producing exclusively ther-",
+    "mal energy. Supernovae also produce substantial amounts of radiation, which can not only heat the gas, but can also exert radiation pressure. The computational cost necessary to do radiative transfer in cosmological calculations is currently too expensive to follow the evolution of haloes down to z = 0, however several groups have explored its effect at high redshift (e.g. (<>)Wise et al. (<>)2012b). There are also other effects such as magnetic fields and cosmic rays which we neglect and may potentially be important in galaxies of this size ((<>)Wadepuhl & Springel (<>)2011). "
+  ],
+  "5 SUMMARY ": [
+    "We have conducted the highest resolution cosmological simulations to date of a 109 M dwarf halo down to a redshift of zero. Our resolution of 11 comoving pc means we achieve physical resolutions of a few parsecs during the epoch of greatest star formation in our haloes, between redshifts of 6 and 10. Our canonical runs includes metal cooling, molecular hydrogen formation and cooling, photoionization and photodissociation from a metagalactic background (with a simple prescription for self-shielding), star formation, and a model for supernovae driven energetic feedback. Our main results are summarized below: ",
+    "H2 line cooling is a crucial and necessary ingredient to start star formation in these low mass haloes. Atomic line cooling in the absence of metals is insufficient by itself to cool gas to the densities required for star formation in such shallow potential wells. Without a first generation of star ",
+    "formation to pollute the ISM with metals, there is no coolant sufficiently effective to cool gas at subsequent epochs. ",
+    "We conclude that while we do reproduce many of the properties of dwarf systems, such as high mass-to-light ratios and low luminosities, more work is required to understand how stellar feedback works to regulate star formation and metal ejection in low mass dwarf galaxies, and hence the properties of stellar populations in dwarf haloes. The feedback scheme we adopted was deliberately simple, and not tuned to reproduce observations. Future work will involve more realistic modeling of supernovae, a model of local sources of ionization, an expansion of the halo we simulate to larger masses and potentially haloes in different environments. "
+  ],
+  "6 ACKNOWLEDGEMENTS ": [
+    "This work was supported by National Science Foundation (NSF) grant AST-0806558 and NASA grant NNX12AH41G. We also acknowledge support from NSF grants AST-0547823, AST-0908390, and AST-1008134, as well as computational resources from NASA, NSF XSEDE, TACC and Columbia University’s Hotfoot cluster. BDS was supported in part by NASA through grant NNX09AD80G and by the NSF through grant AST-0908819. M-MML also acknowledges partial support from NSF grant AST11-09395. ",
+    "CMS would like to thank Mary Putman and David Schiminovich for their support and guidance in the development of this work. She would also like to thank Jacqueline Van Gorkom for her feedback on our manuscript. "
+  ]
+}

jsons_folder/2013MNRAS.434.2556W.json

@@ -0,0 +1,221 @@
+{
+  "ABSTRACT ": [
+    "Dark matter N-body simulations provide a powerful tool to model the clustering of galaxies and help interpret the results of galaxy redshift surveys. However, the galaxy properties predicted from N-body simulations are not necessarily representative of the observed galaxy populations; for example, theoretical uncertainties arise from the absence of baryons in N-body simulations. In this work, we assess how the uncertainties in N-body simulations impact the cosmological parameters inferred from galaxy redshift surveys. Applying the halo model framework, we find that the velocity bias of galaxies in modelling the redshift-space distortions is likely to be the predominant source of systematic bias. For a deep, wide survey like BigBOSS, current 10 per cent uncertainties in the velocity bias limit kmax to 0.14 h Mpc−1 . In contrast, we find that the uncertainties related to the density profiles and the galaxy occupation statistics lead to relatively insignificant systematic biases. Therefore, the ability to calibrate the velocity bias accurately – from observations as well as simulations – will likely set the ultimate limit on the smallest length scale that can be used to infer cosmological information from galaxy clustering. ",
+    "Key words: cosmological parameters – dark energy – dark matter – large-scale structure of Universe "
+  ],
+  "1 INTRODUCTION ": [
+    "The large-scale distribution of galaxies has been used to probe the structure and composition of the universe for over three decades. From the pioneering analyses of the Lick cata-logue ((<>)Groth & Peebles (<>)1977) and the CfA Redshift Survey ((<>)Huchra et al. (<>)1983; (<>)Geller & Huchra (<>)1989) revealing the cosmic web, the APM Galaxy Survey hinting the departure from the standard cold dark matter model ((<>)Maddox et al. (<>)1990) to the subsequent 2dF Galaxy Redshift Survey ((<>)Col-(<>)less et al. (<>)2001), the Sloan Digital Sky Survey (SDSS; (<>)York (<>)et al. (<>)2000) and the VIMOS-VLT Deep Survey ((<>)Le F`evre (<>)et al. (<>)2005), galaxy redshift surveys have revolutionized the view of the large-scale structure of the universe. Recently, the WiggleZ Dark Energy Survey ((<>)Drinkwater et al. (<>)2010) and the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS; (<>)Schlegel et al. (<>)2009) have measured the galaxy clustering to unprecedented precision and provided stringent constraints on the cosmological parameters. ",
+    "One of the most important features in the galaxy clustering is the baryon acoustic oscillations (BAO), originating ",
+    "from the waves in the primordial electron–photon plasma before the recombination. The sound horizon at the end of recombination is manifested as a peak in the real-space two-point correlation function or as wiggles in the Fourier-space power spectrum. This characteristic scale of BAO is considered as a standard ruler of the different evolution stages of the universe, and as a dark energy probe with relatively well-controlled systematics ((<>)Blake & Glazebrook (<>)2003; (<>)Seo (<>)& Eisenstein (<>)2003). Indeed, since its discovery ((<>)Miller et al. (<>)2001; (<>)Cole et al. (<>)2005; (<>)Eisenstein et al. (<>)2005), BAO has been providing ever improving constraints on cosmological parameters (e.g., (<>)Percival et al. (<>)2010; (<>)Blake et al. (<>)2011; (<>)An-(<>)derson et al. (<>)2012). ",
+    "Beyond the BAO feature, the full scale-dependence of the clustering of galaxies contains much more information and can be used to constrain cosmology (e.g., (<>)Tegmark et al. (<>)2006; (<>)Reid et al. (<>)2010; (<>)Tinker et al. (<>)2012; (<>)Cacciato et al. (<>)2013) and the halo occupation statistics (e.g., (<>)Abazajian (<>)et al. (<>)2005; (<>)Tinker et al. (<>)2005; (<>)van den Bosch et al. (<>)2007; (<>)Zheng & Weinberg (<>)2007; (<>)Zehavi et al. (<>)2011). From the perspective of power spectrum P (k), the number of modes increases as k3 , and the information content increases dramatically as one goes to smaller scales. However, when one tries to draw information from high k, especially at low redshift, ",
+    "the density perturbations become non-linear and difficult to model (e.g., (<>)Smith et al. (<>)2003; (<>)Heitmann et al. (<>)2010; (<>)Jen-(<>)nings et al. (<>)2011), which can introduce significant systematic errors in the recovered cosmological parameters (e.g., (<>)de la (<>)Torre & Guzzo (<>)2012; (<>)Smith et al. (<>)2012). ",
+    "The analysis of galaxy clustering often relies on N-body simulations and synthetic galaxy catalogues to model the non-linearity on small scales, as well as to estimate the cosmic and sample covariances. For example, the WiggleZ team has validated their model for the non-linear galaxy power spectrum using the GiggleZ Simulation 1 (<>)((<>)Parkinson et al. (<>)2012), while synthetic galaxy catalogues based on the Large Suite of Dark Matter Simulations (LasDamas 2(<>)) have been used in the galaxy clustering analysis of SDSS ((<>)Chuang & (<>)Wang (<>)2012; (<>)Xu et al. (<>)2013). ",
+    "For upcoming surveys, synthetic catalogues generated from N-body simulations will likely be routinely used to calibrate galaxy surveys. However, N-body simulations are not free from systematics. In N-body simulations, galaxies are assigned to haloes or dark matter particles based on models such as halo occupation distribution (HOD; (<>)Pea-(<>)cock & Smith (<>)2000; (<>)Scoccimarro et al. (<>)2001; (<>)Berlind & (<>)Weinberg (<>)2002), abundance matching ((<>)Kravtsov et al. (<>)2004; (<>)Vale & Ostriker (<>)2004), or semi-analytic models ((<>)White & (<>)Frenk (<>)1991; (<>)Kauffmann et al. (<>)1993; (<>)Somerville & Primack (<>)1999; (<>)Cole et al. (<>)2000). The galaxy populations predicted by simulations can be affected by intensive stripping in dense environment (e.g., (<>)Wetzel & White (<>)2010) and the absence of baryons (e.g., (<>)Weinberg et al. (<>)2008; (<>)Simha et al. (<>)2012). On the other hand, when one uses dark matter particles to model the behaviour of galaxies, systematic errors may arise because the positions and velocities of galaxies do not necessarily follow those of dark matter particles ((<>)Wu et al. 2013a). Hydrodynamical simulations that include proper treatments of baryonic physics can be another avenue to predict the properties of galaxies more reliably; however, because these simulations are more computationally intensive, it is not yet practical to use them to achieve the statistics and high resolution required by upcoming large surveys. ",
+    "In addition, it has been shown that galaxies predicted from N-body simulations cannot recover the spatial distribution of observed galaxies. For example, Wu et al. (in preparation) have shown that in high-resolution N-body simulations of galaxy clusters, subhaloes tend to be prematurely destroyed and fail to predict the location of galaxies (also see Appendix (<>)A). The need to include “orphan galaxies” (galaxies not associated with subhaloes in simulations) to improve the completeness of predicted galaxies has been frequently addressed in the community (e.g., (<>)Gao et al. (<>)2004; (<>)Wang et al. (<>)2006; (<>)Guo et al. (<>)2011); however, even including orphan galaxies does not lead to consistent galaxy clustering at all scales . For example, (<>)Guo et al. ((<>)2011) have shown that the galaxy population generated using the semi-analytic model applied to the Millennium Simulations overestimates the small scale clustering (also see (<>)Contreras et al. (<>)2013). ",
+    "In this paper, we examine the impact of the systematics in N-body simulations on the predictions of galaxy clustering. We calculate the galaxy power spectrum based on the halo model, with inputs from the results of recent N-body simulations. We use the information of the full power spectrum of galaxies to forecast the cosmological parameter constraints and determine at which scale these systematics start to become relevant. We specifically explore how these uncertainties will limit our ability to utilize the cosmological information from small scale. ",
+    "This paper is organized as follows. In Section (<>)2, we review the halo model prediction for galaxy power spectrum. In Section (<>)3, we present our fiducial assumptions and discuss the information content associated with P (k). Section (<>)4 explores the self-calibration of HOD parameters. Section (<>)5 addresses the impact of the uncertainties in the halo mass function on the cosmological constraints from galaxy clustering. Section (<>)6 focuses on various systematics associated with the properties of galaxies in dark matter haloes in N-body simulations and presents the required control of these sources of systematic error. We conclude in Section (<>)7. In Appendix (<>)A, we present the galaxy number density profile model used in this work. In Appendix (<>)B, we provide detailed derivation of the galaxy power spectrum based on the halo model. In Appendix (<>)C, we derive the power spectrum covariance. "
+  ],
+  "2 HALO MODEL AND GALAXY POWER SPECTRUM: A REVIEW ": [
+    "Throughout this work, we use the power spectrum of galaxies P (k) as our clustering statistic. Possible alternatives include the three-dimensional correlation function ξ(r) and its two-dimensional analogue – the angular two-point function w(θ) or the projected two-point function wp(rp). While the Fourier-space power is more difficult to measure from the galaxy distribution, it is ‘closest to theory’ in the sense that the other aforementioned quantities are weighted integrals over P (k). Therefore, it is easiest to see the effect of the uncertainties in theoretical modelling by using the power spectrum. While these different functions measured in a given galaxy survey contain the same information in principle, in data analysis sometimes discrepancies occur (e.g., (<>)Anderson (<>)et al. (<>)2012). "
+  ],
+  "2.1 Basic model ": [
+    "In this section, we provide the key equations of the galaxy power spectrum derived from the halo model, following (<>)Scherrer & Bertschinger ((<>)1991), (<>)Seljak ((<>)2000), and (<>)Cooray (<>)& Sheth ((<>)2002). The detailed derivation is provided in Appendix (<>)B. ",
+    "The halo model assumes that all galaxies are inside dark matter haloes. To model the distribution of galaxies, we need the following distributions. ",
+    "Statistics and spatial distribution of dark matter haloes: ",
+    "• Halo bias, b2(M) = Phh(k)/Plin(k), where Phh is the power spectrum of haloes and Plin is the linear matter power spectrum. We limit our use of b(M) to large scales where b(M) is scale independent. ",
+    "Statistics and spatial distribution of galaxies in a halo: ",
+    "Galaxy number density profile, u(r|M), the radial dependence of the galaxy number densityinside a halo of a given mass. We normalize u such that u(r|M)d3 r = 1. We also use the density profile in Fourier space, u˜(k|M) = ",
+    "d3 xu(x|M)e−ik·x , and u˜ → 1 for small k. ",
+    ". ",
+    "(1) ",
+    "The power spectrum is contributed by two galaxies in two different haloes (the two-halo term, Pgg 2h) and two galaxies 1h in the same halo (the one-halo term, Pgg ): ",
+    "Here X|M indicates the average value of quantity X at a given halo mass M. In the one-halo term, ",
+    "which takes into account the contribution from central– satellite and satellite–satellite pairs ((<>)Berlind & Weinberg (<>)2002). "
+  ],
+  "2.2 Redshift-space distortions ": [
+    "In observations, one cannot recover the exact three-dimensional spatial distribution of galaxies, because the redshifts of galaxies are impacted by their motions due to the local gravitational field and do not reflect their true distances. On larger scales, galaxies tend to move towards high-density regions along filaments, and these motions tend to squash the galaxy distribution along the line of sight and boost the clustering, a phenomenon known as the Kaiser effect ((<>)Kaiser (<>)1987). On small scales, the virial motions of galaxies inside a halo tend to make the galaxy distribution in the redshift space elongated along the line-of-sight, causing the so-called Fingers-of-God effect and reducing the small-scale power. In this section, we briefly describe the model we use ",
+    "for the redshift-space distortions (RSD) for P (k), following (<>)Seljak ((<>)2001), (<>)White ((<>)2001), and (<>)Cooray & Sheth ((<>)2002). We adopt one of the simplified models – assuming the velocity distribution function to be Gaussian – and note that the improvement of the RSD model is currently an active research area. ",
+    "Since the one-halo term involves the halo scale, we only consider the virial motions of galaxies inside a halo, which can be modelled as ((<>)Peacock (<>)1999) ",
+    "(5) ",
+    "where δ˜z and ˜ are the number density fluctuations ofgal δgal galaxies with and without the effect of RSD, σv(M) is the velocity dispersion of galaxies inside a halo of mass M and µ = kˆ · rˆ. We average over µ to obtain the angular averaged one-halo term ",
+    "(6) ",
+    "The factor ",
+    "(7) ",
+    "comes from averaging over µ. ",
+    "For the two-halo term, we multiply the large-scale and small-scale effects together (see (<>)Peacock (<>)1999 and section 4 in (<>)Peacock & Dodds (<>)1994) ",
+    "The first part is the familiar Kaiser result with f(ΩM) ≡ d ln D/d ln a, where D(a) is the linear growth function of density fluctuations and a is the scale factor. The density fluctuation of dark matter is denoted by δ˜m. The calculation thus includes not only the galaxy power spectrum, but also the matter power spectrum and the matter–galaxy cross power spectrum. After averaging over µ, we obtain ",
+    "(9) ",
+    "comes from the contribution of δ˜gal, and  ",
+    "comes from the contribution of δ˜m. Here u˜m(k|M) denotes the dark matter density profile normalized the same way as u˜, and ρ¯ is the average matter density of the universe. We assume that u˜m(k|M) follows the Navarro–Frenk–White (NFW) profile ((<>)Navarro et al. (<>)1997) throughout the paper. The left-hand panel of Fig. (<>)1 shows an example of the ",
+    "Figure 1. Galaxy power spectrum calculated based on the halo model. Left: the blue and red curves show the one-and two-halo terms, respectively. The solid curves include the RSD, while the dashed curves do not. RSD greatly reduce the power spectrum at small scale (the ‘Fingers-of-God’ effect), and only slightly shift the scale where one-and two-halo terms cross. Right: Our model fit to WiggleZ data from (<>)Parkinson et al. ((<>)2012). The blue solid curve shows the theoretical P (k) with the best-fitting HOD parameters and has been convolved with the observational window function. ",
+    "contribution to the total galaxy power spectrum by the one-halo (blue) and two-halo (red) terms. The input of halo model will be detailed in Section (<>)3.1. The solid and dashed curves correspond to including and excluding the effect of RSD. As can be seen, including RSD significantly reduces the power at small scale. We also note that the scale where one- and two-halo terms cross shifts very slightly due to RSD. ",
+    "The right-hand panel of Fig. (<>)1 presents the comparison between our model and one of the power spectra from the WiggleZ survey, provided by (<>)Parkinson et al. ((<>)2012). The green dashed/blue solid curve corresponds to the theoretical P (k) before/after convolving with the window function of WiggleZ. We assume that the HOD is described by the five parameters in equation ((<>)27); we fit for these five parameters and show the model corresponding to the best-fitting parameters. This figure is only for the purposes of illustration; details of the fitting procedure will be presented in a future paper. "
+  ],
+  "3 BASELINE MODEL AND FIDUCIAL DARK ENERGY CONSTRAINTS ": [],
+  "3.1 Baseline assumptions ": [
+    "We use the virial mass Mvir of dark matter haloes throughout this work and adopt the following functions in our halo model calculations: ",
+    "Density profile: based on the universal NFW profile ((<>)Navarro et al. (<>)1997), which is described by one concentration parameter cvir ",
+    "(12) ",
+    "Concentration–mass relation: based on the relation in (<>)Bhattacharya et al. ((<>)2013), which will be further discussed in Section (<>)6.1. In the presence of significant scatter in the c–M relation, we perform the integration  ",
+    "Throughout this paper, we assume that cvir has a Gaussian distribution for a given Mvir with a scatter of 0.33, based on the finding of (<>)Bhattacharya et al. ((<>)2013). ",
+    "We convert the mass M200 to Mvir based on (<>)Hu & Kravtsov ((<>)2003). Since the scatter in the velocity dispersion is expected to be small (4 per cent), it is not included in our calculation. ",
+    "• HOD: based on the parametrization from (<>)Zheng et al. ((<>)2005) and the fiducial parameters from (<>)Coupon et al. ((<>)2012), both of which will be discussed in detail in Section (<>)4. ",
+    "We assume a fiducial galaxy survey covering fsky = 1/3 of the full sky (about 14 000 square degrees), similar to the BigBOSS experiment 3 (<>). We assume that the survey depth is comparable to the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS) results presented in (<>)Coupon et al. ((<>)2012); specifically, we assume five redshift bins in the range 0.2 < z < 1.2, and the limiting magnitude in each bin is summarized in Table (<>)1. We assume no uncertainties in the redshift measurements of galaxies. Given that the assumption of such a deep, wide spectroscopic survey may be somewhat optimistic, our required control of systematic errors may be somewhat more stringent than what BigBOSS needs. ",
+    "We include seven cosmological parameters, whose fidu-cial values are based on the Wilkinson Microwave Anisotropy Probe 7 constraints ((<>)Komatsu et al. (<>)2011): total matter density relative to critical ΩM = 0.275; dark energy equation of state today and its variation with scale factor w0 = −1 and wa = 0 respectively; physical baryon and matter densities Ωbh2 = 0.02255 and ΩMh2 = 0.1352; spectral index ns = 0.968; and the amplitude of primordial fluctuations A = Δ2ζ (k = 0.002h−1Mpc) = 2.43×10−9 . We assume a flat universe; thus, dark energy density ΩDE = 1 − ΩM. "
+  ],
+  "3.2 Likelihood function of P(k) and error forecasting ": [
+    "Here we follow the derivations in (<>)Scoccimarro et al. ((<>)1999) and (<>)Cooray & Hu ((<>)2001) but use a different convention for the Fourier transform (see Appendix (<>)B). If we assume a thin shell in ln k space with width δ ln k around ln ki, the power spectrum estimator reads ",
+    "(15) ",
+    "where ",
+    "(16) ",
+    "and 1/n¯gal accounts for the effect of shot noise. The first term of Pˆ is calculated based on the halo model results described in Section (<>)2.2. ",
+    "The covariance of is given byspectrumpower  ",
+    "describing the non-Gaussian nature of the random field ",
+    "We provide the detailed derivation in Appendix (<>)C. In equation ((<>)17) Vz is the volume of the redshift bin, Vz = Ωsurvey r 2(z)/H(z)dz, where the integral is performed  over the redshift extent of the bin. ",
+    "The calculation of T¯ij involves four-point statistics, which is non-trivial to calculate. Fortunately, (<>)Cooray & Hu ((<>)2001) have shown that only the one-halo term dominates at the scale where the contribution of T¯ij to Cij is not negligible; therefore, we only need to calculate the one-halo contribution: ",
+    "where ",
+    "Analogous to the case of considered in Section (<>)2.1, the first term accounts for quadruplets composed of one central and three satellite galaxies, and the second term accounts for the quadruplets composed of four satellite galaxNsat|M4 /4!. ",
+    "We employ the Fisher matrix formalism to forecast the statistical errors of the cosmological and nuisance parameters based on the fiducial survey. The Fisher matrix reads ",
+    "where α and β are indices of model parameters, while i and j refer to bins in wavenumber which have a constant logarithmic width δ ln k and extend out to the maximum wavenumber kmax. We adopt δ ln k = 0.1, which has been tested to be small enough to ensure convergence. The best achievable error in the parameter θα is given by ",
+    "(21) ",
+    "Throughout this work, unless otherwise indicated, the full set of parameters considered is given by ",
+    "Figure 2. Dark energy information content from P (k), based on our fiducial survey assumptions. The x-axis corresponds to the largest k (smallest scale) assumed to be reliably measured and interpreted. The blue curve corresponds to a Gaussian likelihood function and assumes no RSD; it leads to unrealistically tight constraints for large kmax. The green curve includes RSD, and the red curve further includes the trispectrum correction to the covariance matrix. As can be seen, including these two effects reduces the small-scale information. ",
+    "The first seven are the cosmological parameters introduced in Section (<>)3.1, while the last five are the nuisance parameters describing the HOD and will be discussed in Section (<>)4.1. "
+  ],
+  "3.3 Fiducial constraints without systematics ": [
+    "ht",
+    " ",
+    "200",
+    "et al. ",
+    "To represent the statistical power of an upcoming galaxy redshift survey, in the limiting case of no nuisance parameters, we consider the inverse of the square root of the dark energy figure of merit, originally defined as the inverse of the forecasted 95 per cent area of the ellipse in the w0–wa plane ((<>)Huterer & Turner (<>)2001; (<>)Albrec6). In other words, our parameter of interest is σ(wa)σ(wp), where wp is the pivot that physically corresponds to w(a) evaluated at the scale factor where the constraint is the best. This quantity takes into account the temporal variation of dark energy, and the square root serves to compare it fairly to the constant w; the two quantities, σ(w) and σ(w0)σ(wp), tend to show very similar behaviour. For our fiducial survey, the in our parameter combination of interest is σ(wa)σ(wp) = 0.4 (or 0.003) for kmax = 0.1 (or 1) h Mpc−1 , without external priors. When we add the Planck Fisher matrix (Hu, private communication), σ(wa)σ(wp) becomes 0.002 (or 0.0002) for Mpc−1 . ",
+    "Fig. (<>)2 presents the expected dark energy constraints as a function of kmax, without nuisance parameters or systematic errors for the moment, for three levels of sophistication in the theory. We proceed in steps: the blue curve corresponds to ",
+    "no RSD (Section (<>)2.1) with a Gaussian likelihood function. In this case, the dark energy constraints increase sharply with kmax, indicating that these assumptions are unrealistic. The green curve includes the RSD (Section (<>)2.2), which reduce the dark energy information from small scales. The red curve further includes the effect of non-Gaussian likelihood [T¯ij from equation ((<>)18)], which reduces the information at high k even more. "
+  ],
+  "3.4 Systematic bias in model parameters ": [
+    "In this work, we estimate the systematic shifts in parameter inference caused by using an inadequate model. In particular, if we assume a problematic model that produces a power spectrum Psys(k) that systematically deviates from the truth Pfid(k), we will obtain parameters that systematically deviate from their true values: θsys = θfid + Δθ. The systematic shifts in parameters can be obtained through a modified Fisher matrix formalism ((<>)Knox et al. (<>)1998): ",
+    "(23) ",
+    "(24) ",
+    "To determine the significance of systematic errors, we calculate the systematic shifts Δχ2tot in the full high-dimensional parameter space, ",
+    "(25) ",
+    "where Δθ is the vector of the systematic shifts of parameters. Both Δθ and the Fisher matrix F include cosmological and nuisance parameters. The systematic bias is considered significant if the inferred θsys lies outside the 68.3 per cent confidence interval of the Gaussian likelihood function cen-tred on θfid; in other words, the bias is ‘greater than the 1 σ dispersion’. For example, in a full 12-dimensional parameter space considered here, the 68.3 per cent confidence interval corresponds to Δχ2tot = 13.7. "
+  ],
+  "4 SELF-CALIBRATION OF HOD PARAMETERS ": [
+    "In this section, we focus on the efficacy of self-calibrating the HOD parameters, that is, determining these parameters from the survey concurrently with cosmological parameters. Since these HOD parameters are not known a priori, one usually marginalizes over them along with cosmological parameters (e.g., (<>)Tinker et al. (<>)2012), which inevitably increases the uncertainties in cosmological parameters. Here we focus on the statistical uncertainties and assume no systematic error; in the next section, we will compare these statistical errors with systematic shifts of parameters. ",
+    "We focus on two parametrizations of HOD: one is based on (<>)Zheng et al. ((<>)2005) and the other is based on a piecewise continuous parametrization. ",
+    "Table 1. Fiducial values for the HOD parameters, adopted from (<>)Coupon et al. ((<>)2012) based on CFHTLS. ",
+    "Figure 3. Self-calibration of HOD parameters. We show the dark energy constraints as a function of the highest k used in the survey. The red curve corresponds to no nuisance parameters. The dark blue curve corresponds to five nuisance parameters based on the parametrization in (<>)Zheng et al. ((<>)2005), while the cyan curve corresponds to a piecewise continuous parametrization for satellite galaxies, with one parameter in each of the five mass bins. Including nuisance parameters in either parametrization systematically increases the dark energy uncertainties by one or two orders of magnitude. The dashed curves include the Planck prior and assume the same nuisance parameters as their solid-curve counterparts. "
+  ],
+  "4.1 Zheng et al. parametrization ": [
+    "The HOD describes the probability distribution of having N galaxies in a halo of mass M. In principle, the HOD is spec-ified by the full distribution P (N|M); in practice, modelling of the two-point statistics only requires Ncen|M, Nsat|M, and Nsat(Nsat − 1)|M. We follow the HOD parametrization from (<>)Zheng et al. ((<>)2005), which separates the contribu-",
+    " ",
+    "(26) ",
+    "(27) ",
+    "The first equation describes the contribution from the central galaxy; Mmin corresponds to the threshold mass where a halo can start to host a galaxy that is observable to the survey, and σlog10 M describes the transition width of this threshold. The second equation describes the contribution from satellite galaxies, whose number is assumed to follow a power law, and M0 is the cutoff mass. In addition, we make the widely-adopted assumption that P (Nsat|M) follows a Poisson distribution, i.e., ",
+    "(28) ",
+    "We adopt the fiducial values from (<>)Coupon et al. ((<>)2012), which are constrained using the projected angular two-point correlation function w(θ) from the CFHTLS out to z = 1.2. We use the same binning and limiting magnitude as in (<>)Coupon et al. ((<>)2012); the values are summarized in Table (<>)1. We do not use the error bars quoted there as our priors because we would like all parameters to be self-calibrated consistently. ",
+    "Under these assumptions, we have five nuisance parameters (log10 Mmin, σlog10 M , log10 M0, log10 M1, αsat) for each of the five redshift bins, i.e., 25 parameters in total. We assume that each of the five distinct nuisance parameters varies coherently across the five redshift bins, and is therefore described by a single parameter. Under this assumption, instead of 25 nuisance parameters, we only use five nuisance parameters to describe the uncertainties of all HOD parameters. We parametrize the variations around the fiducial values: ",
+    "(29) ",
+    "where hi are the dimensionless parameters describing the uncertainties of the aforementioned 5 HOD parameters. We note that this choice of five HOD parameters only represents one possible model; depending on the data available and the astrophysical motivation, in principle one can use a more general model to describe the evolution of HOD. Increasing the number of degrees of freedom describing the evolution of HOD will inevitably lead to degradation in the dark energy constraints, and it will be very important to establish the total number of degrees of freedom necessary to model the HOD and its uncertainties. ",
+    "We explore how well these parameters can be self-calibrated by P (k) without the aid of priors. Fig. (<>)3 shows the dark energy constraints as a function of kmax, with fixed nuisance parameters (red) and with these 5 marginalized nuisance parameters (dark blue). The RSD and the full covariances of P (k) are included in this calculation. Clearly, the dark energy constraints are weakened by approximately about one or two orders of magnitude when we marginalize over HOD parameters. "
+  ],
+  "4.2 Piecewise continuous parametrization of HOD parameters ": [
+    "One potential worry with the parametrization in equation ((<>)27) is whether Nsat|M is accurately described by a power law. To address this, we propose a less model-dependent, piecewise continuous parametrization for Nsat|M. We divide the halo mass range into nbins bins and assign a parameter describing the uncertainties of HOD in each bin. That is, ",
+    "(30) ",
+    "where Θi(M) defines the binning and equals 1 in [Mi, Mi+1] and 0 elsewhere, while fi is the free parameter in bin i and describes the uncertainty of Nsat|M in this bin. ",
+    "(31) ",
+    "We start with one parameter per decade in mass, using nbins = 5 parameters between 1011 and 1016 h−1M, equally spaced in log10 M. We assume these parameters to be independent of redshift. The cyan curve in Fig. (<>)3 corresponds to marginalizing over these five piecewise continuous parameters for Nsat|M and two parameters (log10 Mmin, σlog10 M ) for Ncen|M, with no prior on them. ",
+    "Fig. (<>)4 shows the dependence of dark energy constraints on the number of parameters describing Nsat|M per decade of mass, Nper decade. The three panels correspond to kmax = 0.1, 0.4, and 1 h Mpc−1 . The Planck prior is included in this calculation. The black curve corresponds to no prior on fi and shows strong degradation with increasing Nper decade as one would expect. When kmax is small, the prior knowledge of HOD is important to improve the dark energy constraints. On the other hand, when kmax is large, HOD can be well self-calibrated, and the prior is not as important. ",
+    "To enable a fair comparison of priors, however, we would like to increase the freedom in the HOD model while fixing the overall uncertainty per decade. To do this, we impose a fixed prior per decade of mass:  ",
+    "(32) ",
+    "so that the total prior per unit log10 M, when we add the Fisher information from all fi, is σ0 regardless of the value of Nper decade. ",
+    "Figure 5. Impact of the uncertainty in the halo mass function on P (k). The main panel shows the systematic shifts of P (k) when the mass function is shifted by a constant 5 per cent (independent of mass and redshift). The inset shows Δχtot 2 as a function of kmax when the mass function is shifted by 1 or 5 per cent. The horizontal dashed line marks Δχtot 2 = 13.7, the 1-σ deviation in the 12-dimensional parameter space. As can be seen, 5 per cent (1 per cent) allows kmax up to 0.15 (0.25) h Mpc−1 . ",
+    "The red/green/blue curves in Fig. (<>)4 correspond to imposing σ0 = 1/0.1/0.01. For kmax = 0.1 h Mpc−1 , the dark energy constraints converge when we use one parameter per decade of mass regardless of the prior on nuisance parameters. When kmax > 0.1 h Mpc−1 , a few more parameters per decade in mass are required for the results to converge. For example, for kmax = 0.4 (1.0) h Mpc−1 , we need two (three) parameters per decade to ensure convergence. The required number of parameters also somewhat depends on the prior. ",
+    "We note that the HOD parameters are progressively better self-calibrated when we go to higher kmax; when kmax = 1 h Mpc−1 , self-calibrating the five HOD parameters only moderately degrades the dark energy constraints. This finding encourages future surveys to further push towards high kmax for rich cosmological and astrophysical information. "
+  ],
+  "5 SYSTEMATIC ERRORS DUE TO THE UNCERTAINTIES IN HALO MASS FUNCTION ": [
+    "In this section, we focus on the effect of the uncertainties in the halo mass function on the cosmological constraints from galaxy clustering. The mass function has been widely explored analytically (e.g., (<>)Press & Schechter (<>)1974) as well as numerically using dark matter N-body simulations (e.g., (<>)Sheth & Tormen (<>)1999; (<>)Sheth et al. (<>)2001; (<>)Jenkins et al. (<>)2001; (<>)Evrard et al. (<>)2002; (<>)Reed et al. (<>)2003; (<>)Warren et al. (<>)2006; ",
+    "Figure 4. Dark energy constraints with self-calibrated piecewise continuous HODs. The three panels correspond to kmax = 0.1, 0.4 and 1 h Mpc−1 . The x-axis corresponds to the number of parameters used to describe Nsat|M per decade of mass, and the y-axis corresponds to the dark energy constraints. The black curve corresponds to no prior, and the constraints are degraded with larger number of parameters. The other curves correspond to consistently adding a fixed total prior per decade of mass; that is, σfi = σ0 Nper decade , where σ0 = 1, 0.1, or 0.01. We note that one parameter per decade is sufficient for kmax = 0.1 h Mpc−1 , while two or three parameters are needed for higher kmax. Note that for higher kmax, the HOD parameters are better self-calibrated, and the dark energy constraints are less dependent on the prior on HOD nuisance parameters. ",
+    "(<>)Luki´c et al. (<>)2007; (<>)Cohn & White (<>)2008; (<>)Tinker et al. (<>)2008; (<>)Luki´c et al. (<>)2009; (<>)Crocce et al. (<>)2010; (<>)Bhattacharya et al. (<>)2013; (<>)Reed et al. (<>)2013; (<>)Watson et al. (<>)2013) and hydrodynamical simulations (e.g., (<>)Rudd et al. (<>)2008; (<>)Stanek et al. (<>)2010; (<>)Cui et al. (<>)2012). The different fitting formulae for the mass function are often based on different halo identification methods and mass definitions; therefore, instead of drawing a direct comparison between different fitting formulae, we choose one specific fiducial model and explore the uncertainties relative to this model. 4 (<>)",
+    "We use the fitting function from (<>)Tinker et al. ((<>)2008, described in Section (<>)3.1), which has been calibrated based on a large suite of simulations implementing different N-body algorithms and different versions of ΛCDM cosmology; therefore, it is likely to fairly represent the uncertainties in the mass function calibration. (<>)Tinker et al. ((<>)2008) quoted a statistical uncertainty of  5 per cent at z = 0 (∼ 1 per cent around M∗). However, the uncertainties are presumably larger at higher redshift and can further increase if the effects of baryons are taken into account. ",
+    "We explore the effect of a small constant shift of the halo mass function, parametrized as ",
+    "(33) ",
+    "The main panel of Fig. (<>)5 shows the impact of  = 0.05 on P (k). For the two-halo term (small k), P (k) changes by ",
+    "less than 1 per cent, because a constant shift in the mass function only affects Fv describing the large-scale RSD (see equation (<>)9). For the one-halo term (large k), P (k) changes by −5 per cent, which can be easily seen from equation (<>)6; the numerator includes one integration of dn/dM (galaxy pairs in one halo) while the denominator includes the square of such an integration. ",
+    "We next see how this systematic shift in P (k) impacts cosmological parameters. We use Δχ2tot = 13.7 [1 σ errors in a 12-dimensional parameter space; see equation ((<>)25)] as our criterion of significant impact from the systematic error. We calculate Δχ2tot using the Fisher matrix for seven cosmological parameters (Section (<>)3.1) and five HOD parameters (Section (<>)4.1). Throughout this and the next section, we use the Planck prior but no priors on HOD parameters. We believe that these two assumptions reflect reality in the next 5–10 years, when Planck data will firmly pin down certain combinations of cosmological parameters, while the determination of the nuisance HOD quantities will still be in flux. We note that unbiased priors always decrease the resulting systematic bias (for a proof, see appendix A of (<>)Bernstein (<>)& Huterer (<>)2010) and make the theoretical requirements less stringent. Thus, any prior on HOD parameters will alleviate the systematic biases and make the required accuracy of theory less stringent. ",
+    "The inset of Fig. (<>)5 shows how Δχ2 depends on kmax, for 5 per cent (blue) and 1 per cent (green) systematic shifts in the mass function. As can be seen, a 5 per cent (1 per cent) shift in the mass function can cause a significant systematic error at kmax = 0.15 (0.25) h Mpc−1 . We note that at these scales, P (k) is still dominated by the two-halo term; therefore, the systematic shifts caused by the mass function are mainly related to the large-scale redshift distortion (the Kaiser effect). However, this large-scale effect can ",
+    "be mitigated by prior knowledge of σ8 (e.g., σ8 constraints from galaxy cluster counts; (<>)Rozo et al. (<>)2010), with which the large-scale galaxy bias can be calibrated. Therefore, by calibrating the large-scale clustering amplitude, one can in principle reduce the impact of the uncertainties in the mass function. ",
+    "Finally, we note that the halo bias b(M) is also currently being actively studied (e.g., (<>)Tinker et al. (<>)2010; (<>)Ma (<>)et al. (<>)2011; (<>)Manera & Gazta˜naga (<>)2011; (<>)Paranjape et al. (<>)2013). The uncertainty in the halo bias is related to the uncertainty in the mass function; for example, (<>)Tinker et al. ((<>)2010) have indicated that their fitting function for the halo bias has an ∼ 6 per cent uncertainty, which is related to the uncertainty of their mass function. In addition, the uncertainties and systematics in b(M) will lead to a constant shift in the two-halo term (see equation (<>)9). In this case, holding the galaxy bias fixed will cause a huge systematic shift in cosmological parameters (for example, σ8); therefore, it is necessary to fit the overall galaxy bias to the large-scale clustering data. In this work, we do not specifically explore the impact of uncertainties of the halo bias because the halo bias determines the large-scale clustering amplitude, which can be observationally calibrated when combined with independent knowledge of σ8. On the other hand, we note that a scale-dependent bias can arise from the primordial non-Gaussianity (e.g., (<>)Dalal et al. (<>)2008) or small-scale nonlinearity (e.g., (<>)Smith et al. (<>)2007). In this case, one could resort to multiple tracers of large-scale structure (e.g., (<>)Seljak (<>)2009; (<>)Cacciato et al. (<>)2013), knowledge of primordial non-Gaussianity from the cosmic microwave background (e.g., (<>)Planck Collaboration (<>)2013) or higher order statistics (e.g., (<>)Mar´ın et al. (<>)2013) to better calibrate the scale dependence of the galaxy bias. "
+  ],
+  "6 SYSTEMATIC ERRORS DUE TO THE UNCERTAINTIES IN HALO PROPERTIES ": [
+    "In this section, we explore the impact of four sources of theoretical uncertainties related to the properties of dark matter haloes coming from N-body simulations on the constraining power of P (k). These sources of systematics are as follows: ",
+    "In particular, we address the following points. ",
+    "We again use Δχ2tot to assess the impact of systematic errors on the cosmological parameters, as described in the previous section. The summary of the impact of these systematics is presented in Fig. (<>)6 and Table (<>)2. "
+  ],
+  "6.1 Concentration–mass relation ": [
+    "In the halo model, the one-halo term depends on the number density profile of galaxies, u˜(k|M). We assume that the galaxy distribution follows the dark matter distribution, which is well described by an NFW profile. We then use the concentration–mass relation of dark matter haloes from the literature to compute u˜(k|M). ",
+    "The concentration–mass relation has been calibrated with dark matter N-body simulations (e.g., (<>)Bullock et al. (<>)2001; (<>)Neto et al. (<>)2007; (<>)Duffy et al. (<>)2008; (<>)Macci`o et al. (<>)2008; (<>)Kwan et al. (<>)2013; (<>)Prada et al. (<>)2012; (<>)Bhattacharya et al. (<>)2013) and hydrodynamical simulations (e.g., (<>)Lau et al. (<>)2009; (<>)Duffy et al. (<>)2010; (<>)Rasia et al. (<>)2013). Several observational programmes are also working towards pinning down this relation (e.g., (<>)Coe et al. (<>)2012; (<>)Oguri et al. (<>)2012). However, 10–20 per cent of uncertainties in the concentration–mass relation remain, and the concentration–mass relation also varies with cosmology and the implementation of baryonic physics (see, e.g., the review in (<>)Bhattacharya et al. (<>)2013). ",
+    "We investigate the impact of uncertainties in the concentration–mass relation by comparing the models from (<>)Bullock et al. ((<>)2001, B01 hereafter) and the recent calibration from (<>)Bhattacharya et al. ((<>)2013, B13 hereafter). These two models represent two extreme cases of the concentration–mass relation; therefore, using these two extreme cases sets the upper limit of the systematic bias caused by the c–M relation. We assume a scatter of 0.33 for the c–M relation in both cases. Ignoring this scatter will lead to an approximately 0.5 per cent difference in P (k) at k ≈ 1 h Mpc−1 . ",
+    "Our baseline model is from the recent formula given by B13 (based on virial overdensity): ",
+    "We compare it with the model from B01: ",
+    "(35) ",
+    "These two calibrations agree near M∗ at z = 0. ",
+    "The top-left panel of Fig. (<>)6 shows the relative change in the power spectrum P (k), evaluated at five redshifts, due to the difference between B01 and B13. We find that P (k) based on B01 is in general lower than that based on B13, because B01 predict lower concentrations at the high-mass end. Although B01 predict higher concentrations at the low-mass end, these haloes rarely contribute to the one-halo term and thus do not significantly boost clustering. ",
+    "The inset in this panel shows the systematic shifts in the parameter space caused by different models, which are characterized by Δχ2tot. It can be seen that the systematic error starts to be comparable to the statistical error (Δχ2tot = 13.7, marked by a horizontal dashed line) at kmax = 1.2 h Mpc−1 , which makes it a relatively unimportant source of systematic error. ",
+    "We would now like to study the effects of improved calibration in the c–M relation. A natural way to do this is to assume that the difference between the two extreme predic-",
+    "Figure 6. Systematic differences in P (k) caused by the four sources of errors discussed in Section (<>)6. In each panel, the main figure shows the fractional difference in P (k) in the five redshift bins, while the inset shows the systematic error Δχtot 2 as a function of kmax. The 1 σ deviation in the 12-dimensional parameter space, Δχtot 2 = 13.7, is marked by the horizontal dashed line in each inset. ",
+    "tions has been reduced by some constant factor, and that the new value interpolates between the two original extremes. We define the interpolated value as ",
+    "where cfid(M) and calt(M) are respectively the fiducial (say, B13) and the alternate (say, B01) models for the concentration–mass relation. Here fsys is a tunable parameter that allows us to assess the effect of a fraction of the full ",
+    "systematics. The limiting cases are: ",
+    "fsys = 0 ⇐⇒ no systematics ",
+    "fsys = 1 ⇐⇒ fiducial systematics . ",
+    "For a higher kmax, the tolerance of systematics is smaller, and fsys provides a measure for required reduction of systematics. For a given kmax, we search for the appropriate fsys value that makes the systematic negligible 5 (<>). ",
+    "Figure 7. Required reduction of systematic errors, shown as the fraction of the current errors, for the four sources of systematic errors discussed in this paper, as a function of the maximum wavenumber considered in the survey. Note that the velocity bias requires the greatest improvement relative to the current knowledge. ",
+    "The blue curve in Fig. (<>)7 shows the requirement on fsys from the c-M relation as a function of kmax. For all practical kmax values, c–M does not require more precise calibrations from N-body simulations. The results are summarized in the ‘c–M relation’ row of Table (<>)2. "
+  ],
+  "6.2 Galaxy number density profile: deviation from NFW ": [
+    "Our fiducial model assumes that the galaxy distribution inside a halo is described by the NFW profile. However, N-",
+    "ially lead to the same fractional shift in P (k) because the c–M relation (and most other systematics) enters non-linearly into P (k). We therefore need to perform a separate calculation of P (k) for each fsys. ",
+    "body simulations have shown that the distribution of sub-haloes in cluster-size haloes tends to be shallower than the NFW profile, and also shallower than the observed galaxy number density profile (e.g., (<>)Diemand et al. (<>)2004; (<>)Nagai & (<>)Kravtsov (<>)2005). These deviations could be related to insuf-ficient resolution or the absence of baryons in N-body simulations – the so-called overmerging issue. Several authors have proposed models for ‘orphan galaxies’ to compensate the overmerging issue; however, these models do not always recover the observed galaxy clustering (e.g., (<>)Guo et al. (<>)2011). The exact cause for these issues is still uncertain; nevertheless, the uncertainties associated with the distribution of subhaloes will likely impact the modelling of galaxy clustering. Based on the comparisons between dark matter and hydrodynamical simulations (e.g., (<>)Macci`o et al. (<>)2006; (<>)Wein-(<>)berg et al. (<>)2008), the observed galaxy density profile is likely to be bracketed by the density profiles of the subhalo number and dark matter. ",
+    "In this section, we investigate whether the uncertainties in the galaxy number density profile lead to a significant systematic bias. To model the possibility that the galaxy distribution is shallower than dark matter in the inner region of clusters, we adopt the subhalo number density profile measured from Wu et al. (in preparation), which is also illustrated in Appendix (<>)A. Fig. (<>)A1 presents one example of the galaxy number density profile measured from an N-body simulation. Based on this result, we model the subhalo number density profile as ",
+    "where uNFW(r|M) is the NFW profile , and fsurv is the “surviving fraction” of galaxies given by ",
+    "(38) ",
+    "We note that fsurv is smaller for higher host halo mass and smaller radius, where the effect of overmerging is stronger. ",
+    "The top-right panel of Fig. (<>)6 shows the difference in P (k) caused by this cored profile. As expected, the deficit of the galaxy number at small scales leads to lower power at high k. In addition, the suppression is stronger at low redshift because massive clusters are more abundant at low z. The inset shows the corresponding Δχ 2tot as a function of kmax; the systematic shifts dominate at kmax = 1 h Mpc−1 . ",
+    "We model the interpolated systematic error in the density profile as ",
+    "(39) ",
+    "Here our fiducial model is the NFW profile, and the alternative profile is given by equation (<>)37. We again search for the required fsys as a function of kmax. The result is shown by the green curve in Fig. (<>)7. Like the c–M relation, the density profile of galaxies does not require more precise calibrations for all practical kmax. The results are summarized in the ‘Profile’ row of Table (<>)2. "
+  ],
+  "6.3 Deviation from the Poisson distribution ": [
+    "In our fiducial model, P(Nsat|M) is assumed to be Poisson distributed; that is, the second mo(<>)Kolchin et al. ((<>)2010) have shown that the number of subhaloes for a given halo mass deviates from the Poisson distribution (their fig. 8). In addition, (<>)Wu et al. (2013a) have shown that the extra-Poisson scatter depends on how subhaloes are chosen and depends on the resolution. Therefore, it is still unclear whether P(Nsat|M) follows a Poisson distribution. To assess the impact of the possible extra-Poisson scatter, we adopt α = 1.02 in our one-halo term (following (<>)Boylan-Kolchin et al. (<>)2010), noting that this choice of α brackets the various possibilities explored in (<>)Wu et al. (2013a, fig. 3 therein). ",
+    "The bottom-left panel in Fig. (<>)6 shows the impact of α = 1.02 on P(k), relative to the fiducial Poisson case with α = 1. The extra-Poisson scatter only impacts the one-halo term; therefore, the large-scale P(k) is unaffected. At small scales, P(k) is boosted by less than 3 per cent. For different redshifts, ΔP/P takes off at different k, reflect-ing the varying scale where one-halo and two-halo terms cross. We also note that at high k, ΔP/P bends downwards, reflecting the fact that the one-halo term includes When P(Nsat|M) is super-Poisson, more galaxy pairs are expected, and the one-halo term gets more weighting of thus, P(k) becomes lower at high k. ",
+    "The inset in the bottom-left panel of Fig. (<>)6 shows that the systematic shifts dominate statistical errors at kmax = 0.3 h Mpc−1 . We model the partial uncertainties in α as ",
+    "(40) ",
+    "The red curve in Fig. (<>)7 shows the required fsys as a function of kmax; for kmax = 1 h Mpc−1 , the required fsys = 0.2. The results are summarized in the P(Nsat) row of Table (<>)2. "
+  ],
+  "6.4 Velocity bias ": [
+    "The small-scale RSD (also known as the ‘Fingers-of-God’ effect) are usually modelled as an exponential suppression of power with the term e −(kσv µ)2 . Here σv is the velocity dispersion of galaxies inside a cluster σvgal(Mvir). Assuming that the motions of galaxies trace those of dark matter particles, we use the velocity dispersion of dark matter particles ",
+    "inside a halo, σvDM(Mvir), which has been well established using simulations ((<>)Evrard et al. (<>)2008). However, the velocity dispersion of galaxies inside a cluster σvgal is not necessarily the same as σvDM . The ratio between the two is defined as the velocity bias ",
+    "(41) ",
+    "The exact value of bv and its redshift dependence are still under debate. Subhaloes from N-body simulations have shown bv > 1 (e.g., (<>)Col´ın et al. (<>)2000). In addition, (<>)Wu et al. (2013b) have shown that the exact value of bv depends on the selection criteria applied to subhaloes, on the resolution of simulations, and on the location of subhaloes. On the other hand, a simulated galaxy population based on assigning sub-haloes to dark matter particles (e.g., (<>)Faltenbacher & Die-(<>)mand (<>)2006) or based on hydrodynamical simulations with cooling and star formation (e.g., (<>)Lau et al. (<>)2010; (<>)Munari (<>)et al. (<>)2013) tends to have unbiased velocities. ",
+    "Since this paper focuses on the possible systematics from N-body simulations, we adopt bv > 1 observed in N-body simulations. Based on the recent calibration from (<>)Munari et al. ((<>)2013), we adopt the value of velocity bias to be ",
+    "(42) ",
+    "(estimated from the dotted curve in their fig. 7A, which corresponds to subhaloes in their N-body simulations.) The bottom-right panel of Fig. (<>)6 shows the systematic error in P(k) caused by this velocity bias. Introducing higher velocity dispersion of galaxies clearly leads to larger suppression on small scales. Note that each curve showcases a dip near k ≈ 1 h Mpc−1 , which roughly corresponds to the scale where one-halo and two-halo terms cross. As shown in Section (<>)2.2, the exponential suppression of RSD enters the one-halo and two-halo terms differently; modifying the RSD will therefore slightly change the scale of one-halo to two-halo transition. Also note that the shift in P(k) does not vanish even for very small k, because the exponential suppression enters the two-halo term as well. ",
+    "The inset in the bottom-right panel of Fig. (<>)6 shows that the systematic shifts associated with velocity bias (difference between no velocity bias and positive velocity bias) dominate the statistical error even for kmax = 0.14 h Mpc−1 . Because the deviation of P(k) starts at large scales and increases towards small scales, the velocity bias is dominant among the four sources of systematic errors studied in this paper. ",
+    "As before, we consider values of the velocity bias that interpolate between the two extreme values considered: ",
+    "(43) ",
+    "where fsys = 0 corresponds to bv = bfid = 1.0 while fsys = 1.0 corresponds to bv = 1.1 − z/15. The cyan curve= bv, alt in Fig. (<>)7 shows the required reduction of fsys for a given kmax. For example, to extend the survey just out to the usually conservative wavenumber kmax = 0.3 h Mpc−1 , better-",
+    "than-current knowledge of the velocity bias (fsys = 0.11 < 1) is required.6 (<>)",
+    "Given that a biased bv value can lead to a significant systematic error, it is necessary to marginalize over bv to mitigate the systematic bias. We find that marginalizing over an additional parameter bv in the Fisher matrix calculation does not significantlydegrade the dark energy constraints; the statistical error σ(wa)σ(wp) is increased by a factor of 2 at most. Since P (k) is sensitive to the change in bv (as shown in the last panel of Fig. (<>)6), it is not surprising that bv can be well constrained by data when set free. In addition, the effect of bv does not seem to be degenerate with the effects of other nuisance parameters and is likely to be well constrained. ",
+    "While the preparation of this paper was near completion, we learned about the related work from (<>)Linder & Sam-(<>)sing ((<>)2013). These authors have focused on a particular RSD model from (<>)Kwan et al. ((<>)2012) and assess the impact of uncertainties in this model on cosmological constraints. These authors have found that, if the model parameters are fixed, they often require sub-per cent accuracy; on the other hand, if these model parameters are self-calibrated using the data, they do not significantly degrade the cosmological constraints. This trend is consistent with our findings regarding fixing versus marginalizing over the velocity bias. ",
+    "We emphasize that the main goal of this paper is to see to what extent the theoretical uncertainties associated with calibrating galaxy clustering using N-body simulations lead to errors in the cosmological parameters. Given the diffi-culty of predicting clustering beyond k  0.5 h Mpc−1 using purely theoretical methods (e.g., the perturbation theory), resorting to calibration with N-body simulations is required, and this will remain to be the case for years to come. Our findings suggest that the velocity information of galaxies predicted from N-body simulations is likely to generate biases. "
+  ],
+  "7 SUMMARY ": [
+    "As the interpretation of the galaxy clustering measurements from deep, wide redshift surveys often relies on synthetic galaxy catalogues from N-body simulations, the systematic uncertainties in N-body simulations are likely to lead to systematic errors in the cosmological results. In this paper, we have studied several theoretical uncertainties in the predictions of N-body simulations, including the statistics, the spatial distribution and the velocity dispersion of subhaloes. In particular, we have applied the halo model to calculate the galaxy power spectrum P (k), with inputs from recent N-body simulations. We have investigated how the uncertainties from these inputs impact the cosmological interpretation of P (k), and how well these systematics need to be ",
+    "controlled for future surveys. Our main findings can be summarized as follows: ",
+    "Velocity bias is likely to be the most important source of systematic error for upcoming surveys. The current uncertainty of 10 per cent at z = 0 is likely to introduce 3 ",
+    "The sensitivity of P (k) to velocity bias leads to the question of what can be done to alleviate the potential systematic bias. Calibration through both observations and simulations is certainly one obvious solution. Another trick that is increasingly being used for large-scale structure surveys is to self-calibrate the systematic error(s); in the velocity-bias case, this would mean marginalizing over bv. With this marginalization, we expect to be left with vastly diminished biases and only a modest degradation in the cosmological parameters. We do not expect the bias to vanish completely, however, since second-order effects (e.g., redshift-and scale-dependence of bv) will remain and will cause systematic shifts. Given that we currently do not have a good model of bv(z, k), we have not attempted the full self-calibration exercise, but we definitely expect this to be modus operandi of galaxy clustering analyses in the future. "
+  ],
+  "ACKNOWLEDGEMENTS ": [
+    "We thank Andrew Hearin, Eric Linder, Chris Miller, and Zheng Zheng for many helpful suggestions. We also thank the anonymous referee for helpful comments. This work was supported by the U.S. Department of Energy under contract number DE-FG02-95ER40899. "
+  ]
+}

jsons_folder/2013MSAIS..24..128A.json

@@ -0,0 +1,62 @@
+{
+  "Abstract": [
+    "Abstract. We review recent advancements in modeling the stellar to substellar transition. The revised molecular opacities, solar oxygen abundances and cloud models allow to reproduce the photometric and spectroscopic properties of this transition to a degree never achieved before, but problems remain in the important M-L transition characteristic of the e ective temperature range of characterizable exoplanets. We discuss of the validity of these classical models. We also present new preliminary global Radiation HydroDynamical M dwarfs simulations. "
+  ],
+  "1. Introduction ": [
+    "The spectral transition from very low mass stars (VLMs) to the latest type brown dwarfs is remarkable by the magnitude of the transformation of the spectral features over a small change in e ective temperature. It is characterized by i) the condensation onto seeds of strong opacity-bearing molecules such as CaH, TiO and VO which govern the entire visual to near-infrared part (0.4 − 1.2 µm) of the spectral energy distribution (hereafter SED); ii) a •veiling• by Rayleigh and Mie scattering of sub-micron to micron-sized aerosols; iii) a weakening of the infrared water vapor bands due to oxygen condensation and to the greenhouse (or blanketing e ect) caused by silicate dust in the line forming regions; iv) methane and ammonia band formation in T and Y dwarfs; and •nally v) water vapor condensation in Y dwarfs (Te ≤ 500 K). Condensation begins to occur ",
+    "Send o print requests to: F. Allard ",
+    "in M dwarfs with Te < 3000 K. In T dwarfs the visual to red part of the SED is dominated by the wings of the Na I D and 0.77 µm K I alkali doublets which form out to as much as 2000Å from the line center ((<>)Allard et al. (<>)2007b,(<>)a). The SED of those dwarfs is therefore dominated by molecular opacities and resonance atomic transitions under pressure (≈ 3 bars) broadening conditions, leaving no window onto the continuum ((<>)Allard (<>)1990, 1997). ",
+    "With the absence of magnetic breaking due to a neutral atmosphere ((<>)Mohanty et al. (<>)2002), brown dwarfs should present di erential rotation and clouds should be distributed in bands around their surface much as is shown for Jupiter. (<>)Burgasser et al. ((<>)2002) have suggested that brown dwarfs in the L-T transition are affected by cloud cover disruption. And indeed, several objects show even large-scale photometric variability (Artigau et al. 2009, Radigan et al. 2012) • on the order of 5% to even 10-30% in the best studied case. (<>)Buenzli et al. ",
+    "((<>)2012) •nd periodic variability both in near-IR and mid-IR for a T6.5 brown dwarf in simultaneous observations conducted with HST and Spitzer. The phase of the variability varies considerably between wavelengths, suggesting a complex atmospheric structure. Recent large-scale surveys of brown dwarf variability with Spitzer (PI Metchev) have revealed mid-IR variability on order of a few percent in > 50% of L and T type brown dwarfs. On the basis of these results, variability may be expected for young extrasolar planets, which share similar Te and spectral types. And the ubiquity of cloud structures in L3-T8 dwarfs strongly suggests that these may persist into the cooler (> T8) objects. ",
+    "The models developed for VLMs and brown dwarfs are a unique tool for the characterization of imaged exoplanets, if they can explain the stellar-substellar transition. And global circulation models subjected to cloud formation in presence of rotation are necessary to explain the observed weathering phenomena. Recently, Allard et al. (2012a,b) and (<>)Rajpurohit et al. ((<>)2012) have published the preliminary results of a new model atmosphere grid computed with the PHOENIX atmosphere code accounting for cloud formation and mixing from Radiation HydroDynamical (RHD) simulations ((<>)Freytag et al. (<>)2010). In this paper, we present the latest evolution in modeling their SED and their observed photometric variability and present new prospectives for this •eld of research. "
+  ],
+  "2. M dwarfs ": [
+    "Because oxygen compounds dominate the opacities in the SED of VLMs, their synthetic spectra and colors respond sensibly to the abundance of oxygen assumed. Allard et al. (2012a,b) compare models using di erent solar abundance values ((<>)Grevesse et al. (<>)1993, 2007, Asplund et al. 2009) and found an improved agreement with constraints ((<>)Casagrande et al. (<>)2008a) for the solar abundances obtained using RHD simulations by Asplund et al. In this paper, we present models based on the (<>)Ca au et al. ((<>)2011) solar abundances. Taking the (<>)Grevesse et al. ((<>)1993) solar abundance val-",
+    "ues as reference, the Grevesse et al. (2007) results show a reduced oxygen abundance by -39%, while Asplund et al. obtain a reduction by -34%. These values poses problem for the interpretation of solar astero-se¨•smological results ((<>)Basu & Antia (<>)2008, Antia & Basu 2011). More recently, (<>)Ca au et al. ((<>)2011) used the CO5BOLD code to obtain a more conservative reduction of oxygen by -22%. The latter value still allows an acceptable representation of the VLMs while preserving the astero-se¨•smological solar results. Higher spectral resolution and up-to-date opacities also contributed to improve VLMs models compared to previous versions ((<>)Hauschildt et al. (<>)1999, Allard et al. 2001). These models rely on lists of molecular transition determined ab initio. See the review by Homeier et al. elsewhere in this journal for the opacities used in the BT-Settl models presented in this paper. ",
+    "The comparison of the BT-Settl PHOENIX models based on the (<>)Ca au et al. ((<>)2011) solar abundances to the low resolution spectra and to the (<>)Casagrande et al. ((<>)2008b) temperature scale is shown in Figs. (<>)1 and (<>)2. Fig. (<>)1 shows an unprecedented agreement with spectral type through the M dwarf spectral sequence of the models. One can see in Fig. (<>)2 that the new BT-Settl models lie slightly to the blue of the BT-Dusty models by (<>)Allard et al. ((<>)2012) based on the (<>)Asplund et al. ((<>)2009) solar abundances, but largely to the red of the AMES-Cond/Dusty models by (<>)Allard et al. ((<>)2001) and the BT-NextGen models (<>)Allard et al. ((<>)2012) based on the (<>)Grevesse et al. ((<>)1993) solar abundances. The even lower oxygen abundance values of (<>)Grevesse et al. ((<>)2007) cause the MARCS models by (<>)Gustafsson et al. ((<>)2008) to lie to the right of the diagram. The NextGen models by (<>)Hauschildt et al. ((<>)1999) also lie to the right of the diagram due, among others, to the missing and incomplete molecular opacities. ",
+    "The BT-Settl models are computed solving the radiative transfer in spherical symmetry and the convective transfer using the Mixing Length Theory ((<>)Bohm-Vitense¨ (<>)1958, see also Ludwig et al. 2002 for the exact formalism used in PHOENIX) using a mixing length as derived by the RHD convection simulations ((<>)Ludwig et al. (<>)2002, (<>)2006, Freytag et al. 2012) ",
+    "Fig. 1. Fig. 1 of the article by Rajpurohit et al. (in prep.). The optical to red SED of M dwarfs from M0 to M9 observed with the NTT at a spectral resolution of 10.4 Å are compared to the the best •tting (chi-square minimization) BT-Settl synthetic spectra (dotted lines), assuming a solar composition according to Ca au et al. (2011). The models displayed have a surface gravity of long=5.0 to 5.5 from top to bottom. The best •t is determined by a chi-square minimization technic. The slope of the SED is particularly well reproduced all through the M dwarfs spectral sequence. However, some indications of missing opacities (mainly hydrides) persist to the blue of the late-type M dwarf cases such as missing opacities in the B• 2+<… X 2+ system of MgH by (<>)Skory et al. ((<>)2003) and the opacities are totally missing for the CaOH band near 5500 Å. Note that chromospheric emission “ls the Na I D transitions in the latest-type M dwarfs displayed here, and that the M9.5 dwarf has a ”atten optical spectrum due to dust scattering. Telluric features near 7600 Å have been ignored from the chi-square minimization. ",
+    "and a radius as determined by interior models ((<>)Bara e et al. (<>)1998, 2003, Chabrier et al. 2000) as a function of the atmospheric parameters (Te , surface gravity, and composition). PHOENIX use the classical approach consisting in neglecting the magnetic •eld, convective and/or rotational motions and other multidimensional aspects of the problem, and assuming that the averaged properties of stars can be approximated by modeling their properties radially (uni-dimensionally) and statically. Neglecting motions in modeling the pho-tospheres of VLMs, brown dwarfs, and planets ",
+    "is acceptable since the convective velocity •uctuation e ects on line broadening are hidden by the strong van der Waals broadening and the important molecular line overlapping prevailing in these atmospheres. But this is not the case of the impact of the velocity •elds on the cloud formation and wind processes (see section (<>)5 below). "
+  ],
+  "3. Global RHD M dwarf simulation ": [
+    "VLMs and brown dwarfs are fully convective, and their convection zone extends into ",
+    "Fig. 2. Estimated Te and metallicity (decreasing from lighter to darker tones) for M dwarfs by (<>)Casagrande et al. ((<>)2008a) on the left, and brown dwarfs by Golimowski et al. (2004) and Vrba et al. (2004) on the right are compared to the NextGen isochrones for 5 Gyrs (<>)Bara e et al. ((<>)1998) using model atmospheres by various authors: MARCS by (<>)Gustafsson et al. ((<>)2008), ATLAS9 by (<>)Castelli & Kurucz ((<>)2004), DRIFT-PHOENIX by (<>)Helling et al. ((<>)2008), UCM by (<>)Tsuji ((<>)2002), Clear/Cloudy by (<>)Burrows et al. ((<>)2006), NextGen by (<>)Hauschildt et al. ((<>)1999), AMES-Cond/Dusty by (<>)Allard et al. ((<>)2001), the BT-Cond/Dusty/NextGen models by Allard et al. (2012) and the current BT-Settl models. Some curves labeled in the legend can only be seen in the more extended Fig. (<>)4. ",
+    "their atmosphere up to optical depths of even 10−3 ((<>)Allard (<>)1990, 1997). Convection is eÿ-cient in M dwarfs and their atmosphere, except in the case of 1 Myr-old dwarfs which dissociate H2, little sensitive to the choice of mixing length ((<>)Allard et al. (<>)1997). A mixing length value between = l/Hp = 1.8 − 2.2 has been determined by (<>)Ludwig et al. ((<>)2002, (<>)2006) depending on surface gravity. These simulations have been recently extended to the late-type brown dwarf regime using CO5BOLD by (<>)Freytag et al. ((<>)2010). In brown dwarfs the internal convection zone retreats progressively to deeper layers with decreasing Te . ",
+    "The magnetic breaking known to operate in low mass stars is not or less eÿciently op-",
+    "erating in fully convective M dwarfs (< M3) and brown dwarfs. Brown dwarfs can therefore rotate with equatorial speeds as large as 60 km/sec or periods of typically 1.5 hour. Some have even been observed with periods nearly as low as their breakup velocity (1 hour). In comparison, planets of our solar system have a larger rotation period, such as 10 hours for Jupiter, and 24 hours for the Earth. This rapid rotation (as well as their magnetic •eld) causes a suppression of the interior convection ef•ciency leading to a slowed down contraction during their evolution, and to larger radii then predicted by classical evolution models ((<>)Chabrier et al. (<>)2007). ",
+    "Fig. 4.    (<>)                                          ,           ,      T   −,    T =                         ,   −       (T ≤  ) ",
+    "           −      −    −          (   )             −−−  (   )      −−−      (<>)  &  ((<>))        −      ,           , −                    ,   (<>),  −",
+    "     −                          (  & ,  )        ,          (   )               "
+  ],
+  "4. Cloud formation in PHOENIX ": [
+    "      PHOENIX (<>)   ((<>))             ",
+    "Fig. 3.              T = . , g = .,      ⊙      /  ,     − / ,      ,     + /  ,     − /                  PHOENIX                            −                        ",
+    "       ((<>) (<>))   −−       (, , ,   )         ((<>)   (<>),   (<>)   )      (,) −   − ,                           (Pg(t)/Psv/)    −            −−  ,           ( ) ",
+    "                       ",
+    "            ,                                 ,                                              ()    (   , )  − ,   (, , )  − ,    (, , )   (, , )  −                    ( , ,   )          ,           −,                −                           −   ",
+    "      (<>)    −           ((<>)    (<>))         −      "
+  ],
+  "5. Cloud Formation in CO5BOLD ": [
+    "             ((<>)   (<>))                  −,       −",
+    "100 200 300 x [km] mt22g50mm00n08  time=4505sec    ",
+    "100 200 300 x [km] mt18g50mm00n11  time=7955sec    ",
+    "100 200 300 400 x [km] mt20g50mm00n09  time=7945sec    ",
+    "100 200 300 x [km] mt15g50mm00n06  time=13920sec    ",
+    "Fig. 5.     CO5BOLD ((<>)   (<>))               , , ,       g=,       ,                                       ",
+    "                           (<>) ((<>))           µ     −       −−  (<>)    −−−          ,        (   )     (    )   ,                                           ",
+    "   − ,             ,      (≈   )                                    −−                     surface ,                        (            )                                                   ,                    "
+  ],
+  "6. Summary and Prospectives ": [
+    "          −−        (<>)    ((<>))          − ((<>) &  (<>))                                                       ((<>)   (<>)) ",
+    "                −−                            T =  ,              (J − Ks < .)  −   −   −    < T <    −                  ( < T < ,  )     ,       −    (<>)    ((<>))                 ,  −      ,    V        (       ,        −  ),        ( ) ,    ,      (<>) ((<>))     ,   −              −           T        (   )     ( ) , (<>)   ((<>), (<>))         −",
+    "   −       ",
+    "                        ( , −,            , ) ",
+    "  ,                                                            ,                ((<>)    (<>))         (T =   g ≤ . )        ÿ                         ((<>)   (<>))                                      , ,            −      ,      ",
+    "                    ,                      −  ,  ,                           ",
+    "                   ",
+    " (      )                              ,          ,     (    T )     ÿ                  ,                   −  ((<>)   (<>))    ()                        −                     ÿ             ((<>)   (<>),    ,−   )               (               ,     )  ,                              ((<>)   (<>))                −                  ,  ,      −         PHOENIX   (<>) ",
+    "Acknowledgements.                  (),       ",
+    "()   (),         '    (/−    )             −−− "
+  ]
+}

jsons_folder/2013MmSAI..84.1053A.json

@@ -0,0 +1,66 @@
+{
+  "Abstract": [
+    "Abstract. Within the next few years, several instruments aiming at imaging extrasolar planets will see first light. In parallel, low mass planets are being searched around red dwarfs which offer more favorable conditions, both for radial velocity detection and transit studies, than solar-type stars. We review recent advancements in modeling the stellar to substellar transition. The revised solar oxygen abundances and cloud models allow to reproduce the photometric and spectroscopic properties of this transition to a degree never achieved before, but problems remain in the important M-L transition characteristic of the Teff range of characterisable exoplanets. "
+  ],
+  "1. Introduction ": [
+    "Since spectroscopic observations of very low mass stars (late 80s), brown dwarfs (mid 90s), and extrasolar planets (mid 2000s) are available, one of the most important challenges in modeling their atmospheres and spectroscopic properties lies in high temperature molecular opacities and cloud formation. K dwarfs show the onset of formation metal hydrides (starting around Teff ∼ 4500 K), TiO and CO (below Teff ∼ 4000 K), while water vapor forms in early M dwarfs (Teff ∼ 3900 − 2000 K), and methane, ammonia and carbon dioxide are detected in late-type brown dwarfs (Teff ∼ 300−1600 K) and in extrasolar giant planets. Cloud formation is also an important factor in the detectability of biosignatures, and for the habitability of exoplanets ((<>)Paillet et al. (<>)2005; (<>)Kasting (<>)2001) ",
+    "Send offprint requests to: F. Allard ",
+    "Extrasolar planets for which we can currently characterize their atmospheres are either those observed by transit (Teff ∼ 1000−2000 K depending on their radius relative to that of the central star) or by imaging (young planets of Teff ∼ 500 − 2000 K depending on their mass and age). Several infrared integral field spectrographs combined with coronagraph and adaptive optic instruments are coming online before 2013 (SPHERE at the VLT, the Gemini Planet Imager at Gemini south, Project1640 at Mount Palomar, etc.). The E-ELT 39 m telescope in Chile due around 2020 will also be ideally suited for planet imaging. ",
+    "M dwarfs are the most numerous stars, constituting 70% of the stellar budget of the Galaxy ((<>)Chabrier (<>)2003, (<>)2005), and 1281 brown dwarfs1 (<>)and 891 planets2 (<>)are currently ",
+    "known despite their faintness in the solar neighborhood vicinity. Single very low mass (VLM) stars and brown dwarfs are therefore more directly observable and characterizable then exoplanets. They represent, beyond their own importance, a wonderful testbed for the understanding of exo-planetary atmospheric properties together with solar system studies. ",
+    "matrix and a · b = k akbk the scalar product of the two vectors a and b. The dyadic tensor product of two vectors a and b is the tensor ab = C with elements cmn = ambn and the nth componentof the divergence of the tensor C is (∇ · C)n = m ∂cmn/∂xm. In this case, the total energy is given by "
+  ],
+  "2. Model construction ": [
+    "The modeling of the atmospheres of VLMs has evolved (as here illustrated with the development of the PHOENIX atmosphere code) with the extension of computing capacities from an analytical treatment of the transfer equation using moments of the radiation field ((<>)Allard (<>)1990), to a line-by-line opacity sampling in spherical symmetry ((<>)Allard et al. (<>)1994, (<>)1997; (<>)Hauschildt et al. (<>)1999) and more recently to 3D radiation transfer ((<>)Seelmann et al. (<>)2010). ",
+    "To illustrate the various assumptions made by constructing model atmospheres, let us begin with the description of the equations of ideal magnetohydrodynamics (MHD) — adapted here for the stellar case by specifying the role of gravity, radiative transfer, and energy transport — which are themselves a special case (no resistivity) of the more general equations (see for example (<>)Landau & Lifshitz (<>)1960). These are written in the compact vector notation as: ",
+    "The vectors are noted with boldface characters, while scalars are not. For example, P is the gas pressure, ρ the mass density, g the gravity, and v is the gas velocity at each point in space. B is the magnetic field vector, where the units were chosen such that the magnetic permeability µ is equal to one. I is the identity ",
+    "where ei is again the internal energy per unit mass, and Φ the gravitational potential. The additional constraint for the absence of magnetic monopoles, ",
+    "∇ · B = 0 , (3) must also be fulfilled. ",
+    "The first, third, and last equations in Eq. (<>)1 correspond to the mass, magnetic field, and energy conservation, while the second equation is the budget of forces acting on the gas. In the case of stellar astrophysics, gravitational acceleration is an important source term, while the radiative flux participates in the energy budget. Further assumptions are made in the numerical solution of these equations to address different astrophysical problems in very different regimes. The chromospheres correspond to a regime of high Mach numbers and strong magnetic fields where ionized gas has to follow the magnetic field lines, and where the radiative transfer must be solved for the case of a non-ideal gas.The photospheric convection simulations correspond to a regime where the thermal and convective turnover timescales are comparable i.e. Mach numbers are around 1, and the non-local radiative transfer must be solved, often for an ideal gas. And the interior convection and/or dynamo simulations correspond to a regime where the thermal timescale is much larger then the turnover timescale, which in turn is much larger then the acoustic timescale. The radiative flux can be estimated by the diffusion approximation, and the magnetic field lines are dragged by the ionized gas. ",
+    "The classical approach for interior and atmosphere models consists in simplifying the problem for a gain of computing effi-ciency, neglecting the magnetic field, convective and/or rotational motions and other multi-",
+    "dimensional aspects of the problem, and assuming that the averaged properties of stars can be approximated by modeling their properties radially (uni-dimensionally) and statically. We also assume that the atmosphere does neither create nor destroy the radiation emitted through it. Neglecting motions in modeling the photospheres of VLM stars, brown dwarfs, and planets is acceptable since the convective velocity fluctuation effects on line broadening is hidden by the strong van der Waals broadening prevailing in these atmospheres. But this is not the case of the impact of the velocity fields on the cloud formation and wind processes (see section (<>)3 below). In this case, equation (<>)1 reduces to the so-called hydrostatic equation and constant flux approximation for the radial or z direction used in classical models: ",
+    "can be seen from Eq. (<>)4) with a good enough spectral resolution to account for all cooling and heating processes. ",
+    "The PHOENIX code ((<>)Allard et al. (<>)1994, (<>)2012) distinguishes itself by computing the opacities during the model execution (or on-the-fly). This involves computing the opacities for billions of atomic and molecular transitions on-the-fly, though with a selection of the most important lines. This different approach makes PHOENIX much slower then former codes, but allows to take into account more consistently important physical phenomena, such as those involving a modification of local elemental abundances along the atmospheric structure (e.g. non-LTE, photoionisa-tion, diffusion and cloud formation). "
+  ],
+  "3. Mixing": [
+    "This allows computing the interior evo-lutive properties of stars throughout the Hertzsprung-Russell diagram, and to solve the radiative transfer in the atmosphere for a much larger number of wavelengths (line-by-line or opacity sampling) or wavelength bins (Opacity Distribution Function or ODF, K-Coefficient) compared to R(M)HD simulations. Classical model atmospheres impose therefore the independent parameter Frad (= σ Teff , where σ is the Stefan-Boltzmann constant) and compute Fλ so that, after model convergence, the target Frad is reached. Other independent parameters are the surface gravity g and the abundances of the elements i. This makes it possible to create extensive databases of synthetic spectra and photometry that provide the basis for the interpretation of stellar observations. ",
+    "All the model atmospheres compared in this review are classical models in this sense, and differ mainly in the completeness and accuracy of their opacity database including their cloud model assumptions), and the assumed solar abundances used for the particular grid shown. They must resolve the radiative transfer for the entire spectral energy distribution (as ",
+    "(4) Stars becomes fully convective throughout their interior and convection reaches furthest out in the optically thin regions of the photosphere in M3 and later dwarfs with Teff below 3200 K ((<>)Allard (<>)1990; (<>)Chabrier & Baraffe (<>)2000). In most model atmospheres discussed in this review paper, the convective energy transfer is treated using the Mixing Length Theory (or MLT, see (<>)Kippenhahn & Weigert (<>)1994), using at best a unique fixed value of the mixing length of 1.0 (1.25 for the ATLAS9 models, 1.5 for the MARCS models, etc). However, since convection becomes efficient in M dwarfs, the precise value of the mixing length matters only for the deep atmospheric structure and as a surface boundary condition for interior models. ",
+    "(<>)Ludwig et al. ((<>)2002, (<>)2006) have been able to compare the PHOENIX thermal structure obtained using the MLT with that of RHD simulations. They showed that the MLT could reproduce adequately (except for the overshoot region) the horizontally averaged thermal structure of the hydro simulations when using an adequate value of the mixing length parameter. This value has been estimated for M dwarfs to vary with a gravity from α=l/Hp=1.8 to 2.2 (2.5 to 3.0 for the photosphere). The BT-Settl models use the mass and gravity dependent prescription of (<>)Ludwig et al. ((<>)1999) for hotter stars, together with an average (2.0) of ",
+    "the values derived for M dwarfs by (<>)Ludwig (<>)et al. ((<>)2002, (<>)2006). They also use the micro-turbulence velocities from the RHD simulations ((<>)Freytag et al. (<>)2010), and the velocity field from RHD simulations from (<>)Ludwig et al. ((<>)2006) and (<>)Freytag et al. ((<>)2010) to calibrate the scale height of overshoot, which becomes important in forming thick clouds in L dwarfs but is negligible for the SED of VLMs and brown dwarfs otherwise. "
+  ],
+  "3.1. The revision of solar abundances ": [
+    "Model atmospheres assume scaled solar abundances for all elements relative to hydrogen. Additionally, some enrichment of α-process elements (C, O, Ne, Mg, Si, S, Ar, Ca, and Ti) resulting from a ”pollution” of the star-forming gas by the explosion of a supernova is appropriate in the case of metal-poor subdwarfs of the Galactic thick disk, halo, and globular clusters, and the stars towards the galactic center ((<>)Gaidos et al. (<>)2009). ",
+    "Since the overall SED of late K dwarfs, M dwarfs, brown dwarfs, and exoplanets is governed by oxygen compounds (TiO, VO in the optical and water vapor and CO in the infrared), the elemental oxygen abundance is of major importance. Important revisions have been made to the solar abundances based on radiation hydrodynamical simulations of the solar photosphere, and to improvements in the detailed line profile analysis. Indeed, two separate groups using independent RHD and spectral synthesis codes ((<>)Asplund et al. (<>)2009; (<>)Caffau et al. (<>)2011) obtain an oxygen reduction of 34% and 22% respectively) compared to the abundances of (<>)Grevesse et al. ((<>)1993) previously used in the NextGen and AMES-Cond/Dusty models. ",
+    "Figs. 8 and 9 of (<>)Rajpurohit et al. ((<>)2012) shows an example of these effects, where several models are compared to the optical to infrared SED of the M5.5, M9.5, and L0 dwarfs of the LHS 1070 system. The BT-Settl model by Allard et al. (2012) is based on the (<>)Caffau (<>)et al. ((<>)2011) solar abundance values, while DRIFT models by (<>)Helling et al. ((<>)2008b) use the (<>)Grevesse et al. ((<>)1993) solar abundances, and the MARCS model by (<>)Gustafsson et al. ",
+    "((<>)2008) uses the values of (<>)Grevesse et al. ((<>)2007, 39%). The MARCS model show a systematic near-infrared flux excess, compared both to observations and the other models, which is probably caused by the much lower oxygen abundance values of (<>)Grevesse et al. ((<>)2007). The oxygen abundances sensitivity of TiO bands is expressed as a reduced line blanketing effect at longer wavelengths, participating in the water vapor profile changes ((<>)Allard et al. (<>)2000). ",
+    "The influence of the solar oxygen abundance can also be clearly seen in Fig. (<>)1 which compares the (<>)Casagrande et al. ((<>)2008) Teff and metallicity estimates with the (<>)Baraffe et al. ((<>)1998) NextGen isochrones (assuming an age of 5 Gyrs) using model atmospheres from various authors. The oxygen abundance effects are particularly highlighted by comparing the BT-Settl model based on the (<>)Caffau et al. ((<>)2011) values with models based on earlier solar abundance values. This is the case of the AMES-Cond/Dusty and BT-NextGen models which are based on the Grevesse et al. (1993) solar abundances. On can see that the higher oxygen abundance causes models to appear too blue by as much as 0.75 mag compared to models based on the (<>)Caffau et al. ((<>)2011) values. The MARCS models ((<>)Gustafsson et al. (<>)2008) based on the (<>)Grevesse et al. ((<>)2007) values show on the contrary a systematically increasing excess in J − Ks with decreasing Teff . The models are most sensitive on the solar oxygen abundances for M dwarfs around 3300 K, i.e. at the onset of water vapor formation. ",
+    "By comparing the BT-Settl 2012 isochrone, computed using the (<>)Caffau et al. ((<>)2011) solar abundances, to the BT-Dusty isochrone computed using the (<>)Asplund et al. ((<>)2009) values, we note that the remaining uncertainties tied to the solar abundance determination correspond only to 0.02 mag in the J −Ks color. (<>)Rajpurohit (<>)et al. ((<>)2013) have compared the BT-Settl 2012 models to the observed optical spectra and colors of M dwarfs from M0 to M9, and found an excellent agreement of the models with observations except in the Teff = 2000 − 2500 K regime affected by the onset of important cloud formation (see section (<>)4). ",
+    "The NextGen model by (<>)Hauschildt et al. ((<>)1999) dates too far back and suffers from too ",
+    "much opacity differences (incompleteness essentially) to participate in this illustration. In fact, this plot helps to conclude that using the NextGen models caused a systematic overestimation of Teff for VLM stars. It is interesting to note that all models appear too red in the K dwarf range above 4000 K. This may be due to an under representation of the K dwarfs in this diagram. The unified cloud model (hereafter UCM) by (<>)Tsuji ((<>)2002) show a completely different behavior in this diagram, sharing the colors of NextGen or even MARCS models at 4000 K, but diverging towards the BT-Settl colors at 3500 K to finally cross-over to bluer colors as dust begin to form and affect the SED below 2600 K. ",
+    "The various model atmospheres have not been used as surface boundary condition to interior and evolution calculations, and simply provide the synthetic color tables interpolated on the published theoretical isochrones ((<>)Baraffe et al. (<>)1998). Even if the atmospheres partly control the cooling and evolution of M dwarfs ((<>)Chabrier & Baraffe (<>)1997), differences introduced in the surface boundary conditions by changes in the model atmosphere composition have negligible effect. ",
+    "In the substellar regime, the composition of brown dwarfs varies rapidly with decreasing Teff , and the variation is responsible for the immense change in their SED across the very narrow Teff regime of the M-L-T spectral transition. If water vapor opacities only became recently reliable ((<>)Allard et al. (<>)2012), this is not the case of the more complex methane molecule which is so important in brown dwarfs, and planetary atmospheres. The ExoMol Project supported by an European Research Council grant to Jonathan Tennyson (University College London) will allow important advances on these fronts in the coming years. New ammonia line lists are already available through this project ((<>)Yurchenko et (<>)al. (<>)2011) and from the NASA-Ames group ((<>)Huang et al. (<>)2011a,(<>)b). "
+  ],
+  "4. Cloud formation ": [
+    "One of the most important challenges in modeling these atmospheres is the formation ",
+    "of clouds. (<>)Tsuji et al. ((<>)1996) had identified dust formation by recognizing the condensation temperatures of hot dust grains (enstatite, forsterite, corundum: MgSiO3, Mg2SiO4, and Al2O3 crystals) to occur in the line-forming layers (τ ≈ 10−4 − 10−2) of their models. The onset of this phase transition occurs in M dwarfs below Teff = 3000 K, but the cloud layers are too sparse and optically thin to affect the SED above Teff = 2600 K. The cloud composition, according to equilibrium chemistry, is going from zirconium oxide (ZrO2), refractory ceramics (perovskite and corundum; CaTiO3, Al2O3), silicates (e.g. forsterite; Mg2SiO4), to salts (CsCl, RbCl, NaCl), and finally to ices (H2O, NH3, NH4SH) as brown dwarfs cool down over time from M through L, T, and Y spectral types ((<>)Allard et al. (<>)2001; (<>)Lodders & (<>)Fegley (<>)2006). This crystal formation causes the weakening and vanishing of TiO and VO molecular bands (via CaTiO3, TiO2, and VO2 grains) from the optical spectra of late M and L dwarfs, revealing CrH and FeH bands otherwise hidden by the molecular pseudo-continuum, and the resonance doublets of alkali transitions which are only condensing onto salts in late-T dwarfs. The scattering effects of this fine dust is Rayleigh scattering which provides veiling to the optical SED, while the greenhouse effect due to the dust cloud causes their infrared colors to become extremely red compared to those of hotter dwarfs. The upper atmosphere, above the cloud layers, is depleted from condensible material and significantly cooled down by the reduced or missing pseudo-continuum opacities. ",
+    "One common approach has been to explore the limiting properties of cloud formation. One limit is the case where sedimentation or gravitational settling is assumed to be fully efficient. This is the case of the Case B model of (<>)Tsuji ((<>)2002), the AMES-Cond model of (<>)Allard et al. ((<>)2001), the Clear model of ((<>)Burgasser et al. (<>)2002), and the Clear model of (<>)Burrows et al. ((<>)2006). The other limit is the case where gravitational settling is assumed inefficient and dust, often only forsterite, forms in equilibrium with the gas phase. This is the case of of the Case A model of (<>)Tsuji ((<>)2002), the AMES-Dusty models of (<>)Allard et al. ((<>)2001), the BT-Dusty mod-",
+    "Fig. 1. Estimated Teff and metallicity (lighter to darker tones) for M dwarfs by (<>)Casagrande et al. ((<>)2008) on the left, and brown dwarfs by (<>)Golimowski et al. ((<>)2004) and (<>)Vrba et al. ((<>)2004) on the right are compared to the NextGen isochrones for 5 Gyrs (<>)Baraffe et al. ((<>)1998) using model atmospheres by various authors: MARCS by (<>)Gustafsson et al. ((<>)2008), ATLAS9 by (<>)Castelli & Kurucz ((<>)2004), DRIFT-PHOENIX by (<>)Helling (<>)et al. ((<>)2008b), UCM by (<>)Tsuji ((<>)2002), Clear/Cloudy by (<>)Burrows et al. ((<>)2006), NextGen by (<>)Hauschildt et al. ((<>)1999), AMES-Cond/Dusty by (<>)Allard et al. ((<>)2001), and the BT models by Allard et al. (2012). The region below 2900 K is dominated by dust formation. The dust free models occupy the blue part of the diagram and only at best explain T dwarf colors, while the Dusty and DRIFT models explain at best L dwarfs, becoming only redder with decreasing Teff . The BT-Settl, Cloudy and UCM Tcrit = 1700 K models describe a complete transition to the red in the L dwarf regime before turning to the blue into the T dwarf regime. The Cloudy model however does not explain the reddest L dwarfs. ",
+    "els of (<>)Allard et al. ((<>)2012), the Dusty model of (<>)Burgasser et al. ((<>)2002), and the Cloudy model of (<>)Burrows et al. ((<>)2006). To these two limiting cases we can add a third case also explored by several, which is the case where condensation is not efficient and the phase transition does not take place. This is the case of the NextGen models of (<>)Hauschildt et al. ((<>)1999), of the BT-NextGen models of (<>)Allard et al. ((<>)2012), and the Case B models of ((<>)Tsuji (<>)2002, not shown). ",
+    "The purpose of a cloud model is to go beyond these limiting cases and define the number density and size distribution of condensates as a function of depth in the atmosphere, and as a function of the atmospheric parameters. (<>)Helling et al. ((<>)2008a) have compared different cloud models and their impact on model atmospheres of M and brown dwarfs. Most cloud models define the cloud base as the evaporation layer provided by equilibrium chemistry. In the unified cloud model of (<>)Tsuji ((<>)2002) and (<>)Tsuji et al. ((<>)2004) a parametrization of the radial location of the cloud top by way of an ad-",
+    "justable parameter Tcrit was used. This choice permits to parametrize the cloud extension effects on the spectra of these objects without resolving the cloud model equations. In principle, this approach does not allow to reproduce the stellar-substellar transition with a unique value of Tcrit since the cloud extension depends on Teff . Indeed, the transparent T dwarf atmospheres can only exist if the forsterite cloud layers retract below the line-forming regions in those atmospheres. ",
+    "(<>)Ackerman & Marley ((<>)2001) have solved the particle diffusion problem assuming a parametrized sedimentation efficiency fsed (constant through the atmosphere) and a mixing assumed constant and fixed to its maximum value (maximum of the inner convection zone). (<>)Burgasser et al. ((<>)2002) and (<>)Saumon & Marley ((<>)2008) found that their so-called Cloudy models could not produce the M-L-T spectral transition with a single value of fsed. This conclusion prompted them to propose a patchy cloud model (<>)Marley et al. ((<>)2010). ",
+    "2012",
+    "(<>)Fig. 2. Color-magnitude diagram of late-type dwarfs (MKO system, Dupuy & Liu ) and di-rectly imaged HR8799 exoplanets ((<>)Marois et al. (<>)2008) compared to two isogravity tracks of the BT-Settl models, representative of old and young brown dwarfs or planetary mass objects. The models span most of the observed locus of L and early T dwarfs and show the transition from cloudy to (nearly) clear atmospheres around Teff = 1000 − 1500 K, at practically constant J-band luminosity. Late T dwarfs show systematically redder NIR colors possibly explained by sulfide and chloride clouds forming at lower temperatures ((<>)Morley et al. (<>)2012). ",
+    "Allard et al. ((<>)2003, (<>)2012) have developed PHOENIX version 15.05 using the index of refraction of 55 condensible species, and a slightly modified version of the Rossow cloud model obtained by ignoring the coalescence and coagulation, and computing the supersaturation consistently. Their density and grain size distribution with depth in the atmosphere is obtained by comparing the timescales for nucleation, condensation, gravitational settling or sedimentation, and mixing derived from the MLT for the convective mixing in the convection zones, exponential overshoot according to (<>)Ludwig et al. ((<>)2002, (<>)2006), and from gravity waves according to (<>)Freytag et al. ((<>)2010). The cloud model is solved layer by layer inside out (bottom up) to account for the sequence of grain species formation as a function of cooling of the gas. Among the most important species forming in the BT-Settl model are ZrO2, Al2O3, CaTiO3, Ca2Al2SiO7, MgAl2O4, Ti2O3, Ti4O7, Ca2MgSi2O7, CaMgSi2O6, ",
+    "CaSiO3, Fe, Mg2SiO4, MgSiO3, Ca2SiO4, MgTiO3, MgTi2O5, Al2Si2O13, VO, V2O3, and Ni. At each step, the gas phase is adjusted for the depletion caused by grain formation and sedimentation. The grain sizes (a unique maximum value per atmospheric layer) are determined by the comparison of the different timescales and thus varies with depth to reach a few times the interstellar values (used in the dusty limiting case models) at the cloud base for the effective temperatures discussed in this paper. While the BT-Settl model assumes dirty spherical grains in the timescales equations to calculate the growth and settling of the grains, it only sums the opacity contributions of each species in each layer as for an ensemble of pure spherical grains. ",
+    "(<>)Helling et al. ((<>)2008b) and (<>)Witte et al. ((<>)2009) modified the PHOENIX code to compute the DRIFT-PHOENIX models, considering the nucleation of only seven of the most important solids (TiO2, Al2O3, Fe, SiO2, MgO, MgSiO3, Mg2SiO4) made of six different elements. The cloud model is based on resolving the moment equations for the dust density accounting for nucleation on seed particles and their subsequent growth or evaporation, solving from top to bottom of the atmosphere. This model assumes dirty grains mixed according to the composition of each atmospheric layer. It uses composite optical constants resulting in absorption and scattering properties of the grains that are therefore different than those of the BT-Settl models, possibly producing more opaque clouds. However, since the opacities are dominated by atomic and molecular opacities over most of the spectral distribution in this spectral type range, the impact of those differ-ences are difficult to identify. The largest differences between the BT-Dusty, BT-Settl and DRIFT models are the differences in the local number density, the size of dust grains, as well as their mean composition, which are the direct results of the cloud model approach. ",
+    "The models using the limiting cases of maximum dust content describe adequately (given the prevailing uncertainties) the infrared colors of L dwarfs. The cloud-free limiting case models, on the other hand, allow to reproduce to some degree the colors of T ",
+    "dwarfs. But pure equilibrium chemistry models without parametrization of the cloud extension in the atmosphere cannot reproduce the observed behaviour of the M-L-T transition, the dusty models only becoming redder and dustier with decreasing Teff , while dust-free models miss completely the reddening due to the dust greenhouse effects in the L dwarf regime. Fig. (<>)1 shows this situation compared with the effective temperatures estimates obtained by integration of the observed SED ((<>)Golimowski et al. (<>)2004; (<>)Vrba et al. (<>)2004). One can see that the late-type M and early-type L dwarfs behave as if dust is formed nearly in equilibrium with the gas phase with extremely red colors in some agreement with the AMES-Dusty models. The BT-Settl models reproduce the main sequence down to the L-type brown dwarf regime, before turning to the blue in the late-L and T dwarf regime as a result of the onset of methane formation in the Ks bandpass. The BT-Settl models succeed as good as the limiting case AMES-Dusty, BT-Dusty, and UCM Tcrit = 1700 K at explaining the reddest colors of L dwarfs (assuming an age of 5 Gyrs). The fact that a UCM model with Tcrit value of 1700 K succeeds rather well in reproducing the L-T transition suggest that the cloud extension is somewhat constant through that transition. The DRIFT models, on the other hand, reach slightly less to the red and do not extend low enough in temperature to explain the L-T transition. The M-L transition is not reproduced by any models where the BT-Settl models shows a J-band flux excess. This suggests that an additional element neglected thus far is at play, such as larger maybe porous grains. Indeed, all models assume thus far spherical and nonporous grains. The choice of solar abundances and the completeness of the opacity databases used is also important. "
+  ],
+  "5. Conclusions ": [
+    "We have compared the behavior of the recently published model atmospheres from various authors across the M-L-T spectral transition from M dwarfs through L type and T type brown dwarfs and confronted them to constraints. If the onset of dust formation is occurring be-",
+    "low Teff = 2900 K, the greenhouse effects of silicate dust cloud formation impact strongly (J − Ks < 2.0) the near-infrared SED of late-M and L-type atmospheres with 1300 < Teff < 2600 K. The BT-Settl models by (<>)Allard et (<>)al. ((<>)2012) are the only models to span the entire regime from stars to Y type brown dwarfs. In the M dwarf range, the results appear to favor the BT-Settl models based on the (<>)Caffau (<>)et al. ((<>)2011) solar abundances versus MARCS and ATLAS 9 models based on other values. In the brown dwarf (and planetary) regime, on the other hand, the unified cloud model by (<>)Tsuji ((<>)2002) succeeds extremely well in reproducing the constraints, while the BT-Settl models also show a plausible transition. However, no models succeed in reproducing the M-L transition between 2500 and 2000 K. The BT-Settl models also reproduce the redder infrared colors of young planets directly observable by imaging as an effect of their lower surface gravities. ",
+    "Acknowledgements. The research leading to these results has received funding from the French “Agence Nationale de la Recherche” (ANR), the “Programme National de Physique Stellaire” (PNPS) of CNRS (INSU), and the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 247060). "
+  ]
+}

jsons_folder/2013PhRvD..88h3507B.json

@@ -0,0 +1,225 @@
+{
+  "arXiv:1305.2917v1  [astro-ph.CO]  13 May 2013 ": [],
+  "I. INTRODUCTION ": [
+    "The three dimensional distribution of galaxies has the potential to tell us a lot about the physics governing our Universe. However, the imprint of the composition and history of our Universe on its structure is usually quantified in terms of the linear power spectrum. From there it is a fair way to go to connect to the distribution of luminous objects. Due to the stochastic nature of the initial conditions the comparison between theory and observation has to be made at a statistical level. Thus, it has become common practice to reduce the data to n-spectra and to find a way to push the theory as far as possible in order to make predictions for the observed spectra. This means that the theoretical prediction needs to account for the fact that galaxies are only sampling the underlying matter distribution. While their distribution is clearly related to the matter distribution, there are a number of distinct features present in the galaxy distribution that are related to their discrete nature and the fact that galaxies form preferentially in high density regions. ",
+    "Due to the complicated nature of galaxy formation, cosmological constraints from galaxy surveys are usually obtained using a bias model [(<>)1]. The simplest local bias models [(<>)2] assume a proportionality between the galaxy and matter overdensities. As we will review in detail below in §(<>)II A, the auto power spectrum of a sample of N particles in a volume V is expected to have an additional scale independent shot noise component V/N . We will refer to this Poisson prediction as fiducial stochasticity. On top of the fiducial Poisson shot noise there are further contributions to the halo power spectrum that are white only over a limited range of wavenumbers and lead to modifications in the k → 0 limit. The latter will be referred to as stochasticity corrections. For instance, the studies of [(<>)3, (<>)4] found evidence for a sub-Poissonian noise in the halo distribution in N -body simulations (see also [(<>)5, (<>)6]) and used this concept to increase the information content extractable from surveys by weighting haloes accordingly. Subsequently, this approach was used to improve constraints on primordial non-Gaussianity [(<>)7] and redshift space distortions [(<>)8]. ",
+    "Thus far, the origin of these stochasticity corrections has not been understood consistently. However, some authors noted that realistic bias models would at some point need to account for the finite size of haloes and the resulting exclusion effects [(<>)9]. The effect of halo exclusion on the power spectrum was previously discussed in [(<>)10] in a an Eulerian setting. Here, we will argue that the exclusion effect can not be seen in isolation but has to be combined with the non-linear clustering, which can lead to positive corrections on large scales. This approach partially alleviates the longstanding problem of non-vanishing contributions of the perturbative bias model on the largest scales, where perturbative corrections are considered unphysical. This paper aims at shedding light at the stochasticity properties of halo and galaxy samples and tries to quantify them where possible. ",
+    "The paper breaks down as follows: We begin in §(<>)II with a short review of the standard Poisson shot noise for a sample of discrete tracers. Then, in §(<>)III we consider some simple toy models to understand the effects of exclusion on the power spectrum, before we go on to discuss more realistic models for the clustering of dark matter haloes in §(<>)IV. In §(<>)V we study the stochasticity and correlation function for a sample of dark matter haloes and a HOD galaxy sample in N -body simulations. Finally, we summarize our findings in §(<>)VI. "
+  ],
+  "II. DISCRETE TRACERS ": [],
+  "A. Correlation and Power Spectrum ": [
+    "The overdensity of discrete tracer particles (dark matter haloes, galaxies etc.) can generically be written as ",
+    "(1) ",
+    "where n¯ is the mean number density of the point-like objects whereas n(r) is their local number density. The two-point correlation of this fluctuation field is the expectation value ",
+    "(2) ",
+    "We split the sum into an i = j and and i  = j part, corresponding to the correlation of the discrete particles with themselves and the correlation between different particles, respectively. The second term in the last equality is the reduced two-point correlation function of the tracers. The first term arises owing to “self-pairs”, which are usually ignored in the calculation of real space correlations. Taking the Fourier transform of the last expression, the power spectrum of the discrete tracers is ",
+    "(3) ",
+    "Self-pairs contribute the usual Poisson white noise 1/n¯. The only requirement is that the power spectrum be positive definite. This implies that the Fourier transform of the two-point correlation ξ(d)(r) can be anything equal or greater than − 1/n¯. In the limit k → 0 in particular, the power spectrum tends towards ",
+    "(4) ",
+    "where the intregal of ξ(d)(r) over the whole space can be positive, zero or negative (but greater than − 1/n¯) depending on the nature of the discrete tracers. This can lead to super-poisson or sub-poisson white noise in the low-k limit. At k = 0, the power spectrum is P(d)(0) = 0 because the fluctuation field δ(d)(r) is defined relative to the mean number density, hence  δ(d) = 0. This implies that P(d)(k) drops precipitously on very large scales (so it must be discontinuous at k = 0) regardless the value of To convince ourselves that this is indeed the case, wed3r ξ(d)(r). can write the Fourier modes of the tracer fluctuation field as ",
+    "(5) ",
+    "To calculate δ(d)(k = 0) (which is formally the difference between two infinite quantities), we first assume N, V  1 at fixed average number density n¯ ≡ N/V , and then take the limit N, V → ∞ . We thus have for the Fourier transform of the density field ",
+    "(6) ",
+    "which for k = 0 yields ",
+    "(7) ",
+    " This obviously holds also for a finite number N of tracers in a finite volume V . Therefore, the fact that d3r ξ(d)(r) can be different from zero has nothing to do with the fact that  δ(d) = 0, nor with the so-called “integral constraint” that appears when measuring an excess of pairs relative to a random distribution in a finite volume [(<>)11, (<>)12]. "
+  ],
+  "B. The Effect of Exclusion with Clustering ": [
+    "Let us now account for the fact that haloes are the centre of an ensemble of particles, which by definition can not overlap, and that these are clustered. Exclusion means it is forbidden to have two haloes closer than the sum of their radii R. This fact can be accounted for by writing the correlation function of the discrete tracers as ",
+    "(8) ",
+    "where the fictitious continuous correlation function ξhh (c)(r) is defined for r ∈ [0, ∞ ] and would for instance be related to the matter correlation function by the local bias model (see § (<>)IV A below). Enforcing this step at the exclusion radius is certainly overly simplistic, since any triaxiality or variation of radius within the sample will smooth this step out. We will come back to this issue later. ",
+    "For generic continuous clustering models, we can write the Fourier transform of the correlation function as ",
+    "(9) ",
+    "where the exclusion volume is Vexcl = 4πR3/3, j0 is the zeroth order spherical Bessel function and the Fourier transform of the top-hat window is given by ",
+    "(10) ",
+    "and where the notation [A ∗ B](k) describes a convolution integral ",
+    "(11) ",
+    "We also defined the continuous power spectrum as the full Fourier transform of the continuous correlation function ",
+    "(12) ",
+    "Combining the above results with the fiducial stochasticity contribution we finally have for the power spectrum of the discrete tracers ",
+    "(13) ",
+    "This equation is the basis of our paper and we will thus explore it in detail. ",
+    "It is common practice to ignore the exclusion window and to approximate the continuous power spectrum by the linear local bias model, which yields for the power spectrum of the discrete tracers in the Poisson model ",
+    "(14) ",
+    "This needs to be modified because of exclusion and non-linear effects. In practice, for k > 0, it is difficult to separate the effects. Here we will formally define the stochasticity effects discussed in this paper as a stochasticity power spectrum [(<>)4] ",
+    "(15) ",
+    "where b1 = Phm(k)/Pmm(k) is the first order bias from the cross-correlation in the low-k limit. We then have in the low-k limit ",
+    "(16) ",
+    "One could make this generally valid at all k by defining b(k) = Phm(k)/Pmm(k), but we will not do this here, and instead explore physically motivated models of non-linear bias. In this paper we are interested in the stochasticity power spectrum C(k) and in particular its limit as k → 0. ",
+    "What are the corrections arising from the exclusion and deviations from the local bias model? In the low k-limit, the window function scales as WR(k) −−−→ k→0 1 − k2R2/10. Hence, the convolution integral leads to a constant term plus corrections scaling as k2R2 times moments of the continuous power spectrum ",
+    "(17) ",
+    "FIG. 1. Cartoon version of the correlation function of discrete tracers. Continuous linear correlation function (black dashed) and non-linear correlation function (red dashed). The true correlation function of discrete tracers (green solid line) agrees with the non-linear continuous correlation function outside the exclusion scale and is -1 below, except for the delta function at the origin arising from discreteness. Thus, there are two corrections compared to the continuous linear bias model, a negative correction inside the exclusion radius (red shaded) and a positive one outside the exclusion radius due to non-linear clustering (blue shaded). ",
+    "Thus, irrespective of the shape of the continuous power spectrum on large scales, exclusion always introduces a white (k0) correction on large scales. ",
+    "Fig. (<>)1 illustrates the behaviour of the correlation function of discrete tracers. In the very popular local bias model, the clustering of dark matter haloes is modeled at leading order as In configuration space this leads to shown by the black dashed line. We will consider this linear bias model as the fiducial model on top of which we define corrections. Non-linear halo clustering suggests an enhancement proportional to higher powers of the linear correlation function as exemplified by the red dashed line. Our above arguments suggest that this clustering model, if at all, can only be true outside the exclusion radius. Inside this radius the probability to find another halo is zero, leading to ξhh (d)(r < R) = −1. ",
+    "An intuitive understanding of the corrections can be obtained in the k → 0 limit, where the halo power spectrum is given by an integral over the correlation function and can thus be written as ",
+    "(18) ",
+    "where we introduced ξhh,NL (c) (r) to account for generic non-linear continuous models of the halo clustering. The red and blue shaded regions in Fig. (<>)1 show the negative and positive corrections with respect to the linear bias model for which we would have in absence of exclusion Phh (d)(k) −− k→−→ 0 1/n¯. Note that the non-linear halo-halo correlation function could in principle be smaller than the linear bias prediction. Our above notion of a positive correction arising from the non-linear correction outside the exclusion radius is solely based on local bias arguments. In general this statement should be relaxed (for an example see App. (<>)A) and the blue region could have either sign. "
+  ],
+  "III. TOY MODELS ": [
+    "To show that the exclusion can indeed lower the stochasticity we perform a simple numerical experiment. We consider a set of hard sphere haloes of radius R/2. For this purpose, we distribute N particles randomly in a cubic box ensuring that | xi − xj | > R for all pairs of particles (i, j). The corresponding correlation function is expected to be zero except for scales r < R, where ξ = − 1 due to exclusion. Thus we expect the fiducial stochasticity to be lowered by 4πR3/3 in the k → 0 limit. For an intuitive derivation of the corrections to the power spectrum we will consider a fixed number of particles N in a finite volume V . Using Eq. ((<>)6) the auto-power spectrum of the tracer ",
+    "particles can be written as [(<>)13] ",
+    "(19) ",
+    "This yields for the hard sphere sample, which we consider as a proxy for excluded haloes ",
+    "(20) ",
+    "In Fig. (<>)2 we show the power spectrum of this toy halo sample for R = 8 h−1Mpc, N = 800 and V = 3003 h−3Mpc3 . We clearly see that the measured power follows the exclusion corrected stochasticity. The window is close to unity on large scales and decays at k ≈ 1/R, i.e., the fiducial shot noise is recovered for high k. This is a first indication for stochasticity not being scale independent. Note that the above derivations are only true in the limit, where the total exclusion volume is small compared to the total volume and thus allows for a quasi random distribution (about 0.8% volume coverage in our case). "
+  ],
+  "A. Satellite Galaxies ": [
+    "Galaxies are believed to populate dark matter haloes. Let us consider the simple case that each of the dark matter haloes under consideration hosts a central galaxy that, as the name suggests, coincides with the halo centre plus a fixed number Ns,h of satellite galaxies, such that the total number of satellite galaxies is given by Ns = Ns,hNh. For simplicity, we will assume that the galaxies are distributed according to a profile ρs(r) with typical scale Rs around the centers of the host halo centers. For long wavelength modes k < 1/Rs the Ns,h galaxies within one halo are effectively one particle, which is why on large scales we expect the stochasticity of the satellite galaxy sample to be equal to the one of the host haloes and only for scales k > 1/Rs the modes can probe the distinct nature of the particles and the stochasticity goes to 1/n¯s. ",
+    "We can evaluate our model Eq. ((<>)19) to obtain the satellite-satellite power spectrum ",
+    "(21) ",
+    "Here µ is the cosine of the angle between k and Δrij = ri − rj that is averaged over, us(k) is the normalized Fourier transform of the galaxy profile ρs(r). For definiteness we will assume a delta function profile ρ(r) = δ(D)(r − Rs)/r2 corresponding to us(k) = j0(kRs), where j0 is the zeroth order spherical Bessel function. The two terms in the above equation correspond to the one and two halo terms in the halo model [(<>)14, (<>)15], the profile and the fiducial shot noise arise from correlations between particles in the same halo, whereas the exclusion term is dominated by the correlation between distinct haloes. The results of the numerical experiment are shown in Fig. (<>)2 as the green points. The model prediction is shown as the green solid line and describes the simulation measurement very well. On small scales the power is dominated by the fiducial galaxy shot noise and on large scales the host halo stochasticity dominates ",
+    "(22) ",
+    "While the distribution of satellite galaxies on a sphere of fixed radius around the halo centre is very peculiar and unrealistic, the qualitative behaviour is the same for all profiles with finite support. In the case studied above, the corrections to the fiducial galaxy shot noise 1/n¯h are always positive. This is due to the high satellite fraction. As we will discuss below, this behaviour might be completely different for galaxy samples with small satellite fraction, where the exclusion effect can be more important than the enhancement due to the satellites. ",
+    "FIG. 2. Power spectrum of a randomly distributed halo sample obeying exclusion (red points) and corresponding model with (red solid line) and without (red dashed line) exclusion. In a second step we populate these haloes with Ngal = 2 satellite galaxies, and calculate the auto power spectrum of the satellite galaxies (green points) and their cross power spectrum with the halo centers (blue points). The blue and green solid lines show our model predictions, whereas the dashed lines show the naive expectation of Poisson shot noise. "
+  ],
+  "B. Central and Satellite Galaxies ": [
+    "We can also consider the cross power spectrum between halo centers (central galaxies) and the satellite galaxies. In this case there is no Poisson shot noise, since the samples are non-overlapping and the power is dominated by a one-halo term describing the radial distribution of the satellites around the halo centre ",
+    "(23) ",
+    "Here we have again a one halo term arising from correlations of the halo center with satellites in the same halo and a two halo term arising from the correlation of satellite galaxies in one halo with the center of another halo. The comparison with the result of the numerical experiment in Fig. (<>)2 shows very good agreement. ",
+    "The above discussion is overly simplified as we assume all haloes to be of the same mass and to host the same number of galaxies. Any realistic galaxy sample will be hosted by a range of halo masses (i.e. a range of exclusion radii) and the number of galaxies per halo will also be a function of mass. The total galaxy power spectrum of the combined central and satellite samples can be obtained as a combination of the central-central, central-satellite and satellite-satellite contributions ",
+    "(24) ",
+    "where fs = Ns/(Nc + Ns) is the satellite fraction. For realistic satellite fractions for SDSS LRGs [(<>)16] fs ≈ 0.1, the weighting of the central-central power spectrum dominates over the contributions from the central-satellite and satellite-satellite power spectra by factors of 9 and 81, respectively. A more realistic galaxy sample based on a HOD population of dark matter haloes in a N-body simulation will be discussed in Sec. (<>)V F. "
+  ],
+  "C. Toy Model with Clustering ": [
+    "Haloes are clustered, i.e., there is an enhanced probability to find two collapsed objects in the vicinity of each other to finding them widely separated. Let us discuss the influence of this phenomenological result on our toy model. For the sake of simplicity let us assume that haloes always come in pairs, i.e., that there is a second halo outside the exclusion scale at typical separation Rclust. This will similarly to satellite galaxies residing in one halo, lead to a ",
+    "FIG. 3. Kaiser bias [(<>)1] in configuration and Fourier space. Left panel: Un-smoothed (black dashed) and R = 4 h−1Mpc smoothed (black solid) linearly biased matter correlation functions b12 ,trξ(r) and continuous correlation function of the thresholded regions ξtr(r) (red dashed). The red solid line shows a simple implementation of exclusion imposed on the correlation function of the thresholded regions. Right panel: Power spectrum correction arising from the non-linear biasing (top line) and effect of increasing exclusion for R = 0, 4, 6, 8 h−1Mpc from top to bottom. ",
+    "0.01 0.02 0.05 0.10 0.20 0.50 1.00 4000 3000 Pk h3 Mpc3 0 1000 2000 1000 2000 k h Mpc1 ",
+    "positive k0 term on large scales, that decays for k > 1/Rclust. In a more realistic setting, not all haloes will come in pairs, some of them will be single objects, others will come in clusters of n-haloes. Furthermore not all of them will be separated by exactly the clustering scale. ",
+    "Some authors argued that any large scale k0-behavior in the perturbation theory description of biasing is unphysical and should be suppressed by constant but aggressive smoothing [(<>)17] or by a k-dependent smoothing [(<>)18]. Based on the above considerations, we argue that such terms are just a result of the clustering of haloes and thus not unphysical. Whether the magnitude of these effects can be covered by a perturbative treatment such as second order bias combined with perturbation theory, is a different question, which we will pick up later in §(<>)IV B. For now, let us note that such a k0 term is also predicted by biasing models that go beyond the local bias model as for instance the correlation of thresholded regions as discussed briefly in the next subsection and for instance in [(<>)19]. Generally the clustering scale exceeds the exclusion scale and thus one should expect that the enhancement due to clustering decays at lower k than the suppression due to exclusion. This is actually what happens in the simulations as we will show in §(<>)V. "
+  ],
+  "D. Density Threshold Bias ": [
+    "The spherical collapse model suggests that spherical Lagrangian regions exceeding the critical collapse density δc ≈ 1.686 segregate from the background expansion and form gravitationally bound objects. Hence, the clustering statistics of regions above threshold can tell us something about the clustering of dark matter haloes and galaxies. The study of [(<>)1] considered the correlation function of regions whose density exceeds a certain value in a Gaussian random field, smoothed with a top-hat window of scale R. At the same time this paper pioneered bias models, which are nothing but a large scale expansion of the full correlation function of thresholded regions. Let us see how non-linear or non-perturbative clustering can affect the power spectrum on the largest scales in the full model. The root mean square overdensity within the smoothed regions is given by ",
+    "(25) ",
+    "The correlation of thresholded regions can be calculated exactly employing the two point probability density function of Gaussian random fields. For simplicity, we will consider regions of a fixed overdensity rather than regions above threshold. The peak height ν = δc/σR can be chosen based on the spherical collapse argument. For the correlation function of regions of fixed overdensity one obtains [(<>)1, (<>)19] ",
+    "(26) ",
+    "FIG. 4. Clustering of peaks in a one dimensional skewer through a density field smoothed with a Gaussian filter of scale R = 2 h−1Mpc (M ≈ 8.6 × 1012 h−1M). Left panel: For fixed peak height the correlation function flattens out on small scales (black), but with increasing bin width the exclusion becomes stronger. The width of the bin in peak height increases from dark to light red. The linear local bias expansion is the same for all of these models and is shown by the dashed line. For reference we overplot the Gaussian smoothing (dash-dotted) and the top-hat smoothing scale containing the same mass (dashed). Right panel: Corresponding stochasticity correction ΔPpk(k) = FT[ξpk](k) − b12 ,pkPlin(k) for the fiducial bin width. ",
+    "where . Here ξR(r) is the linear correlation function smoothed on scale R. In the large distance, small correlation limit, the correlation function of the thresholded regions can be approximated by a linearly biased version of the linear correlation function ξtr(r) = b21,trξR(r) with b1,tr ≈ ν/σR. If one is interested in an accurate description of the non-perturbative correlation function on smaller scales, higher orders in the expansion need to be considered. Comparing the expansion of the correlation of thresholded regions in powers of the smoothed correlation to the full non-perturbative result in Eq. ((<>)26), we can investigate the convergence properties of the linear bias model. The left panel of Fig. (<>)3 shows the correlation function of thresholded regions for a Gaussian random field smoothed on R = 4 h−1Mpc and the linearly biased versions of the smoothed and un-smoothed linear correlation functions. ",
+    "We can now Fourier transform the correlation function of thresholded regions and subtract out the linearly biased power spectrum to obtain the correction introduced by the non-linear clustering ",
+    "(27) ",
+    "As we show in Fig. (<>)3, there is a non-vanishing correction in the k → 0 limit that is approximately constant on large scales and goes to zero on small scales. The presence of such a correction was discussed in a slightly different context in [(<>)19]. ",
+    "In its original form, the thresholded regions are a continuous field and thus do not include any exclusion. One could however imagine that the patches defining the smoothing scale do not overlap. In this case the correlation function of thresholded regions should go to −1 for r < 2R. To show how the exclusion scale affects the correction in the power spectrum we consider a few exclusion radii smaller than two smoothing radii. As obvious in Fig. (<>)3, increasing the smoothing scale first reduces the scale independent correction on large scales, compensates it completely and eventually leads to a negative scale independent correction for r = 2R. "
+  ],
+  "E. Peak Bias Model ": [
+    "While the thresholded regions provide a continuous bias model, the peak model [(<>)20, (<>)21] goes beyond in identifying a discrete set of points and providing the correlation function of these points. Most studies of the peak model to date have focused on the large separation limit [(<>)22–(<>)24], where closed form expressions for the peak correlation in terms of the underlying linear correlation function and its derivatives are possible. However, [(<>)25] calculated the one dimensional peak correlation function for a set of power law power spectra and [(<>)26] computed the two dimensional peak correlation function for peaks in the CMB. The reason for the restriction to one or two dimensions owes to the dimensionality of the covariance matrix that needs to be inverted for the calculation of the peak correlation. In a ",
+    "one dimensional field the covariance matrix is a six by six matrix (field amplitude, first and second derivative at two points). ",
+    "Here we consider realistic ΛCDM power spectra in three dimensions, smooth them on a realistic Lagrangian scale R = 2 h−1Mpc and evaluate the exact non-perturbative one dimensional correlation of peaks following the approach of [(<>)25] (see App. (<>)B for a brief review). Note that the correlation of field derivatives diverges for top-hat smoothing, which is why we follow common praxis and employ a Gaussian smoothing. The Gaussian smoothing makes the correlators of field derivatives well behaved but beyond that there is no physical motivation to employ this filter. We study a range of peak heights ν and also a range of bin widths in ν. The peak correlation function for four different bin widths is shown in the left panel of Fig. (<>)4. ",
+    "The first remarkable observation is that peaks of a fixed height don’t seem to obey exclusion, only after considering a finite width in peak height, we can observe that the correlation function goes to −1 on small scales. The transition scale to the fixed peak height case increases with bin with, i.e., wider bins have a larger exclusion region. As above for the thresholded regions we can expand the peak correlation function in the large distance limit and obtain a bias expansion that has contributions from the underlying matter correlation function and correlation functions of the derivatives. Doing that, it becomes obvious, that the linear matter bias is only assumed outside of the BAO scale and that there is a distinct scale dependent bias that is partially described by the derivative terms in the bias expansion. Fourier transforming the full peak correlation function and subtracting out the linear biased power spectrum we obtain the correction shown in the right panel of Fig. (<>)4. The qualitative behaviour agrees with the result obtained above for the thresholded sample with an ad hoc exclusion scale. On large scales there is a combination of clustering and exclusion effects, the clustering decays first and then also the exclusion correction goes to zero. Note that the projected one dimensional matter power spectrum scales as k0 one large scales and thus doesn’t vanish in the k → 0 limit. This fact makes the distinction between clustering and stochasticity terms in the one dimensional peak model very difficult. We hope to report on results for the full three dimensional peak model in the near future. "
+  ],
+  "IV. QUANTIFYING THE CORRECTIONS ": [
+    "Let us now try to quantify the stochasticity corrections for a realistic halo sample. We expect the effect to be time independent in the k → 0 limit if the same sample of particles is evolved under gravity. Thus, to minimize the influence of non-linearities, we will consider the protohaloes in Lagrangian space. In numerical studies of the effect, we will later define the protohalo as the initial ensemble of particles that form the Friends-of-Friends (FoF) haloes in our final output at redshift zf = 0. "
+  ],
+  "A. Continuous Halo Power Spectrum from Local Bias ": [
+    "The local Lagrangian bias model assumes that the initial halo density field can be written as a Taylor series in the matter fluctuations at the same Lagrangian position q ",
+    "(28) ",
+    "here ηi is the conformal time of the initial conditions and q is the Lagrangian coordinate. We will follow the approach of [(<>)27] where the smoothing scale is an unobservable scale, which should not affect n-point clustering statistics on scales exceeding the smoothing scale. The above model can be used as the starting point for a coevolution of haloes and dark matter, which finally leads to a Eulerian bias prescription. Recently, such a calculation was shown to correctly predict non-local Eulerian bias terms [(<>)28, (<>)29]. The peak-background-split (PBS) [(<>)30] makes predictions for the Lagrangian bias parameters in the above equation, and the corresponding late time Eulerian local bias parameters can then be obtained based on the spherical collapse model. There is some evidence that the peak model yields a better description of some aspects of the initial halo clustering than the local Lagrangian bias model. While we will briefly discuss these effects in App. (<>)A, we refrain from using this model for the modelling of the stochasticity corrections, since the the peak bias expansion beyond leading order has not been studied in great detail and its implementation goes beyond the scope of this study. ",
+    "For the continuous power spectrum in the initial conditions the local Lagrangian bias model predicts ",
+    "(29) ",
+    "where D(η) is the linear growth factor and the scale dependent bias correction is described by ",
+    "(30) ",
+    "This term leads to a positive k0 contribution in the low-k regime. In this sense it deviates from typical perturbative contributions to the power spectrum, which start to dominate on small scales. For this reason, this term was partially absorbed into the shot noise by [(<>)27]. We will explicitly consider the term, since it describes the effect of non-linear clustering and is responsible for super-Poissonian stochasticity. The cross power spectrum between haloes and matter is given by ",
+    "(31) ",
+    "and does obviously not contain any second order bias corrections. This statement remains true if higher order biasing schemes are considered, since higher order biases only renormalise the bare bias parameters [(<>)27]. ",
+    "Truncating the bias expansion is only valid if δ2  1, which is certainly satisfied on large scales in the initial conditions, but not necessarily on the scales relevant for halo clustering outside the exclusion radius. On these scales one might have to consider all the higher order local bias parameters. It is beneficial to calculate this effect in configuration space where the local bias model leads to a power series in the linear correlation function ",
+    "(32) ",
+    "The limit applies only in the high peak limit and Press-Schechter bias parameters [(<>)31]. We will restrict ourselves to the quadratic bias model since it can account for the main effects and since using higher order biasing schemes also requires more parameters to be determined. The Press-Schechter and Sheth-Tormen prescriptions provide a rough guideline for the scaling of bias with mass and redshift, but fail to provide correct predictions for the bias amplitude. Thus we obtain the bias parameters from fits to observables not affected by stochasticity (such as the halo-matter cross power spectrum) and obtaining higher order biases would require higher order spectra such as the bispectrum. Since our discussion is mostly in Lagrangian space we will drop the superscripts E and L from now on and absorb the growth factors into the linear power spectra and correlation functions. "
+  ],
+  "B. Theory Including Clustering and Exclusion ": [
+    "We can now use the bias model introduced above to evaluate the discrete power spectrum Eq. ((<>)13). We have ",
+    "(33) ",
+    "The splitting of I22, the non-linear clustering term arising from b2, is somewhat counterintuitive, since we expect this term to be active only outside the exclusion scale. Furthermore, there is no corresponding term in the halo-matter or matter-matter power spectra that would cancel the continuous I22. Thus we combine the continuous part and the exclusion correction for the non-linear clustering term into a positive correction whose small scale contributions have been removed. ",
+    "(34) ",
+    "Here we defined the correction term ",
+    "(35) ",
+    "A simpler version of Eq. ((<>)34) has been presented in [(<>)10], where the non-linear clustering is neglected and the results are presented in Eulerian rather than Lagrangian space. ",
+    "In the k → 0 limit the Fourier transform simplifies to a spatial average over the correlation function ",
+    "(36) ",
+    "where the linear bias term vanishes due to Plin(k) −k−−→→ 0 0. The fact that the integral over ξ2 runs only from the exclusion scale to infinity mitigates the smoothing dependence of the correction, since smoothing on the scale of the halo affects the correlation function only on the halo scale, which is by definition smaller than the exclusion scale. ",
+    "TABLE I. Mean masses, exclusion radii, first and second order Lagrangian and Eulerian bias parameters for our z = 0 halo sample. Masses are in units of h−1M and radii in units of h−1Mpc. The mass dependence of these parameters is also plotted in Fig. (<>)6. Note that the second order bias parameter is just a phenomenological fitting parameter used to get a reasonable representation of the correlation function. We do not claim that our fitting procedure yields an accurate second order bias parameter for the sample. For this purpose on has to employ the bispectrum, which yields second order bias parameters that are in much better agreement with the peak-background split expectation but fail to describe the correlation function. "
+  ],
+  "C. Stochasticity Matrix ": [
+    "In Fig. (<>)7 we show the diagonals of the stochasticity matrix measured in our simulations in Lagrangian space (zi = 49) and Eulerian space (zf = 0). The most remarkable observation in this plot is the agreement between the results, given the different amplitude of the growth factors and the linear bias parameters at these two times. This is a result of the fact, that gravity can not introduce or alter k0 dependencies [(<>)41] due to mass and momentum conservation. This can for instance be seen in the low k-limit of standard perturbation theory [(<>)32]: The mode coupling term P22 is a gravity-gravity correlator and thus scales as k4 , whereas the propagator term P13 is a gravity-initial condition correlator and scales as k2Plin. ",
+    "For the highest mass bin there is a clear suppression of the noise level on the largest scales which then asymptotes to the fiducial value 1/n¯h at a scale k ≈ 1/R ≈ 0.3 hMpc−1 . Since the radius of the halo shrinks during collapse, this scale is found at a higher wavenumber in Eulerian space. For the less massive haloes the behavior is not completely ",
+    "FIG. 7. Diagonals of the stochasticity matrix σij . Left panel: Initial conditions zi = 49 Right panel: Final field zf = 0. There is remarkable agreement in the large scale amplitude between initial conditions and final field besides the strong difference in the bias parameters and growth factors. We highlight this fact by the horizontal dashed lines that have the same amplitude in both panels and are matched to the large scale stochasticity matrix in the initial conditions. For both panels, there is clear evidence for stochasticity going to fiducial 1/n¯ for high wavenumbers, and a modification due to exclusion and clustering for k ≤ 1/R, where R is the scale of the halo at the corresponding redshift. Note the different scaling of the k-scale in the two plots. The mass increases from blue to orange, i.e., top to bottom. ",
+    "monotonic. On large scales we find a noise level slightly exceeding the fiducial value. Going to higher wavenumbers the fiducial value is crossed, the residual reaches a minimum and finally asymptotes to 1/n¯. This behavior can be explained as follows: the clustering scale exceeds the exclusion scale and as we have argued in §(<>)III C, the enhanced correlation on the clustering scale leads to a positive contribution on the largest scales that decays for lower wavenumbers than the negative exclusion correction. ",
+    "The wavenumber at which the stochasticity asymptotes to its fiducial value in the final field is at fairly high wavenumbers, exceeding the Nyquist frequencies of both Nc = 512 and Nc = 1024 grids. To probe smaller scales we employ a mapping technique [(<>)42, (<>)43] that allows us to resolve small scales without having to increase the grid size beyond Nc = 512. The technique consists of splitting the box into n parts per dimension and adding these parts to the same grid. This allows inference of each l-th mode but also increases the Nyquist frequency by a factor l. We use several different mapping factors l = 4, 6, 12, 20, 50 to probe all the scales up to k ≈ 20 hMpc−1 . ",
+    "In Fig. (<>)8 we show the diagonals of the stochasticity matrix for one and two mass bins respectively. For the one bin case we select all the haloes in our simulation, effectively combining all the ten mass bins resulting in M1bin = 3.84 × 1013 h−1M. For the two bin case we combine the five lightest and the five heaviest mass bins resulting in masses M2bin,I = 1.47 × 1013 h−1M and M2bin,II = 6.21 × 1013 h−1M. The plot shows both the initial condition and the final stochasticity and the two agree very well in the low-k limit. The stochasticity correction does not depend on the fiducial stochasticity and thus the scale dependence of the total stochasticity is more pronounced in the wider mass bins due to their lower fiducial shot noise. Interestingly the stochasticity correction for the 1-bin case vanishes in the low-k limit, but is negative in the intermediate regime. This is a sign of a perfect cancellation between exclusion and non-linear clustering. The final stochasticity seems to be a k-rescaled version of the initial stochasticity. Finally, let us stress that the power spectrum of the wide bins can not be obtained by a summation of the contributing bin-power spectra from the ten bin case since one has to account for the off-diagonal components of the stochasticity matrix. ",
+    "In the left panel of Fig. (<>)10 we compare our model Eq. ((<>)39) to the measured stochasticity matrix of the ten bins in the initial conditions. The only modification to the model is that we replace the hard cutoff by the smoothed transition Eq. ((<>)43). We employ the parameters obtained in the fit to the corresponding halo correlation functions in §(<>)V B. The data points in the plot are copied from Fig. (<>)7. Given the differences between the model and the correlation functions in Fig. (<>)5, there is a reasonably good agreement both in large scale amplitude and scale dependence of the stochasticity correction. We can conclude that while being a relatively crude fit to the correlation function, our model can account for the major effects, exclusion and non-linear clustering. The drawback is that this model lives in Lagrangian space and can not be straightforwardly applied to the halo power spectrum in Eulerian space. In Fig. (<>)15 we show the off-diagonal terms of the stochasticity matrix in the initial conditions and our corresponding model predictions. As for the diagonals discussed above, the corrections can be either positive or negative, depending ",
+    "FIG. 8. Left panel: Diagonals of the stochasticity matrix for one mass bin containing all the haloes in our simulation. Open points show the initial condition measurement, whereas the filled points show the final value. The horizontal thick solid line shows the fiducial shot noise 1/n¯ = 2680 h−1Mpc. The Eulerian bias is b(E) 1 = 1.49. On the largest scales there seems to be a cancellation between the exclusion and non-linear clustering contributions resulting in no net correction to the fiducial shot noise. Right panel: Same as left panel but for splitting our haloes into two mass bins with equal number density. The upper red points are the measurement for the lighter, lower bias bin b(E) 1 = 1.25 and the lower blue points are for the more massive, higher bias bin b(E) 1 = 1.74. The fiducial shot noise is 1/n¯ = 5362 h−1Mpc. Note that both mass bins show a significant scale dependence of the stochasticity. ",
+    "on whether exclusion or nonlinear clustering dominates The model predictions are in reasonable agreement with the measurements except for the highest mass bin. This failure is connected to the fact that the b2 parameter for the highest mass bin is imaginary, i.e., we have to set the second order bias term in the cross correlations to zero. This is a severe problem of our overly simplistic model, which is related to the importance of the peak effects for the correlation function of the highest mass bin (see App. (<>)A). ",
+    "Let us try to gain some more insight on where the stochasticity corrections arise in Lagrangian and Eulerian space. For this purpose we consider the configuration space version of the diagonal of the stochasticity matrix defined in Eq. ((<>)38) ",
+    "(45) ",
+    "The stochasticity level in the k → 0 limit is then given by ",
+    "(46) ",
+    "In Fig. (<>)9, we show the above integral as a function of the upper integration boundary where the full large scale stochasticity correction would be obtained by taking this boundary to infinity. Comparing the contributions in the initial conditions and the final configuration, we clearly see that the large scale stochasticity arises on different scales at the two times. We clearly see that the negative stochasticity corrections are dominated at much smaller scales in the final configuration as compared to the initial conditions. At these scales the halo-matter and matter-matter correlation functions are dominated by the one halo term, i.e., the halo profile, which complicates quantitative predictions of the exclusion effect in the final configuration and motivates our Lagrangian approach. "
+  ],
+  "V. EVALUATIONS AND COMPARISON TO SIMULATIONS ": [],
+  "A. The Simulations & Halo Sample ": [
+    "Our numerical results are based on the Z¨urich horizon zHORIZON simulations, a suite of 30 pure dissipationless dark matter simulations of the ΛCDM cosmology in which the matter density field is sampled by Np = 7503 dark matter particles. The box length of 1500 h−1Mpc, together with the WMAP3 [(<>)33] inspired cosmological parameters (Ωm = 0.25, ΩΛ = 0.75, ns = 1, σ8 = 0.8), then implies a particle mass of Mp = 5.55 × 1011 h−1M. The total simulation volume is V ≈ 100 h−3Gpc3 and enables precision studies of the clustering statistics on scales up to a few hundred comoving megaparsecs. ",
+    "The simulations were carried out on the ZBOX2 and ZBOX3 computer-clusters of the Institute for Theoretical Physics at the University of Zurich using the publicly available GADGET-II code [(<>)34]. The force softening length of the simulations used for this work was set to 60 h−1kpc, consequently limiting our considerations to larger scales. The transfer function at redshift zf = 0 was calculated using the CMBFAST code of [(<>)35] and then rescaled to the initial redshift zi = 49 using the linear growth factor. For each simulation, a realization of the power spectrum and the corresponding gravitational potential were calculated. Particles were then placed on a Cartesian grid of spacing Δx = 2 h−1Mpc and displaced according to a second order Lagrangian perturbation theory. The displacements and initial conditions were computed with the 2LPT code of [(<>)36], which leads to slightly non-Gaussian initial conditions. Gravitationally bound structures are identified at redshift zf = 0 using the B-FoF algorithm kindly provided by Volker Springel with a linking length of 0.2 mean inter-particle spacings. Haloes with less than 20 particles were rejected such that we resolve haloes with M > 1.2 × 1013 h−1M. The halo particles are then traced back to the initial conditions at zi = 49 and the corresponding centre of mass is identified. We split the halo sample into 10 equal number density bins with a number density of n¯ = 3.72 × 10−5h3Mpc−3 leading to a shot noise contribution to the power at the level of PSN ≈ 2.7 × 104 h−3Mpc3 . "
+  ],
+  "B. The Correlation Function in Lagrangian Space ": [
+    "The corrections to the halo power spectrum in our model are motivated by certain features in the halo-halo correlation function. While the fiducial stochasticity affects the correlation function only at the origin, the two other effects, exclusion and non-linear clustering, should be clearly visible in the correlation function at finite distances. For this purpose we measure the correlation function of the traced back haloes for our 10 halo mass bins using direct pair counting. ",
+    "In Fig. (<>)5 we show the correlation function for mass bin V. The log-linear plot clearly shows that the correlation function is −1 on small scales and shows a smooth transition to positive values around the exclusion scale visualized ",
+    "FIG. 6. Upper left panel: Exclusion radii measured in the initial and final halo-halo correlation functions. The exclusion radius is defined as a fixed fraction of the maximum in the halo-halo correlation function (see Fig. (<>)5). The red line shows the na¨ıve estimate of the exclusion radius R = (3M/4πρ¯)1/3 , whereas the blue line shows R = (3M/4πρ¯(1 + δ))1/3 with δ ≈ 30. This fitted overdensity is clearly distinct from the spherical collapse prediction of δ = 180. Lower left panel: Ratio of the initial and final exclusion radii. Right panel: Bias parameters fitted from the halo-matter cross power spectrum (b1), the halo-matter bispectrum and the correlation function (b2). Note that b2 fitted from the correlation function deviates strongly from the value predicted by the peak-background split (blue solid and dashed for positive and negative) and the value inferred from the bispectrum. The dash-dotted lines show a fit used for extrapolation purposes. ",
+    "by the vertical black line. The exclusion scale is fitted both in the initial and final conditions as 0.8 times the maximum in the correlation function and is shown in Fig. (<>)6. The ratio between the initial and final exclusion radii is roughly 3 for all mass bins. The spherical collapse model suggests that haloes collapse by a factor 5, but there is no reason to believe that protohaloes that are in direct contact in Lagrangian space are still touching each other in Eulerian space. Thus it is reasonable to expect a somewhat smaller reduction in the exclusion scale. On large scales 30 h−1Mpc < r < 90 h−1Mpc the correlation function is reasonably well described by linear bias shown in the Figure as a dot-dashed line. We infer the linear bias parameter from the ratio of halo-matter cross power spectrum and matter power spectrum on scales k < 1.5 × 10−2 hMpc−1 ",
+    "(41) ",
+    "See Fig. (<>)14 and App. (<>)A for why we have to restrict the linear bias fitting to large scales even in the initial conditions. The advantage of the cross power spectrum is that it should be free of stochasticity contributions and fully described by linear bias [(<>)37] on large scales. ",
+    "There is a clear enhancement of the data in Fig. (<>)5 compared to the linear bias model on small scales. Thus we consider the quadratic bias model ",
+    "(42) ",
+    "and fit for the quadratic bias parameter on scales exceeding the maximum. The resulting continuous correlation function is shown as the dashed line in Fig. (<>)5. It does not fully account for the enhanced clustering outside the exclusion scale. The inferred bias parameters are shown in Fig. (<>)6 and will be discussed in more detail below. Note that the above fit is performed using an un-smoothed version of the linear correlation function, whereas the local bias model relies on an explicit smoothing scale. Here, we argue that the smoothing scale for the local bias model should be related to the Lagrangian scale of the haloes and thus be smaller than the exclusion scale. In this case, the smoothing scale does typically not affect the scale dependence of the correlation function (except for around the BAO scale). ",
+    "In our above discussion we have assumed a sharp transition between the exclusion regime and the clustering regime. This is certainly unphysical as is obvious in Fig. (<>)5. The smoothness is probably caused by a number of phenomena, for instance mass variation within the mass bins (should be quite small < 1.3 h−1Mpc for the highest mass bin which has R ≈ 8 h−1Mpc and even smaller for the lower mass bins) or alignment of triaxial haloes. The lack of a physically ",
+    "motivated, working model for the transition forces us to employ a somewhat ad hoc functional form for the step, which is based on a lognormal distribution of halo distances (see App. (<>)C) ",
+    "(43) ",
+    "For alternative implementations of exclusion windows in the context of the halo model see [(<>)38, (<>)39]. The resulting shape of the correlation function is shown as the red solid line, where the smoothing was chosen to be σ ≈ 0.09 and seems to be quite independent of halo mass. The model clearly underestimates the peak in the data in the log-linear plot. Our final goal is to construct an accurate model for the effect of exclusion and non-linear clustering on the power spectrum. Thus, we should not only check the validity of our model on plots of the correlation function itself but also on the integrand in the Fourier integrals r3ξhh(r) d ln r. We do so in the right panel of Fig. (<>)5, where it is obvious that the model does not reproduce the exact shape of the correlation function outside of the exclusion scale. However, we certainly improved over the naive linear biasing on all scales and obtained a reasonable parametrization of exclusion and non-linear clustering effects. ",
+    "Let us now come back to the mass dependence of the inferred bias and exclusion parameters. As we show in Fig. (<>)6, the linear bias b1 is in very good agreement with the bias parameters inferred from a Sheth-Tormen mass function [(<>)40] rescaled to the initial conditions at zi = 49. For the second order bias we compare the measurement from the correlation function to measurements from the bispectrum of the protohaloes and the second order bias inferred from the Sheth-Tormen mass function. The latter agrees reasonably well with the bispectrum measurement reproducing the zero crossing in the theoretical bias function. Note that the bispectrum measurement (for details of the approach see [(<>)28]) uses only large scale information and is thus a clean probe for second order bias. Isolating second order bias effects in the correlation function is less straightforward. With decreasing scale higher and higher bias parameters become important, and to our knowledge there is no established scale down to which a certain order of bias can be trusted to a given precision. Our fitting procedure was led by the goal of obtaining a good parametrization of the correlation function, which could subsequently be used to calculate the corresponding power spectra and the corrections to the linear bias model. Note that due to the functional form of Eq. ((<>)42) this fitting approach allows inference of the magnitude of b2, but not its sign. The second order bias parameters obtained in this way deviate significantly from the theoretical bias function and the bispectrum measurement. The most severe failure of the model is the imaginary b2 for the highest mass bin. In this case the deviation is connected to corrections arising from the peak constraint, as we explain in App. (<>)A. We find that the initial Lagrangian second order bias parameter in Fig. (<>)6 can be roughly fitted as follows ",
+    "(44) ",
+    "We will use this fitting function for extrapolation in mass and redshift in §(<>)V D. The initial second order bias parameters for halo samples identified at higher redshifts (z = 0.5 and z = 1) are roughly the same as for the z = 0 halo sample. Although we will use this b2 fit to predict the resulting stochasticity corrections, we do not believe that the observed scale dependence of the correlation function is solely a second order bias effect. We checked an expansion of Eq. ((<>)42) to higher orders in the correlation function using peak-background split bias parameters. Even up to tenth order there is no considerable improvement in the fit. Thus we argue that the enhancement is a non-perturbative effect (e.g. peak bias) and consider the ξ2 scale dependence as a reasonably well working phenomenological parametrization rather than a physical truth. We hope to shed more light on this issue in a forthcoming paper. "
+  ],
+  "D. Redshift and Mass Dependence of the Correction ": [
+    "The subtraction of the fiducial 1/n¯ shot noise from the power spectrum will lead to a biased estimate of the continuous halo power spectrum. Thus, estimating the bias as ",
+    "(47) ",
+    "FIG. 9. Cumulative contributions to the stochasticity correction up to scale r (see Eq. (<>)46) in configuration space for our 10 mass bin sample. Open symbols show negative contributions and filled symbols positive contributions. Left panel: Initial conditions. Right panel: Final configuration at z = 0. We clearly see, that the corrections in the initial conditions are dominated on larger scales than in the final configuration, where the negative corrections are clearly in the one halo regime, where both the halo-matter and matter-matter correlation functions are highly non-linear. This gives further motivation for the modelling of the effect in Lagrangian space. The horizontal solid (dashed) lines show the positive (negative) stochasticity corrections inferred from Fig. (<>)7. ",
+    "FIG. 10. Left panel: Theoretical prediction for the diagonals of the stochasticity matrix for the ten mass bins. The parameters b2 and R are measured from the correlation function. The points are the coarsly binned simulation measurement taken from the left panel of Fig. (<>)7. Right panel: Bias correction as defined in Eq. ((<>)49). While there is clear scale dependence for weakly non-linear wavenumbers k > 0.1 hMpc−1 the correction is fairly flat on large scales, where the cosmic variance errors are largest. It could thus be easily interpreted as a higher or lower bias value. The points show the relative deviation of the bias inferred from the halo-halo power spectrum in the final configuration from the bias inferred from the halo-matter cross power spectrum. ",
+    "will lead to a flawed estimate of the bias. Indeed, it has been found in simulations that the biases estimated from the auto-and cross-power spectra are generally not in agreement [(<>)44, (<>)45]. Studying for instance Table I in [(<>)45] we see that ˆb1,hh exceeds ˆb1,hm for low mass haloes at redshift 0 indicating that the fiducial shot noise subtraction underestimates the true noise level. For high mass objects the opposite happens, the bias from the cross-power exceeds the bias from the auto power indicating that the employed 1/n¯ shot noise subtraction overestimates the true noise level. Let us try to understand this effect in more detail. Based on our model, subtraction of the fiducial shot noise on large ",
+    "scales leaves us with the linear bias term plus the stochasticity correction ",
+    "(48) ",
+    "where in absence of shot noise in the cross-power spectrum b1 = ˆb1,hm. Thus we have for systematic error on the linear bias parameter ",
+    "(49) ",
+    "Consequently the ratio ˆb1,hh/ˆb1,hm is a function of mass and redshift due to the mass and redshift dependence of the parameters of the model. We show the k-dependence of the bias correction in Fig. (<>)10. Since we don’t have a reliable model to relate the scale dependent stochasticity matrix from Lagrangian space to the one in Eulerian space we employ the scale dependent stochasticity model from Lagrangian space but divide by the present day linear power spectrum. This procedure should provide a reasonable estimate for the bias corrections on large scales. The linear bias is usually estimated close to the peak of the linear power spectrum, where it is approximately flat and where non-linear corrections are believed to be negligible. As a result, the bias correction is also fairly flat and would lead to a 1% overestimation of bias for low mass objects and a 3 − 4% underestimation for clusters. This behaviour can qualitatively explain the deviations found in [(<>)45]. ",
+    "In Fig. (<>)11 we show the amplitude of the low-k limit of the stochasticity correction for ten equal halo mass bins at redshifts z = 0, 0.5, 1. We overplot the theoretical expectation based on our model, linear bias parameters from the peak background split and second order bias parameters obtained from our phenomenological b2 relation in Eq. ((<>)44). In particular, we calculate the Lagrangian bias parameters and exclusion radii corresponding to the halo samples at z = 0, 0.5, 1 and use them to predict the stochasticity correction. As a general result we can see that there is a negative correction for high masses and a positive correction for low masses with a zero crossing scale that decreases with increasing redshift. The model captures the trends in the measurements relatively well. We are also overplotting the low-k amplitude of the SN for the one and two bin samples at z = 0 as the squares and diamonds. Besides the fact that these bins are much wider and thus have lower fiducial shot noise, the low-k amplitude is in accordance with the model and also narrower mass bins of the same mass. This fact supports our conjecture, that the stochasticity correction does not depend on the fiducial shot noise, but rather on mass (via the exclusion scale and the linear and non-linear bias parameters). The negative correction for high masses is dominated by the exclusion term, whose amplitude depends on the linear bias parameter and the exclusion scale. The latter is a function of mass but not a function of redshift, whereas the bias increases with redshift and thus the negative correction at high masses also increases with redshift. The positive correction at the low mass end depends on the second order bias parameter. In our fits to the correlation function we found that this parameter is roughly constant for the three different redshifts under consideration. "
+  ],
+  "E. Eigensystem and Combination of Mass Bins ": [
+    "The stochasticity matrix can be diagonalized as ",
+    "(50) ",
+    "where Vi(l) are the eigenvectors and λ(l) the corresponding eigenvalues. The eigenvector corresponding to a low eigenvalue can be used as a weighting function in order to construct a halo sample that has the lowest possible stochasticity contamination [(<>)4]. Furthermore, the eigenvalues allow for a clean separation of the exclusion and clustering contributions to the total noise correction. We show the measurement and comparison to our model in Fig. (<>)12. The data show pronounced low and high eigenvalues with most of the eigenvalues identical to the fiducial shot noise. The high eigenvalue is probably related to the non-linear clustering and the low eigenvalue to exclusion. The model also predicts eight of the ten eigenvalues to agree with the fiducial shot noise as well as one high and one low eigenvalue. The exact agreement is not perfect, which is probably due to an imperfect representation of the off-diagonal stochasticity terms. The main problem with the off-diagonals is to estimate the exclusion radii. The right panel of Fig. (<>)12 shows the eigenvectors corresponding to the eigenvalues. The eigenvector corresponding to the low eigenvalue is clearly connected to the mass, i.e., the exclusion volume, whereas the eigenvector corresponding to the high eigenvalue is clearly connected to the second order bias. ",
+    "FIG. 11. Dependence of the stochasticity correction on halo mass and redshift. The lines are based on linear bias parameters from the peak-background split and a fitting function modelling b2. The dashed lines and open points describe negative values. We also include the low-k limits of the one and two bin splitting as the diamond and squares, respectively. The dotted line shows the positive low mass correction arising from non-linear biasing whereas the dash-dotted blue, green and red lines show the negative high mass exclusion corrections for the three different redshifts. ",
+    "FIG. 12. Left panel: Eigenvalues of the stochasticity matrix for the traced back z = 0 haloes. The lines show our prediction based on the modelling of the initial correlation function whereas the points are based on the diagonalization of the measured stochasticity matrix of the traced back haloes. Right panel: Eigenvectors in the k → 0 limit. The black and red filled points show the measured eigenvectors for the lowest and highest eigenvalue in the initial conditions, whereas the open points show the respective prediction of our model. The blue line shows mass weighting, the red line b2-weighting and the magenta line shows the modified mass weighting proposed by [(<>)4]. ",
+    "So far we have concentrated on the stochasticity correction for narrow mass bins and quantified them in terms of the corresponding stochasticity matrix. If all the corrections were linear in the parameters of the model, all we needed to do is to calculate the corresponding mean parameters of the sample and use them to calculate the stochasticity correction for the combined sample. However, the corrections are in general a non-linear function of the parameters. The wider the mass bins the less exact is a bulk description by a set of mean parameters. It should be more exact to consider subbins and combine them. Thus we need to calculate the stochasticity correction for narrow mass bins Then, when considering samples that span a wide range of halo masses or realistic galaxy samples, we need to weight the prediction for the stochasticity correction accordingly. The weighted density field is then ",
+    "(51) ",
+    "FIG. 13. Stochasticity of an HOD implementation of a Luminous Red Galaxy sample. We split the sample into the central-central (cyan), satellite-satellite (green) and central-satellite (black) contributions. The constituent stochasticity levels are weighted according to their contribution to the full galaxy power spectrum (see Eq. (<>)24). The horizontal thick lines show the correspondingly weighted fiducial stochasticity. Left panel: Halo occupation distribution model with a satellite fraction of fs = 4.9% ([(<>)46, (<>)47]). Right panel: Same as left panel, but for a satellite fraction of fs = 8.5%. ",
+    "and the corresponding noise level of the combined sample is given by ",
+    "(52) ",
+    "For halo samples the weighting is given by the mean number density in a mass bin ",
+    "(53) ",
+    "A similar weighting scheme can be derived for galaxies for the two-halo term in the context of the halo model. "
+  ],
+  "F. A realistic Galaxy Sample ": [
+    "Let us now see how the stochasticity matrix behaves for a realistic galaxy sample. In Halo Occupation Distribution (HOD) models [(<>)48, (<>)49] the occupation number Ng(M) is usually split into a central and a satellite component Ng = Nc + Ns. In Fig. (<>)13 we show the stochasticity of the Luminous Red Galaxy (LRG) sample described in [(<>)46, (<>)47]. The total number density of the LRGs is n¯ g = 7.97 × 10−5 h−3Mpc3 corresponding to a fiducial shot noise of 1/n¯ g ≈ 1.25 × 104 h−3Mpc3 . The effective stochasticity level for the full sample is SNeff = 1.09 × 104 h−3Mpc3 , corresponding to a correction of ΔPgg = −1.8 × 103 h−3Mpc3 . The satellite fraction of the galaxy sample is 4.9%. Let us try to understand the total correction based on the constituent central, satellite and central-satellite cross-power spectra. The sum of these three components weighted according to Eq. ((<>)24) agrees with the measured stochasticity of the full sample. The central-central power spectrum dominates the negative stochasticity correction on large scales with a weighted correction of (1 − fs)2ΔPcc = −2100 h−3Mpc3 The satellite-satellite power spectrum has a positive one halo contribution on large scales that contributes a weighted correction of fs2ΔPss = +570 h−3Mpc3 The central-satellite cross power spectrum changes sign but contributes about ΔPcs = −370 h−3Mpc3 at k = 0.03 hMpc−1 . The amplitude of these corrections could in principle be understood based on a accurate model for the stochasticity correction of the host haloes and the halo model. In this context the corrections are given as [(<>)14, (<>)15] ",
+    "(54) ",
+    "(55) ",
+    "(56) ",
+    "(57) ",
+    "(58) ",
+    "(59) ",
+    "On large scales we have u(k|M) → 1. Furthermore the halo-halo power spectra can be again split into a linear bias part b(M)b(M)P(k) and a correction term accounting for the discreteness of the host haloes. For the central galaxy sample our model yields a correction of ΔPcc ≈ −1000 h−3Mpc3 . More accurate predictions would require a better model of the stochasticity corrections, which in turn requires a better model of exclusion and non-linear biasing. We also consider a slightly modified galaxy sample with a larger satellite fraction fs = 8.47%. For this purpose we create a copy of each satellite galaxy at twice its separation from the host halo centre. The resulting stochasticity properties are shown in the right panel of Fig. (<>)13. In contrast to the previous case the actual stochasticity now exceeds the fiducial shot noise due to the strong positive contribution of the satellite-satellite one halo term. "
+  ],
+  "VI. CONCLUSIONS ": [
+    "In this paper we discuss effects of the discreteness and non-linear clustering of haloes on their stochasticity in the power spectrum. The standard model for stochasticity is the Poisson shot noise model with stochasticity given as the inverse of the number density of galaxies, 1/n¯. Motivated by the results in [(<>)4], we study the distribution of haloes in Lagrangian space and estimate the effect of exclusion and non-linear clustering of protohaloes on the stochasticity. These induce corrections relative to 1/n¯ in the low-k limit. Exclusion lowers and non-linear clustering enhances the large scale stochasticity. The total value of the large scale stochasticity depends on which of the two effects is stronger but the amplitude of the correction does not directly depend on the abundance of the sample. These stochasticity corrections must decay to zero for high-k, implying they are scale dependent in the intermediate regime. The transition scale is related to either the exclusion scale of the halo sample under consideration or to the non-linear clustering scale. At the final time (Eulerian space) these transition scales shrink due to the non-linear collapse, but the low-k amplitude of the stochasticity agrees with Lagrangian space, as expected from mass and momentum conservation. ",
+    "While the presented model can explain the observed trend of modified stochasticity at a qualitative level, the quantitative agreement is not perfect. This is related to our imperfect modelling of the Lagrangian halo correlation function with a local bias ansatz. A more realistic modelling might be possible in the full framework of peak biasing in three dimensions, as the one dimensional results in §(<>)III E indicate. ",
+    "We also discuss the effects of satellite galaxies, when a galaxy sample with a non-vanishing satellite fraction is considered. In this case the stochasticity can dramatically deviate from the auxiliary 1/n¯ value on large scales. In this case one has to identify the number density of host haloes to infer the stochasticity on large scales and account for the fact that on scales below the typical scale of the satellite profile there is a transition to the fiducial Poisson shot noise of the galaxy sample. ",
+    "Finally, we consider the stochasticity matrix of haloes of different mass. We show that diagoalization of this matrix gives rise to one eigenvaue with a low amplitude, with the eigenvector that aproximately scales with the halo mass. This provides an explanation to the stochasticity suppression with mass weighting explored in [(<>)3, (<>)4]. It would be interesting to explore, how the stochasticity corrections imprint themselves in the halo bispectrum, which is a promising probe of inflationary physics [(<>)50] and whose measurement becomes realistic in present and upcoming surveys [(<>)51]. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "The authors would like to thank Niayesh Afshordi, Kwan Chuen Chan, Donghui Jeong, Patrick McDonald, Teppei Okumura, Fabian Schmidt, Ravi Sheth, Zvonimir Vlah and Jaiyul Yoo for useful discussions. The simulations were carried out on the ZBOX3 supercomputer at the Institute for Theoretical Physics of the University of Zurich. This work is supported in part by NASA ATP Grant number NNX12AG71G, Swiss National Foundation (SNF) under contract 200021-116696/1, WCU grant R32-10130, National Science Foundation Grant No. 1066293. T.B. acknowledges the hospitality of the Aspen Center for Physics. "
+  ]
+}

jsons_folder/2013arXiv1308.6569C.json

@@ -0,0 +1,164 @@
+{
+  "MAGNIFICATION BIAS IN GRAVITATIONAL ARC STATISTICS ": [
+    "G. B. Caminha ",
+    "Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil ",
+    "J. Estrada ",
+    "Fermi National Accelerator Laboratory, Batavia, Illinois, USA ",
+    "and ",
+    "M. Makler ",
+    "Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil ",
+    "Draft version September 17, 2013 "
+  ],
+  "ABSTRACT ": [
+    "The statistics of gravitational arcs in galaxy clusters is a powerful probe of cluster structure and may provide complementary cosmological constraints. Despite recent progresses, discrepancies still remain among modelling and observations of arc abundance, specially regarding the redshift distribution of strong lensing clusters. Besides, fast “semi-analytic” methods still have to incorporate the success obtained with simulations. In this paper we discuss the contribution of the magnification in gravitational arc statistics. Although lensing conserves surface brightness, the magnification increases the signal-to-noise ratio of the arcs, enhancing their detectability. We present an approach to include this and other observational effects in semi-analytic calculations for arc statistics. The cross section for arc formation (σ) is computed through a semi-analytic method based on the ratio of the eigenvalues of the magnification tensor. Using this approach we obtained the scaling of σ with respect to the mag-nification, and other parameters, allowing for a fast computation of the cross section. We apply this method to evaluate the expected number of arcs per cluster using an elliptical Navarro–Frenk–White matter distribution. We include the effect of magnification using two methods: by considering the magnification dependent arc cross section and by assuming that all sources in the arc forming region are magnified by the same amount. We show that both methods are in excellent agreement and it is thus sufficient to consider the effect of the mean magnification in arc statistics. Our results show that the magnification has a strong effect on the arc abundance, enhancing the fraction of arcs, moving the peak of the arc fraction to higher redshifts, and softening its decrease at high redshifts. We argue that the effect of magnification should be included in arc statistics modelling and that it could help to reconcile arcs statistics predictions with the observational data. ",
+    "Subject headings: gravitational lensing: strong, galaxies: clusters: general, dark matter, cosmological parameters "
+  ],
+  "1. INTRODUCTION ": [
+    "Gravitational arcs are highly distorted images of background galaxies (sources) due to the gravitational field of a foreground object (lens), usually a galaxy or cluster of galaxies. After the discovery of the first gravitational arcs (Lynds & Petrosian 1986; Soucail et al. 1987), it was soon realized that the statistics of arcs in galaxy clusters could provide powerful probes of both cluster structure (see, e.g., Wu & Hammer 1993; Bartelmann & Weiss 1994; Hattori, Watanabe, & Yamashita 1997; Oguri, Lee, & Suto 2003) and cosmology (see, e.g., Grossman & Saha 1994; Wu & Mao 1996; Bartelmann et al. 1998; Zieser & Bartelmann 2012). For a complete review on arc statistics, see Meneghetti et al. (2013). ",
+    "With this in mind, several arc searches were undertaken, both in imaging surveys (Gladders et al. 2003; Cabanaˇc, et al. 2007; Estrada et al. 2007; Faure et al. 2008; Belokurov et al. 2009; Kubo et al. 2010; Gilbank et al. 2011; More et al. 2012; Wen et al. 2011; Bayliss 2012; Wiesner et al. 2012; Pawase et al. 2012; Erben et al. 2013, More et al., in prep, Caminha et al., in prep.), as well as in fields targeting X-ray and optical clusters, with observations from the ground (Luppino et al. 1999; Zaritsky & Gonzalez 2003; Campusano et al. 2006; Hennawi et al. 2008; Kausch et al. 2010; Furlanetto et al. 2013b) and from space (Ebeling, Edge, & Henry 2001; Smith et al. 2005; Sand et al. 2005; Horesh et al. 2010; Okabe et al. 2013). With these surveys, the homogeneous samples of arcs are reaching the order of hundreds of objects.1 In the near future, the next generation wide-field surveys such as the Dark Energy Survey 2 (DES; The Dark Energy Survey Collaboration 2005; Annis, et al. 2005; Ngeow, et al. 2006, Lahav et al., in preparation, Frieman et al., in preparation), which started its first observing season this year, are expected to lead to the discovery of thousands of gravitational arcs. ",
+    "In parallel to the growing size of arc samples, the theoretical modelling of arc statistics has also experienced significant improvements. The earliest predictions for arc abundance used idealised lenses (from axially symmetric singular isothermal models to halos from low resolution pure CDM simulations) and sources (constant surface brightness sources distributed in a single plane) and strongly underestimated the number of arcs in the now standard ΛCDM cosmology with respect to observational data (see, e.g., Wu & Hammer 1993; Wu & Mao 1996; Bartelmann et al. 1998). Several degrees of realism were added subsequently, investigating the role of each in arc statistics. For example, on the lens side, the effects of cluster ellipticity, asymmetries, and substructures (e.g., Hennawi, Dalal, Bode, & Ostriker 2007; Meneghetti et al. 2007), triaxiality (Oguri, Lee, & Suto 2003; Dalal, Holder, & Hennawi 2004; Meneghetti et al. 2010), and mergers (Torri et al. 2004; Fedeli et al. 2006; Hennawi, Dalal, Bode, & Ostriker 2007; Redlich et al. 2012) were investigated. The effects of baryonic processes of cooling (Puchwein et al. 2005; Rozo, Nagai, Keeton, & Kravtsov 2006; Wambsganss, Ostriker & Bode 2008), star formation rate, and AGN feedback (Mead et al. 2010; Killedar et al. 2012) on the cluster structure, as well as the contribution of cluster galaxies (Flores, Maller & Primack 2000; Meneghetti et al. 2000) to the cluster lensing potential were taken into account. The contribution of structures along the line of sight (Hilbert, White, Hartlap, & Schneider 2007; Puchwein & Hilbert 2009) was also addressed. On the sources side, the impact of their size and ellipticity was investigated (e.g., Oguri 2002), including the effect of arc formation by the merging of multiple images (Rozo, Nagai, Keeton, & Kravtsov 2006). The impact of the redshift distribution of sources was also considered (Wambsganss, Bode, Ostriker 2004; Dalal, Holder, & Hennawi 2004; Li et al. 2005). ",
+    "The inclusion of the effects above helped to shed light on their contribution on arc statistics. Most of them increase the arc incidence up to factors of a few and their inclusion has reduced the overall discrepancy between observed and predicted arc abundances (e.g., Dalal, Holder, & Hennawi 2004; Horesh et al. 2005; Hennawi, Dalal, Bode, & Ostriker 2007). One of the key factors to reduce this discrepancy was the inclusion of realistic source distributions in the theoretical predictions (Horesh et al. 2005; Wu & Chiueh 2006; Hennawi, Dalal, Bode, & Ostriker 2007). Another key progress was the development of simulations at the image level (Meneghetti et al. 2008; Horesh et al. 2011; Boldrin et al. 2012), which led to the inclusion of new levels of realism, such as sources with surface brightness variations and noise, and allowed for a more direct comparison with the observations, including the use of the same tools for arc detection. The study of selection biases also contributed to a more accurate comparison between simulated and real data (Meneghetti et al. 2010). Overall, these developments have, if not solved, at least mitigated the longstanding arc statistics problem (Meneghetti et al. 2011). ",
+    "If on one hand the simulations are generally beginning to broadly agree with the observational data, on the other hand several open issues remain, among which the variation of arc abundance with respect to the cluster redshift. For example, Gladders et al. (2003) found an over-abundance of arcs in high-redshift clusters as compared to lower redshift ones in the Red Sequence Cluster Survey (RCS). In particular, they found no arcs in clusters at z  0.6. However, theoretical investigations did not predict such an enhanced incidence of arcs at high z. For example, Hennawi, Dalal, Bode, & Ostriker (2007) found no increase in arc abundance at the redshift implied by RCS. Gonzalez et al. (2012) found arcs in a cluster at z = 1.75, which should not be present at their image depths according to their modelling. ",
+    "Up to the present, most of the focus of theoretical studies in this field — from idealized analytical treatments to fully numerical ray tracing methods in simulated mass distributions — has been on the modelling of the lens potential and on gravitational lensing aspects of arc formation in general. However, observational effects such as finite PSF size and the noise present in real images play a fundamental role in arc detection. An important progress to include these effects was undertaken by Horesh et al. (2005), who added noise (sky and detector backgrounds, Poisson noise, and readout noise), PSF, and light from cluster galaxies to the arc simulations (see also Meneghetti et al. 2005, 2008; ",
+    "Horesh et al. 2011; Boldrin et al. 2012). However, the full image simulation process, including the generation of clusters in N-body/hydrodynamical simulations, the computation of deflection angles, the association of images to sources, and the addition of observational effects; together with the detection of arcs in the simulated images, can be extremely expensive in terms of computational time. ",
+    "An alternative to this “fully numerical” treatment is to use semi-analytical approaches, which can incorporate, to a certain degree, some of the features of the realistic modelling described above. For example, analytic density profiles can be used instead of N-body simulations, local prescriptions to define the formation of arcs instead of finding images of finite sources, etc. Although this approach is expected to be less accurate, it is useful to investigate the qualitative behavior of the arc abundance with respect to several variables. It can also provide a valuable insight to isolate the key factors that contribute to the modelling of arc abundance, being helpful for interpreting and understanding the outcome of simulations. Furthermore, if calibrated with realistic simulations, the semi-analytic modelling may provide fitting formulae for fast parameter estimation (e.g., to obtain cluster parameters from arc statistics) and for producing forecasts. ",
+    "In this paper, we use a semi-analytic approach to compute the expected number of arcs per cluster as a function of cluster redshift, mass, and ellipticity. We discuss how to include some observational effects and, in particular, we take into account, for the first time in this approach, the effect of the noise in the images. The signal-to-noise ratio (S/N) of the arc images is enhanced by the magnification, effectively changing the limiting magnitude of the image in the region of arc formation, enhancing the efficiency of arc detection. This results in a kind of magnification bias and leads us to include this quantity in the arc abundance modelling. ",
+    "We obtain scaling relations that allow for a fast computation of the cross section for arc formation, taking into account its variation with respect to magnification. We apply this method to an elliptical Navarro–Frenk–White matter distribution in clusters and compute the number of arcs per cluster considering a realistic redshift distribution of sources, which is effectively modified due to the effect of the magnification. ",
+    "The paper is organized as follows. In the next section we present the semi-analytic modelling for the arc fraction in clusters. In section 3 we discuss the importance of the signal-to-noise ratio for arc detection and how to incorporate the effect of S/N enhancement through the magnification in gravitational arc statistics. In section 4 we review the semi-analytic computation of the arc cross section and the lens model that will be used. In section 5 we obtain the scaling of the cross section with respect to the magnification, which is needed to take the noise into account in the modelling. Finally, in section 6 we apply these results to compute the expected number of arcs per cluster — showing the importance of magnification — and discuss its evolution with respect to the cluster redshift. We summarize our results and present some concluding remarks in section 7. In the Appendix we derive useful expressions for the lensing quantities of elliptical lens models for any parameterisation of the ellipticity. "
+  ],
+  "2. SEMI-ANALYTICAL MODELLING FOR ARC ABUNDANCE: INCLUDING OBSERVATIONAL EFFECTS ": [
+    "Our aim is to compute the average number of arcs per cluster farcs, for clusters with given properties, such as mass and ellipticity (see, e.g., Cypriano et al. 2001; Hattori, Watanabe, & Yamashita 1997; Oguri, Lee, & Suto 2003; Horesh et al. 2005, for other works using this same statistical measure). For a sample of clusters selected with uniform criteria, for example a given richness and redshift interval, this fraction is easily calculated as farcs = Narc/Ncluster, where Ncluster is the number of clusters in the sample and Narcs is the total number of arcs found in this sample. While many studies on arc statistics have focused on predictions for the total number of arcs, this quantity is not very suitable to probe properties associated with gravitational lensing (such as lens mass profiles or cosmological distances), since it is extremely sensitive to the cosmological parameters in a way not related to lensing at all. More specifically, the total number of arcs depends on cluster abundance, which is in turn very sensitive to σ8 and the growth factor. Some inconsistencies among arc abundance predictions were due to the different choices of the cosmological parameters, rather than the modelling of the lensing aspects of the problem (see, e.g., Li et al. 2005). By focusing on farcs we may decouple the generation of arcs from cluster abundance, minimizing the explicit dependence on cosmology. Moreover, this statistic is also well suited for targeted surveys, were a sample of clusters is selected to be observed with better imaging to search for arcs. Finally, the fraction of arcs is less dependent on the cluster selection function than the total arc number (of course, as long as the selection is not based on the presence of arcs). A careful selection of the clusters for this statistic could also mitigate the selection biases (Meneghetti et al. 2010). ",
+    "A direct method to evaluate the expected number of arcs per cluster is to perform simulations where a given mass distribution is used to lens objects from a real astronomical image. The resulting images of these sources are identified as arcs, according to their properties. As mentioned in section 1, the source redshift distribution must be taken into account in computing the arc abundance. For this sake, redshifts can be associated to each source in the image, as in Horesh et al. (2005). A similar approach is to lens sources distributed in multiple planes (Hennawi, Dalal, Bode, & Ostriker 2007). Another possibility, which we refer to as “semi-analytic modelling for arc abundance”, consists in computing the cross section for arc formation σ for a given cluster (i.e., the effective area in the source plane where a source gives rise to an arc in the lens plane) as a function of source redshift zS and convolving it with the source surface number density ΣS as a function of zS . ",
+    "The cross section is generally defined in terms of a given set of parameters of a lensed object. For example, a standard criterium, which we shall apply in this work, is to use the length-to-width ratio (R := L/W ) of the images. Whenever this ratio is above a given threshold (Rth) the image is said to form an arc. Other parameters that are relevant for detection include the magnitude and, possibly, the curvature. Naturally, σ is a function of the lens properties, such as mass M, ellipticity e, slope of the density profile γ, and characteristic radius rs, and also depends on the lens and ",
+    "source redshifts, zL and zS, through the cosmological distances. It may also depend on source properties, such as ellipticity eS and angular size θS. Therefore, we may write the cross section as σ = σ (ΠL, zL; ΠS, zS; QP ), where ΠL is a set of cluster properties (M, rs, γ, e, etc.), ΠS is a set of source properties (θS , eS ), and QP is a set of arc properties (L/W , S/N, µ, etc.).3 ",
+    "Besides its dependence on zS, the source distribution ΣS is a function of θS , eS , and magnitude m. In principle, ΣS (zS, ΠS) can be estimated from deep space-based surveys, such as the COSMOS field4 (see, e.g., Scoville 2007). If we do not take into account the source sizes and ellipticies, ΣS can be estimated from ground based observations. ",
+    "A third key ingredient is related to the observational effects, which transform the “proper” arc parameters QP , that would be measured in noise free images without PSF effects, into their observed ones QO. For example, the seeing will change the width of the arcs in a way that can be modelled approximately by WO = WP2 + σs2 , where σs is the seeing FWHM. These effects are encoded in the “transfer” function T (QP |QO). ",
+    "The final important ingredient in the arc fraction calculation is the detection efficiency, which depends only on the observed arc properties QO (i.e., of the objects identified in real images, which are PSF convolved and include all sources of noise) in a given survey. Usually it is assumed that all arcs with observed (L/W )O and peak surface brightness above some threshold will be detected in a given image. However, in realistic arc finding methods the efficiency is a more complicated function of these quantities. The efficiency P (QO) can be determined, for each survey, using image simulations containing fake arcs, as in Estrada et al. (2007) (see also Horesh et al. 2005; Furlanetto et al. 2013a). ",
+    "Taking into account the above aspects, we may express the arc fraction for clusters with properties ΠL as ",
+    ". ",
+    "(1) ",
+    "In practical applications this expression can be simplified. For example, we shall see in section 4 that a scaling of σ with zL, and zS can be taken into account analytically. Besides, in section 5 we obtain a good approximation for the scaling of the cross section with an arc parameter QP (in this case, the magnification µ). Finally, in our modelling of section 6, σ will be independent of ΠS . Therefore, the number of degrees of freedom in equation 1 can be substantially reduced, and some of the remaining ones can be included in an analytic form. Furthermore, in many cases we may explicitly write QP in terms of QO (as the relation among WP and WQ discussed above), instead of using T (QP |QO). ",
+    "The formalism described above allows us to take into account some observational effects together with the detection efficiency, which are usually considered only in full image simulations. A useful aspect of this approach is that it naturally separates the problem into various components, enabling investigations on the influence of each part in the arc statistics predictions. ",
+    "In this work we shall discuss the effects of the signal-to-noise ratio in the images, which leads us to consider the role of the magnification in the computation of the arc fraction in clusters. "
+  ],
+  "3. THE ROLE OF MAGNIFICATION ": [
+    "Since gravitational lensing conserves surface brightness, it is commonly assumed that the magnification is not important for the detection of extended objects such as arcs. This would indeed be true if no noise was present in the images. However, in a real astronomical situation the total flux may have an important role in the detection, due to the signal-to-noise ratio of the arcs. In fact, arcs will not be identified by their peak surface brightness, but rather by the coherence of the signal produced by that object compared to the noise in the image. Therefore, the signal-to-noise ratio (S/N) must play an important role in arc detection. ",
+    "Here we assume that the dominant sources of noise are Poisson noise from the background and from the object counts. The signal is simply given by the total flux of the object (counts) and the noise is the integrated noise on the object from the Poisson noise of the background and the object. For an object with surface brightness F and occupying the area A in an image whose background has a surface brightness b, this ratio is ",
+    "(2) ",
+    "The gravitational lensing effect changes only the image area, with the new area being Alensed = µ × A, where µ is the magnification. Taking this into account, the lensed object has ",
+    "(3) ",
+    "The enhancement of the signal-to-noise of the lensed objects will lead to an increase of the effective depth of the image in the magnified regions, which will be translated into an effective change of the distribution of sources that can be mapped into arcs. Let us assume that the objects in an image are identified and selected in terms of their S/N (e.g.,√imposing a cut of 5σ above noise for detection). In this case, the effective flux limit will decrease by a factor of 1/ µ (c.f. Eq. 3) in comparison to a non-lensed region, due to the effect of magnification. In other words, the effective limiting magnitude will be given by ",
+    "(4) ",
+    "To include this effect in gravitational arc statistics, we use the formalism of section 2. The arc detection efficiency P (QO), which will be a function of the arc S/N, is connected to the source distribution in an intricate way through Eq. (1). The cross section will depend on arc and source properties and the transfer function will map the intrinsic to observed arc properties. Here we will make a few simplifying assumptions as a first approach to the problem. First, we assume that the total signal-to-noise and the length-to-width ratios are the dominant factors to determine the detectability of the arcs. We will further assume that the sensitivity to these quantities is uncorrelated and that all arcs with L/W above a given threshold Rth and with S/N above a threshold (S/N)th can be detected. In other words, the selection function will be given by ",
+    "(5) ",
+    "where θ(x) is the step function. In reality the situation is a bit more complicated since other factors, such as curvature and surface brightness, may impact the detection efficiency and also the sensitivity to S/N and L/W may be correlated. Furthermore, in realistic situations the selection function P (QO) will be dependent on the arc finding method. Here we assume that the object pixels are selected as part of the object identification or arc finding methods. This can be achieved, for example, by requiring a low significance for each object pixel with respect to the background. The S/N is then computed taking into account all object pixels and a higher significance is required for the object to be selected as an arc (provided that the L/W restriction is met). As for the hard cut in L/W in Eq. (5), this is implicitly assumed in most arc statistics calculations. In any case, the novel aspect that we shall address in this work is the dependency on S/N, which will be shown to have a large impact on the arc abundance predictions. ",
+    "We shall also neglect for now the explicit dependence of the arc L/W and S/N on the image PSF, such that the transfer function is given simply by ",
+    "(6) ",
+    "where δ is the Dirac delta function, and the quantities with O refer to the observed ones and those with P correspond to what would be measured without the effects of the PSF (but same instrument and other observing conditions). ",
+    "A third ingredient in the arc abundance calculation is the source distribution. In this paper we will neglect any dependence of the cross section on the properties of finite sources, such as size and ellipticity (see Sect. 4). Therefore, we only need to consider its dependence on redshift and source S/N, i.e. ΣS (zS, (S/N)source). The condition (6) implies that we need to consider all arcs with S/N above a given threshold. This will imply that all sources above a certain S/N (as would be seen in the same observing conditions, but no lensing) may give rise to arcs and the connection  √ among these thresholds is given by equation (3). In other words, we need to consider ΣS zS, > (S/N)th/ µ . Here we are of course assuming the same observing conditions for the determination of the source density and the arcs, such that we can use Eq. (3). In practice we only need to know how ΣS(zS) scales in terms of an S/N threshold. Usually the source distribution determined from imaging surveys is expressed in terms of zS and a limiting magnitude mlim (as long as mlim is well below the detection limit of the images), not a S/N threshold. However, this limiting magnitude is dependent on the threshold. We mimic this effect following Eq. (4). Therefore, after integrating on the arc properties QO in Eq. (1) and applying the selection function (6), we only need to consider the surface density of sources per unit redshift, for a given limiting magnitude, An explicit form for this function will be used in Sect. 6. ",
+    "Finally, we need to consider the cross section and its dependence on source and arc properties. As mentioned above, for simplicity we will not consider the effect of finite sources. Besides, the cross section will not depend on S/N. The only dependence on the arc parameters will be on L/W and µ. Also, as in the case of the integral over (S/N)O, the integral over (L/W )O will lead to a threshold in (L/W )P , Rth. Thus we only need to compute the cross section for (L/W ) > Rth, which we will refer to as σ (ΠL, zL; zS; µ, Rth). ",
+    "Inserting all these ingredients in Eq. (1) and integrating over the arc parameters µ, (L/W )O, and (S/N)O we finally obtain the expression for the arc fraction including the effect of magnification ",
+    "(7) ",
+    "In the next section we discuss the computation of the cross section, and in particular the inclusion of its explicit dependence on the magnification, employing a semi-analytic approach. "
+  ],
+  "4. SEMI-ANALYTICAL CROSS SECTION ": [
+    "To compute the cross section for the production of arcs, a simple approach is to resort to the local mapping given by the magnification tensor, which determines the distortion of infinitesimal sources. For this sake, we evaluate the two eigenvalues of the magnification tensor to determine the region in the image plane in which their ratio exceeds a certain threshold Rth. It is in this region that arcs with L/W exceeding Rth are expected to be formed. ",
+    "The magnification eigenvalues are given by ",
+    "(8) ",
+    "where the convergence κ and the shear strength, γ = γ12 + γ22 , can be obtained from the derivatives of the lens potential Ψ: ",
+    "(9) ",
+    "where the subindices 1 and 2 refer to derivatives with respect to θ1 and θ2 respectively and Ψ = 2ψ DLS/(DOSDOL), where ψ is the projected gravitational potential of the lens, DOS denotes the angular diameter distance from the observer to the source, DOL that from the observer to the lens, and DLS that from the lens to the source 5 (see, e.g., Schneider, Ehlers, & Falco 1992; Mollerach & Roulet 2002). ",
+    "Usually, µt corresponds to a deformation approximately in the tangential direction, while µr corresponds to the deformation along the radial direction. Therefore tangential arcs are expected to be formed in regions where R := |µt/µr| ≫ 1. For infinitesimal circular sources, the length to width ratio (L/W ) of tangentially distorted images will be approximately given by the local deformation R (Hattori, Watanabe, & Yamashita 1997; Hamana & Futamase 1997). Arcs are usually defined as objects with axial ratio above a given threshold L/W > Rth (a typical value considered is Rth = 10) and, according to the approximation discussed above, they will be produced in a region ΩL around the lens for which the local eigenvalue ratio satisfies the condition R > Rth. ",
+    "This region in the image plane is mapped through the lens equation into a region in the source plane. The cross section for arc production σ (which we will refer to as deformation cross section) will be given by the corresponding solid angle in the source plane. Since the solid angles in the image and source planes are related by dΩS = dΩL/|µ(θ)| (where |µ| = |µt × µr| is the magnification) we hence have (see, e.g., Blandford & Narayan 1986; Fedeli et al. 2006; D´umet-Montoya et al. 2012) ",
+    "(10) ",
+    "Notice that, through this procedure, two points in the lens plane with R > Rth that are mapped into the same point in the source plane are accounted for twice in the computation of σ. This is the appropriate definition for computing farcs since this region in the source plane will give rise to two arcs. Hence σ is an effective area in the source plane, already accounting for the multiplicity of the images. ",
+    "Throughout this work we model the lenses by an elliptical Navarro, Frenk, & White (1996, 1997, hereafter NFW) mass distribution, whose radial (i.e. angle averaged) profile is given by ",
+    "(11) ",
+    "where the parameters rs and ρs can be expressed in terms of the mass M200 and the concentration parameter c (see Sect. 6). ",
+    "The lensing properties may be obtained from the projected mass distribution, which in the case of the NFW profile is determined by two parameters (see, e.g., Bartelmann 1996): rs and ",
+    "(12) ",
+    "where Σcr = DOS/(4πGDOLDLS). ",
+    "An elliptical surface density distribution can be obtained from the projected z2)dz (Bartelmann 1996) by replacing the radial coordinate ξ by ",
+    "(13) ",
+    "where the parameter e denotes the ellipticity. With this choice, the projected mass contained inside contours of constant ξ is independent of e. The relevant quantities for the lensing mapping can be expressed in terms of integrals, which are given in the Appendix. ",
+    "Since the lens equation can be written in terms of an arbitrary length scale (see, e.g., Schneider, Ehlers, & Falco 1992), we may work with all distances in units of rs and eliminate this quantity from the analysis, such that the (rescaled) cross section σ˜ becomes a function of κs and e only (for a given L/W threshold). The cross section in steradians is then given by6 (D´umet-Montoya et al. 2012) ",
+    "(14) ",
+    "This already simplifies the calculation of the cross section by eliminating one degree of freedom from the problem (see, e.g., Oguri 2002; Oguri, Lee, & Suto 2003; Fedeli et al. 2006, for similar transformations). We will refer to σ˜ as the dimensionless cross section. To recover the cosmological and mass dependence of the parameters, one has to write κs and rs in terms of the NFW model parameters M200 and c, and the cosmological distances (see Sect. 6). ",
+    "A similar procedure as the one described above for computing the arc cross section is often used for computing the magnification cross section for point-like sources (although, of course, the integration domain is defined by the constraint µ > µth, rather than R > Rth). For finite-size objects such as arcs, the validity of this method has to be checked. Indeed, due to the extended nature of the images, variations of the local eigenvalue ratio throughout the sources may be important. Source ellipticity will break the direct relation between L/W and R. Moreover, it is well ",
+    "Fig. 1.— Dependence of the cross section with κs. A steep reduction in σ˜(κs) is seen for low values of κs. ",
+    "known that arcs can be formed as the result of the merging of multiple images. The criterium based on the local eigenvalue ratio can only take into account arcs generated through the high distortion of single images, produced when sources are close to any caustic, but not those formed by image merging (Rozo, Nagai, Keeton, & Kravtsov 2006). Some of these finite source effects can be accounted for in the semi-analytic computation of the cross section. For example Fedeli et al. (2006) introduce a method to include the gradients of R across the source. Keeton (2001c) proposed an approximation to obtain L/W from the magnification eigenvalues considering source ellipticity and orientation. ",
+    "Any detailed prediction of arc abundance should take into account these effects. Nevertheless, it has been show that including finite size and source ellipticity does not change the cross section by large factors (Hattori, Watanabe, & Yamashita 1997; Bartelmann et al. 1998; Oguri 2002; Fedeli et al. 2006) and their impact is considerably smaller than lens ellipticity, for example (Oguri 2002). Li et al. (2005) made a comparison of the cross section of lensing clusters with randomly oriented elliptical sources of fixed area. They found that the cross section derived from |µt/µr| agrees within ∼ 30% with the ray-tracing simulations for Rth = 10 for an average of many simulated clusters and for a generalized NFW profile. As will be shown, the impact of the magnification on arc statistics is much stronger than the above mentioned effects. Therefore, for simplicity, we will ignore the effects of finite size throughout this work and use Eq. (10) to compute the arc cross section. ",
+    "In figure 1 we show the dimensionless cross section σ˜ as a function of κs for three ellipticities. From this figure we see that the cross section has a sharp drop for low values of κs and is, in general, not very sensitive to the ellipticity, which is in agreement with Rozo, Nagai, Keeton, & Kravtsov (2006) for distortion arcs. However, the sensitivity to e increases for lower κs. Therefore, the ellipticity will play a more important role for clusters of lower masses and those at lower redshifts (see the results of Sect. 6). "
+  ],
+  "5. SCALING OF THE CROSS SECTION WITH MAGNIFICATION ": [
+    "As discussed in Sect. 3, the magnification may have an important role in determining the observed abundance of arcs by enhancing their signal-to-noise ratio in the images. To include the effect of the magnification in farcs following the method of section 3 we need to determine the cross section as a function of µ. For this sake, we obtain the cross section as a function of a magnification threshold µth, σ˜(κs, e; µth), which is computed using the method described in section 4 above (Eq. 10) by adding the constraint that µ > µth in the integration region (besides requiring that R > Rth). In figure 2 we show σ˜(κs, e; µth), for e = 0.2, and κs = 0.5, 0.75, 1 (full lines). We see that for low values of µth the cross section is insensitive to this parameter. This is easy to understand, since all sources which lead to images ",
+    "with R ≥ Rth will have a magnification above some minimum value µmin. For µth > µmin the cross section begins to decrease (since not all regions that lead to R ≥ Rth will have µ ≥ µth), exhibiting an approximately quadratic decay with µth for large magnifications. This is exactly what would be expected if the cross section is dominated by arcs whose sources are close to fold caustics. Indeed, it is well known that the magnification cross section (i.e., with no constraint on R) scales as σ ∝ µ−2 for high µ (see, e.g., Chang & Refsdal 1979; Blandford & Narayan 1986; Blandford & Kochaneck 1987). In fact, for a source approaching a tangential (radial) fold, the tangential (radial) magnification µt (µr) is inversely proportional to the square root of the distance between the sources and the caustic (β − βc) ",
+    "(15) ",
+    "(see, e.g., Mollerach & Roulet 2002), which leads to the quadratic scaling for the cross section.7 A simple approximation for the dependence of the cross cross section on µth is given by ",
+    "(16) ",
+    "where σ˜(κs, e) is the cross section computed with no restriction on µ and µcr(κs, e) is a critical value above which the scaling is quadratic. Notice that, by construction, the expression above is exact for µ < µmin. ",
+    "(17) ",
+    "where d˜σ(κs, e; µ) is the cross section for images with magnification between µ and µ + dµ. Using approximation (16) we have ",
+    "(18) ",
+    "if µ > µcr, and zero otherwise. ",
+    "Expression (16) provides an excellent approximation for σ˜(κs, e; µ) if µcr is determined as follows. First we note that the mean magnification for images with R > Rth is given by ",
+    "(19) ",
+    "Then, using equation (18) we obtain ",
+    "(20) ",
+    "The mean magnification µ¯ (κs, e) is computed using the definition (19). In figure 3 we show µ¯ as a function of κs for several values of the ellipticity. The mean magnification has a steep increase for lower values of κs and is very sensitive to the ellipticity. As for the dimensionless cross section, the dependence with ellipticity is inverted close at κs ≃ 0.75. ",
+    "In figure 2 we plot the scaling of σ˜ with µ, computed numerically for each magnification threshold µth, together with the approximation defined by equations (16) and (20). We see that they provide a good approximation in the whole µ range displayed.8 Therefore, to obtain the cross section for a given Rth and for any specified magnification threshold we only need two functions: σ˜(κs, e) and µ¯(κs, e). In the remaining of this work we shall use this approximation to account for the behavior of the cross section as a function of the magnification threshold. "
+  ],
+  "6. THE EFFECT OF MAGNIFICATION ON ARC STATISTICS ": [
+    "Now we are ready to compute the expected number of arcs per cluster including the effect of magnification following Eq. (7). The first ingredient is the dimension-full magnification-dependent cross section, which is obtained by combining Eqs. (14), (18) and (20): ",
+    "(21) ",
+    "The explicit dependence of κs and rs in terms of the cluster mass and concentration parameter, lens and source redshifts, and cosmological model is obtained as follows. First rs and ρs are written in terms of the concentration parameter c and mass9 M200 as ",
+    "(22) ",
+    "(23) ",
+    "Fig. 2.— Scaling of the cross section σ˜(κs, e; µth), with respect to the magnification threshold µth, for the elliptic NFW model with e = 0.2. The full lines show the numerical computation using the conditions R > Rth and µ > µth in equation (10). The dashed lines show the results of the approximation defined by equations (16) and (20). The vertical lines indicate the values of µmin and µcrit for κs = 0.5. ",
+    "where g(c) = c2/ (ln (1 + c) − c/ (1 + c)). ",
+    "Obviously the relation (22) among the mass and radius holds for a spherical cluster. Our elliptical clusters are obtained by “deforming” the mass distribution in the direction perpendicular to the line of sight according to equation (13). In other words, a region of constant density would define a shell ξ2 + z2 = const. Since, by construction, the area of a ξ = const. curve is independent of e, the mass is independent of the ellipticity and equation (22) will hold even in the elliptical case. It is worth stressing that, by this procedure, the elliptical clusters are oblate spheroids with the smaller axis perpendicular to the line of sight. We are thus neglecting the triaxiality of these objects. However, this situation is somewhat intermediate to having a triaxial cluster aligned along the major or minor axes. For a full treatment of triaxiality, see e.g., Oguri, Lee, & Suto (2003). For the purposes of this paper it is sufficient to proceed with the approximation described above. ",
+    "Then, using Eqs. (12), (22), and (23), and inserting the relevant units, the projected NFW profile parameters are ",
+    "Fig. 3.— Average magnification within the region with |µt/µr | > Rth = 10 as a function of κs for several values of the ellipticity. ",
+    "finally given by ",
+    "(24) ",
+    "(25) ",
+    "where ILS is the transverse commoving distance from lens to source in units of the Hubble radius (and equivalently for IOL and with and sinh χ, for ",
+    "0, respectively. Here we adopt a flat ΛCDM model, such that E(z) = Ωm(1 + z)3 + ΩΛ and Ωk = 1 − Ωm − ΩΛ = 0, with parameters Ωm = 0.3, ΩΛ = 0.7. Notice that if the mass is expressed in units of h−1 , the results will be independent on the Hubble parameter. ",
+    "For a given background cosmological model (and fixed zL and zS), κs and rs are functions of M200 and c only. Although c is in principle independent of M200, these two quantities are strongly correlated, as seen in simulations (see, e.g. Klypin, et al. 1999) and in observational data (Comerford & Natarajan 2007). Here we use the expression for c(M200) from Neto et al. (2007), with the redshift dependence given in Macci`o et al. (2008). Although the distribution of halo concentrations for a given mass and redshift follows a log-normal distribution, we shall use only the mean ",
+    "relation in this work. ",
+    "The second ingredient to compute the arc fraction is the source distribution as a function of redshift and limiting magnitude. The redshift dependence is modelled as in Baugh & Efstathiou (1993) and we take the total surface density of sources and the scaling with mlim from the COMBO-17 survey (Taylor et al. 2007), such that ",
+    "(26) ",
+    "where z∗ = zm/1.412 and zm is the median redshift, which depends on the limiting magnitude mlim in the relevant band. For an R-band survey zm ≃ 0.23(mlim − 20.6) (Brown et al. 2003). ",
+    "Although we do not explicitly take into account the effects of the PSF in this work, we point out that the distribution above was obtained from ground-based observations. Therefore, our arc fraction computation will include, to some extent, the effect of the seeing. Ideally one would determine the source distribution from deep space based observations and include the effects of the PSF through the formalism of Sect. 2. This is left for future work. ",
+    "With the relations above, we may finally compute the expected number of arcs per cluster, which is given by a convolution of the cross section with the source surface density, integrated over all sources behind the cluster and all the magnifications (Eq. 7): ",
+    "(27) ",
+    "We also test an approximation by which the whole area defined by the condition R > Rth has the mean magnification µ¯ (Eq. 19), such that σ˜(κs, e; µth) = σ˜(κs, e)θ (µ − µ¯). In this case, Eq. (27) simplifies to ",
+    "(28) ",
+    "where σ is the dimension-full cross section without imposing any cut in magnification. In other words, all sources are assumed to be magnified by the mean magnification µ¯. As above, the dependence on zL, zS, and M enters on both σ and µ¯(κs, e; Rth) through κs. ",
+    "For the sake of comparison, we also compute the arc fraction neglecting the effect of magnification, i.e., using mlim eff = mlim in the equation above, which is the more standard computation. In figure 4 we show the results of these 3 computations for the arc fraction farcs as a function of lens redshift for a cluster with M = 5 × 1014h−1M⊙ and e = 0.5 and a survey with limiting magnitude Rlim = 24. We see that the magnification has a dramatic impact on arc abundance, enhancing the fraction of arcs by more than an order of magnitude. Furthermore, the inclusion of the effect of magnification shifts the peak of the arc incidence to higher redshifts and modifies the slope of the decay at large zL, showing a softer decrease with lens redshift. ",
+    "We also notice that the results including the dependence of the cross section with µ as in Eqs. (18) and (27) (full line in Fig. 4) or considering only the mean magnification, as in Eq. (28) (dashed line), are very similar. Indeed, the relative difference is less than 10% for a broad range of parameters. Therefore, from now on we will use the constant magnification approximation given by (28), since it makes calculations much faster, by avoiding the integration in µ. ",
+    "In Fig. 5 we show the impact of the depth of the survey on farcs(z) for the same lens parameters as in the previous figure. The bottom line corresponds to Rlim = 22, typical of the Sloan Digital Sky Survey,10 while the upper line corresponds to Rlim = 28, close to what would be achieved from the final Large Synoptic Survey Telescope11 (LSST) coadded data (Ivezi´c et al. 2008). As expected, the change in limiting magnitude has a large impact on arc incidence, which could explain the differences in arc abundance found in the various surveys. Also, by comparing Figs. 4 and 5, it is clear that the effect of magnification is qualitatively akin to changing the limiting magnitude of the survey. ",
+    "In Fig. 6 we show the result of the integration of Eq. (28) as a function of zL for several values of M and e. The qualitative behaviour is similar in all cases, with the expected number of arcs increasing as a function of cluster redshift at low redshifts and decreasing at higher redshifts. These results can be simply understood in terms of the scaling of the cross section with the characteristic convergence κs (Fig. 1), the scaling of κs with mass and redshift (Eq. 24), and the source redshift distribution (Eq. 26). First, for a given mass and ellipticity, the maximum value of κs increases with zL. In other words, the lensing efficiency has the potential to grow with zL, as long as there are far enough sources to be lensed. Therefore, for low lens redshifts, farcs will always increase with zL. On the other hand, for high zL the exponential decay of sources will end up causing a fall down in farcs. The arc fraction is more sensitive to zL for lower masses, ellipticities, and lens redshifts. This occurs because the cross section is much more sensitive to κs for smaller values of this parameter and smaller ellipticites. ",
+    "From these figures we see that the arc fraction is more sensitive to the ellipticity than to the mass, with roughly a linear dependence on mass at the peak and exponential with ellipticity. The transition redshift (i.e. the redshift at which farcs starts to decrease) is weakly dependent on M and e. ",
+    "The dependence of arc abundance on the source distribution and its dependence on the limiting magnitude highlight the importance of the magnification effects for farcs. For example, for κs ≃ 1, we have µmin ≃ 20 (see Fig. 3), which implies that the effective limiting magnitude is increased by at least 1.25 (see Eq. 4), changing both the normalization and shape of farcs(zL). ",
+    "Fig. 4.— The expected fraction of arcs as a function of lens redshift computed in three different ways: ignoring the magnification (dotted line), taking into account the mean magnification (dashed line), and considering the quadratic scaling of the cross section with magnification (full line). The results are shown for a NFW cluster with M = 5 × 1014h−1M⊙ and e = 0.5, assuming Rlim = 24. "
+  ],
+  "7. CONCLUDING REMARKS ": [
+    "In this paper we have introduced a method to include the effect of noise and other observational effects in semi-analytic computations of gravitational arc statistics. We argue that the expected fraction of arcs per cluster farcs is a well suited indicator to study arc statistics. On the theoretical side this quantity is less dependent on cosmological parameters not directly related to lensing (such as σ8) than the total arc number. On the observational side farcs is less affected by selection effects. The procedure to compute farcs involves the arc cross section σ, the source distribution, and a combination of observational effects with the selection function (see Eq. 1). In particular, to include the effect of the increased S/N of the arcs due to the magnification on their detectability, we are lead to consider the magnification dependent cross section. This cross section is obtained by adding an additional constraint on the image properties. Besides requiring that L/W > Rth, we also impose that the sources must be magnified by a minimum factor µth. ",
+    "The cross section was computed through a semi-analytic method based on the local eigenvalue ratio of the magnifi-cation tensor. This method has been used in previous studies (see, e.g., Hattori, Watanabe, & Yamashita 1997; Fedeli et al. 2006), and was validated using simulations of extended sources. For distortion arcs, the local eigenvalue ratio gives a good approximation for the cross section and is much faster than ray tracing finite sources. Using this method we investigated the scaling of σ with respect to the magnification threshold µth. We found that σ scales approximately as µ−th2 for high magnifications — which is expected from the properties of the lens mapping close to folds — and obtained a good approximation for all values of µth using the mean magnification µ¯. This approximation is expected to be valid for generic lens models (as long as the scaling is close to the one expected by fold arcs). ",
+    "Given a cluster mass model, the cosmological dependence of the cross section is encoded on the projected characteristic density and characteristic scale. In the case of the elliptical NFW profile, the problem of computing σ(M, e, zL; zS) is simplified to the one of obtaining σ˜(κs, e). Further, if one wishes to approximate the cross section for arbitrary µth it suffices to obtain σ˜(κs, e) and µ¯(κs, e). Obviously, the scaling of σ with projected mass and (arbitrary) length scale is a property of the lensing geometry. This feature could be used to scale the cross sections of simulated clusters for different lens and source redshifts if the lens parameters are scaled accordingly. ",
+    "To obtain the arc fraction we assume that the objects are identified and selected in terms of their S/N in the images. The arc selection function is given by a constant threshold in L/W and S/N. The enhanced detectability due to the magnification acts effectively as an increased depth of the image in the magnified region, which translates into a ",
+    "Fig. 5.— The expected fraction of arcs as a function of lens redshift for different limiting magnitudes for a NFW cluster with M = 5 × 1014 h−1M⊙ and e = 0.5. The bottom line shows the results for Rlim = 22, increasing in steps of unity, to reach Rlim = 28 for the upper curve. ",
+    "Fig. 6.— Expected fraction of arcs as a function of lens redshift for different masses and ellipticities for a NFW cluster in a survey with Rlim = 24. Left: fixed ellipticity (e = 0.5) and varying the mass in steps of 1014 h−1M⊙, from M = 1 × 1014h−1M⊙ (lower curve) up to M = 1015 M⊙ (upper curve). Right: fixed mass (M = 5 × 1014 h−1M⊙) and varying ellipticity, from e = 0 (bottom line), increasing in steps of 0.2 up to e = 0.8 for the upper curve. ",
+    "(magnification dependent) modification of the source distribution. We account for this effect by effectively changing the limiting magnitude used to determine the source distribution as in equation (4). We take the source surface density as a function of redshift and its scaling with mlim from the COMBO-17 survey. ",
+    "The resulting arc fraction is shown as a function of zL in figure 4. We see that the inclusion of the magnification has a very strong impact on the arc incidence, both enhancing the arc fraction by over an order of magnitude, as well as changing the shape of its redshift distribution. In particular, the peak in the arc fraction shifts towards higher zL and the tail of farcs has a less steep decrease with the cluster redshift. All these features are qualitatively in the right direction for improving the agreement between the predictions and observations of arc abundance, though the modelling used in this work is still oversimplified to allow for a direct comparison. Also, the detailed form and magnitude of the ",
+    "arc fraction is sensitive to the redshift variation of the mass-concentration relation, the mass definition, etc. Besides, it must be pointed out that the impact of the magnification may be a bit overemphasised in these results, given our assumption on the direct dependence of detection on the arc S/N . Other quantities may also play an important role, such as the surface brightness, which is not directly affected by the magnification. In any case, we emphasise the importance of including the effect of magnification, which is often ignored in semi-analytic predictions of arc abundance and is not accounted for in simulations that use constant surface brightness sources. ",
+    "The magnification bias considered in this work is different from the standard magnification bias in the statistics of multiple imaging of point sources (see, e.g., Turner 1980; Turner et al. 1984), in that the effect scales with the square root of magnification (i.e. S/N enhancement) and not the magnification itself. The magnification has been considered in previous arc statistics studies (see, e.g., Oguri, Lee, & Suto 2003), but through the enhancement of the total flux, which should not be the dominant factor for arc detection. ",
+    "As far as we know, this is the first work to take into account the effect of the magnification through the S/N on arc statistics and to consider the dependence of the cross section on the magnification for computing the arc abundance. We compute the arc fraction using two methods: by using the magnification dependent cross section (Eq. 27) and by using the cross section with no cut in µth but associating to all arcs the mean magnification µ¯ (Eq. 28). Both methods turn out to be in very good agreement. Therefore, it is sufficient to consider the magnification independent cross section and carry out the integration only on the source redshift, as in the more standard approach, as long as we consider the effect of the mean magnification (which depends on the lens parameters and source redshift) on the source distribution. The inclusion of magnification on arc statistics through this procedure requires only the additional computation of µ¯ in addition to the cross section. ",
+    "Several aspects of this work could be improved to yield more realistic predictions for the arc cross section and the expected number of arcs per cluster. Regarding the lens model, two key features that should be considered are the triaxial mass distribution (see, e.g., Oguri, Lee, & Suto 2003; Hennawi, Dalal, Bode, & Ostriker 2007) and the mass-concentration relation c(M ), including its scatter. More sophisticated mass distributions could also be dealt with, including different radial profiles, external perturbations, asymmetries, and substructures. Regarding the sources, the effects of finite sizes and ellipticities could be included with the methods discussed in section 4. Finally, given the observed morphological properties of the sources (e.g. their size distribution), the effects of the seeing should be taken into account, as outlined in section 2. This is left for future work. In any case, we argue that the enhancement of the S/N of the arcs due to the magnification must be included in more sophisticated semi-analytic modelling of arc abundance. Furthermore, the inclusion of this effect could help to bring a better agreement between observations and theoretical modelling of arc abundance. ",
+    "With the upcoming wide-field surveys such as DES, which has just started its first observing season, and LSST, and future space based projects such as EUCLID12 (Laureijs et al. 2011), the observed number of gravitational arcs is expected to reach ∼ 103 −104 . This will become a promising new era for doing precision statistical studies of the cluster inner matter distribution and its evolution through strong lensing. For such a program to be successful, end-to-end simulations to generate fake images are starting to be extensively used in combination with arcfinding codes, allowing for a direct comparison of theoretical predictions with observational data, taking into account the physical processes involved and the observational effects. As in many areas of cosmology, the interplay between detailed simulations and simple semi-analytic models is a useful and necessary step. The semi-analytic approach allows for a qualitative understanding of the problem and provides a framework to interpret the outcome of simulations. Furthermore, the semi-analytic modelling provides a way to make fast computations allowing a large parameter space to be probed for performing parameter estimations and forecasts. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "The authors are grateful to Silvia Mollerach and Esteban Roulet for providing fundamental contributions to this work in its earlier stages. We thank Eduardo Rozo for numerous remarks that lead to a significant improvement of this work. The authors acknowledge Chuck Keeton for making his gravlens code publicly available, which was used to test our numerical codes. MM wishes to thank Eduardo Cypriano, Laerte Sodr´e, and Joan-Marc Miralles for useful comments and suggestions. JE and MM acknowledge the hospitality of Instituto Balseiro, where this work was initiated. MM acknowledges the hospitality of the Particle Astrophysics Center at Fermilab were part of this work was done. GBC is partially funded by CNPq and CAPES. MM is partially supported by CNPq (grant 309804/2012-4) and FAPERJ (grant E-26/110.516/2012). "
+  ]
+}

jsons_folder/2014AdSpR..54.1108Z.json

@@ -0,0 +1,47 @@
+{
+  "Abstract ": [
+    "Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the Rn gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the Rn gravity which could be obtained by the present and next generations of large telescopes. Our results show that Rn gravity a ects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newton’s gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter in Rn gravity is noticeably smaller, due to the fact that the both extended mass and Rn gravity cause the retrograde orbital precession. "
+  ],
+  "keywords": [
+    "Keywords: Black hole physics; Galactic Center; Astrometry; Alternative theories of gravity "
+  ],
+  "1. Introduction ": [
+    "Dark matter (DM) ((<>)Zwicky, (<>)1933) and Dark Energy ((<>)Turner, (<>)1999) problems are fundamental and diÿcult for the conventional General Relativity approach for gravity, ((<>)Zakharov et al., (<>)2009) see also the monograph by (<>)Weinberg ((<>)2008) for a more comprehensive review. ",
+    "There is an opinion that an introduction of alternative theories of gravity (including so-called f(R) theories ((<>)Capozziello and Fang, (<>)2002; Capozziello et al., (<>)2003, (<>)2006; (<>)Carroll et al., (<>)2004; (<>)Capozziello et al., (<>)2007; Capozziello and Faraoni, (<>)2012; (<>)Mazumdar and Nadathur, (<>)2012)) could after all give explanation of observational data without DM and DE problems. However, a proposed gravity theory has to explain not only cosmological problems but many other observational data because sometimes these theories do not have Newtonian limit for a weak gravitational field case, so parameters of these theories have to be very close to values which correspond to general relativity ((<>)Zakharov et al., (<>)2006). Earlier, constraints on f(R) = Rn have been obtained from an analysis of trajectories of bright stars near the Galactic Center ((<>)Borka et al., (<>)2012, (<>)2013), assuming a potential of bulk distribution of matter is negligible in comparison with a potential of a point like mass. In this paper we consider modifications of results due to a potential of a bulk distribution of matter assuming that this potential is small in comparison with point like mass one. For the standard GR approach these calculations have been done ((<>)Zakharov et al., (<>)2007; (<>)Nucita et al., (<>)2007). ",
+    "We would like to mention that not only trajectories of bright stars but also probes such as LAGEOS and LARES ((<>)Ciufolini and Pavlis, (<>)2004; (<>)Ciufolini, (<>)2007) could provide important test for alternative theories of gravity, see for instance constraints on the Chern–Simons gravity ((<>)Smith et al., (<>)2008). "
+  ],
+  "2. Method ": [
+    "We simulated orbits of S2 star around Galactic Center in the Rn gravity potential, assuming a bulk distribution of mass in the central regions of our Galaxy. The Rn gravity potential is given by (<>)Capozziello et al. ((<>)2006, (<>)2007): ",
+    "(1) ",
+    "where rc is an arbitrary parameter, depending on the typical scale of the considered system and is a universal constant depending on n (Capozziello ",
+    "et al., (<>)2006; (<>)Zakharov et al., (<>)2006) ",
+    "(2) ",
+    "We use two component model for a potential in the central region of our Galaxy which is constituted by the central black hole of mass MBH = 4.3 ×106M⊙((<>)Gillessen et al., (<>)2009) and an extended distribution of matter with total mass Mext(r) (including a stellar cluster and dark matter) contained within some radius r. For the density distribution of extended matter we adopted the following broken power law proposed by (<>)Genzel et al. ((<>)2003): ",
+    "(3) ",
+    "where ˆ0 = 1.2 ×106 M⊙·pc−3 and r0 = 10 ′′. This leads to the following expression for the extended mass distribution: ",
+    "(4) ",
+    "Figure 1: Parameter space for Rn gravity with di erent contributions of extended mass under the constraint that, during one orbital period, S2-star orbits in Rn gravity di er less than 10 mas (\" = 0 ′′.01) from its Keplerian orbit. The assumed values for mass density constant ˆ0 from Eq. ((<>)3) are denoted in the title of each panel. ",
+    "The corresponding potential for extended distribution of matter is then: ",
+    "(5) ",
+    "Figure 2: The same as in Fig. (<>)1, but for 10 times higher astrometric precision of 1 mas (\" = 0′′.001). ",
+    "where r∞is the outer radius for extended distribution of matter which is enclosed within the orbit of S2 star. The total gravitational potential for the two component model can be evaluated as a sum of Rn potential for central object with mass MBH and potential for extended matter with mass Mext(r): ",
+    "(6) ",
+    "Thus, the simulated orbits of S2 star could be obtained by numerical integration of the following di erential equations of motion in the total gravitational potential: ",
+    "(7) "
+  ],
+  "3. Results ": [
+    "In Figs. (<>)1–(<>)3 we present the parameter space for Rn gravity with di erent contributions of extended mass for which the discrepancies between the orbits ",
+    "Figure 3: The same as in Fig. (<>)1, but for 100 times higher astrometric precision of 0.1 mas (\" = 0′′.0001). ",
+    "of S2-star in Rn gravity and its Keplerian orbit during one orbital period are less than an assumed astrometric precision. As it can be seen from Fig. (<>)1, it is very diÿcult to detect the contribution of extended mass with the astrometric precision of 10 mas, which was the actual limit during the first part of the observational period of S2 star, some 10–15 years ago. The blue area of parameter space changing very little with variations of ˆ0. However, with the current astrometric limit reaching less than 1 mas, this contribution significantly constrains the maximum allowed value (see Fig. (<>)2). In the cases where the density of extended mass is higher, the maximum allowed value of is noticeably smaller, due to the fact that the both extended mass and Rn gravity have the similar e ect on S2 star orbit, i.e. they both cause the retrograde orbital precession. However, the astrometric limit is constantly improving and in the future it will be possible to measure the stellar positions with much better accuracy of ∼10 µas ((<>)Gillessen et al., (<>)2010). The parameter space for currently unreachable accuracy of 0.1 mas ",
+    "Figure 4: Comparison between the simulated orbits of S2 star in the Rn gravity potential with (solid line) and without (dashed line) contribution of extended mass, and NTT/VLT (left) and Keck (right) astrometric observations. The parameters of Rn gravity are obtained by fitting the simulated orbits in total potential to the observations, assuming astrometric accuracy of 10 mas and the density constant ˆ0 = 12 ×106 M⊙·pc−3 . ",
+    "is presented in Fig. (<>)3, from which one can see that even a small amount of extended mass would practically exclude the Rn term from the total gravity potential. Even more, we found that in such a case expression ((<>)3) would result with overestimated amount of extended mass at Galactic center, and therefore, we assumed 2 and 10 times smaller densities ˆ0. Besides, from Figs. (<>)1–(<>)3 it is obvious that both astrometric precision and amount of extended mass have significant influence on the value of rc for which maximum is expected. For example, in the top right panel of Fig. (<>)1 the maximum ≈0.027 is expected for rc ≈250 AU, while in the top right panel of Fig. (<>)3 the maximum ≈0.00023 is expected for rc ≈450 AU. ",
+    "Several comparisons of the simulated S2 star orbits in the Rn gravity potential with and without contribution of extended mass with NTT/VLT and Keck astrometric observations are given in Fig. (<>)4, assuming the as-trometric accuracy of 10 mas. In this case, influence of extended mass for ˆ0 = 1.2 ×106 M⊙·pc−3 ((<>)Genzel et al., (<>)2003) is almost negligible, and hence it cannot explain the observed precession of S2 star orbit. Therefore, in order to explain the observed precession, either a higher value of in Rn gravity ",
+    "potential (see e.g. (<>)Borka et al., (<>)2012), or much higher density of extended mass are necessary (as it is the case in Fig. (<>)4). "
+  ],
+  "4. Conclusions ": [
+    "In this paper we analyze stellar orbits around Galactic Center in the Rn gravity with extended mass distribution. Our results show that Rn gravity with extended mass distribution could significantly a ect the simulated orbits. Both Rn gravity and extended mass distribution give retrograde direction of the precession of the S2 orbit. In the cases if the density of extended mass is higher, the maximum value of which is consistent with observations in Rn gravity is noticeably smaller. We confirmed that the Rn gravity parameter must be very close to those corresponding to the Newtonian limit of the theory. When parameter is vanishing, we recover the value of the Keplerian orbit for S2 star. When we take into account extended mass distribution, parameter is less than in case without extended mass distribution and faster approaching to zero. Even more, one can see that relatively small amount of extended mass would practically exclude the Rn term from the total gravity potential. ",
+    "We can conclude that both e ects, additional term in Rn gravity and extended mass distribution, produce a retrograde shift, that results in rosette shaped orbits. Also, we can conclude that both astrometric precision and extended mass distribution have significant influence on the value of rc for which maximum could be expected. ",
+    "Although both observational sets (NTT/VLT and Keck) indicate that the orbit of S2 star might not be closed, the current astrometric limit is not suÿcient to unambiguously confirm such a claim. However, the astrometric accuracy is constantly improving from around 10 mas during the first part of the observational period, currently reaching less than 1 mas. ",
+    "Acknowledgments. D. B., V. B. J. and P. J. acknowledge support of the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project 176003 ”Gravitation and the large scale structure of the Universe”. A. F. Z. acknowledges a partial support of the NSF (HRD-0833184) and NASA (NNX09AV07A) grants at NCCU (Durham, NC, USA) and RFBR 14-02-00754a at ICAD of RAS (Moscow). Authors thank anonymous referees for their useful critical remarks. "
+  ]
+}

jsons_folder/2014Ap&SS.354...55S.json

@@ -0,0 +1,83 @@
+{
+  "R. Smiljanic1 ": [
+    "arXiv:1403.6276v1  [astro-ph.SR]  25 Mar 2014"
+  ],
+  "Abstract": [
+    "Abstract Stellar abundances of beryllium are useful in different areas of astrophysics, including studies of the Galactic chemical evolution, of stellar evolution, and of the formation of globular clusters. Determining Be abundances in stars is, however, a challenging endeavor. The two Be II resonance lines useful for abundance analyses are in the near UV, a region strongly affected by atmospheric extinction. CUBES is a new spectrograph planned for the VLT that will be more sensitive than current instruments in the near UV spectral region. It will allow the observation of fainter stars, expanding the number of targets where Be abundances can be determined. Here, a brief review of stellar abundances of Be is presented together with a discussion of science cases for CUBES. In particular, preliminary simulations of CUBES spectra are presented, highlighting its possible impact in investigations of Be abundances of extremely metal-poor stars and of stars in globular clusters. "
+  ],
+  "keywords": [
+    "Keywords globular clusters: general – stars: abundances – stars: late-type – stars: population II "
+  ],
+  "1 Introduction ": [
+    "Beryllium has one single stable isotope, 9Be. Spectral lines of Be have been identified in the Sun, in the near UV region that is observable from the ground, quite some time ago by (<>)Rowland and Tatnall ((<>)1895). The lines tentatively identified included the Be I lines at λ 3321.011, 3321.079 and 3321.340 A,˚and the Be II resonance lines at λ 3130.422 and 3131.067 ˚A (wavelengths from (<>)Kramida and Martin (<>)1997; (<>)Kramida (<>)2005). ",
+    "However, it has been shown that the identification of the Be I lines was erroneous ((<>)Grevesse (<>)1968; (<>)Hauge and (<>)Engvold (<>)1968). Only the Be II 2S–2P0 resonance lines at ∼ 3130 ˚A are now used to determine Be abundances in late-type stars. Other Be lines can be found in the UV below 3000 ˚A, but are only observable from space and seem to be of limited use ((<>)Garcia Lopez (<>)1996). Isotopic shifted lines of unstable 7Be and 10Be have been searched for, but were never detected ((<>)Warner (<>)1968; (<>)Boesgaard and Heacox (<>)1973; (<>)Chmielewski et al. (<>)1975). ",
+    "High signal-to-noise (S/N) spectra in the near UV is hard to obtain because of atmospheric extinction. In addition, the spectral region of the Be lines is crowded with other atomic and molecular lines (see the solar spectrum in Fig. (<>)1). Some of these blending lines are still unidentified, as for example the one contaminating the blue wing of the 3131.067 ˚A line (see e.g. (<>)Ross and (<>)Aller (<>)1974; (<>)Garcia Lopez et al. (<>)1995; (<>)Primas et al. (<>)1997; (<>)Smiljanic et al. (<>)2011). ",
+    "Early analyses of Be abundances were reviewed by (<>)Wallerstein and Conti ((<>)1969) and (<>)Boesgaard ((<>)1976). The solar Be abundance seems to have been first determined by (<>)Russell ((<>)1929). The approximation of local thermodynamic equilibrium (LTE) has been shown to result in correct abundances for the Sun ((<>)Chmielewski (<>)et al. (<>)1975; (<>)Shipman and Auer (<>)1979; (<>)Asplund (<>)2005). The solar Be abundance also seems to be largely insensitive to 3D hydrodynamical effects ((<>)Asplund (<>)2004; (<>)Asplund et al. (<>)2009). The current value of the solar meteoritic abundance of Be is A(Be)1 (<>)= 1.32 ((<>)Mak-(<>)ishima and Nakamura (<>)2006; (<>)Lodders (<>)2010) while the photospheric abundance is A(Be) = 1.38 ((<>)Asplund et al. (<>)2009). Nevertheless, most 1D LTE model atmosphere analyses of Be in the Sun tend to find values between ",
+    "Fig. 1 The Be lines in the solar spectrum ",
+    "A(Be) = 1.10 and 1.15. The difference is ascribed to near-UV continuum opacity missing in the computations ((<>)Balachandran and Bell (<>)1998; (<>)Bell et al. (<>)2001). ",
+    "Beryllium is not produced in significant amounts by the primordial nucleosynthesis, because there are no stable elements with mass number 5 or 8 to act as an intermediate step in synthesising 9Be ((<>)Wagoner et al. (<>)1967; (<>)Thomas et al. (<>)1993; (<>)Coc et al. (<>)2012). In addition, Be is rapidly destroyed by proton capture reactions when in regions inside a star with a temperature above ∼ 3.5 ×106 K ((<>)Greenstein and Tandberg Hanssen (<>)1954; (<>)Salpeter (<>)1955). Therefore, stars do not produce Be. ",
+    "In stars like the Sun, for example, Be is only present in the external regions of lower temperature (see Fig. 1 of (<>)Barnes et al. (<>)1999). In evolved stars, where the convective envelope has increased in size and mixed the surface material with the interior, Be, unlike Li, is usually not detected ((<>)Boesgaard et al. (<>)1977; (<>)Garc´ıa P´erez (<>)and Primas (<>)2006; (<>)Smiljanic et al. (<>)2010). Beryllium has never been detected in Li-rich giants ((<>)de Medeiros et al. (<>)1997; (<>)Castilho et al. (<>)1999; (<>)Melo et al. (<>)2005). ",
+    "Long ago, it was understood that Be can only be produced by the spallation of heavier nuclei, mostly from carbon, nitrogen, and oxygen ((<>)Fowler et al. (<>)1955; (<>)Bernas et al. (<>)1967). The only known way to produce significant amounts of Be is by cosmic-ray induced spal-lation in the interstellar medium (ISM), as first shown by (<>)Reeves ((<>)1970) and (<>)Meneguzzi et al. ((<>)1971). ",
+    "Two channels of cosmic-ray spallation might work to produce Be. In the so-called direct process, Be is produced by accelerated protons and α-particles that collide with CNO nuclei of the ISM ((<>)Meneguzzi and (<>)Reeves (<>)1975; (<>)Vangioni-Flam et al. (<>)1990; (<>)Prantzos et al. ",
+    "Fig. 2 The Be abundances as a function of metallicty in the metal-poor stars analyzed by (<>)Smiljanic et al. ((<>)2009). Also shown are the slopes expected for primary and secondary elements. Clearly, the inverse process dominates the Be production and it behaves as a primary element ",
+    "(<>)1993). In the inverse process, accelerated CNO nuclei collide with protons and α-particles of the ISM ((<>)Ra-(<>)maty et al. (<>)1997; (<>)Lemoine et al. (<>)1998; (<>)Vangioni-Flam (<>)et al. (<>)1998; (<>)Valle et al. (<>)2002; (<>)Prantzos (<>)2012). ",
+    "If the first channel dominates in the early Galaxy, Be should behave as a secondary element, as its production rate would be proportional to the metallicity of the ISM. If the second channel dominates, Be should instead behave as a primary element. The two behaviors can be distinguished by the analysis of Be abundances in metal-poor stars. For primary elements, one should observe a linear correlation between log(Be/H) and the metallicity [Fe/H]2 (<>)with a slope close to one. For secondary elements, the slope should be around two. ",
+    "Linear relations with the two slopes are compared in Fig. (<>)2. Also shown are the Be abundances of metal-poor stars determined by (<>)Smiljanic et al. ((<>)2009). It is clear then that Be behaves as a primary element, meaning that the inverse process dominates (as first suggested by (<>)Duncan et al. (<>)1992). The determination of abundances of Be in metal-poor stars were first attempted by (<>)Molaro and Beckman ((<>)1984) and (<>)Rebolo (<>)et al. ((<>)1988). But it was with the works of (<>)Ryan et al. ((<>)1992) and (<>)Gilmore et al. ((<>)1992) that the linear correlation with slope of one became well established. Beryllium abundances in metal-poor stars have been further investigated in several works since then (e.g. (<>)Boesgaard (<>)and King (<>)1993; (<>)Molaro et al. (<>)1997; (<>)Boesgaard et al. (<>)1999; (<>)Smiljanic et al. (<>)2009; (<>)Tan et al. (<>)2009; (<>)Rich and ",
+    "(<>)Boesgaard (<>)2009; (<>)Tan and Zhao (<>)2011; (<>)Boesgaard et al. (<>)2011). ",
+    "With the inverse process dominating, and considering that cosmic-rays are globally transported across the Galaxy, then the Be production in the early Galaxy should be a widespread process. It follows that, at a given time, the abundance of Be across the Galaxy should have a smaller scatter than the products of stellar nucleosynthesis (such as Fe and O), as suggested by (<>)Beers et al. ((<>)2000) and (<>)Suzuki and Yoshii ((<>)2001). In this case, Be abundances could be used as a time scale for the early Galaxy ((<>)Pasquini et al. (<>)2005; (<>)Smiljanic (<>)et al. (<>)2009). This is an interesting application that still needs to be further constrained. "
+  ],
+  "2 CUBES ": [
+    "CUBES (Cassegrain U-Band Brazil-ESO Spectrograph) is a new medium-resolution ground based near UV spectrograph for use at the VLT (Very Large Telescope). CUBES is being constructed by Brazilian institutions together with ESO (see Barbuy et al. this volume, for more details). The properties of CUBES are still not finalized, but it will have a resolution of at least R = 20 000 and should provide access to the wavelength range between 3000–4000 A.˚",
+    "CUBES will be more efficient than UVES ((<>)Dekker (<>)et al. (<>)2000) in the near UV. UVES (Ultraviolet and Visual Echelle Spectrograph) is the current spectrograph at the VLT that is able to obtain high-resolution spectra in this region. There is an expected gain of about three magnitudes at 3200 ˚A. This gain in sensitivity will expand the number of targets that can be observed. Among the main science cases for CUBES are the study of abundances of Be, C, N, O, and of heavy neutron-capture elements in metal-poor stars (see also Siqueira-Mello, this volume and Bonifacio, this volume). ",
+    "Most of the future new instruments and facilities (such as the E-ELT, European Extremely Large Telescope) are now being optimized for the red and near-infrared spectral regions. Thus, CUBES has the potential of being an unique instrument in terms of sensitivity, spectral range, and resolution. With respect to current ESO instruments, CUBES will outperform both UVES and X-Shooter ((<>)Vernet et al. (<>)2011). CUBES should also be more efficient than other ground-based near-UV capable spectrographs, such as HIRES (High Resolution Echelle Spectrometer) at the Keck Observatory and HDS (High Dispersion Spectrograph) at the Subaru telescope. ",
+    "Regarding space-based telescopes, the HST (Hubble Space Telescope) has two UV spectrographs, the ",
+    "Fig. 3 Beryllium abundances as a function of metallicty. The stars from (<>)Smiljanic et al. ((<>)2009) are shown as filled circles, together with stars BD+03 740 ([Fe/H] = −2.85), BD−13 3442 ([Fe/H] = −2.80), G64-12 ([Fe/H] = −3.20), G64-37 ([Fe/H] = −3.15), and LP 815-43 ([Fe/H] = −2.75) as open circles. Also shown is the upper limit for star BD+44 493 ([Fe/H] = −3.80), as an open triangle ",
+    "Space Telescope Imaging Spectrograph (STIS) and the Cosmic Origins Spectrograph (COS). Nevertheless, the HST will likely not be operational when CUBES comes online (∼ 2017/2018). The WSO-UV (World Space Observatory -Ultraviolet), a 170 cm space based telescope, that should be launched in 2016 will provide access to the UV region (see Shustov, this volume). The WSOUV is however optimized for the region between 1150-3200 ˚A. It is thus not a competitor but complementary to CUBES. "
+  ],
+  "3 Science with beryllium abundances and CUBES ": [],
+  "3.1 Extremely metal-poor stars ": [
+    "The linear relation with slope close to one between log(Be/H) and [Fe/H] is well established down to [Fe/H] = −2.5/−3.0 (but see also (<>)Rich and Boesgaard (<>)2009, for a slightly different view). Going to the extremely metal-poor regime ([Fe/H] ≤ −3.00), however, the situation is less clear. ",
+    "The detection of Be in two stars (LP 815-43 and G64-12) with [Fe/H] ∼ −3.00 by (<>)Primas et al. ((<>)2000a,(<>)b) seems to suggest some deviation from the linear trend, with a possible flattening of the relation between log(Be/H) and [Fe/H]. The Be abundance of a third star (G64-37), analyzed by (<>)Boesgaard and Novicki ((<>)2006), ",
+    "Fig. 4 Comparison of three spectra with R = 20 000 of a metal-poor star with [Fe/H] = −3.00. The black spectrum was calculated without Be, the blue with log(Be/H) = −13.10 (simulating an abundance plateau), and the red one with an abundance decreased by 0.60 dex. The lines at the red spectra can never be detected ",
+    "seems to be consistent with this flattening, although these authors argue that there is only evidence for a dispersion of the Be abundances. The Be abundances of these three stars, together with the stars from (<>)Smiljanic (<>)et al. ((<>)2009), and of stars BD+03 740 and BD−13 3442 ([Fe/H] = −2.85 and −2.80, respectively) are shown in Fig. (<>)3. The Be abundances and metallicities of these extremely metal-poor stars were redetermined by (<>)Smil-(<>)janic et al. ((<>)2012). ",
+    "A Be upper limit of log(Be/H) < −13.80 was determined for the carbon-enhanced metal-poor star BD+44◦ 493 with [Fe/H] = −3.80 by (<>)Ito et al. ((<>)2009, (<>)2013). This limit is in principle consistent with an extension of the linear trend between Be and metallicity to lower values of Fe (see Fig. (<>)3). Care in the interpretation is needed because the origin of the carbon enhancement in this type of stars is also not well established. If any kind of transfer of material from evolved stars (which are depleted in Be) is involved, the surface abundance of Be would be diluted. ",
+    "Whether the flattening exists or not is thus still not clear, because Be abundances have been determined in only a few stars with metallicity around or below [Fe/H] = −3.00 (see (<>)Boesgaard et al. (<>)2011; (<>)Smiljanic et al. (<>)2012). A number of different scenarios could cause such flattening, each one with its own astrophysical implication. (<>)Orito et al. ((<>)1997), for example, suggest that a Be plateau, although an order of magnitude below of the current detections, could be the result of an inhomogeneous primordial nucleosynthesis. The identification of such a primordial plateau of Be, similar to the one observed for Li ((<>)Spite and Spite (<>)1982), might be an important test of the standard big bang model. Other possibilities include: 1) the accretion of metal-enriched interstellar gas onto metal-poor halo stars, while crossing the Galactic plane (see (<>)Yoshii et al. (<>)1995 for the case of beryllium, but see also (<>)Hattori et al. (<>)2014 for a more recent assessment of this effect on stellar metallic-ities); 2) pre-Galactic production by cosmic-rays in the intergalactic medium ((<>)Rollinde et al. (<>)2008; (<>)Kusakabe (<>)2008); and 3) although a plateau is not predicted, Be ",
+    "Fig. 5 Comparison of three spectra with R = 20 000 of a metal-poor star with [Fe/H] = −3.50. The black spectrum was calculated without Be, the blue with log(Be/H) = −13.10 (simulating an abundance plateau), and the red one with an abundance decreased by 1.00 dex. The lines at the red spectra can never be detected ",
+    "enriched stars with [Fe/H] ≥ −3.2 might be associated to population III quark-novae ((<>)Ouyed (<>)2013). ",
+    "To address the existence of the flattening, it is important to expand the number of stars with [Fe/H] < −3.00 where Be abundances have been determined. All additional known stars with this or lower metallicity are too faint to be observed with current instrumentation. CUBES will then offer an unique opportunity to obtain the spectra needed to test this possibility. ",
+    "For this science case, it is important to establish whether a sample of stars has Be abundances at the level of a given plateau or whether the Be abundances follow an extension of the linear relation between log(Be/H) and [Fe/H]. Therefore, the key requirement is to detect the Be lines at low-metallicities and derive proper abundances, not only upper-limits. ",
+    "To test if this will be possible with CUBES, spectra of two different stars were simulated, one with [Fe/H] = −3.00 and the other with Fe/H] = −3.50. Synthetic spectra were computed with the same codes and line lists used in (<>)Smiljanic et al. ((<>)2009). The spectra of ",
+    "each star was computed with two different Be abundances. The higher abundance for the two stars is the same, chosen to simulate the presence of a plateau. This abundance is log(Be/H) = −13.10, i.e. the Be abundance found for star G64-12 by (<>)Primas et al. ((<>)2000b). The smaller Be abundance, was decreased by 0.60 dex for the star with [Fe/H] = −3.00 and by 1.00 dex for the star with [Fe/H] = −3.50: ",
+    "The Be abundances reflect a scale where A(Be) = 1.10, as derived by (<>)Smiljanic et al. ((<>)2009). In addition, all the spectra were computed with the abundance of the alpha-elements increased, [α/Fe] = +0.40. ",
+    "The spectra were computed with three different spectral resolutions, R = 15 000, 20 000, and 25 000, although only the case of R = 20 000 is shown here, as this currently seems to be the favored CUBES value. To ",
+    "Fig. 6 Comparison between turn-off stars of NGC6752 with R = 20 000. A difference in abundances of ΔBe = 0.60 dex can be detected in all cases except the lowest S/N case, where a detection is marginal at best ",
+    "simulate the observations, noise was added to the spectra with four different levels in 10 different realizations (kindly computed by H. Kuntschner). The signal-to-noise levels were S/N = 20, 50, 100, and 150 for the case with R = 25 000. For the other cases the S/N was scaled to try to simulate the gain in S/N given by the decrease in resolution. Thus, the values used were S/N = 22, 56, 112, 168 for the R = 20 000 case and S/N = 26, 65, 129, 194 for the R = 15 000 case. ",
+    "Example are shown in Figs. (<>)4 and (<>)5. It is possible to see that detecting low Be abundances (log(Be/H) ≤ −13.70) is not possible, in the simulated spectra. This is also valid for the cases with different resolutions not shown here. Nevertheless, it is also shown that if there is a plateau around log(Be/H) = −13.10, the Be lines can be detected in both metal-poor stars, if S/N  100. Therefore, with CUBES data it would be possible to detect the flattening, if it has a level of Be abundances similar to the one currently found for stars with [Fe/H] ∼ −3.00. The exact limit of Be detection for CUBES remains to be determined. To calculate ",
+    "that, more information is needed also to understand which level of S/N can be reached. "
+  ],
+  "3.2 Stars in globular clusters ": [
+    "Globular clusters host multiple generations of stars (see e.g. (<>)Gratton et al. (<>)2012, and references therein). Second generation stars are formed out of material contaminated by proton-capture nucleosynthetic products. The polluters are usually thought to be either first-generation massive asymptotic-giant-branch stars (AGBs) or first-generation fast-rotating massive stars ((<>)Ventura and D’Antona (<>)2009; (<>)Decressin et al. (<>)2007). ",
+    "That these peculiarities have a pristine origin, and are not the result of deep mixing inside the stars themselves, became clear when the same chemical pattern was found in turn-off stars ((<>)Gratton et al. (<>)2001). The most obvious observational result of mixing pristine and processed material is the appearance of the correlations and anti-correlations between light-element abundances. Proton-capture reactions can decrease the abundances of Li, C, O, and Mg and enhance the abun-",
+    "Fig. 7 Comparison between stars at the metal-poor turn-off of Ω Cen with R = 20 000. A difference in abundances of ΔBe = 0.60 dex can not be easily detected in the lowest S/N case. It seems possible in the three other cases ",
+    "dances of N, Na, and Al. All the globular clusters analyzed so far with sufficient depth show signs of these chemical inhomogeneities ((<>)Carretta et al. (<>)2009). ",
+    "Beryllium, another light element, should also be affected by the polluting material. In particular, and as discussed before, Be is not produced inside stars but only destroyed. Thus the polluting material from the first generation of evolved stars, regardless of the exact nature of the polluting star, is completely devoid of Be. A star formed with only pristine material should have the original Be abundance of that material. Stars with different amounts of polluted material should have diluted the surface Be abundance to different levels. Stars with bigger fraction of polluted material should have stronger correlations and anti-correlations between the light elements and should be strongly depleted in Be. ",
+    "Lithium abundances should in principle behave in a similar way. However, AGB stars can produce Li via the Cameron-Fowler mechanism ((<>)Cameron and Fowler (<>)1971). Even though some extreme fine tuning might be needed to explain the full range of oxygen abundances in stars with seemly normal Li, this option can ",
+    "not be completely excluded as of yet (see e.g. (<>)Shen et al. (<>)2010). In this situation, Be offers an important complementary test. As Be is never produced in stars, it is an unique tracer of the amount of pollution suffered by the globular cluster stars. ",
+    "In this science case for CUBES, the objective is to detect differences in the Be abundance among different turn-off stars of the same cluster. These different stars should have been polluted to different levels. If differ-ent Be abundances are detected, then one can use them to quantify the fraction of polluting material. On the other hand, if stars with different levels of pollution are found to have the same Be abundance, this would definitely show that all the simple dilution-pollution scenarios currently proposed to explain the chemical properties of globular clusters are too simplistic and not valid. It would show that the true formation scenario was more complex than that. ",
+    "Measurements of Be abundances have been attempted in two globular clusters so far: i) In NGC6397, Be was detected in two turn-off stars by (<>)Pasquini (<>)et al. ((<>)2004), and an upper limit was derived for the ",
+    "Fig. 8 Comparison between stars at the metal-rich turn-off of Ω Cen with R = 20 000. A difference in abundances of ΔBe = 0.60 dex can be detected in all cases ",
+    "extremely Li-rich main-sequence star NGC6397 1657 ((<>)Pasquini et al. (<>)2014) and ii) two turn-off stars in NGC6752 were analyzed by (<>)Pasquini et al. ((<>)2007), resulting in one detection and one upper limit. The results seem to indicate that the stars have the same Be abundance, even though they have different abundances of oxygen (and thus were polluted to different levels). Nevertheless, the results are uncertain due to the low S/N of the spectra (S/N ∼ 10–15), even though they were obtained with long total exposure time (∼ 900 min). CUBES will allow better spectra to be acquired with shorter exposure times, increasing also the number of globular clusters were Be abundances can be investigated. ",
+    "To test this science case, synthetic spectra of three different stars were computed. One star represents turn-off stars in the cluster NGC6752, the other stars represent the metal-poor and metal-rich turn-off members of Ω Cen. For each star, two different Be abundances were adopted. The higher abundance in NGC6752 is the one derived by (<>)Pasquini et al. ((<>)2007), log (Be/H) = −12.05. The smaller abundance was de-",
+    "creased by 0.60 dex. For the stars in Ω Cen, the Be abundances were scaled according to the metallicity – log(Be/H) = −12.6 and −13.2 for turn-off star 1 and log(Be/H) = −11.7 and −12.3 for turn-off star 2: ",
+    "The same combinations of resolving power and S/N used before were adopted. The results are shown in Figs. (<>)6, (<>)7, and (<>)8. It can be seen that basically in all cases a difference in Be abundances can be detected, the only exception being the metal-poor turn-off of Ω Cen with low-S/N. Therefore, with CUBES it will be possible to use Be as a tracer of the dilution-pollution processes in globular clusters. More sound quantitative predictions have to wait until the CUBES properties are better defined. Then, it will be possible to define the list of clusters were the measurements will be possible ",
+    "and better determine the limit of detection of the Be abundances in these stars. "
+  ],
+  "4 Summary ": [
+    "Abundances of the fragile element Be can be used in different areas of astrophysics, including studies of the Galactic chemical evolution, of stellar evolution, and of the formation of globular clusters. Only the Be II resonance lines at λ 3130.422 and 3131.067 ˚A are used for abundance studies. The lines are in the near UV spectral region, a region strongly affected by atmospheric absorption. It is very time demanding to obtain the high-resolution, high-S/N spectra needed to study Be. ",
+    "Because of that, Be abundances have not been used to its full potential yet. To increase the number of stars where Be abundances can be determined, and to decrease the time cost of obtaining high-quality spectra, new UV sensitive instruments are needed. CUBES is one such instrument. It has an expected sensitivity gain of about three magnitudes at 3200 ˚A over UVES. ",
+    "In the near future, CUBES will likely be the only instrument offering the opportunity to measure Be abundances in samples of extremely metal-poor stars and in turn-o�� stars of globular clusters. Here, preliminary simulations of CUBES-like spectra for these types of stars were presented. ",
+    "For the first case, the simulations indicate that with CUBES spectra it will be possible to investigate the suggested flattening of the relation between Be and Fe at low metallicities ([Fe/H] < −3.00). This flattening might have implications, for example, to primordial nu-cleosynthesis models. ",
+    "With CUBES, it will also be possible to investigate Be abundances in turn-off stars of globular clusters. Beryllium can be used as a tracer of the fraction of polluting material accreted by the second generation stars. If stars with different levels of pollution are found to have the same Be abundances, this would argue against the currently favored dilution-pollution scenarios invoked to explain the chemical properties of globular clusters. ",
+    "Acknowledgements I thank the organizers of the “Challenges in UV Astronomy” workshop for the invitation to give the review talk on beryllium abundances. I acknowledge financial support by the National Science Center of Poland through grant 2012/07/B/ST9/04428. I am pleased to thank L. Pasquini and H. Kuntschner for sharing their enthusiasm for the CUBES project. "
+  ]
+}

jsons_folder/2014ApJ...785...91M.json

@@ -0,0 +1,112 @@
+{
+  "ABSTRACT ": [
+    "The classic optical nebular diagnostics [N II], [O II], [O III], [S II], [S III], and [Ar III] are employed to search for evidence of non-Maxwellian electron distributions, namely  distributions, in a sample of well-observed Galactic H II regions. By computing new e ective collision strengths for all these systems and A-values when necessary (e.g. S II), and by comparing with previous collisional and radiative datasets, we have been able to obtain realistic estimates of the electron-temperature dispersion caused by the atomic data, which in most cases are not larger than ∼10%. If the uncertainties due to both observation and atomic data are then taken into account, it is plausible to determine for some nebulae a representative average temperature while in others there are at least two plasma excitation regions. For the latter, it is found that the diagnostic temperature di erences in the high-excitation region, e.g. Te(O III), Te(S III), and Te(Ar III), cannot be conciliated by invoking  distributions. For the low excitation region, it is possible in some, but not all, cases to arrive at a common, lower temperature for [N II], [O II], and [S II] with  ≈10, which would then lead to significant abundance enhancements for these ions. An analytic formula is proposed to generate accurate -averaged excitation rate coeÿcients (better than 10% for  ≥5) from temperature tabulations of the Maxwell–Boltzmann e ective collision strengths. ",
+    "Subject headings: atomic data—atomic processes—H II regions "
+  ],
+  "1. Introduction ": [
+    "A fundamental and still unresolved problem in the understanding of astronomical photoionized plasmas, particularly H II regions and planetary nebulae, is the systematic higher metal abundances derived from recombination lines (RL) relative to those from collisionally excited lines (CEL). The magnitude of these discrepancies varies from a few percent up to puzzling factors as large as 70 (see, for instance, (<>)Liu et al. (<>)2000, (<>)2001). Several plausible explanations have been proposed to account for their cause, among them temperature fluctuations ((<>)Peimbert (<>)1967), hydrogen deficient inclusions ((<>)Liu et al. (<>)2000; (<>)Stasi´nska et al. (<>)2007), and dense clumps ionized by X rays ((<>)Ercolano (<>)2009). However, all these hypotheses present certain limitations and no conclusive evidence has been put forward to either prove or dispute them. ",
+    "(<>)Nicholls et al. ((<>)2012) have suggested that the apparent temperature variations in nebular plasmas are the result of electron velocity distributions that deviate from the generally assumed Maxwell–Boltzmann (MB), proposing the  distribution as a more functional alternative. It is therein argued that excitation rates suÿciently boosted from the MB values are obtained with 10 ≤ ≤20, implying that the traditional temperature diagnostics from forbidden line ratios systematically overestimate the true kinetic temperature; therefore, ion abundances derived from CEL would be underestimated. In their analysis, two crucial approximations are made: (i) electron impact collision strengths are constant with energy, which in practice is not the case due to strong resonance contributions; and (ii) the e ects of the  distribution on the de-excitation rate coeÿcients are ignored. ",
+    "(<>)Binette et al. ((<>)2012) have found that the O III temperatures from CEL are consistently higher than those of S III in an extensive group of both Galactic and extragalatic H II regions with gas metallicities higher than 0.2 solar. Among the causes for this excess, the ",
+    " distribution has again been invoked. (<>)Nicholls et al. ((<>)2013) have continued their work on the  distributions by revising the e ects of di erent datasets of e ective collision strengths on the electron temperatures obtained from nebular diagnostics such as [N II], [O II], [O III], [S II], and [S III]. In particular, by comparing the O III electron temperature obtained using recent collision strengths ((<>)Palay et al. (<>)2012) with those derived from earlier datasets, they have concluded that the previous electron temperatures have been seriously overestimated. Since any spectroscopic evidence of non-Maxwellian electron distributions must rely on accurate atomic data, it is indispensable to verify this claim. It must be added that (<>)Nicholls et al. ((<>)2013) did not consider the accuracy of the radiative rates (A-values) which is also a source of uncertainty in spectral diagnostics. For a full treatment of the propagation of atomic data uncertainties in spectral diagnostics, see (<>)Bautista et al. ((<>)2013). ",
+    "More recently, (<>)Dopita et al. ((<>)2013) have made an e ort to estimate both MB and -averaged collisional rates from energy tabulations of raw collision strengths, and stress the need for a systematic inventory and assessment of the newer atomic data and their e ects on photoionization models before really establishing the prevalence of the  distribution in nebular plasmas. This is in fact the main motive of the present work. We make use of the familiar nebular diagnostics—namely [N II], [O II], [O III], [S II], [S III], and [Ar III]—to search for evidence of  distributions in well-observed H II regions. In Section (<>)2 we describe the e ects of the  distribution on both the electron excitation and de-excitation rate coeÿcients for forbidden transitions. Since energy-tabulated electron collision strengths with at least a similar degree of reliability are required in this analysis, we decided to recalculate them from scratch (Section (<>)3). The sensitivity of the electron temperature to the A-values is also evaluated in Section (<>)4. With the new data, we derive in Section (<>)5 electron temperatures for the H II regions studied by (<>)Nicholls et al. ((<>)2012) and compare them with those obtained with representative e ective collision strengths published in the past two decades. The possibilities of the  distribution in reducing CEL temperatures ",
+    "and in conciliating the temperature di erences in plasma regions are also investigated (Section (<>)6). Conclusions are finally discussed in Section (<>)7. "
+  ],
+  "2. -averaged rates ": [
+    "Spectral emission of non-Maxwellian plasmas has been studied in detail by (<>)Bryans ((<>)2005) from which we recapitulate the formalism for electron impact excitation and de-excitation within the -distribution framework. For an ionic transition between levels i →j induced by electron impact, the excitation and de-excitation generalized rate coeÿcients may be written as ",
+    "(1) ",
+    "and ",
+    "(2) ",
+    "T ≡2E/3kB is defined in terms of the mean energy where Eij is the energy separation between the two levels and gi and gj are their respective statistical weights. The other quantities are the standard fine structure constant, , speed of light, c, Bohr radius, a0, Rydberg constant, R, and Boltzmann constant, kB. For a particular normalized electron-energy distribution function f(E), the kinetic temperature ",
+    "(3) ",
+    "The e ective collision strengths for excitation, ij, and de-excitation, ji, involve energy averages over the quantum mechanical cross section ˙(E) for the transition, which may be conveniently expressed in terms of the symmetric collision strength ",
+    "(4) ",
+    "where Ei and Ej are the free-electron energies relative to the ith and jth levels, respectively. ",
+    "They are then expressed through the integrals ",
+    "(5) ",
+    "and ",
+    "(6) ",
+    "For the MB electron distribution ",
+    "(7) ",
+    "T becomes the familiar electron temperature Te and the e ective collision strengths for excitation and de-excitation are also symmetric ",
+    "(8) ",
+    "an unmistakeable signature of detailed balance for this distribution. ",
+    "On the other hand, the  distribution of electron energies ",
+    "(9) ",
+    "has a characteristic energy E that is related to the kinetic temperature ",
+    "(10) ",
+    "where the  parameter (3/2 ≤ ≤∞) gives a measure of the deviation from the MB distribution, converging to the latter as  →∞. Detailed balance is now broken and the asymmetric e ective collision strengths are given by ",
+    "and ",
+    "In Figure (<>)1, the ratio /MB is plotted as a function of  for the forbidden transitions arising from the ground states of O II and O III. It may be seen that the  distribution increases the de-excitation e ective collision strength by up to a factor of two for  . 5, while for higher  the enhancements are marginal. For excitation, the  distribution causes large di erences for  . 5, in particular increments as large as a factor of six for the transitions with the larger Eij; for such transitions, they remain sizeable (> 50%) even for  > 20. The behavior of this ratio with temperature in O III is depicted in Figure (<>)2, where it may be appreciated that, for de-excitation, the ratio is temperature independent and not larger than 10%; for excitation, on the other hand, exponential increases are found with decreasing temperature for T < 104 K especially for the transition 3P0 −1S0 due to its comparatively larger Eij. In Figure (<>)3, the [O III] (4959 + 5007)/4363 line ratio is plotted as a function of temperature for both the MB and  distributions at an electron density of Ne = 1.5 ×104 cm−3 . It is therein shown that, for an observed line ratio of 200 say, MB results in Te = 9700 K while the  distribution gives significantly lower values: T = 8000 K and T = 6100 K for  = 20 and  = 10, respectively. ",
+    "These findings are in general agreement with (<>)Nicholls et al. ((<>)2012), and support their approximation of neglecting the contributions of the  distribution to the de-excitation rate coeÿcient. Regarding their assumption of estimating the -averaged excitation rate coeÿcient with a constant collision strength, we have found that a better choice would be to derive it from the MB temperature-dependent e ective collision strength for the transition ",
+    "which can be integrated analytically to give ",
+    "Equation ((<>)14) is a small yet significant improvement over equation (16) in (<>)Nicholls et al. ((<>)2012) inasmuch as now the MB e ective collision strength MB ji (T) is temperature dependent rather than constant, and enables the accurate determination of -averaged excitation rate coeÿcients (better than 10% for  ≥5) from temperature tabulations of the MB e ective collision strengths. Furthermore, as mentioned in (<>)Nicholls et al. ((<>)2012), the key term in equation ((<>)14) is T/Tex, the ratio of the kinetic temperature relative to the excitation temperature Tex ≡Eij/kB, since -distribution enhancements to the excitation rate coeÿcient become conspicuous for T/Tex ≪1. Hence, IR transitions within the ionic ground term, where usually Tex < 103 K, are not expected to show noticeable departures from MB conditions in nebular plasmas. ",
+    "The optical diagnostics we study in the present work are those widely used in observational work to determine nebular plasma properties—namely [N II], [O II], [O III], [S II], [S III], and [Ar III]—the specific line ratios being listed in Table (<>)1. Since the collision strengths for these transitions are not readily available from the original sources, and the present analysis requires at least an even degree of reliability, we had no alterative but to recalculate them. [They are openly available from the AtomPy1 (<>)atomic data curation service on Google Drive; for an ion identified by the tuple (zz,nn), where zz (two-character ",
+    "strengths is located at IsonuclearSequences/zz/zz nn.] string) and nn (two-character string) stand for the atomic and electron numbers, the spreadsheet containing level energies, A-values, collision strengths, and e ective collision "
+  ],
+  "3. Collision strengths ": [
+    "When computing e ective collision strengths for both the MB and  distributions used in Figures (<>)1–(<>)2, it is important to take into account that the collision strengths for forbidden transitions are dominated by dense packs of resonances in the region near the excitation threshold; therefore, it is the mesh between Ej = 0 (threshold) and ∼1 Ryd that determines their value at typical nebular temperatures (Te ∼104 K). ",
+    "In the present work, collision strengths for the forbidden transitions within the ground configuration of the ions specified in Table (<>)1 are computed with the Breit–Pauli R-matrix method ((<>)Berrington et al. (<>)1978, (<>)1987; (<>)Scott & Burke (<>)1980; (<>)Scott & Taylor (<>)1982). Multi-configuration wave functions for the target representations have been obtained in a Thomas–Fermi–Dirac potential with the atomic structure code autostructure 2 (<>)((<>)Eissner et al. (<>)1974; (<>)Badnell (<>)1986, (<>)1997). The scattering calculations are carried out in LS-coupling taking into account partial wave contributions with L ≤9 and including the non-fine-structure mass, velocity, and Darwin one-body relativistic corrections. The intermediate coupling (IC) collision strengths for fine-structure levels are obtained by means of the Intermediate Coupling Frame Transformation (ICFT) method of (<>)Griÿn et al. ((<>)1998) using energy meshes with a resolution of 10−4 Ryd for most ions except Ar III where a finer step of 5 ×10−5 Ryd was required. The ICFT method is computationally less demanding than a fully relativistic Breit–Pauli calculation without compromising accuracy, ",
+    "thus allowing the handling of more complex target representations. The ionic targets are specified in Table (<>)2 and will be henceforth briefly described (Sections (<>)3.1–(<>)3.6). The resulting e ective collision strengths are also compared with other representative datasets in order to estimate their accuracy. In this respect, since one-to-one comparisons are usually hindered by the diverse temperature tabulations found in publication, a useful measure (see Table (<>)3) is the scatter of the e ective collision strengths at Te = 104 K for the leading transitions that populate the diagnostic upper levels (this temperature, representative of the order of nebular temperatures, is always given). As shown in Table (<>)3, the mean dispersions are not greater than 15%. "
+  ],
+  "3.1. N II ": [
+    "As indicated in Table (<>)2, our N II target representation includes in the close-coupling expansion the ten lowest LS terms and configuration interaction within complexes with principal quantum number n ≤3. The resulting e ective collision strengths are compared with two other datasets: (i) the R-matrix calculation by (<>)Lennon & Burke ((<>)1994) with a 12-term target representation in an LS-coupling framework, the IC collision strengths being obtained by algebraic recoupling of the LS reactance matrices; and (ii) the IC B-spline, Breit–Pauli R-matrix method of (<>)Tayal ((<>)2011) with a target containing 58 fine-structure levels. The present scheme is similar to that by (<>)Lennon & Burke ((<>)1994), but our IC collision strengths are obtained with the ICFT method based on multi-channel quantum defect theory ((<>)Griÿn et al. (<>)1998). The agreement with (<>)Tayal ((<>)2011) is in general within 10% except for the 2s22p2 1D2 −1S0 transition at the lower temperatures (Te < 104 K) where larger discrepancies are found (see Fig. (<>)4). Significant di erences (∼20%) are also found with the data of (<>)Lennon & Burke ((<>)1994) for this same transition as shown in Fig. (<>)4 and for ",
+    "The outcome of this comparison, i.e. good agreement for most transitions but noticeable discrepancies for a selected few, is typical of collisional rates dominated by resonances, where small variations in resonance patterns can cause unexpected e ects. Nonetheless, the discrepancies for the 3PJ −3PJ′transitions have little impact on the optical emission spectra of typical nebulae since the fine-structure levels within the ground multiplet are nearly thermalized at electron densities of Ne ∼104 cm−3 and temperatures of Te ∼104 K, while the optical transitions arising from the first and second excited terms are dominated by excitations from the ground multiplet. "
+  ],
+  "3.2. O II ": [
+    "E ective collision strengths for the forbidden transitions in O II have been recently assessed in Appendix A of (<>)Stasi´nska et al. ((<>)2012), where the most elaborate Breit–Pauli R-matrix calculation by (<>)Kisielius et al. ((<>)2009) (21-level target) is in very good accord (a few percent) with (<>)Montenegro et al. ((<>)2006); (<>)Pradhan et al. ((<>)2006) (16-level target, Breit–Pauli R-matrix) and (<>)Tayal ((<>)2007) (62-level target, B-spline, Breit–Pauli R-matrix) except for the 2s22p3 2D3o /2 −2D5o /2 transition; for this transition, di erences at the lower temperatures are around 36% and 25%, respectively. Notoriously larger discrepancies are found with the data by (<>)McLaughlin & Bell ((<>)1998); hence, they will not be further considered in the present analyses. ",
+    "Our target expansion includes 19 LS terms in the close-coupling expansion and correlation configurations with n ≤3 (see Table (<>)2). Our resulting e ective collision strengths are found to be in general around 25% higher than those of (<>)Kisielius et al. ((<>)2009) which are believed to be due to our smaller target representation. "
+  ],
+  "3.3. O III ": [
+    "The level of agreement between the e ective collision strengths computed for O III by (<>)Lennon & Burke ((<>)1994), (<>)Aggarwal & Keenan ((<>)1999), and (<>)Palay et al. ((<>)2012) is unimpressively ∼20%. (<>)Lennon & Burke ((<>)1994) computed their R-matrix data in LS-coupling in a 12-term target approximation, obtaining IC e ective collision strengths by algebraic recoupling of the reactance matrix. The data by (<>)Aggarwal & Keenan ((<>)1999) were computed in a similar fashion but with a 26-term target representation. The recent calculation by (<>)Palay et al. ((<>)2012) was performed with an IC Breit–Pauli R-matrix method with a 19-level target and extensive configuration interaction within n ≤4 complexes. This approach implements experimental thresholds, and also includes in the relativistic Hamiltonian the two-body Breit terms that are usually neglected in relativistic scattering work. ",
+    "As shown in Table (<>)2, the present R-matrix calculation has been carried out with a model target of 9 LS terms and extensive configuration interaction within the n ≤3 complexes. The resulting e ective collision strengths are found to be around 30% below those of (<>)Palay et al. ((<>)2012) except for the 2s22p2 1D2 −1S0 quadrupole transition where this trend is reversed. Such di erences are perhaps caused by our shorter close-coupling expansion. "
+  ],
+  "3.4. S II ": [
+    "S II has been the most diÿcult of all the systems treated here. We have explored several configuration expansions including orbitals up to n = 4 and n = 5. It is found that the best representation is obtained with a relatively small expansion that allows for single electron promotions from the 2p sub-shell and including in the close-coupling expansion ",
+    "the lowest 17 LS terms (see Table (<>)2). Previous R-matrix work has been carried out by (<>)Cai & Pradhan ((<>)1993) and (<>)Ramsbottom et al. ((<>)1996) with target expansions including the lower 12 and 18 LS terms, respectively; the IC e ective collision strengths were obtained by algebraic recoupling of the reactance matrices. (<>)Tayal & Zatsarinny ((<>)2010) have performed an IC B-spline, Breit–Pauli R-matrix calculation with a 70-level target. In general, we find good agreement (within ∼20%) with (<>)Tayal & Zatsarinny ((<>)2010) but discrepancies around a factor of two for the 3s23p3 4S3o /2 −2PJo and 2P3o /2 −2P1o /2 transitions in Ramsbottom et al. (see Fig. (<>)5). Due to these gross discrepancies, this latter dataset is excluded from further consideration. "
+  ],
+  "3.5. S III ": [
+    "As indicated in Table (<>)2, our target expansion includes the lowest ten LS terms and 31 correlation configurations with n ≤4 orbitals. Previous R-matrix work has been carried in LS-coupling by (<>)Galav´ıs et al. ((<>)1995) (15-term target) and (<>)Hudson et al. ((<>)2012) (29-term target), whereby the IC collision strengths are obtained by a method of algebraic recoupling of the reactance matrices that allows for target fine-structure splittings. The general agreement of the present e ective collision strengths with these two datasets is ∼25%. "
+  ],
+  "3.6. Ar III ": [
+    "The target model for this system involves 10 LS terms and correlation configurations with n ≤4 orbitals, including an open 2p sub-shell (see Table (<>)2). Agreement with the previous computations by (<>)Galav´ıs et al. ((<>)1995) and (<>)Munoz Burgos et al. ((<>)2009) is ∼20% (see Table (<>)3), but a larger discrepancy of a factor of two stands out for the 3s23p4 1D2 −1S0 quadrupole transition due to correlation e ects arising from the open 2p sub-shell in the ",
+    "present target model. "
+  ],
+  "4. A-values ": [
+    "The forbidden line ratios that are studied in the present work are listed in Table (<>)1, and correspond to those employed by observers to derive electron temperatures for the Galactic H II regions under consideration. The radiative transition probabilities (A-values) that we have adopted to determine the line emissivities have been obtained from di erent compilations—mainly from (<>)Badnell et al. ((<>)2006), Appendix A of (<>)Stasi´nska et al. ((<>)2012), and the MCHF/MCDHF (Version 2) database3 (<>)((<>)Tachiev & Froese Fischer (<>)2001; (<>)Irimia & Froese Fischer (<>)2005)—in order to evaluate temperature sensitivity. It is generally found that, for the characteristic electron densities (Ne . 2 ×104 cm−3) and temperatures (Te . 15000 K) of our H II sources, the line ratios are practically insensitive to the A-value choice, i.e. between (<>)Badnell et al. ((<>)2006) and (<>)Tachiev & Froese Fischer ((<>)2001) say, except for [S II]. For this species, the (6716 + 6731)/(4069 + 4076) line ratio, even at the lower densities (Ne ∼102 cm−3), shows a noticeable A-value dependence, and as previously discussed by (<>)Tayal & Zatsarinny ((<>)2010), an undesirable wide scatter is encountered among the published radiative data. We have therefore been encouraged to compute with the atomic structure code autostructure new A-values for this system with extensive configuration interaction, and in particular, taking into account the Breit correction to the magnetic dipole operator that has been shown by (<>)Mendoza & Zeippen ((<>)1982) to be important for ions such as S II with a 3p3 ground configuration. ",
+    "In Table (<>)4 we tabulate A-values for [S II] from several theoretical datasets where the ",
+    "aforementioned wide scatter is confirmed. In the present context, the A-value ratios ",
+    "(15) ",
+    "and ",
+    "(16) ",
+    "are of interest. As pointed out by (<>)Mendoza & Zeippen ((<>)1982), R1 tends to the ratio of the line intensities ",
+    "(17) ",
+    "as Ne →∞which gives rise to a useful benchmark with observations of dense nebulae. In this respect, (<>)Zhang et al. ((<>)2005) report a ratio of R1 = 0.443 for the dense (Ne = 4.7×104 cm−3) planetary nebula NGC 7027, which is only matched accurately (better than 10%) in Table (<>)4 by (<>)Mendoza & Zeippen ((<>)1982), (<>)Fritzsche et al. ((<>)1999), (<>)Irimia & Froese Fischer ((<>)2005) (with adjusted level energies), and the present work. R2 is associated to the [S II] temperature diagnostic, and the agreement of the present value with those by (<>)Mendoza & Zeippen ((<>)1982) and (<>)Fritzsche et al. ((<>)1999) is within 1% while only ∼10% with (<>)Irimia & Froese Fischer ((<>)2005). The poorer accord with the latter may be due to their exclusion of the relativistic correction to the magnetic dipole operator. In the light of this outcome, the radiative data by (<>)Keenan et al. ((<>)1993), (<>)Irimia & Froese Fischer ((<>)2005) (with ab-initio level energies), and (<>)Tayal & Zatsarinny ((<>)2010) for [S II] will not be further discussed. "
+  ],
+  "5. Temperature diagnostics ": [
+    "In order to study the impact of the atomic data on nebular temperature diagnostics, we have selected the same group of spectra of Galactic H II regions considered by (<>)Nicholls et al. ((<>)2012), namely ",
+    "We have not included here the spectra of extragalactic H II regions also taken into account by (<>)Nicholls et al. ((<>)2012) as some of the lines of our comprehensive set of temperature diagnostics are not reported. Also, we have not extended our study to planetary nebulae as the CEL fluxes of at least [N II] and [O II] in many of these objects are usually contaminated with recombination-line contributions. Although these fluxes are usually corrected with the widely used formula of (<>)Liu et al. ((<>)2001), we do not have a reliable measure of its accuracy. Such flux corrections in the present set of H II regions, as reported in the observational papers, are found to be less than ∼5%. ",
+    "In Table (<>)5, we tabulate for the di erent H II regions (in increasing density order) the electron temperatures derived with our selected datasets of e ective collision strengths, which allow for each diagnostic the estimate of an average electron temperature Tth e for ob in the observational It be appreciatedcomparison with the quoted value, T papers. may, e that the agreement between for most diagnostics is better than 10% except for [S II] in S311, M20, M16, HH 202 (shock region), and NGC 3603 where di erences of oband T e thT e 20–25% are found and of ∼12% for [O II] in M20 and Orion. Such discrepancies in our opinion are caused by the use of poor atomic data in previous analyses, i.e. either radiative, collisional or both. ",
+    "It must be pointed out that the scatter of Tthin Table (<>)5 is a direct consequence of e the inherent statistical uncertainties of resonance phenomena in electron–ion collisional processes, where small variations in quantum mechanical models can give rise to large rate ",
+    "discrepancies. By comparing the magnitudes of the error margins of Tethand Teob in Table (<>)5, we are inclined to believe that the errors due to the atomic data have not always been taken into account in estimates of Teob , and therefore, a more reliable temperature uncertainty would perhaps be Teth + Teob . In this light, it is then plausible to derive for certain sources, namely M20, S311, and NGC 3576, an average temperature with a standard deviation comparable to the specified error bars; for other objects, e.g. NGC 3603, there seems to be at least two well-defined plasma regions associated with ionic excitation. ",
+    "The noticeable dependence of the [S II] electron temperature on the A-values, specially at the higher densities, is further illustrated in Table (<>)6 where the electron temperatures have been obtained with our e ective collision strengths but di erent radiative datasets. Di erences between the present temperatures with those obtained with the A-values of (<>)Mendoza & Zeippen ((<>)1982) and (<>)Fritzsche et al. ((<>)1999) are not larger than 4% while those derived with the A-values by (<>)Irimia & Froese Fischer ((<>)2005) are lower by as much as 15% at the higher densities. "
+  ],
+  "6. -distribution e ects ": [
+    "It may be noted in Table (<>)5 that the [O III] temperature in most objects is distinctively lower than other diagnostics, in particular Te(O III) < Te(S III). Such standing di erences have been previously reported by, for instance, (<>)Binette et al. ((<>)2012) in an extensive sampling of Galatic and extragalactic H II regions, but in their case it is the converse: Te(O III) > Te(S III) mostly when gas metallicities are greater than 0.2 solar. In this context, we plot in Fig. (<>)6 the line-ratio map for [O III] 4363/(4959 + 5007) vs. [S III] 6312/(9069 + 9352) at Ne = 8.9 ×103 cm−3 . It is seen that, in spite of the inaccuracies in both observation and atomic data, the observed [O III] and [S III] line ratios in the Orion nebula ((<>)Esteban et al. (<>)2004) neither conduce to a common ",
+    "MB Te nor to a common T when di erent values of  are considered. This trend prevails in all the H II regions of our sample as further illustrated in Fig. (<>)7: for MB, 0 . Te(S III) −Te(O III) . 1.5 ×103 K while for  = 20 both temperatures are significantly reduced but now 103 . T(S III) −T(O III) . 2.4 ×103 K; i.e. the temperature di erences are significantly increased (∼103 K) by the  distribution. In Fig. (<>)7 we also include the temperatures determined in the larger sample of (<>)Binette et al. ((<>)2012), where the scatter is much larger (−5 ×103 . Te(S III) −Te(O III) . 104 K) and, in contrast to the present dataset, most of their objects have Te(O III) > 104 K. It must be noted that in Fig. (<>)7 we have plotted the T−T relation rather than the usual T−T since we would like to emphasize several points: T is found to take positive and negative values; the T reduction by the  distribution does not necessarily lead to a diminished T as desired; and unlike previous reports, we have avoided displaying the apparent -distribution T as it is density dependent and, thus, arguably reliable for a large nebula sample such as that of (<>)Binette et al. ((<>)2012) for which we are unaware of the density range. ",
+    "A similar situation is found in the [O III] vs. [Ar III] line-ratio map of our sample which implies that, in the high-excitation region, the diagnostic temperature di erences do not seem to be caused by non-Maxwellian distributions. Evidently, this conclusion cannot be extended to the sample by (<>)Binette et al. ((<>)2012) where the  distribution may indeed contribute to reduce some of the [O III] and [S III] temperature disparities, at least for the large population for which Te(S III) −Te(O III) < 0 K (see Fig. (<>)7). ",
+    "For the low-excitation region, the situation is somewhat di erent as the  distribution can lead in some circumstances to a lower common temperature for the [N II], [O II], and [S II] diagnostics. This is the case, as shown in Fig. (<>)8, of the nebular component of HH 202 where the three di erent MB temperatures Te(N ii) = 9700 K, Te(O ii) = 8800 K, and Te(S ii) = 8300 K can be reduced to a single, lower temperature of T ≈7400 K with ",
+    " = 10. As a result, the lower temperature leads to abundance increases for N II, O II, and S II of factors of 1.79, 2.21, and 1.32, respectively. It must be pointed out that the reliability of these findings is highly limited by the confidence levels of both the observations and atomic data; for instance, it may be seen in Fig. (<>)8 that the error bar of the [N II] line ratio is fairly large (∼19%) thus hampering the choice of an accurate  value or even a reliable departure from the MB distribution. ",
+    "In the Orion nebula (see Fig. (<>)9), the two MB temperatures of Te(N ii) = 10000 K and Te(S ii) = 8700 K can also be reduced to a common  temperature of T ≈8400 K with  = 12, the abundance enhancements for N II and S II in this case being smaller: 32% and 8%, respectively; however, this procedure cannot be extended to the low Te(O ii) = 7900 K which could perhaps be due to errors in our atomic data since the temperatures obtained with other collisionally datasets are significantly higher (see Table (<>)5). Furthermore, in other sources, e.g. M16, there is no conclusive evidence that the  distribution would lead to a common lower temperature in the low-excitation region. "
+  ],
+  "7. Summary and conclusions ": [
+    "It has become clear in the work of (<>)Nicholls et al. ((<>)2013) and (<>)Dopita et al. ((<>)2013) on non-Maxwellian electron distributions in nebular plasmas that reliable e ective collision strengths and A-values are essential before any recommendations can be drawn. We have therefore been encouraged to make an attempt at quantifying the impact of such atomic data on the electron temperatures of a sample of Galactic H II regions for which accurate spectra are available, and to search for evidence to substantiate departures from the MB framework. This initiative has implied extensive computations of new collisional datasets for the ionic systems that give rise in nebulae to CEL plasma diagnostics in order to derive both MB and -averaged rate coeÿcients with a comparable degree of accuracy. These ",
+    "energy-tabulated collision strengths are currently available for download from the AtomPy4 (<>)data curation service. ",
+    "By extensive comparisons with other datasets of e ective collision strengths computed in the past two decades, we have found that their statistical consistency is around the ∼20−30% level although larger discrepancies (factor of 2, say) may be detected for the odd transition. This inherent dispersion, which in our opinion would be hard to reduce in practice, is due in forbidden transitions to the strong sensitivity of the resonance contribution to the scattering numerical approach, target atomic model, energy mesh, and small interactions such as relativistic corrections. However, with the exception of the diÿcult [S II] system, the theoretical temperature dispersion in most diagnostics has been found to be not larger than 10%, and the agreement with the temperatures estimated in the observational papers is within this similar satisfactory range. Therefore, there is room for optimism. As shown in the present analysis, Te(S II) has been proven to be strongly dependent on both the radiative and collisional datasets, and in this context, only the A-values by (<>)Mendoza & Zeippen ((<>)1982), (<>)Fritzsche et al. ((<>)1999), and the present comply with all the stringent specifications required. On the other hand, the collisional dataset for this ion still needs more refinement before a firm ranking can be put forward on its accuracy. ",
+    "In the present study, which has relied on high-quality sets of astronomically observed line intensities for H II regions with fairly low electron temperatures (Te . 1.5 ×104 K), it has been shown that the error margins due to the atomic data are not always taken into account in observational work when quoting electron temperature uncertainties. When they are included, rather than trying to di erentiate plasma regions, an average temperature may be defined in some sources with a standard deviation comparable to the error margins ",
+    "of each temperature diagnostic. If multi-region plasmas are indeed in evidence, the observed diagnostic temperature variation in our sample might be resolved by  distributions only in the low-excitation region, thus leading to a single lower temperature for diagnostics such as [N II], [O II], and [S II] with the consequent abundance enhancements. However, even in these cases the di erences between observed line ratios and the predictions of the MB distribution di er by less than 2˙ if proper uncertainties are taken into account. In the high-excitation region, on the other hand, diagnostic temperature di erences in [O III], [S III], and [Ar III] do not seem to be reconciled by invoking  distributions, which then leaves the problem open to other unaccounted physical processes. It must be emphasized that these findings are not the rule as indicated by the extensive sample by (<>)Binette et al. ((<>)2012) of H II regions with mostly higher temperature (Te > 104 K); thus further detailed work would be required before  distributions can be firmly established. ",
+    "Regarding the e ects of the  distribution on the collisional rate coeÿcients, we have confirmed the reliability of their neglect for de-excitation, and an accurate (better than 10%) analytic expression has been derived to readily estimate -averaged rates for excitation from temperature tabulations of MB e ective collision strengths. The measure that regulates level-excitation departures from MB is T/Tex ≪1; hence, for IR transitions within the ionic ground terms with very low excitation energies (Tex < 103 K), the MB and -distribution electron impact excitation rates are essentially identical at nebular temperatures. IR abundance discrepancies with respect to the optical would then be a further indication of the relevance of  distributions. However, such discrepancies have not been reported; for instance, all planetary nebulae observed with ISO show consistent abundances as estimated from both IR and optical CEL ((<>)Wesson et al. (<>)2005), which then suggests that the MB distribution dominates. ",
+    "In the present work it has been demonstrated that error-margin capping in the ",
+    "collisional data relevant to nebular diagnostic implies—apart from detailed comparisons with previous datasets and in some cases recalculations—comprehensive benchmarks with spectral models and observations, and this is a task we intend to pursue in the ongoing discussion concerning the CEL–RL abundance discrepancies. ",
+    "We would like to thank Christophe Morisset, Instituto de Astronom´ıa, UNAM, Mexico, for sending us the temperature diagnostics for the H II region sample by (<>)Binette et al. ((<>)2012). We are also indebted to Grazyna Stasi´nska, Observatoire de Paris, France, for useful discussions regarding several aspects of the paper. "
+  ]
+}

jsons_folder/2014ApJ...791..117A.json

@@ -0,0 +1,157 @@
+{
+  "TESTING X-RAY MEASUREMENTS OF GALAXY CLUSTER OUTSKIRTS WITH COSMOLOGICAL SIMULATIONS ": [
+    "(<http://arxiv.org/abs/1404.4634v3>)arXiv:1404.4634v3  [astro-ph.CO]  23 Oct 2014 "
+  ],
+  "ABSTRACT ": [
+    "The study of galaxy cluster outskirts has emerged as one of the new frontiers in extragalactic astrophysics and cosmology with the advent of new observations in X-ray and microwave. However, the thermodynamic properties and chemical enrichment of this diffuse and azimuthally asymmetric component of the intra-cluster medium are still not well understood. This work, for the •rst time, systematically explores potential observational biases in these regions. To assess X-ray measurements of galaxy cluster properties at large radii (>R500c), we use mock Chandra analyses of cosmological galaxy cluster simulations. The pipeline is identical to that used for Chandra observations, but the biases discussed in this paper are relevant for all X-ray observations outside of R500c. We “nd the following from our analysis: (1) “lament regions can contribute as much as 50% at R200c to the emission measure, (2) X-ray temperatures and metal abundances from model “tted mock X-ray spectra in a multi-temperature ICM respectively vary to the level of 10% and 50%, (3) resulting density pro“les vary to within 10% out to R200c, and gas mass, total mass, and baryon fractions vary all to within a few percent, (4) the bias from a metal abundance extrapolated a factor of 5 higher than the true metal abundance results in total mass measurements biased high by 20% and total gas measurements biased low by 10% and (5) differences in projection and dynamical state of a cluster can lead to gas density slope measurements that differ by a factor of 15% and 30%, respectively. The presented results can partially account for some of the recent gas pro“le measurements in cluster outskirts by e.g., Suzaku. Our “ndings are pertinent to future X-ray cosmological constraints with cluster outskirts, which are least affected by non-gravitational gas physics, as well as to measurements probing gas properties in “lamentary structures. ",
+    "Subject headings: cosmology: theory • clusters: general • galaxies • methods : numerical • X-rays:galaxies:clusters "
+  ],
+  "1. INTRODUCTION ": [
+    "Clusters of galaxies are the largest gravitationally bound objects in our universe. These objects are massive enough to probe the tension between dark matter and dark energy in structure formation, making them powerful cosmological tools. Cluster-based cosmological tests use observed cluster number counts, the precision of which depends on how well observable-mass relations can constrain cluster masses. Finely tuned observable-mass relations require an understanding of the thermal and chemical structure of galaxy clusters out to large radii, as well as an understanding of systematic biases that may enter into observational measurements of the intracluster medium (ICM). ",
+    "A new area of study lies in studying the ICM in the outskirts of clusters, a region where the understanding of ICM physics remains incomplete (e.g., see (<>)Reiprich et al. (<>)2013, for an overview). Cluster outskirts can be considered to be a cosmic melting pot, where infalling substructure is undergoing virialization and the associated infalling gas clumps are being stripped due to ram pressure, depositing metal-rich gas in the cluster atmosphere, changing thermal and chemical structure of the ICM. Measurements at these regions will allow us to form a more complete assessment of the astrophysical processes, e.g. gas stripping and quenching of star formation in infalling galaxies, that govern the formation and evolution of galaxy clusters and their galaxies. ",
+    "Gas properties in cluster outskirts are also more suitable for ",
+    "cosmological measurements; the effects of dissipative non-gravitational gas physics, such as radiative cooling and feedback, are minimal in the outskirts compared with the inner regions. Gas density measurements in cluster outskirts will also help constrain the baryon budget. While recent X-ray cluster surveys have provided an independent con•rmation of cosmic acceleration and tightened constraints on the nature of dark energy ((<>)Allen et al. (<>)2008; (<>)Vikhlinin et al. (<>)2009), the best X-ray data, circa 2009, were limited to radii within half of the virial radius, and cluster outskirts were largely unobserved. ",
+    "Recent measurements from the Suzaku X-ray satellite have pioneered the study of the X-ray emitting ICM in cluster outskirts beyond R200c 1 (<>)(e.g., (<>)Bautz et al. (<>)2009; (<>)Reiprich et al. (<>)2009; (<>)Hoshino et al. (<>)2010; (<>)Kawaharada et al. (<>)2010). These measurements had unexpected results in both entropy and enclosed gas mass fraction at large radii. Entropy pro•les from Suzaku data were signi•cantly •atter than theoretical predictions from hydrodynamical simulations ((<>)George et al. (<>)2009; (<>)Walker et al. (<>)2012), and the enclosed gas mass fraction from gas mass measurements of the Perseus cluster exceeded the cosmic baryon fraction ((<>)Simionescu et al. (<>)2011). These results suggest that gasesous inhomogeneities might cause an overestimate in gas density at large radii. Suzaku observations and subsequent studies demonstrated that measurements of the ICM in cluster outskirts are complicated by contributions from the cosmic X-ray background, excess emission from gasesous substructures ((<>)Nagai & Lau (<>)2011; (<>)Zhuravleva et al. (<>)2013; (<>)Vazza et al. ",
+    "(<>)2013; (<>)Roncarelli et al. (<>)2013), and poorly understood ICM physics in the outskirts. However, analyses of cluster outskirts with both Planck Sunyaev-Zel•dovich and ROSAT X-ray measurements found otherwise ((<>)Eckert et al. (<>)2013a,(<>)b). The mysteries surrounding these X-ray measurements of cluster outskirts are still unsettled due to a number of observational systematic uncertainties, such as X-ray background subtraction. ",
+    "The latest deep Chandra observations of the outskirts of galaxy cluster Abell 133, a visually relaxed cluster with X-ray temperature TX = 4.1 keV, have given us an unprecedented opportunity to probe the ICM structure in cluster outskirts (Vikhlinin et al., in prep.). First, the high sub-arcsec angular resolution allows for ef•cient point source removal, the isolation of the cosmic X-ray background, and the detection of small-scale clumps, which dominate the X-ray •ux at large radii. Second, the long exposure time of 2.4 Msec also enables direct observations of the •lamentary distribution of gas out to R200c. ",
+    "To address potential biases that could affect observed ICM properties at large radii, we use mock Chandra observations from high-resolution cosmological simulations of galaxy clusters. The goal of this paper is to characterize the properties of diffuse components of the X-ray emitting ICM in the outskirts of galaxy clusters, and to assess the implications for X-ray measurements. Our analysis focuses on the effects that come from a combination of limited spectral resolution and low photon counts in cluster outskirts, where spectral contributions from metal line emissions become more signi•cant than those from thermal bremsstrahlung emissions. ",
+    "Our approach is similar in spirit as in (<>)Rasia et al. ((<>)2008) which pioneered the study of systematics on abundance measurements on the ICM by analyzing the spectral properties of mock plasma spectra generated with XSPEC. We extend the study of XSPEC generated mock spectra to the outskirt regions. Our results are valid for all observations of spectra from plasma with a multicomponent temperature. ",
+    "Speci•cally, we look at the accuracy of metal abundance measurements from spectral •tting and their consequential effects on the measurements of projected X-ray temperature, emission measure, deprojected temperature, gas density, gas mass, and hydrostatic mass derived from these pro•les. We explore potential biases by (1) measuring contributions of clumps and •laments to emission measurements, (2) testing the modeling of bremsstrahlung and metal line emissions in low density regions, and (3) checking for line of sight dependence in the density slope in cluster outskirts and differences in observed ICM pro•les for an unrelaxed cluster. ",
+    "This work will be useful in assessing the robustness of X-ray measurements beyond R500c, as we test both the spectral •tting of X-ray photons in low density regions, and the validity of •tting formulae that are used to reconstruct ICM pro•les. ",
+    "Our paper is organized as follows: in Section (<>)2 we describe the simulations we used and the mock Chandra analysis pipeline. We present our results in Section (<>)3, and give our summary and discussion in Section (<>)4. "
+  ],
+  "2. METHODOLOGY ": [],
+  "2.1. Cosmological simulations ": [
+    "We use a sample of high-resolution cosmological simulations of cluster-sized systems from (<>)Nagai et al. ((<>)2007a,(<>)b, hereafter N07) that assumes a ”at CDM universe with m = 1   = 0.3, b = 0.04286, h = 0.7, and σ8 = 0.9. The Hub-",
+    "ble constant is de•ned as 100h km and σ8 is the mass variance within spheres of radius 8 h1Mpc. We simulate these clusters with the Adaptive Re“nement Tree (ART) N-body+gas-dynamics code ((<>)Kravtsov (<>)1999; (<>)Kravtsov et al. (<>)2002; (<>)Rudd et al. (<>)2008), an Eulerian code with spatial and temporal adaptive re“nement, and non-adaptive mass re“nement ((<>)Klypin et al. (<>)2001). ",
+    "Our simulations include radiative cooling, star formation, metal enrichment, stellar feedback, and energy feedback from supermassive black holes (see Avestruz et al., in prep. for more details). Brie•y, we seed black hole particles with a seed mass of in dark matter halos with M500c >and allow the black holes to accrete gas according to a modi“ed Bondi accretion model with a density dependent boost factor ((<>)Booth & Schaye (<>)2009). Black holes feed back a fraction of the accreted rest mass energy in the form of thermal energy, ",
+    "(1) ",
+    "where ǫr = 0.1 is the radiative ef“ciency for a Schwarzschild black hole undergoing radiatively ef“cient Shakura & Sun-yaev accretion ((<>)Shakura & Sunyaev (<>)1973), and ǫf = 0.2 is the feedback ef“ciency parameter tuned to regulate the z = 0 black hole mass. ",
+    "We focus on two X-ray luminous clusters from the N07 sample to study the effects of metallicity, line of sight, and dynamical state on X-ray measurements in cluster outskirts. The core-excised X-ray temperatures of CL6 and CL7 are TX = 4.18 and TX = 4.11, respectively. The cluster mass and radii are and for CL6, and and for CL7. Each cluster is selected from simulation box with size Mpc, run on a 1283 uniform grid with 8 levels of re•nement, and has peak spatial resolution of ˇ 2.4h1 kpc. The corresponding dark matter particle mass in our regions of interest is is an unre-laxed cluster that experienced a 1:1 major merger at z ˇ 0.6, and CL7 is a typical relaxed cluster which has not undergone a major merger for z <1. We refer the reader to N07 for further details. "
+  ],
+  "2.2. Mock Chandra Pipeline ": [
+    "Using our simulated cluster sample, we create realistic mock X-ray maps of simulated clusters by (1) generating an X-ray •ux map, and (2) convolving the •ux map with the Chandra response •les to create photon maps. Below we outline our mock Chandra pipeline, where details can be found in (<>)Nagai et al. ((<>)2007b). "
+  ],
+  "2.2.1. X-ray Flux maps ": [
+    "We generate X-ray •ux maps for each of the simulated clusters along three orthogonal line-of-sight projections. To calculate the •ux map, we project X-ray emission from hydrodynamical cells along each line of sight within 3 × Rvir (ˇ 4 × R200c for the clusters in this work) of the cluster center. The X-ray emission as a function of energy from a single hydrodynamical cell of volume Vi is given as, ",
+    "(2) ",
+    "where ne,i, np,i, Ti, and Zi are respectively the electron number density, proton number density, temperature, and metal-licity in that cell volume. We compute the X-ray emissivity, E(Ti,Zi,z), using the MEKAL plasma code ((<>)Mewe et al. ",
+    "(<>)1985; (<>)Kaastra & Jansen (<>)1993; (<>)Liedahl et al. (<>)1995) and the solar abundance table from (<>)Anders & Grevesse ((<>)1989). We multiply the plasma spectrum by the photoelectric absorption corresponding to a hydrogen column density of NH = 2 ×1020 cm2 . ",
+    "We include results from four different •ux maps: (1) Zsim, (2) Z0.5, (3) Z0.05, and (4) Z0.5TX,1 keV. We generate the Zsim •ux map from X-ray spectra using all hydrodynamic values directly output from our simulation runs. To isolate the effects of metallicity on our simulated spectra, we use Zi = 0.5Z⊙ for all i-th cell elements in our Z0.5 ”ux maps and a constant Zi = 0.05Z⊙ for all i-th cell elements in our Z0.05 ”ux maps. Current observations do not yet probe metal abundance pro“les in cluster outskirts, and often extrapolate the abundance at radii beyond R500c. Given the typical range of metallicity that observers have found near R500c (Z ˇ 0.3Z⊙) (e.g., (<>)Matsushita et al. (<>)2007; (<>)Leccardi & Molendi (<>)2008; (<>)Komiyama et al. (<>)2009; (<>)Werner et al. (<>)2013), we choose these two values for Zi to bracket a potential range of metal-licities in the outskirts. The order of magnitude difference probes how X-ray measurements of the ICM and inferred quantities might be affected by an incorrect extrapolation or mis-measurement of both a metal rich and metal poor environment. ",
+    "We remove the effects of a multi-temperature medium by •xing both the metal abundance to Zi = 0.5Z⊙, and the temperature to TX = 1 keV in the Z0.5TX,1 keV map, which is a characteristic temperature in the outskirts of a galaxy cluster in our probed mass range. "
+  ],
+  "2.2.2. Mock Chandra Photon Maps and Spectra ": [
+    "To simulate mock Chandra data, we convolve the emission spectrum with the response of the Chandra front-illuminated CCDs ACIS (both the Chandra auxiliary response •le (ARF) and redistribution matrix •le (RMF)) and draw a number of photons at each position and spectral channel from the corresponding Poisson distribution. The photon maps for our mock Chandra data has an exposure time of 2 Msec, comparable to the 2.4 Msec deep Chandra observations of Abell 133. Since we are interested in probing physical causes for biased X-ray measurements, we do not include any simulated backgrounds. ",
+    "From our mock photon maps, we generate images in the 0.7  2 keV band, and use them to identify and mask out clumps from our analysis. We use the wavelet decomposition algorithm described in (<>)Vikhlinin et al. ((<>)1998). This procedure is consistent with the small-scale clump removal performed by observers. ",
+    "Detected clumps are within a limited •ux of ˘ 3 × 1015 erg s1 cm2 in the 0.7  2 keV energy band, corresponding to a luminosity of ˘ 1.5 × 1042 erg s1 for clusters at zobs = 0.06, the observational redshift of our clusters. Any remaining small-scale structures fall below our clump detection limit. The total gas mass in excluded clumps is no more than a few percent of the total enclosed gas mass. ",
+    "X-ray emission in cluster outskirts also receive azimuthally asymmetric contributions from •lamentary structures. Similar to the analysis of X-ray emission in A133 outskirts, after clump removal, we identify •lamentary regions as annular sections with an average •ux that exceeds the average •ux within the entire annulus. We exclude the •lamentary contribution from our •nal analysis. We include a sample image map with identi•ed clumps and •laments in Figure (<>)1. ",
+    "From the mock Chandra photon map, we extract a grouped ",
+    "spectrum from concentric annular bins centered on the main X-ray peak. Annular regions are de•ned with rout/rin = 1.25, where rout and rin are the outer and inner edges of the annular bin, respectively. The spectra exclude photons from regions corresponding to clumps and •laments. For each spectrum, we perform a single-temperature •t in the 0.1  10 keV band using XSPEC version 12.8 with the MEKAL model plasma code and a C-statistic •t ((<>)Cash (<>)1979) to extract the projected X-ray temperature TX,proj(r) and abundance Zproj(r). We use the same Chandra ARF and RMF •les to •t a model spectrum to the mock photon spectra. Temperature, metal abundance, and spectral normalization are the only free parameters in the •t. "
+  ],
+  "2.2.3. Analysis of the ICM ": [
+    "To compare with observed Chandra data, we reconstruct the emission measure pro•le and repeat the deprojection analysis by (<>)Vikhlinin et al. ((<>)2006). This analysis reconstructs the spherically averaged density and temperature pro•les of the intracluster medium with 3D analytic models. We also estimate the total cluster mass assuming hydrostatic equilibrium from the reconstructed 3D density and temperature pro•les. ",
+    "To calculate the projected emission measure pro•le EMM = R nenpdl, we use two main input ingredients: (1) the azimuthally averaged X-ray surface brightness pro•le X SB, and (2) the projected 2D X-ray temperature TX,proj and metallic-ity pro•les Zproj described in Section (<>)2.2.2. We can relate the deprojected EMM to the two ingredients as follows, ",
+    "(3) ",
+    "We show the emission measure pro•le for CL7 along the y-axis, where •lamentary features are most prominent in Figure (<>)2, and the corresponding effect of clump and •lament removal from the analysis. The solid blue line corresponds to the emission measure pro•le that include clumps and •lamentary substructure, and dotted line corresponds to the emission measure pro•le that excludes the substructure. The bottom panel shows the ratio between the pro•le with substructure to the pro•le without, and illustrates the extent of the excess emission in cluster outskirts. For this cluster, the excess of the best-•t pro•le can be as much as a factor of 2 at R200c to a factor of 3 at 3 × R200c. The errorbars correspond to the binned data, and the excess in individual bins are as high as a factor of 6 in the •lamentary regions. Excess emission measure from a substructure is visible at R ˇ 2 kpc. ",
+    "We extract the X-ray surface brightness pro•les from photons in the 0.7  2 keV band in concentric annuli of rout/rin = 1.1, giving us a count rate in each annular bin. We use the projected X-ray temperature and metal-licity to calculate the MEKAL model plasma emissivity, (TX,proj(rproj),Zproj(rproj),z). With the relation given by Equation ((<>)3), we use interpolated values of the model plasma emissivity to convert the count rate into a projected emission measure. ",
+    "The deprojection process is fully described in (<>)Vikhlinin et al. ((<>)2006), and can be summarized as follows. The analytic form of our 3D gas density model is given ",
+    "FIG. 1.• Top: Mock Chandra maps of CL6 in 0.7  2 keV band viewed from left to right along the x, y, and z axes. Bottom: Mock Chandra maps of CL7 in 0.7  2 keV band. Each region is 5 Mpc across. Identi•ed clumps and •lamentary structures are respectively outlined by green ellipses annular sections. Both of these regions are excluded from our •nal analysis. ",
+    "FIG. 2.• We show the effects of clump and •lament removal on the emission measure pro•le for a sample projection for CL7 in the y direction. Pro•les with both clumps and •laments are shown in the solid lines, no clumps in the dash-dotted lines, and no clumps nor •laments in the dotted lines. The ratio between solid (dash-dotted) and dotted is shown in the excess panel. Substructure in this cluster can boost the best •t emission measure by up to a factor of 3, and binned emission measure by up to a factor of 6 in the •lamentary regions. ",
+    "by, ",
+    "(4) ",
+    "This is a modi“cation of the β-model that allows for separate “tting of the gas density slope at small, intermediate, and large radii. ",
+    "The analytic form of our 3D temperature pro•le is a product of two terms that describe key features of in observed projected temperature pro•les ((<>)Vikhlinin et al. (<>)2005), ",
+    "(5) ",
+    "The •rst term takes into account the temperature decline at large radii with a broken power law with transition radius, rt , ",
+    "(6) ",
+    "with a and b as free parameters. The second term models the temperature decline in the central region due to radiative cooling, ",
+    "(7) ",
+    "We project the 3D model of the temperature pro•le, weighting multiple temperature components using the algorithm from (<>)Vikhlinin et al. ((<>)2006). We then “t the projected model to the projected X-ray temperature from our mock data, “tting in the radial range between 0.1  r/R200c  3. ",
+    "The 3D models for gas density and temperature pro•les allow us to estimate the total mass of the cluster, assuming hydrostatic equilibrium, ",
+    "(8) ",
+    "where µˇ 0.59 is mean molecular weight for the fully ionized ICM, mp is the proton mass, and we have set the Boltzmann constant to be unity such that the temperature T3D(r) is in unit of energy. "
+  ],
+  "3. RESULTS ": [
+    "To test the MEKAL modeling of bremsstrahlung and metal line emissions in low density regions, we perform the XSPEC •t with a •xed metal abundance parameter: Z•x = 0.5Z⊙ for the Z0.5 map, and Z“x = 0.05Z⊙ for the Z0.05 map. The metal-licity in the Z0.05 map is close to the simulation metallicity in cluster outskirts, but we use the Z0.5 map to also check the effects of a possible scenario where a higher abundance of metals sits in cluster outskirts. We then compare results from each Z“x case with the Z“t case, where we perform the “t for all three parameters. ",
+    "To eliminate the effects of a multi-temperature medium, we also perform the XSPEC •t on our Z0.5 TX,1 keV map. We generate ICM pro•les using a the best-•t metal abundance parameter and •xed temperature, and compare with the pro•les resulting from the known input metal abundance and temperature value. "
+  ],
+  "3.1. Recovered temperature and density pro•les with known abundance measurements ": [
+    "In this section, we check for consistency in gas density measurements from spectral •tting with the XSPEC •t performed using only two free parameters: projected X-ray temperature and normalization of •t. We use the Z0.5 and Z0.05 photon maps for this experiment, and •x the abundance parameter to the true abundance of the map. ",
+    "Figure (<>)3 shows the best-•t value for the projected X-ray temperature for each map. In cluster outskirts, the best •t X-ray temperature for the Z0.05 maps is systematically higher than that of the Z0.5 map, and the gas density differs by ˘ 20%. Note that while the true temperature of the two maps in each radial bin is identical, their measurements differ up to ˘ 15%. The discrepancy points to the degeneracies between •tting parameters. While the •tting procedure assumes a single-temperature •t, the true ICM is a multi-temperature medium, thus requires more degrees of freedom to capture the inhomogeneities. Both the metal abundance and the normalization of the •t offer additional degrees of freedom to minimize the residuals, so it is not surprising that statistically signi•cant differences can arise in measured X-ray temperatures if the metal line contributions are different. We plot the spectra of photons from the radial bin with the largest deviation in measured X-ray temperature (R ˇ 2 × R200c) in Figure (<>)4. Compared to the spectrum from the Z0.5 photon map (red points), the spectrum from the Z0.05 map (blue points) has a much lower emission from metal line cooling, and therefore it has a suppressed peak in the energy spectrum. The solid lines show the best •t model spectrum for each map. ",
+    "With a metal abundance parameter •xed to the true value of Z = 0.5Z⊙, the model spectrum overshoots the peak of the mock photon spectrum at the Fe-L complex between 0.8 and 1.4 keV, and the best “t X-ray temperature is TX = ",
+    "0.81 ± 0.01keV. If we allow the metal abundance to vary as an additional free parameter, both the best •t metal abundance (Z = 0.21 ± 0.03Z⊙) and the X-ray temperature (TX = 0.76 ±0.02keV) are lower and the residual difference between the mock photon counts and the model spectrum improves. ",
+    "In Figure (<>)5, we show how the systematic bias in metal abundance goes away in the absence of a multi-temperature ICM. The axes show the best •t metal abundance as a function of radius along three different lines of sight for our Z0.5 TX,1 keV map. This test isolates biases due to density inhomogeneities, lower photon counts, and instrumental response. For a map with uniform temperature, the •tting procedure well recovers the input constant metallicity, and does not exhibit a systematic decline. The best •t projected X-ray temperature is also well recovered to the •xed input value. ",
+    "The suppressed peak in the mock photon spectrum in Figure (<>)4 can be attributed to a high temperature phase of gas in the outskirts. For gas with an average temperature of TX ˇ 1 keV, the Fe-L line would be sensitive to a higher temperature component of gas, even if the metallicity of that component is the same (e.g., see Figure 3 in (<>)Mazzotta et al. ((<>)2004) and Figure 23 in (<>)Böhringer & Werner ((<>)2010)). ",
+    "Note, if the abundance parameter were not •xed (magenta dotted line in Figure (<>)4, the best •t abundance parameter would have to be lower than the true value Z = 0.5Z⊙ to better minimize the residuals in the “tting procedure. If we were to increase the X-ray temperature in the model spectrum, the residual at the peak would improve, but at the expense of increasing the residual values at other energies. ",
+    "On the other hand, for the Z0.05 spectra in Figure (<>)4, there are fewer photons from metal line cooling. Hence, most of the spectral features are hidden in Poisson noise. Because of the suppressed spectral features, the •tting procedure produces a best-•t X-ray temperature and normalization that will better minimize the residuals near the peak of the spectrum as opposed to at energies with much fewer counts. To minimize the residuals near the peak, the •tted X-ray temperature must then be higher to harden the model spectrum, which is why the best •t projected X-ray temperature for the Z0.05 map is systematically higher in the outskirts, where photon counts are low. "
+  ],
+  "3.2. Testing metal abundance measurements in cluster outskirts ": [
+    "The robustness of metal abundance measurements in the low density outskirts is not well understood. In this section, we compare the abundance measurements from spectral •tting to the true abundance from our photon maps. We also discuss the effects on the projected X-ray temperature, projected emission measure and the reconstructed three dimensional gas density pro•le. We begin by comparing variations in projected X-ray temperature TX,proj and abundance measurements Zproj from our Z0.5 and Z0.05 photon maps, where we have set the input metal abundance to constant values. ",
+    "Figure (<>)6 compares ICM pro•les from our Z0.5 and Z0.05 mock X-ray •ux maps of CL7, projected along the z-axis. Results along other axis projections are qualitatively similar. The top left panel shows the metal abundance measurements retrieved from our mock spectra, •tting the mock spectra to MEKAL model spectra using XSPEC. We de•ne fZ•t /Z•x as the ratio between the best •t abundance parameter to the true abundance of our photon map. The fZ•t /Z•x pro•le shows that the while XSPEC •tting procedure recovers a Z•t value that is within a factor of 2 of the true input abundance of the photon ",
+    "FIG. 3.• (Left) The projected X-ray temperature from spectral •tting and (right) the corresponding deprojected 3-D density pro•le for CL7. Spectral •ts used a •xed abundance parameter set to the true abundance of the photon map. Mock maps were generated with constant •xed metallicity (Z0.5 = 0.5Z⊙ in red solid and in blue dash-dotted). The black line in the fTX and fˆg axes is the ratio between the pro“le obtained using a “xed Z0.5 and the pro“le using a “xed Z0.05. The black circles indicate the ratio between the TX,proj data points. Spectral “tting of two maps with identical gas density and temperature, but differing abundances, yield recovered density pro“les that differ by up to 20%. ",
+    "map, the abundance recovery is signi•cantly worse at larger radii. ",
+    "For the Z0.5 map, the abundance measurements has a systematic decline from the true value at large radii R & 0.7R200c. As discussed in Section (<>)3.1, the metal abundance parameter adjusts to compensate for the multi-temperature medium when we perform a single-temperture spectral •t. Thus, the best •t abundance parameter will be smaller than the true abundance in order to minimize the residual around the suppressed emission lines. However, if there are too few photons from metal line cooling, the poisson errors become large, and therefore this systematic effect is less apparent since the statistical errors dominate. This is why the last two radial bins do not show underestimation in abundance measurements. ",
+    "For the Z0.05 map, the photon counts around the peak of the spectrum (0.7  1 keV) is a factor of three lower than that of the Z0.5 spectrum (See Figure (<>)4). In addition to the intrinsically less pronounced metal lines, the low photon count makes it more dif•cult for the •tting routine to discern between contributions from metal line cooling and thermal bremsstrahlung emissions, leading to more scatter in the abundance measurements shown in Figure (<>)6. Note that similar scatter is seen in the last two radial bins from the Z0.5 map, which also has a very low photon count. ",
+    "The top right panel of Figure (<>)6 shows the projected X-ray temperature pro•le (red and blue points for the respective abundances) from spectral •tting, and the corresponding best •t projected 3D temperature model (thin lines of the same color). We measure the relative bias in TX,proj as the ratio of the projected X-ray temperature measured with abundance as a free parameter (the pro•le in Figure (<>)6 compared with the X-ray temperature measured with the abundance parameter •xed to the true abundance of the map (see Figure (<>)3). The X-ray temperature measurements from •ts with abundance as a free ",
+    "parameter (Z = Z•t) vary up to ˘ 10% of the measurements with a •xed abundance parameter (Z = Ztrue ). Note, the relative bias in projected X-ray temperature from spectral •tting is in the same direction as that of the abundance measurement. ",
+    "The cause of the correlation in the relative bias of both the abundance and X-ray temperature becomes evident when we compare model spectra (see Figure (<>)7). When the best •t abundance is higher (lower) than the true abundance, the peak of the model spectrum will sit above (below) the mock spectrum, and a higher (lower) X-ray temperature is necessary to harden (soften) the spectrum to minimize the residuals. Note, while •xing the metal abundance parameter to a value that is •ve times the true value signi•cantly biases the value of the best •t X-ray temperature parameter, it does not signi•cantly increase the error in the X-ray temperature parameter. The X-ray temperature •t is mostly sensitive to shape of the continuum, and most of the residual contributions to the error in X-ray temperature come from energy bins outside of the Fe-L complex. Here, the model spectra are still within the errorbars of the mock data. ",
+    "An interesting feature to note in the projected X-ray temperature pro•le is that the projected 3D temperature model •ts the data points well only out to R . R200c. While the best-•t model pro•le is within the errorbars of the mock data, it does not capture the emerging trend of the decreasing slope of the projected X-ray temperature at larger radii. The departure from the smooth temperature model pro•le is indicative of the complicated, inhomogeneous temperature structure in cluster outskirts. The smooth temperature model does not have enough degrees of freedom to account for the bumpier features of the TX,proj data points, indicating that perhaps a modi•ed •tting formula would be appropriate for total mass measurements outside of R200c. ",
+    "Note, the errorbars at large radii for the metal abundance ",
+    "FIG. 4.• Energy spectra from the Z0.5 (red) and Z0.05 photon maps corresponding to the third to the last radial bin in Figure (<>)3 (R ˇ 2 ×R200c). Spectra are normalized to the size of the energy bin. The solid lines show the best •t model spectra with the abundance parameter •xed to the true abundance of the photon map. The dotted line corresponds to the best •t model spectrum allowing both the abundance and temperature values to vary. The legend labels the corresponding metallicity and best •t projected X-ray temperature. We show the residual value between the model and our mock data in the lower panel. The statistically signi•cant difference between all of the best •t X-ray temperature values is due to a degeneracy in •tting a multi-temperature medium with a single temperature •t. The best •t abundance parameter for the Z0.5 map in this bin is lower than the true abundance to compensate for the temperature that has been biased low. Note, the lower metal abundance in the Z0.05 map produces fewer photons from metal line cooling, leading to suppressed spectral features. There are 18,800 counts in the bin from the Z0.05 map, and 43,000 counts in the bin from the Z0.5 map. ",
+    "measurements are not as good as those of the X-ray temperature measurements because the abundance •tting requires an order of magnitude more photons to have the same statistical uncertainty as the X-ray temperature. The metal abundance is only affected by line emission contributions as opposed to the X-ray temperature, which also has contributions from thermal bremsstrahlung. ",
+    "From Equation ((<>)3), we can see that for the same X-ray surface brightness X SB at a given radius, a higher (lower) gas density is necessary to compensate for a lower (higher) X-ray emissivity . The bottom two panels in Figure (<>)6 show the corresponding projected emission measure and gas density for the same photon maps as in the top two panels. The projected emission measure varies to 20% at all radii, and the gas density to a level of 15%. ",
+    "We note that the apparent enhanced bias in projected emission measure at intermediate radii for the Z0.5 map, shown in red, is due to effects from integrating over the line of sight. The density pro•le measured with a •xed abundance parameter is steeper at intermediate radii than the density pro•le measured with the best •t values for the abundance parameter. Hence, along an equal line of sight, there is a relatively lower emission measure in the •xed abundance case than in the best •t abundance case. ",
+    "In summary, the relative bias in abundance and projected X-ray temperature are correlated, and vary up to 50% and 10%, ",
+    "FIG. 5.• The best-•t projected metallicity along three different projections of CL7. Mock maps were generated with both a constant •xed metallicity of Z0.5 = 0.5Z⊙ and constant “xed temperature of TX = 1 keV. The lower axis shows the ratio between the best-“t metal abundance and the true metal abundance. X-ray temperature and normalization are free parameters. In the absence of a multi-temperature medium, the abundance is well recovered out to large radii. ",
+    "respectively. Both the resulting projected emission measure and gas density pro•les vary to 10% at low and intermediate radii, but deviate as much as 40% and 20% in emission measure and gas density, respectively. "
+  ],
+  "3.3. Systematic effects of metal abundance measurements on gas pro•le measurements ": [
+    "As described in Section (<>)3.2, a high (low) bias of the abundance and X-ray temperature measurements would lead to a suppressed (enhanced) density measurement in that radial bin. ",
+    "In this section, we examine the systematic effects on gas pro•le measurements with a factor of 2 and 5 bias in the abundance •tting at all radii. For this test, we use the Z0.05 map where we take the metallicity to be constant at Z = 0.05Z⊙ throughout the simulation. We choose this value since it is closer to the metal abundance at large radii R & R200c in our self-consistent cluster simulation with metal enrichment and advection. We run XSPEC “tting by “xing the abundance parameter at metallicities a factor of 2 and 5 from the true value from the map: Z“x/Z⊙ = 0.01,0.025,0.1,0.25, and we compare the results to those “tted with the true value Z = 0.05Z⊙. To isolate the effects from all other quantities, we only allow the projected X-ray temperature and the spectral normalization to be free parameters in the “tting . ",
+    "In Figure (<>)8, we plotted the X-ray temperature, projected emission measure, and gas density for each case of Z•x and compare to the Z•x = Ztrue = 0.05Z⊙ case (black solid line). Consistent with what we found in Section (<>)3.2, an over (under) estimate of the abundance will lead to suppressed (enhanced) emission measurements and subsequently gas density measurements. ",
+    "If the abundance is measured to within a factor of two of the true metal abundance, the resulting density measurements ",
+    "FIG. 6.• From top left panel in a clockwise direction, the projected metallicity, projected X-ray temperature, recovered 3-D density pro•les, and projected emission measure for CL7. Mock maps were generated with constant •xed metallicity (Z0.5 = 0.5Z⊙ in red solid and Z0.05 = 0.05Z⊙ in blue dash-dotted). The lower axes, labeled with an f , show the ratio between pro“les recovered with metal abundance as a free parameter to pro“les recovered with abundance “xed to the known input abundance. The systematic decline of the best-“t projected metallicity beyond R500 is due to the multi-temperature medium, as shown in Figure (<>)4. The effects of low photon count from metal line cooling is visible in both the Z0.05 best “t projected metallicity as well as in the last two bins of Z0.5. The bias in metal abundance measurement introduces variations of up to 15% in recovered density pro“les. ",
+    "in the outskirts will be within 15%. However, for the most extreme case of an abundance measurement biased by a factor of 5, the density measurements will have up to a 35% bias. ",
+    "The emission measure pro•le on the right panel of Figure (<>)8 shows that an abundance measurement that is higher than the true value can steepen the pro•le in cluster outskirts. For observational measurements that extrapolate the abundance at large radii, this could introduce an even larger bias in the emission measure, density and temperature. Our tests that ",
+    "•x the abundance measurement to be a factor of two and •ve times the true abundance show how severely this extrapolation can propagate to inferred quantities, even at R200c. Most notably, for an assumed abundance that is a factor of •ve higher than the true abundance, the gas density is biased low by ˇ 15%. "
+  ],
+  "3.4. Hydrostatic mass and gas mass fraction ": [
+    "FIG. 7.• Grey errorbars show the energy spectrum from the Z0.05 photon map corresponding to the third to the last radial bin in Figure (<>)3 (R ˇ 2 × R200c). Spectra are normalized to the size of the energy bin. The solid lines show the best •t model spectra with the abundance parameter •xed (0.01Z⊙ in blue, 0.05Z⊙ in black, and 0.25Z⊙ in cyan), and the best “t projected X-ray temperature. The dotted lines correspond to model spectra with the projected X-ray temperature “xed to TX,proj = 0.944 keV, which is the value of the best-“t X-ray temperature with Z“x = Ztrue. We show the residual value between the model and our mock data in the lower panel. The model spectra show that the best-“t projected X-ray temperature will be biased in the same direction as the best-“t abundance parameter, as shown in Figure (<>)6. ",
+    "From Equation ((<>)8), we can see that the X-ray measurement of the hydrostatic mass of the cluster is sensitive to three quantities: the best •t 3D model of the temperature pro•le, the logarithmic slope of the 3D temperature pro•le, and the logarithmic slope of the gas density pro•le. The left panel of Figure (<>)9 illustrates how each of these quantities is affected by a systematic over (under) •t abundance. ",
+    "For the case of recovering the metal abundance to within a typical factor of two (Z•x = 0.025Z⊙ and Z“x = 0.1Z⊙), all three quantities are within <10% at intermediate and large radii. At large radii, the bias in the 3D temperature and logarithmic density slope dominate to drive the hydrostatic mass bias in the same direction. A lower temperature “t in the outskirts corresponds to a shallower logarithmic density slope, and therefore a smaller hydrostatic mass (see dotted blue and dot-dashed green thick lines in the right panel of Figure (<>)9). However, the lower “tted temperature and shallower logarithmic slope correspond to a larger enclosed gas mass (see corresponding thin lines in Figure (<>)9), as underestimates in both abundance and temperature lead to overestimates in emission measure, therefore bias the gas density high. ",
+    "Figure (<>)10 shows that the combined bias in enclosed gas mass and the hydrostatic mass drives the bias in gas fraction up for the low •xed abundance values, and down for the high •xed abundance values. This shows that a poor •t to the X-ray temperature and metallicity in cluster outskirts is potentially causing biases in the Suzaku gas mass fraction measurements at large radii. The same magnitude of errors can come from an incorrectly extrapolated metal abundance in cluster outskirts. ",
+    "For a standard factor of 2 error in the abundance measure-",
+    "ment, the gas mass fraction is only affected by 10%, but any underestimate of the 3D temperature at large radii due to an overly steep poor •t in the deprojection procedure could lead to an even higher gas mass fraction by driving the hydrostatic mass low. ",
+    "For an abundance that is measured 5 times lower than the true abundance, the measured gas mass fraction could be biased high by 70% given a true abundance of Z = 0.05Z⊙. ",
+    "While the bias in enclosed gas mass and hydrostatic mass at small radii is rather large, we do not consider this to be representative of biases present in observations; the error in abundance measurement is primarily an issue in the low density outskirts where photon statistics are poor. Additionally, at smaller radii, the gas is much hotter, so the metal abundance and X-ray temperature parameters are less degenerate with each other in the spectral •t. "
+  ],
+  "3.5. Potential issues for gas density slope measurements ": [
+    "We test two potential issues for density slope measurements in cluster outskirts to compare with biases in measurements from spectral •tting and metal abundance extrapolation: projection bias from triaxiality and mass accretion history. ",
+    "To test the bias due to projection effects from traxiality, we compute the inertia tensors of the gas mass at R500c for our clusters. For CL7, the semi-minor and semi-major axes of the inertia tensor lie almost parallel to the x-and y-axes respectively, allowing us to use the projections along these axes to make a preliminary assessment of the effects of cluster shape. ",
+    "To test the effect of accretion history, we compare two clusters, CL6 and CL7 that have similar mass but differ in dynamical states. CL6 has a recent major merger and CL7 has been quiescent since z ˘ 1. We compare these two clusters to identify the extent of steepening that is mainly due to recent accretion history. ",
+    "Figure (<>)11 shows the logarithmic gas density slope for our two test cases along various projections, CL6 and CL7. In our relaxed cluster, CL7, the density slope projected along each axis varies by no more than 15%. We would naively expect a signi•cant difference between a line of sight along the semi-major axis (y-axis) and along the semi-minor axis (x-axis). However, the difference in density slope between these two line of sight projections amounts to only a few percent. Effects due to line of sight projection are not likely to signi•cantly steepen observed density pro•les. ",
+    "CL6 is a dynamically disturbed cluster that experienced a 1:1 major merger at z ˇ 0.6, and has a smaller infalling structure at R & R200c at z = 0. The x-and y-projections correspond to lines of sight that are perpendicular to the plane of accreting substructure. The effects of a merging substructure are visible in the z-projection (dotted green), where the density slope is no longer monotonically increasing at larger radii. The outskirts of CL6 cluster along the x-and y-projections have an observed density pro•le that exceeds the density slope along the x-projection of CL7 by ˇ 30%, con•rming that X-ray observations should be able to see a difference in density slope between clusters of varying accretion histories. ",
+    "These two mechanisms have the potential to contribute additional bias to the observed density slope than the bias introduced from spectral •tting (ˇ 5%). "
+  ],
+  "4. SUMMARY AND DISCUSSION ": [
+    "The study of galaxy cluster outskirts is the new frontier in cluster-based cosmology. In this work, we used cosmological simulations of galaxy clusters to investigate potential bi-",
+    "FIG. 8.• The above •gures are pro•les corresponding to the Z0.05 •ux maps. The plot on the left shows the ratio between pro•les using various values for Z•x, and the corresponding pro•le with Z•x = Ztrue = 0.05Z⊙. From top to bottom panel, these respectively are the ratios in X-ray temperature, gas density, and projected emission measure. The “gure on the right shows the projected emission measure for each value of Z“x. At 3 × R200c, an abundance measurement that is biased by a factor of 2 results in gas densities that are biased by 15%. ",
+    "FIG. 9.• The above •gures are pro•les corresponding to the Z0.05 •ux maps, with various values of Z•x, identical to the data set from Figure (<>)8. Left: Ratios of quantities that contribute to the total mass measurement -the best •t 3D X-ray temperature, the logarithmic slope of the 3D temperature pro•le, and the logarithmic slope of the density pro•le. Right: The total mass pro•le (thick lines), and the gas mass pro•le (thin lines). At 3 × R200c, an abundance measurement that is biased by a factor of 2 results a logarithmic gas density slope that is biased by <5%. ",
+    "FIG. 10.• The above •gures are pro•les corresponding to the Z0.05 •ux maps, with various values of Z•x, identical to the data set from Figure (<>)8. The panels on the left are ratios of the gas mass, hydrostatic mass, and gas mass fraction, and the •gure on the right is the gas mass fraction pro•le for each •xed value of the metal abundance. At 3 × R200c, an abundance measurement that is biased by a factor of 2 results in a fractions that is biased by ˘ 5%. ",
+    "FIG. 11.• The logarithmic gas density slope pro•le of CL6 (dash-dotted lines) and CL7 (solid lines) along different projections. The z projection for CL6 is perpendicular to the plane of a merger. The bottom panel is the ratio of each pro•le to the pro•le of CL7 along the x-projection. The logarithmic gas density slope of CL6, a dynamically disturbed cluster, is steeper than that of the CL7. ",
+    "ases in metal abundance measurements from X-ray spectra in the low density cluster outskirts (R >R500), where metal line cooling contributions become signi“cant. Using X-ray maps with a constant input metal abundance, we showed how systematically biased metal abundance measurements affect ICM quantities such as the gas density and temperature pro“les. ",
+    "In order to test other potential sources of systematic uncertainty in density slope measurements from Chandra observations of Abell 133 (Vikhlinin et al., in prep.), we performed our mock X-ray analysis for projections along the semi-major and semi-minor axes of a relaxed cluster, and for a dynamically disturbed cluster. ",
+    "To summarize our •ndings: ",
+    "We test the extent of biases that may arise from incorrectly extrapolating the metal abundance measurement in galaxy cluster outskirts by •xing the metal abundance to a factor of 2 and a factor of 5 above and below the true abundance. An abundance assumed a factor of ",
+    "5 too high biases the gas density measurement and the enclosed total mass by as much as 15% at R200c. ",
+    "We note that fully testing the accuracy of X-ray measurements in cluster outskirts requires a comparison of measurements of ICM properties directly from the simulation with 3D •laments removed in a self-consistent manner with our projected •lament •nder. While the test cases used in this study do not include high mass clusters, any bias from incorrect abundance measurements would not exceed the bias found in the lower mass counterparts. High mass clusters have larger temperatures at R200c, resulting in a decreased relative contribution of metal line emissions to the X-ray emission measure. This analysis does not include any contributions from simulated backgrounds, and the effects of instrumental and X-ray backgrounds are additional sources of systematic biases that have not been accounted for in our discussions. ",
+    "Furthermore, our analysis does not take into account non-equilibrium electrons at large radii, which have a lower temperature than the mean ICM gas temperature ((<>)Rudd & Nagai (<>)2009). The temperature bias from non-equilibrium electrons is small in clusters of the mass scales we tested, and we expect non-equilibrium electrons to have less of an effect on the emission measure in the cluster outskirts than biases from metal abundance measurements. Metal line contributions have a signi•cant contribution to the X-ray emission in the low density cluster outskirts, and the X-ray emission has a weak dependence on any biases in the temperature at all radii (/ T 1/2 ). Alternatively, in higher mass clusters, non-equilibrium electrons have larger deviations from the mean ICM gas temperature because the equilibration timescale is longer. The corresponding biases in X-ray measurements of the outskirts of high mass clusters is a topic for future work. ",
+    "Our •ndings emphasize the need for long exposure times to have accurate measurements of metal abundance and X-ray temperature in the low density outskirts of galaxy clusters. Accurate X-ray measurements of the hydrostatic mass require an additional term in the temperature modeling in cluster outskirts to account for the shallow slope in the outermost radii. Additionally, accounting for errors in the metal abundance measurement will require more careful modeling of the thermal and chemical structure in cluster outskirts. ",
+    "In addition to gas inhomogeneities (e.g., (<>)Nagai & Lau (<>)2011), biased measurements of the metal abundance in cluster outskirts may partially explain the enhanced gas mass fraction (e.g., (<>)Simionescu et al. (<>)2011) and •attened entropy pro•les (e.g., (<>)Walker et al. (<>)2012) observed in cluster outskirts. Errors in metal abundance could produce enhanced emission measurements and a steeper 3D temperature pro•le, leading to overestimates in gas mass and underestimates in hydrostatic mass. ",
+    "We have identi•ed three potential mechanisms that contribute to density steepening in our mock data, and may affect the observed density slope beyond R200c: (1) overestimation of the abundance, (2) a line of sight corresponding to the semi-minor axis, and (3) rapid recent mass accretion. For (1), the biases introduced by spectral •tting are not likely to exceed 5%. The two physical mechanisms (2) and (3) had respective effects of 15% and 30%. ",
+    "The mass accretion rate of a galaxy cluster can in•uence its DM density ((<>)Cuesta et al. (<>)2008; (<>)Diemer & Kravtsov (<>)2014) and gas pro•les (E.T. Lau et al., in prep.). Accurate measurements of gas density and temperature pro•les from X-ray observations of cluster outskirts will provide information on the recent mass accretion history of a galaxy cluster, which is one of the dominant systematics in mass-observable relations in cluster cosmology. Deep observations of cluster outskirts will allow us to better understand the growth of galaxy clusters though mass accretion from the surrounding •lamentary structures. ",
+    "A careful consideration of all potential biases that enter into ",
+    "ICM measurements in galaxy cluster outskirts will enable us to fully use clusters as cosmological probes. Results from this work will also be useful for future missions, such as SMARTX 2 (<>)and Athena+ 3 (<>), which will begin mapping the denser parts of the •lamentary cosmic web. ",
+    "We thank the referee for the useful feedback, and Elena Rasia for comments on the manuscript. This work is supported by NSF grant AST-1009811, NASA ATP grant NNX11AE07G, NASA Chandra grants GO213004B and TM4-15007X, and by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center. CA acknowledges support from the NSF Graduate Student Research Fellowship and the Alan D. Bromley Fellowship from Yale University. "
+  ]
+}

jsons_folder/2014ApJ...794...74J.json

@@ -0,0 +1,98 @@
+{
+  "EFFECTS OF LARGE-SCALE ENVIRONMENT ON THE ASSEMBLY HISTORY OF CENTRAL GALAXIES ": [
+    "Intae Jung 1,2 , Jaehyun Lee 1 , and Sukyoung K. Yi 1 ",
+    "(<http://arxiv.org/abs/1409.0860v1>)arXiv:1409.0860v1  [astro-ph.GA]  2 Sep 2014 "
+  ],
+  "ABSTRACT ": [
+    "We examine whether large-scale environment a ects the mass assembly history of their central galaxies. To facilitate this, we constructed dark matter halo merger trees from a cosmological N-body simulation and calculated the formation and evolution of galaxies using a semi-analytic method. We confirm earlier results that smaller halos show a notable di erence in formation time with a mild dependence on large-scale environment. However, using a semi-analytic model, we found that on average the growth rate of the stellar mass of central galaxies is largely insensitive to large-scale environment. Although our results show that the star formation rate (SFR) and the stellar mass of central galaxies in smaller halos are slightly a ected by the assembly bias of halos, those galaxies are faint, and the di erence in the SFR is minute, and therefore it is challenging to detect it in real galaxies given the current observational accuracy. Future galaxy surveys, such as the BigBOSS experiment and the Large Synoptic Survey Telescope, which are expected to provide observational data for fainter objects, will provide a chance to test our model predictions. ",
+    "Subject headings: methods : N-body simulations — cosmology: large-scale structure of universe — galaxies: halos — galaxies: evolution "
+  ],
+  "1. INTRODUCTION ": [
+    "In the standard CDM cosmology with the hierarchical structure formation paradigm, dark matter halos not only play an important role in galaxy formation and evolution, but also compose large-scale structures in the universe. Dark matter first collapses and forms a gravitationally bound system, then baryons fall into the pre-existing potential well of dark matter halo and form galaxies ((<>)White & Rees (<>)1978). Small halos grow into larger systems with mergers or accretion, and thus galaxies residing in the halos naturally evolve with the halo growth. Furthermore, in the past decade, large galaxy survey projects such as the 2dF Galaxy Redshift Survey (2dFGRS; (<>)Colless et al. (<>)2001) and the Sloan Digital Sky Survey (SDSS; (<>)York et al. (<>)2000) and large volume simulations using supercomputers like the Millennium simulation ((<>)Springel et al. (<>)2005) and the Horizon runs ((<>)Kim et al. (<>)2009, (<>)2011) have revealed the existence of large-scale structures. ",
+    "Since (<>)Oemler ((<>)1974) and (<>)Dressler ((<>)1980) found that the cluster environment a ects the galaxy color, there have been numerous studies verifying the relations between galaxy properties and their environments. However, most of them have investigated local environments, which can be classified into cluster, group, or field. While the local environments of galaxies are confined to the inner halo regions, large-scale structures, such as super-clusters, filaments, and voids are super-halo scale environments. Therefore, the large-scale environment should be distinguished from the local environments. ",
+    "(<>)Mo & White ((<>)1996) predicted that massive halos are more likely to occupy denser regions in a large-scale distribution. Moreover, (<>)Mo et al. ((<>)2004) depicted that the large-scale environmental dependence of the galaxy luminosity function can be explained by the mass de-",
+    "pendence of the halo bias. Galaxy properties mainly depend on the inner halo environment defined by halo mass, and the bias of halo mass in large-scale distribution can cause large-scale environmental dependence. However, using N-body simulations, (<>)Sheth & Tormen ((<>)2004) showed that halos in denser regions form slightly earlier than those in less dense regions, when halo mass is fixed. In addition, many theoretical works have found that the formation time of small halos (. 1013h−1M⊙ at z = 0) depends on the large-scale environment, which is known as the assembly bias (e.g. (<>)Gao et al. (<>)2005; (<>)Harker et al. (<>)2006; (<>)Wechsler et al. (<>)2006; (<>)Maulbetsch et al. (<>)2007; (<>)Jing et al. (<>)2007; (<>)Gao & White (<>)2007; (<>)Li et al. (<>)2008; (<>)Fakhouri & Ma (<>)2009, (<>)2010). In short, not only is the halo mass biased by the large-scale environment, but the assembly time of halos also depends on the large-scale environment. ",
+    "The large-scale environmental e ects on galaxies have become an active research area with the advent of wide field surveys. (<>)Kau mann et al. ((<>)2004) and (<>)Blanton & Berlind ((<>)2007) attempted to find a correlation between the large-scale environment and the central galaxy color in SDSS galaxy groups; however, they concluded that the large-scale environment does not have any considerable e ects on the central galaxy color. Meanwhile, (<>)Yang et al. ((<>)2006) found, from 2dFGRS data, that galaxy groups with passive central galaxies at a fixed halo mass are strongly clustered, and it was supported by (<>)Wang et al. ((<>)2008) using SDSS galaxies. Furthermore, (<>)Croton et al. ((<>)2007) studied the correlation between the halo assembly bias and galaxy clustering using a semi-analytic model ((<>)Croton et al. (<>)2006) and reached a conclusion similar to the observational study of (<>)Yang et al. ((<>)2006). (<>)Scudder et al. ((<>)2012) also pointed out that the star formation rate of compact group galaxies is mildly dependent on the large-scale environment, based on SDSS data. Currently, it seems that galaxy ",
+    "properties are correlated with the large-scale environment in addition to the mass of host halo. However, there is still no clear understanding of the physical origins of these large-scale environmental e ects in the baryonic universe. ",
+    "The aim of this paper is to study the e ect of large-scale dependence of halo assembly time on the mass assembly of galaxies using a cosmological N-body simulation and a semi-analytic model. In addition to the previous study of (<>)Croton et al. ((<>)2007), which investigates the e ects of the halo assembly bias on galaxy clustering, we examine the e ect of the halo assembly bias on the mass assembly of galaxies. We first measure the mass assembly of halos in di erent large-scale environments from halo merger trees, and trace the evolution of the central galaxies in those halos by using a semi-analytic model. This scheme allows us to study the direct connection between halos and their central galaxies according to the mass assembly history and to test the existence of any e ects of the halo assembly bias on those galaxies. ",
+    "This paper is organized as follows. In section 2, we describe the details of our cosmological N-body simulation and the scheme by which we construct halo merger trees from N-body simulations. In section 3, we explain the measurement of the large-scale environment of halos and the classification of our sample halos and galaxies. We study the mass assembly history of dark matter halos and their central galaxies in section 4, and in the final section, we discuss and summarize our results. "
+  ],
+  "2. METHODOLOGY ": [],
+  "2.1. N-body simulation ": [
+    "We performed a cosmological dark matter-only simulation using parameters of the standard concordance cold dark matter cosmology using a cosmological constant  = 0.728, a current matter density parameter m = 0.272, the normalization factor of the initial power spectrum ˙8 = 0.809, the spectral index n = 0.963, and the Hubble constant H0 = 100hkms−1 with h = 0.704. These parameter values are based on the seven-year Wlikinson Microwave Anisotropy Probe observations (WMAP; (<>)Jarosik et al. (<>)2011). The cosmological hydrodynamic code used in this work is GADGET-2 ((<>)Springel (<>)2005). For the simulation, a periodic box-size was chosen as 100h−1Mpc with 10243 dark matter particles.1 (<>)The dark matter particle mass was 6.9 × 108h−1M⊙, and the gravitational softening length was 2.441h−1kpc. The dark matter particle position and velocity information were stored for 117 time-steps between z=13 and z=0. The initial condition of the simulation was produced using MPgrafics ((<>)Prunet et al. (<>)2008), which is a parallel version of Grafic1 ((<>)Bertschinger (<>)2001). "
+  ],
+  "2.2. Dark matter halo merger trees : ySAMtm ": [
+    "In order to trace the formation and the mass assembly history of halos, we built dark matter halo merger trees from an N-body simulation. Our treebuilder, ySAMtm, was implemented into the semi-analytic model (ySAM; (<>)Lee & Yi (<>)2013). ",
+    "Fig. 1.— Definition of a dark matter halo merger. This schematic diagram shows the processes of a dark matter halo merger. The solid circle indicates a main halo, and the dashed circle is a sub-halo. The black (thin) solid arrow describes the unique descendant-progenitor relation, and the red (thick) solid arrow states the beginning of the dark matter halo merger. ",
+    "The first step in building dark matter halo merger trees is structure detection. We used the structure finding code AHF ((<>)Knollmann & Knebe (<>)2009) in this work. We define the halo center as the position of the densest region in the halo, as the center of mass is not a proper position for halos undergoing mergers. The halos and subhalos in the simulation are supposed to have at least 20 particles. ",
+    "From the results of structure detection, we constructed dark matter halo merger trees. Figure (<>)1 briefly describes the definition of dark matter halo mergers. We define the beginning of the halo mergers using the virial radius criterion. A detailed procedure for building halo merger trees can be explained as follows : "
+  ],
+  "1. Calculate the shared mass between halos ": [
+    "The shared mass between halos at two subsequent snapshots is calculated by tracing the particle transfer between those halos. At this step, particle transfers between halos in two snapshots are tracked using particle indexes, and individual particles should be included in a single halo or sub-halo; particles in a subhalo are not listed in the main halo of the subhalo. "
+  ],
+  "2. Define a unique descendant halo. ": [
+    "In order to be applicable to semi-analytic models, we find the unique descendant halos of individual progenitor halos. For one progenitor halo, the shared masses of its descendant halos are compared, and the descendant halo with the largest shared mass among those descendants is assigned as a unique descendant halo of the progenitor. However, if another descendant halo receives the largest fraction of its mass from the same progenitor, we determine this descendant halo to be a unique descendant of the progenitor, even if the shared mass of the descendant is not the largest ",
+    "compared to the other descendants. This additional process is needed to avoid a situation in which the small descendant halo is considered to be otherwise newly born. Thus far, one descendant halo can be connected to multiple progenitor halos, whereas a single progenitor must have a unique descendant. If one descendant halo has multiple progenitors, the main progenitor halo is determined by maximizing Mshared,i/Mdescendant , where Mshared,i is the shared mass between the descendant halo and the progenitor halo, and i is the list index of the progenitor halo. In Figure (<>)1, the black (thin) solid arrows indicate a unique descendant-progenitor relation. "
+  ],
+  "3. Find the end of the merger events. ": [
+    "The end of the halo mergers is defined as the moment when two progenitor halos have an identical descendant halo at the next snapshot. In Figure (<>)1, the main halo and its subhalo at z=0.02 have the same descendant halo at z=0. In this case, we consider z=0 to be the epoch when a halo merger is complete. "
+  ],
+  "4. Detect the beginnings of halo mergers. ": [],
+  "5. Build the merger trees of individual halos. ": [
+    "For each halo at z=0, the whole merger history is constructed by backwards tracking progenitor halos including all progenitors of the halos which have finally merged into the object halo. ",
+    "Fly-by events between halos can significantly inflate the number of halo mergers by double counting ((<>)Fakhouri & Ma (<>)2008; (<>)Genel et al. (<>)2009). By considering only the subhalos that were supposed to be finally merged and by tracing backward, we avoided the overestimation of halo mergers caused by fly-bys. "
+  ],
+  "3. HALO SAMPLING ": [],
+  "3.1. Measuring the environment: local overdensity ": [
+    "The goal of this study is to investigate the environmental e ects in large scales; therefore we need to define the large-scale environment of halos. In the literature, there are two ways to measure the large-scale environment. The first is to measure the local overdensity in a sphere of radius R centered at a halo (e.g. (<>)Lemson & Kau mann (<>)1999; (<>)Wang et al. (<>)2007; (<>)Maulbetsch et al. (<>)2007; (<>)Fakhouri & Ma (<>)2009; (<>)Hahn et al. (<>)2009; (<>)Tillson et al. (<>)2011), and the other is ",
+    "to measure the halo bias using the two-point correlation function (e.g. (<>)Sheth & Tormen (<>)2004; (<>)Gao et al. (<>)2005; (<>)Harker et al. (<>)2006; (<>)Wechsler et al. (<>)2006; (<>)Gao & White (<>)2007; (<>)Croton et al. (<>)2007; ?). Although the two-point correlation function is widely used to study the relations between halo clustering and halo properties (formation, merger, dynamical structure, etc.), the correlation function itself is only dependent on the number of halo pairs. On the other hand, the local overdensity more directly reflects the matter distribution of both the internal and external regions of halos. Therefore, we chose to use the former method. ",
+    "The definition of the local overdensity (R) is the same as that in (<>)Fakhouri & Ma ((<>)2009, (<>)2010) and can be calculated as follows: ",
+    "(1) ",
+    "where ˆR is the matter density in a sphere with radius R, and ˆ¯m is the mean matter density in a simulation box. The contribution of the central halo mass is removed by ",
+    "(2) ",
+    "where MHalo is the mass of the central halo, and VR is the volume of the sphere. ",
+    "It is worth mentioning how we choose the sphere radius for measuring the local overdensity. In order to understand the impact of di erent sphere radii, we calculated the local overdensity with various values (3h−1Mpc, 5h−1Mpc, 7h−1Mpc, and 9h−1Mpc). The results did not di er significantly with di erent sphere radii, which is consistent with previous studies ((<>)Sheth & Tormen (<>)2004; (<>)Croton et al. (<>)2007; (<>)Maulbetsch et al. (<>)2007). However, similar to the results presented in (<>)Fakhouri & Ma ((<>)2009), we also found that the centric distance of the farthest particle sometimes exceeded 5h−1Mpc for massive halos. Therefore, we used 7h−1Mpc in this study. "
+  ],
+  "3.2. Classification ": [
+    "In order to compare halos at a fixed mass in di erent large-scale environments, we classified the halos in the present universe into three mass bins: 1011.0−11.5h−1M⊙, 1011.5−12.0h−1M⊙, and 1012.0−13.0h−1M⊙. This range of halo mass roughly covers single galaxies to small clusters. We focused on halos with the mass range 1011−13h−1M⊙ at z = 0 because there were not enough massive halos (& 1013h−1M⊙) to be statistically analyzed, and smaller halos (. 1011h−1M⊙) were excluded due to the resolution limits of our simulation. The definitions of high density and low density in large-scale environments were selected to be the top 20% and the bottom 20% of the local overdensity distribution (7−Halo). ",
+    "The spatial distribution of halos is only slightly dependent on halo mass; the average mass of halos in high-density regions is slightly larger than that of the halos in low-density regions even at the same mass bin. For all identified halos with the mass range 1012.0−13.0h−1M⊙, the average mass of halos in denser regions (the top 20%) is 2.73 × 1012h−1M⊙, while that of halos in less dense regions (the bottom 20%) is 1.87× 1012h−1M⊙. To minimize the e ect of halo mass dependence, we selected the ",
+    "TABLE 1 ",
+    "Properties of sample halos residing in different environments. ",
+    "same number of halos for di erent density groups until the average masses of halos in those groups became virtually identical. ",
+    "Table (<>)1 presents the number and the average mass of the sample halos for each group, and Figure (<>)2 illustrates the distribution of dark matter halos. As seen In Figure (<>)2, the upper panel displays the distribution of all halos more massive than 1011h−1M⊙ in a 30h−1Mpc slice in the simulation. The grayscale system represents the local overdensity 7−Halo; the darker circles indicate halos in denser regions. In the bottom panel, our sample halos are over-plotted on the upper-panel image (Table (<>)1). The red and blue circles are halos in high-density (the upper 20%) and low-density (the bottom 20%) regions, respectively. ",
+    "The main purpose of this paper is to investigate the e ects of the halo assembly bias on real galaxies. For the purpose, we used a semi-analytic model (ySAM; (<>)Lee & Yi (<>)2013). In the model, the mass accretion and mergers of galaxies follow the evolution of each halo merger tree, and many processes of baryonic physics (gas cooling, star formation, feedback processes, etc.) are calculated using simple prescriptions. (<>)Lee & Yi ((<>)2013) demonstrated that their model is calibrated to reproduce recent empirical data, and (<>)Yi et al. ((<>)2013) showed that the merger history of galaxies predicted by the model is comparable to the observational results of the cluster galaxies in (<>)Sheen et al. ((<>)2012). ",
+    "To investigate the impact of various SAM parameters on our results presented in the parer, we varied the efficiencies of AGN and supernovae feedbacks, which are considered important mechanisms in galaxy growth, in a factor of two ranges: from half to twice of our fiducial values. These wide ranges of eÿciencies made noticeable di erences in the galaxy stellar mass function at z=0. We confirmed, however, that our result is not sensitive at all to the variation of feedback eÿciencies. ",
+    "We perform our test on central galaxies because our research focus is on the assembly bias of host halos reflecting the outer environments of those halos, and central galaxies directly follow the formation and the mass growth of their host halos. Satellite galaxies, on the other hand, are more likely to be a ected by their host halo environment. "
+  ],
+  "4. MASS ASSEMBLY HISTORY ": [],
+  "4.1. Dark matter halos and gaseous components ": [
+    "In the current galaxy formation theory, the gas accretion in galaxies is strongly a ected by the assembly history of dark matter halos. In this section, we present ",
+    "Fig. 2.— Dark matter halo distributions in a 30h−1Mpc slice in the simulation. The upper panel displays the distribution of all halos more massive than 1011 h−1M⊙ in the region. The size of the circles represents the virial radius. The grayscale system represents the local overdensity 7−Halo. The darker circles indicates halos in denser regions. The bottom panel is the over-plotted image of the upper panel with our sample halos in Table (<>)1. The red and blue circles are halos in high-density (the upper 20%) and low-density (the bottom 20%) regions, respectively. ",
+    "the assembly history of halos and their central galaxies, comparing the average values between di erent density environments at a fixed halo mass, as shown in Table (<>)1. ",
+    "Figure (<>)3 shows the average mass growth of dark matter halo (top row), hot gas (middle), and cold gas (bottom) components. The average masses are compared in three di erent halo mass bins: 1011.0−11.5h−1M⊙, 1011.5−12.0h−1M⊙, and 1012.0−13.0h−1M⊙ at z = 0 (from left to right). The dashed curve was calculated using halos in a high-density environment (the top 20%), and the dotted curve was computed using those in a low-density environment (the bottom 20%). The vertical arrows indicate the formation time2 (<>)of dark matter halos. ",
+    "Fig. 3.— The mass growth of halos and galaxy gaseous components. The average masses of dark matter halo (top row), hot gas (middle), and cold gas (bottom) components were calculated according to the di erent halo mass bins shown in Table (<>)1: 1011.0−11.5 h−1M⊙, 1011.5−12.0 h−1M⊙, and 1012.0−13.0 h−1M⊙ (from left to right). The dashed and dotted curves indicate halos in di erent density environments: high-density (the top 20%) and low-density (the bottom 20%) regions. The vertical arrows present the time at which the mass reaches half of the final mass for each component. The x-axis indicates the cosmic expansion factor. ",
+    "In the top row of Figure (<>)3, the average mass of the halos shows that halos form earlier in denser regions than in less dense regions, and the di erence in the halo formation time is larger in lower-mass halos (panel (a)). This is in agreements with the previous studies (e.g. (<>)Gao et al. (<>)2005; (<>)Harker et al. (<>)2006; (<>)Wechsler et al. (<>)2006; (<>)Fakhouri & Ma (<>)2010). In the case of gaseous components, the growth trend of hot gas (middle row) is very similar to that of dark matter halos, and the cold gas component (bottom row) follows the trend of dark matter halos and hot gas. In the semi-analytic model, the amount of hot gas accreted onto dark matter halos follows the global baryonic fraction, b/ m, and cold gas increases from the cooling of the hot gas component. Thus, the mass growth of hot and cold gas is similar to that of dark matter halos. "
+  ],
+  "4.2. Star formation rate ": [
+    "Following the growth history of gaseous components, we investigate the star formation history and the mass growth of stellar mass in central galaxies. Figure (<>)4 shows the star formation rates (SFRs; upper row) and the specific star formation rates (SSFRs; bottom) in the same mass bins as in Figure (<>)3. ",
+    "In the top row, the SFRs of central galaxies in smaller halos (. 1012h−1M⊙) are slightly higher in denser regions than in less dense regions, although they are almost the same in the case of more massive halos. This is because the central galaxies in smaller halos have more cold gas in high-density regions than in low-density re-",
+    "Fig. 4.— The star formation rates (SFRs; top row) and the specific star formation rates (SSFRs; bottom) in the same halo mass bins as seen in Figure (<>)3. The dashed curve was calculated using halos in a high-density environment (the top 20%), and the dotted curve was computed using those in a low-density environment (the bottom 20%). The x-axis indicates the cosmic expansion factor. gions (see panel (g) in Figure (<>)3), and the SFR is strongly dependent on the amount of cold gas. ",
+    "On the other hand, the SSFRs, the normalized SFRs, shows the same feature in both high-and low-density environments in all of the mass bins (the bottom panels in Figure (<>)4), which indicates that the amount of the newly formed stars per unit stellar mass is almost the same. This is consistent with a previous observational study on the star formation history by (<>)Kau mann et al. ((<>)2004) who concluded that the SSFR minimally depends on environments larger than 1Mpc from a galaxy. "
+  ],
+  "4.3. Mass growth rates of halos and central galaxies ": [
+    "This section describes the mass growth rates of both halos and their central galaxies in an attempt to more directly search for the evidence of the assembly bias in the baryonic universe. (<>)Maulbetsch et al. ((<>)2007) investigated halo mass growth using an N-body simulation and concluded that, at present, low-mass halos are more apt to accrete their mass in low-density regions than in high-density regions, because halos in high-density regions form earlier. This means that halos in denser regions (e.g., filaments) grow faster than those in less dense region (e.g., voids) when halos mass is fixed. ",
+    "As seen in the first row of Figure (<>)5, we reconfirmed that smaller halos in high-density regions grow faster. However, based on the mass growth rates of central galaxies (middle row), we cannot find evidence of any considerable dependence on the large-scale environment in any mass bins. In particular, in low-mass halos where mass growth shows a stronger assembly bias, the di erence between the mass growth rates becomes mostly diminished in galaxies (panel (d)). ",
+    "The panels in the bottom row show the stellar mass of central galaxies. The galaxy formation times (vertical arrows) are not sensitive to the large-scale environments, even in smaller halos, where halos show a relatively stronger bias for assembly time (see panel (a) of figure (<>)3). However, as a consequence of the higher SFR in small halos, stellar mass is slightly larger in denser regions than in less dense regions (panel (g)). "
+  ],
+  "5. SUMMARY AND DISCUSSION ": [
+    "Fig. 5.— The normalized mass growth rates of halos (top row) and central galaxies (middle), and the stellar mass (bottom) in the same halo mass bins as shown in Figure (<>)3. The dashed curve was calculated using halos in a high-density environment (the top 20%), and the dotted curve was computed using those in a low-density environment (the bottom 20%). The vertical arrows indicate the time at which the stellar mass reaches half of the final stellar mass of central galaxies. The x-axis indicates the cosmic expansion factor. ",
+    "This research attempted to address how the assembly bias by the outer environment of halos a ects the mass assembly of their central galaxies. It seems that the assembly time of dark matter halos is a ected by the surrounding large-scale environment in the case of small halos that mainly host isolated galaxies. Since the galaxy properties are strongly governed by the mass assembly of halos, it is supposed that the assembly bias probably a ects the galaxies in various ways. ",
+    "In short, we predict that the SSFR and the normalized growth rate of the stellar mass show no marked sign of the assembly bias for any mass range. Meanwhile, the stellar masses of central galaxies in fixed mass halos are slightly a ected by the assembly bias of the halos. However, this e ect is perhaps too small to detect in real galaxies, in light of the fact that, in observational data, accurate measurement of the halo mass of galaxies is problematic ((<>)Yang et al. (<>)2006). ",
+    "In this paper, we investigated whether central galaxies show the bias of mass assembly due to large-scale environments when considering over the e ect of halo mass using a cosmological simulation and a semi-analytic model. Our study is based on a controlled sample of halos and galaxies, which minimizes the dependence of halo mass. The results can be summarized as follows: ",
+    "The SSFRs and the normalized growth rates of the stellar mass of central galaxies hardly depend ",
+    "on the large-scale environment for all mass bins. For example, according to our models, the average values of the stellar mass-weighted age of central galaxies in those small halos in high-and low-density regions are 6.4 ± 1.4Gyr and 6.1 ± 1.2Gyr, respectively. ",
+    "Even in the case of small halos (1011.0−11.5h−1M⊙), which show a relatively stronger assembly bias, we predict that the growth rate of the stellar mass will not easily show the assembly bias. This is comprehensible in the sense that, unlike the assembly history of halos, galaxies are a ected by complex baryonic physics such as gas cooling, feedback processes, and cluster environmental e ects. Those baryonic physics operate di erently in individual galaxies through cosmic time, which mostly erases the records of the di erences in the halo formation time. ",
+    "Recently, (<>)Wang et al. ((<>)2013) showed that the clustering of central galaxies depends on the SSFR by using two-point correlation function statistics (see their Figure 2): low-SSFR galaxies being more strongly clustered. At first glance, it seemed to be in contradiction to our result, but in truth it is not. The discrepancy arises from the use of di erent approaches, and our result and theirs show the two sides of the same coin. (<>)Wang et al. ((<>)2013) picked high and low SSFR galaxies and compared their spatial correlations. It is generally believed that at a fixed stellar mass, lower SSFR galaxies at z = 0 tend to have earlier formation times. Thus, their SSFR-based classification is inherently based on galaxy assembly time. We on the other hand classified galaxies by large-scale density environment. In our approach, sample galaxies in the same density environment have a variety of star formation histories, and the galaxies showing a strong assembly bias account for a relatively small fraction. As a result of our approach, the mean SFRs and final stellar masses of central galaxies in the di erent environments show up to a factor of two di erence, which is clearly present but challengingly small to be detected in currently available observational data. Future galaxy surveys such as the BigBOSS experiment ((<>)Schlegel et al. (<>)2011) and the Large Synoptic Survey Telescope (LSST; (<>)Ivezic et al. (<>)2008), which are expected to be able to detect fainter objects, and more accurate measurements of host halo mass will provide a better chance to test these model predictions. ",
+    "SKY acknowledges support from National Research Foundation of Korea (Doyak FY2014). Numerical simulation was performed using the KISTI supercomputer under the program of KSC-2013-C3-015. IJ performed numerical simulations. JL calculated semi-analytic models. IJ and SKY wrote the paper. SKY acted as the corresponding author. "
+  ]
+}

jsons_folder/2014CQGra..31x4002V.json

@@ -0,0 +1,120 @@
+{
+  "arXiv:1411.1760v2  [astro-ph.GA]  2 Dec 2014": [],
+  "Eugene Vasiliev ": [
+    "Lebedev Physical Institute, Moscow, Russia ",
+    "eugvas@lpi.ru ",
+    "E-mail: ",
+    "Received 28 February 2014, revised 13 May 2014 ",
+    "Accepted for publication 16 May 2014 "
+  ],
+  "Abstract": [
+    "Abstract. We consider the problem of star consumption by supermassive black holes in non-spherical (axisymmetric, triaxial) galactic nuclei. We review the previous studies of the loss-cone problem and present a novel simulation method which allows to separate out the collisional (relaxation-related) and collisionless (related to non-conservation of angular momentum) processes and determine their relative importance for the capture rates in different geometries. We show that for black holes more massive than 107 M, the enhancement of capture rate in non-spherical galaxies is substantial, with even modest triaxiality being capable of keeping the capture rate at the level of few percent of black hole mass per Hubble time. "
+  ],
+  "1. Introduction ": [
+    "The study of stellar dynamics around massive black holes begins in 1970s in application to (still hypothetical) intermediate-mass black holes in globular clusters ((<>)Bahcall & (<>)Wolf, (<>)1976; (<>)Frank & Rees, (<>)1976; (<>)Lightman & Shapiro, (<>)1977; (<>)Cohn & Kulsrud, (<>)1978). The early studies established the importance of two-body relaxation which changes angular momenta of individual stars and drives them into the loss cone – the region in phase space in which a star would be captured by the black hole in at most one orbital period. Later, the loss cone theory was applied to galactic nuclei ((<>)Duncan & (<>)Shapiro, (<>)1983; (<>)Syer & Ulmer, (<>)1999; (<>)Magorrian & Tremaine, (<>)1999; (<>)Wang & Merritt, (<>)2004). If the black hole mass is not too large ( 108 M), a star lost into the black hole could produce a tidal disruption flare ((<>)Rees, (<>)1988), and several candidate events have been observed to date (e.g. (<>)Strubbe & Quataert, (<>)2009; (<>)van Velzen et al., (<>)2011). ",
+    "To deliver a star into the loss cone, it is necessary to reduce its orbital angular momentum to a very small value. In a spherical geometry, this can only be achieved by two-body relaxation, but relaxation times in galactic nuclei are typically very long, especially in massive galaxies. The predicted rate of capture events is generally rather low, of order 10−5 M/yr per galaxy, weakly depending on the black hole mass M•. On the other hand, if a galaxy is not precisely spherically symmetric, then angular momenta of individual stars are not conserved, so that they may be driven into the loss cone by collisionless torques (as opposed to collisional two-body relaxation). This effect was recognized quite early ((<>)Norman & Silk, (<>)1983; (<>)Gerhard & Binney, (<>)1985), and more recent studies have suggested that particular properties of triaxial galactic nuclei, namely the existence of a large population of centrophilic orbits, may keep the capture rate well above that of a similar spherical system ((<>)Merritt & Poon, (<>)2004; (<>)Holley-Bockelmann & Sigurdsson, (<>)2006; (<>)Merritt & Vasiliev, (<>)2011). These conclusions ",
+    "were obtained based on the properties of orbits, and not on the full-scale dynamical simulations, which are fairly non-trivial to conduct for such a problem. ",
+    "There are several numerical methods that have been used for studying stellar systems with massive black holes. Fokker-Planck models are usually restricted to spherical ((<>)Cohn & Kulsrud, (<>)1978) or at most axisymmetric ((<>)Goodman, (<>)1983; (<>)Fiestas (<>)& Spurzem, (<>)2010; (<>)Vasiliev & Merritt, (<>)2013) geometries, as are gaseous ((<>)Amaro-Seoane (<>)et al., (<>)2004) or Monte-Carlo ((<>)Shapiro & Marchant, (<>)1978; (<>)Freitag & Benz, (<>)2002) models. N-body simulations (e.g. (<>)Baumgardt et al., (<>)2004; (<>)Brockamp et al., (<>)2011; (<>)Fiestas et al., (<>)2012) do not have such limitation, but as we will show below, it is extremely hard to operate them in a regime with realistic proportion between collisional and collisionless effects. We have developed a new variant of Monte-Carlo code that is applicable in any geometry and have used it to study how the non-spherical effects change the rate of star captures by supermassive black holes. ",
+    "We begin by reviewing the basic properties of orbits in galactic nuclei of various geometries in §(<>)2. Then in §(<>)3 we set up the loss-cone problem and consider the interplay between collisional and collisionless relaxation processes. §(<>)4 is devoted to order-of-magnitude estimates and scaling relations. In §(<>)5 we describe the novel Monte-Carlo method for simulating the dynamics of near-equilibrium stellar systems of arbitrary geometry, and in §(<>)6 apply this method for the problem of star capture by supermassive black holes in axisymmetric and triaxial galactic nuclei. §(<>)7 presents the conclusions. "
+  ],
+  "2. Orbital structure of non-spherical galactic nuclei ": [
+    "Throughout this paper, we consider motion of stars in a time-independent potential, which is composed of a Newtonian potential of the supermassive black hole at origin (we ignore relativistic effects for the reasons described later) and the potential of extended distribution of stars: ",
+    "(1) ",
+    "It is clear that depending on the relative contribution of these two terms (or, rather, their derivatives that determine acceleration), there are two limiting regimes and a transition zone between them. Close to the black hole, the motion can be described as a perturbed Keplerian orbit. At larger radii, the black hole almost unnoticed by the majority of stars – except for those with low angular momenta, which are able to approach close to the black hole; nevertheless, even these orbits are mostly determined by the extended stellar distribution rather than the point mass. The boundary between the two cases is conveniently defined by the black hole influence radius rm, which contains stars with the total mass M(< rm) = 2M•. Another commonly used definition of the influence radius is GM•/σ2 , where σ is the stellar velocity dispersion; it is more readily computed from observations but has a more indirect meaning, as σ is determined by the distribution of matter in the entire galaxy and not just close to the black hole, and may well be a function of radius itself. The two definitions of influence radius give the same value for a singular isothermal density profile, but may differ by a factor of few for less cuspy profiles ((<>)Merritt, (<>)2013b, Section 2.2). We will use the first definition henceforth. ",
+    "In general, the only classical integral of motion in a time-independent potential of arbitrary geometry is the total energy (per unit mass) of an orbit E ≡ Φ(r) + v2/2. Obviously, in the spherical and axisymmetric cases there exist additional integrals – three and one components of the angular momentum vector L, correspondingly. In ",
+    "‡",
+    "the vicinity of the black hole, however, the orbits look like almost closed Keplerian ellipses, with the oscillations in radius between peri-and apoapses (r−, r+) occuring on a much shorter timescale (radial period P ) than the changes in the orientation of the ellipse (precession timescale). Under these conditions, one may use the method of orbit √ averaging (e.g. (<>)Sridhar & Touma, (<>)1999) to obtain another conserved quantity I ≡ GM•a, where a is the semimajor axis. Thus the total Hamiltonian is split into the Keplerian and the perturbing part, each one being conserved independently. The perturbing potential Φ, averaged over the radial oscillation period, becomes an additional integral of motion, the so-called secular Hamiltonian. ",
+    "The existence of this additional integral does not add new features in the spherical case, but is important in other cases. In particular, the motion in an axisymmetric nuclear star cluster becomes fully integrable, while in the weakly triaxial case another non-classical integral of motion can be shown to exist ((<>)Merritt & Vasiliev, (<>)2011), so that the system is again fully integrable. Empirical evidence shows that even for rather large deviation from spherical symmetry, orbits in the triaxial case remain regular in the vicinity of the black hole, if one neglects relativistic effects. ",
+    "In a generic triaxial potential there usually exist several types of tube orbits, which conserve the sign of one component of angular momentum, and box orbits, which do not have a definite sense of rotation around any axis ((<>)Binney & Tremaine, (<>)2008, §3.8). The latter have stationary points, in which the velocity (and hence, the angular momentum) comes to zero, and are generally centrophilic, meaning that a star can pass at an arbitrarily small distance from the origin. Centrophilic orbits, by necessity, cannot conserve the sign of any component of angular momentum, however the opposite is not true – there exist various non-tube resonant orbit families which avoid coming too close to the center. These orbits play an important role in the structure of triaxial galaxies with density cusps and/or central black holes ((<>)Merritt (<>)& Valluri, (<>)1999), as the regular box orbits are destroyed by the sharp gradients in the potential near origin and replaced by chaotic orbits and resonant orbit families. Thus the centrophilic orbits outside a few influence radii and up to a radius containing M ∼ 102 M• are generally chaotic ((<>)Valluri & Merritt, (<>)1998), although in some special cases the motion remains fully integrable even in the presence of the black hole ((<>)Sridhar (<>)& Touma, (<>)1997). On the other hand, the motion inside rm is generally regular, with the box orbits being replaced by a related family of pyramid orbits ((<>)Merritt & Valluri, (<>)1999, Fig.11a). These are also centrophilic, and as such, are natural candidates for the capture by the black hole ((<>)Merritt & Vasiliev, (<>)2011). Tube orbits also exist near the black hole, and a special class of short-axis tubes has a noticeably conical shape and are called saucers ((<>)Sambhus & Sridhar, (<>)2000). Figure (<>)1 shows the four major classes of orbits in a triaxial nucleus, of which two exist also in the oblate axisymmetric case. In an even more general case without a triaxial symmetry (for instance, if the black hole is displaced from the center of stellar potential), there are other classes of orbits (e.g. lens orbits, see (<>)Sridhar & Touma, (<>)1999), some of them also being centrophilic. In what follows, we consider systems with at least triaxial symmetry. ",
+    "Given the non-conservation of angular momentum in non-spherical potentials, it is important to know the amplitude and timescale of its variation. Let us describe the deviation from spherical symmetry by a parameter , roughly equal to 1 − x/z, where x and z are the major and minor axes (more precise definition is given by Eq.11b in (<>)Vasiliev & Merritt ((<>)2013), where it is called Rsep). For a triaxial system, ",
+    "Figure 1. Four major orbit families in a triaxial galactic nucleus: short-axis tube (SAT, top left), (inner) long-axis tube (LAT, top right), saucer (bottom left), pyramid (bottom right). The long/intermediate/short axes are x/y/z. There are also outer long-axis tubes which look similar to SAT turned by 90 degrees (with x axis going through the tube). In the axisymmetric case, only the two types of orbits on left panels exist. ",
+    "These orbits are found in the vicinity of the black hole (for r  rm); outside the influence radius pyramid and saucer orbits (and some tubes as well) are largely replaced by chaotic orbits. ",
+    "there is another parameter T = (x2 − y2)/(x2 − z2) which describes the degree of triaxiality (y is the intermediate axis). It ranges from T = 0 for oblate to T = 1 for prolate axisymmetric models; in the rest of the paper we will assume T = 0.5 (maximal triaxiality), having in mind that the importance of triaxial effects decreases as the system approaches axisymmetry. Let Lcirc(E) be the angular momentum of a circular orbit with the given energy, and define the dimensionless squared angular momentum R ≡ L2/Lcirc2 . It turns out that for tube orbits with high enough R the variation in R is rather small, but for saucer and pyramid orbits, both of which appear at R  , this variation can be by order of R itself. (Note, however, that in the axisymmetric case the magnitude of angular momentum is bounded from below by its conserved component Lz). The timescale for such variation is of order −1/2 times the precession time TM = P M•/M(a) ((<>)Vasiliev & Merritt, (<>)2013). The above estimates were valid for the motion in the sphere of influence; outside rm the chaotic centrophilic orbits also typically have R   and the variation of angular momentum by order of itself occurs on the timescale of radial period P . ",
+    "There is ample evidence that a substantial fraction of elliptical galaxies and bulges of disk galaxies might be triaxial ((<>)Tremblay & Merritt, (<>)1996; (<>)M´endez-Abreu et al., (<>)2010), with the minor-to-major axis ratio in the range 0.7 − 0.85 and a large spread in the triaxiality parameter. Nuclear star clusters also are known to exhibit significant departures from spherical symmetry (see (<>)Sch¨odel et al., (<>)2014, for the case of Milky Way), which is also a natural consequence of one of the proposed scenarios of their formation ((<>)Antonini, (<>)2014). Even if the mass distribution in the nuclear star cluster itself is spherical, the distortion of the gravitational potential by asymmetries on larger scales (such as nuclear bars) would still create the centrophilic orbit families. We will take the axis ratio z/x = 0.8 and triaxiality T = 0.5 as our fiducial parameters, but we note that the capture rates do not depend substantially on these values. "
+  ],
+  "3. Collisional and collisionless relaxation and the loss-cone problem ": [
+    "The black hole tidally disrupts or directly captures stars which pass at a distance smaller than a critical radius r•, or, equivalently, pass the periapse while having orbital angular momentum smaller than L•. The former fate occurs for main-sequence stars if M•  107 − 108 M, depending on the mass of the star (see Fig.5 in (<>)Freitag & (<>)Benz, (<>)2002), and for giant stars even for much larger M•; the latter case applies to compact stars, stellar-mass black holes, or for the largest M•. We shall consider only non-rotating black holes; see the paper by L.Dai in this volume for the problem of tidal disruption of stars by Kerr black holes. The critical angular momentum is ",
+    "(2) ",
+    "where m and R are the mass and radius of the star and the coefficient η ∼ 1 depends on the internal structure of the star. The region of phase space with L < L• is called the loss cone. ",
+    "A detailed review of the loss cone theory is given by (<>)Merritt ((<>)2013a); here we remind several key points. Substantial changes in both energy and angular momentum distributions occur on the timescale of relaxation time Trel(E), but the relaxation in angular momentum is more important for the overall rate of capture ((<>)Frank (<>)& Rees, (<>)1976), since near the loss cone boundary a comparatively small change in L can drive a star into the black hole. The relaxation in E would produce a ρ ∝ r−7/4 cusp ((<>)Bahcall & Wolf, (<>)1976) in a time ∼ 0.1Trel(rm); since many galaxies are not that dynamically old, we will not assume this particular density profile and let it to be an unspecified function. The isotropic distribution function of stars in energy f(E) is given by the Eddington formula, while the density of states g(E) = 4π2 P (E) Lcirc 2 (E) provides the link between f and the number of stars in energy interval dE: N(E) dE = f(E) g(E) dE ((<>)Binney & Tremaine, (<>)2008, Eq.4.46, 4.56). In what follows, we will use interchangeably the energy E or the semimajor axis a (for a non-Keplerian potential it should be more appropriately called the radius of a circular orbit with the given energy). ",
+    "In the spherical case, the only mechanism producing changes in angular momentum is the two-body relaxation. It can be substantially enhanced if there are massive perturbing objects such as molecular clouds ((<>)Perets et al., (<>)2007), but the basic physical effect remains the same. Resonant relaxation also enhances the exchange of angular momentum between stars ((<>)Rauch & Tremaine, (<>)1996; (<>)Hopman & (<>)Alexander, (<>)2006), but has a rather moderate effect on the overall rate of capture, so we ",
+    "also ignore it in the discussion. Relativistic effects play an important role close to the black hole ((<>)Merritt et al., (<>)2011, C.Will, this volume), but since the bulk of captured stars come from radii comparable to rm, relativity can be neglected for them. On the other hand, in non-spherical systems the angular momentum changes due to both two-body relaxation and torques from non-spherical mass distribution, the interplay between these two effects being quite complex. ",
+    "In the case of spherical symmetry, the main parameter that determines the flux of stars into the loss cone is the ratio q of mean-square change in angular momentum per one radial period to the width of the loss cone: ",
+    "(3) ",
+    "where D(E) is the limiting value of diffusion coefficient in R for R → 0, roughly equivalent to Trel −1 . This quantity determines the boundary condition for the diffusion in R in the following way ((<>)Lightman & Shapiro, (<>)1977). When q  1, the relaxation is rather weak and as soon as the star reaches the boundary of the loss cone, it is captured within one orbital period; thus the density of stars inside the loss cone is zero – this is called the empty loss cone regime. On the other hand, if q  1, the changes in angular momentum occur so rapidly that in the time-averaged sense, the loss cone remains fully populated: the stars with R < R• are still being captured once per radial period, but this occurs only when the star actually passes the periapse, and for the rest of its orbit it can stay inside the loss cone without impunity. If we introduce the time-averaged value of distribution function in the loss cone as fLC ≡ f(E, R•), then the rate of capture is given by the number of stars inside the loss cone divided by radial period: ",
+    "(4) ",
+    "In the spherical case, the boundary condition fully determines the steady-state solution of the diffusion equation: assuming a particular form of isotropized (averaged over angular momenta) distribution function of stars f(E), the actual two-dimensional function f(E, R) has a nearly logarithmic profile in R, and the rate of capture is ((<>)Vasiliev & Merritt, (<>)2013) ",
+    "(5) ",
+    "It is easy to see that in the full loss cone limit (q  1), this quantity tends to ((<>)4), and fLC ≈ f(E). Close to the black hole the loss cone is empty, and further out it may – or may not – reach a full loss cone regime; for M•  108 M in lower-density galactic nuclei this never happens, while for smaller M• the transition between empty and full loss cone regimes may lie around rm. ",
+    "For non-spherical system, the treatment of two-body relaxation is more difficult and has only been carried out rigorously in the axisymmetric case inside the sphere of influence ((<>)Vasiliev & Merritt, (<>)2013), where the dynamics is fully integrable. The main conclusion is that the steady-state solution at R   is still well described by a logarithmic profile, but at smaller R there exists a more extended “loss wedge” ((<>)Magorrian & Tremaine, (<>)1999), in which the orbits on average have R > R• but may get into the loss cone (below R•) due to torques from non-spherical potential, roughly after one precessiontime TM. The volume of the loss wedge is larger than the loss cone by a factor ∼ /R•, and the boundary condition corresponds to a full loss cone ",
+    "regime (i.e. the distribution function inside the loss cone is almost the same as on the boundary of the loss wedge). In other words, the quantity qaxi, analogous to ((<>)3), is  1 for most orbits, because the change of angular momentum due to precession during one radial period is typically larger than the size of the loss cone. However, now the global shape of the solution is not simply determined by the boundary condition, but rather by the average two-body relaxation rate at the given energy: the non-spherical torques cannot bring an orbit all the way from R ∼ 1 to R• – this still remains the duty of relaxation. Overall, the larger size of the loss wedge increases the steady-state capture rate by a factor of few, compared to the spherical case, but only in the regime when the spherical system would have empty loss cone. Roughly speaking, the star only needs to get down to R ∼  by collisional diffusion, and then it will be driven into the loss cone by collisionless effects; but as the dependence of the flux on the effective size of the loss region is logarithmic ((<>)5), this does not greatly increase the loss rate. ",
+    "A similar picture should be describing triaxial systems; however, for them, and to a lesser extent for axisymmetric systems, another effect may be more important, namely the draining of the loss region. This term refers to the gradual depletion of the region in phase space populated by orbits that may attain angular momentum lower than L• at some point of their evolution in the smooth stationary potential (i.e. in the absense of relaxation). In the triaxial case, this region contains the entire population of centrophilic orbits (which constitute approximately a fraction /4 of total mass), whether these are regular pyramids inside rm or chaotic orbits further out. The lifetime of orbits in the loss region is much longer in the triaxial case; it is roughly given by ((<>)Merritt & Vasiliev, (<>)2011, Eq.117): ",
+    "(6) ",
+    "the latter equation used the radius of direct capture and not tidal disruption and is valid for a  rm. An analogous expression for draining of chaotic orbits in the axisymmetric case ((<>)Merritt, (<>)2013a, Eq.65) gives ",
+    "(7) ",
+    "Thus it is clear that the timescale for draining the loss region can be quite long, especially in the triaxial case; during this time, the capture rate at a given energy is roughly given by the expression ((<>)4) for the full loss cone. The necessary conditions for this are that (i) the initial distribution of stars in R is close to uniform (isotropic), and (ii) the typical change in angular momentum during one radial period is larger than the loss cone size. The first condition is the most neutral, if not natural, choice for the velocity distribution function, although it may be substantially overestimating the capture rate if the low angular momentum part of the phase space is initially depleted due to the slingshot ejection of stars by a binary supermassive black hole ((<>)Milosavljevi´c (<>)& Merritt, (<>)2003). The second condition is satisfied for most orbits which are not too close to the black hole (essentially most orbits that contribute to the total flux), as shown by (<>)Merritt & Vasiliev ((<>)2011, Eq.55) and (<>)Vasiliev & Merritt ((<>)2013, Eq.59). ",
+    "It is also worth noting that the above discussion assumed a steady-state solution for the distribution function (to the extent that we ignore the loss of stars into the black hole, which is reasonable on the Hubble timescale). A time-dependent solution to the Fokker-Planck equation may give the loss rate higher than the steady-state by a factor of few ((<>)Milosavljevi´c & Merritt, (<>)2003; (<>)Vasiliev & Merritt, (<>)2013), or, conversely, ",
+    "lower ((<>)Merritt & Wang, (<>)2005), depending on the initial conditions. There are two separate factors that complicate matters in the non-stationary case. The first is that if the relaxation time is much longer than the Hubble time, then the gradient of the distribution function near the capture boundary, which determines the capture rate in the empty loss cone regime, is not uniquely determined by the isotropized distribution function f (E), as in the steady state (Eq. (<>)5). Rather, it depends on the prior evolution and, ultimately, the initial state. Figure 13 in (<>)Vasiliev & Merritt ((<>)2013) shows that under the assumption of initially isotropic distribution of stars, the time-dependent capture rate for a spherical galaxy may be 2−3 times higher than the steady-state rate for the most massive black holes. On the other hand, these two rates are roughly equal for M•  108 M, when the relaxation is fast enough to establish a nearly steady-state profile. The second factor, more important for non-spherical systems, is related to the collisionless draining of the loss region, which could increase the captured mass by more than an order of magnitude compared to the steady-state solution. However, one should keep in mind that both factors sensitively depend on the initial population of stars in and near the loss region (i.e., on the details of galaxy formation), while the steady-state rates, which differ only by a factor of two between spherical and axisymmetric systems, provide a more robust estimate. "
+  ],
+  "4. Scaling laws ": [
+    "We can obtain a very rough estimate of the total steady-state capture rate for a spherical galaxy by noting that F(E) peaks around E ∼ Φ(rm), so that if the system is in the empty loss cone regime at this energy, then the total flux is ",
+    "To arrive at a single-parameter formula, we use the M• − σ relation, which is typically written as ",
+    "(9) ",
+    "with α ≈ 8, β ≈ 4.5 being the typical values found in the literature (e.g. (<>)Ferrarese & (<>)Merritt, (<>)2000; (<>)Gebhardt et al., (<>)2000; (<>)G¨ultekin et al., (<>)2009). The influence radius then scales as ",
+    "(10) ",
+    "with the parameter r0 depending on the density profile. Taking σ to be the line-of-sight velocity, averaged over the effective radius, we obtain r0 = 45 pc for a (<>)Dehnen ((<>)1993) model with a γ = 1 cusp. Then the estimate ((<>)8) gives Ftotal ∼ 10−5(M•/108 M)−0.3M/yr for more massive galaxies which are in the empty loss cone regime, comparable with more accurate calculations ((<>)Vasiliev & Merritt, (<>)2013, Fig.13). ",
+    "For an axisymmetric galaxy, the steady-state capture rate is only moderately larger than for a spherical one, and have roughly the same functional dependence on galaxy parameters ((<>)Magorrian & Tremaine, (<>)1999). The statement that axisymmetric galaxies have much higher capture rates is often attributed to this paper, but in fact a more careful reading reveals that the effect of axisymmetry increases the capture rates due to relaxation only by a factor of two or so. This ignores the draining of the loss wedge, which is justified since the draining time is substantially shorter than ",
+    "the Hubble time at the radii of interest, as is the case for most realistic situations: substituting ((<>)10) into ((<>)7), we obtain that Tdrain,axi  109 yr at the radius of influence. On the other hand, the mass of stars in the loss wedge, and hence their draining rate, is roughly proportional to the mass of the black hole, while the capture rate due to relaxation scales more slowly with M•. Hence, (<>)Magorrian & Tremaine ((<>)1999) suggest that for the most massive galaxies it is indeed the draining of the loss wedge that is the main source of captured stars, and the capture rate exceed the steady-state value by orders of magnitude, which is apparent in comparing their figures 3 and 5. Thus their study presented two very different conclusions about capture rates in axisymmetric galaxies, without a clear explanation of the discrepancy. It is worth reiterating that the first one, about a moderate increase in the relaxation flux, is more robust, as it does not depend on the initial conditions, while the second one, about a much higher capture rate due to draining, is based on the assumption that the loss wedge was fully populated at the beginning of evolution. Both conclusions were confirmed by (<>)Vasiliev (<>)& Merritt ((<>)2013) using a more elaborate calculation. ",
+    "For a triaxial galaxy, however, the draining times for most galaxies are comparable to or exceed the Hubble time, and the capture rate at a given energy is comparable to the full loss cone rate ((<>)4) if Tdrain,triax(E) > THubble (again under the assumption of initially fully populated loss region). We may make a crude estimate by integrating the expression for the full loss cone flux from the critical energy up to infinity, where the critical energy Edrain is given by the condition that the draining time ((<>)6) is equal to the Hubble time. Hence, the total capture rate is ",
+    "(11) ",
+    "From ((<>)6,(<>)10) we see that, evaluated at the radius of influence, Tdrain ∼ 4×1011  yr, so that unless the triaxiality is very small, most of the draining flux comes from inside rm. We may make the above estimate more quantitative by taking the expressions for f(E) and g(E) in the Newtonian potential ((<>)Merritt, (<>)2013b, Eqs.3.49, 3.51, 5.182). This yields ",
+    "(12) ",
+    "The capture rate increases approximately linearly with M•, a situation rather different from the spherical case. For a γ = 1 cusp, the present-day flux is ∼ 4 × 10−4 1/5(M•/108 M)1.1 Myr−1 . Note that, as the more bound orbits are drained more quickly, the total rate declines with time, although rather slowly. Even with such a high flux, it is not quite correct to say that the capture rate is comparable or exceeds the full loss cone rate, as the latter quantity is poorly defined by itself: the undepleted full loss cone draining rate would increase with increasing |E|, producing a divergent overall total flux ((<>)Merritt, (<>)2013b, Chapter 6). A rough estimate obtained for a singular isothermal sphere (r−2 density cusp), taking the full loss cone rate at the radius of influence, produces another two orders of magnitude larger flux ((<>)Zhao (<>)et al., (<>)2002). ",
+    "The scaling relation ((<>)12) is somewhat different from the one obtained by (<>)Merritt & (<>)Poon ((<>)2004) based on their model of scale-free γ = 1 cusp with x : y : z = 1 : 0.8 : 0.5. There are several reasons for this. First, their models, having a power-law density profile, could not extend to infinity, so were cut off at a few influence radii; second, their plots of capture rate versus energy used the definition of potential without the ",
+    "contribution of black hole, which is strictly valid only well outside influence radius. In short, there is no range of radii such that rm  r  rcutoff , so it is hard to interpret their power-law fits. In particular, the dashed line on their Fig.3, marking the full loss cone flux, is correct for r  rm, and it is indeed apparent that for large energies the points start to follow that asymptote, instead of the power-law fit for smaller energies. On the other hand, a correct expression for the full loss cone flux valid both inside and outside has a peak at roughly E = Φ(rm) and declines towards lower energies as (−E)−1/2; however, as it extends to arbitrarily negative values of E, the overall flux would diverge at low, not at high E as they claim. This divergence is removed by imposing a lower limit at energy Edrain, which introduces the time dependence in the total flux that was derived in the above formulae. Lastly, their normalization is somewhat lower because the capture radius was taken to be at one Schwarzschild radius instead of four. Despite these complications, the basic statement, that the draining rate may be equal to the full loss cone rate during a Hubble time, remains valid if we take into account the proper cutoff at energies below Edrain, and even the numerical estimates are correct to within an order of magnitude. ",
+    "We now discuss scaling relations that may facilitate numerical study of loss rates. State-of-the-art N-body codes on the present-day hardware can simulate systems with ∼ 105 stars for ∼ 105 dynamical times, which takes months to years of wall-clock time (D.Heggie, priv.comm.). A simulation of even the relatively low-mass Milky Way nuclear star cluster would need to follow some 107 stars for 105 dynamical times, clearly beyond the reach of direct N-body simulations in the near future. However, we may design (almost) equivalent systems with suitably scaled parameters. ",
+    "We start from spherical case, in which the important quantity that needs to be preserved by the scaling is the radius (or energy) of transition between empty and full loss cone regimes, i.e. at which q = 1 (Eq.(<>)3). Then it is clear that we need to change R• and D by the same factor β. The flux in the full loss cone regime (Eq.(<>)4) will be also multiplied by β, and the flux in the empty loss cone regime (Eq.(<>)5 with α → 0) will be multiplied by almost the same factor, except for the change in the logarithmic factor in the denominator. The total simulation time, in units of dynamical time, should then be scaled by β−1 . ",
+    "In the axisymmetric case the scaling is largely the same, if we ignore the draining of the loss wedge; furthermore, in this case R• under the logarithm in the denominator is replaced with an effective constant which depends only on  ((<>)Vasiliev & Merritt, (<>)2013). The draining, however, scales differently with β, so we may only ignore its contribution if the scaled draining time is less than the scaled simulation time. ",
+    "In the triaxial case, the flux from draining of centrophilic orbits cannot be ignored as it gives the dominant contribution to the total capture rate. We need to preserve the ratio of draining time ((<>)6) to the simulation time, which, fortunately, means that both should change by the same factor β−1 . Thus the relative importance of collisional and collisionless capture rate will not change under the same scaling of D ∝ β,R• ∝ β,tsim ∝ β−1 . ",
+    "Unfortunately, even with this scaling it is not possible to design a feasible N-body simulation for most of galaxies: since the relaxation rate D ∝ (ln N)/N, and we need to consider galaxies with N  1010 , β should be of order 104 . Thus instead of a system which is ∼ 104 dynamical times old at rm, we get a system which has an age of ∼ 1 dynamical time, and a capture radius which is a substantial fraction of rm; clearly, such an extrapolation is too brave. In addition, for the system with a binary black hole the scaling is impossible to follow, as the stars are lost due to three-body ",
+    "scattering and not to the capture, so that the relevant radius r• is proportional to the size of the binary orbit and cannot be changed at will. In such case, increasing the relaxation rate without adjusting the loss cone size moves the system more into a full loss cone regime, and decreases the relative importance of draining. "
+  ],
+  "5. Monte-Carlo treatment of relaxation in arbitrary geometry ": [
+    "The complexity of interplay between collisional relaxation and collisionless changes in angular momentum makes a direct solution of Fokker-Planck equation impractical in the general case of triaxial system with a mixture of regular and chaotic orbits. On the other hand, direct N-body simulations are presently incapable of achieving the necessary regime of relatively weak two-body relaxation, compared to the collisionless effects. ",
+    "To address this problem, we have developed a novel Monte-Carlo method. The idea is to follow the motion of sample orbits in a smooth, non-spherical potential while adding a random perturbation to the equations of motion, which would mimick two-body relaxation with an adjustable magnitude (unrelated to the actual number of test particles). The approach is actually not so novel, dating back to (<>)Spitzer (<>)& Hart ((<>)1971), who used it for a spherical system with diffusion coefficients being computed under an assumption of Maxwellian distribution of background (field) star velocities. The perturbations were applied directly to the velocity of the test star, its motion being numerically integrated in the given potential. Later on, the idea was modified in (<>)Spitzer & Shapiro ((<>)1972) by using orbit-averaged diffusion coefficients in energy, and further developed by (<>)Shapiro & Marchant ((<>)1978) and (<>)Duncan & (<>)Shapiro ((<>)1983) to study star clusters around supermassive black holes, using two-dimensional orbit-averaged diffusion in {E,L} space with a special treatment of loss-cone ensuring a correct form of the boundary condition. The diffusion coefficients were recomputed regularly, using the distribution function of field stars equal to the isotropized distribution of test stars. At the same time, another branch of Monte-Carlo methods was developed by (<>)Henon ((<>)1971), in which the perturbations were computed between pairs of stars, thus equating the test and the field star population and ensuring conservation of global integrals of motion in each interaction. This method is employed in several presently used Monte-Carlo codes for the evolution of spherically symmetric star clusters (e.g. (<>)Giersz, (<>)1998; (<>)Joshi et al., (<>)2000; (<>)Freitag & Benz, (<>)2002). Unfortunately, it is difficult to generalize it for non-spherical systems, while the Spitzer’s formulation is relatively straightforward to apply in any geometry. ",
+    "The detailed description of the new Monte-Carlo code is given elsewhere ((<>)Vasiliev, (<>)2015); here we outline its main features. As in all previous studies, we consider scattering of test particles by an isotropic spherically symmetric distribution of field particles, which are described by a distribution function f(E) consistent with the terms spherical of local of the potential in which the The scattering is described inpart (position-dependent) velocity stars diffusion move. (e.g. (<>)Merritt, (<>)2013b, Eqs.5.23, 5.55), which represent mean and mean-squared changes in velocity per unit time. The trajectory of a test star is integrated numerically in the given smooth potential, and the perturbations to velocity are applied after each timestep of the ODE integrator, typically several tens of steps per radial period, using locally computed drag and diffusion coefficients. We have checked that the prescription for adding velocity perturbation gives correct rates of orbit-averaged diffusion coefficients in energy and angular momentum in the spherical case. ",
+    "The loss cone is taken into account by computing the radius of each periapse from the numerically integrated trajectory and eliminating the particle if this radius is below r•. This automatically implies an appropriate boundary condition for the angular momentum diffusion in terms of q, which applies for both regular changes of L due to precession in the smooth potential and the random two-body relaxation. ",
+    "In the present study, we neglect the changes in the background potential in the course of evolution. Most galactic nuclei have long enough relaxation times that the change in density profile due to relaxation in energy is negligible during the Hubble time (a few counterexamples exist, notably the Milky Way ((<>)Merritt, (<>)2009)). The change in shape which is responsible for the collisionless changes in angular momentum is more difficult to assess. Early studies ((<>)Gerhard & Binney, (<>)1985; (<>)Merritt & Quinlan, (<>)1998) have found that for a large enough black hole ( 1% of the galaxy mass) the triaxiality of the system is rapidly destroyed, presumably, due to diffusion of chaotic orbits. However, later papers were successful at creating strongly triaxial models with high fraction of chaotic orbits which nevertheless maintained their shape during many dynamical times ((<>)Holley-Bockelmann et al., (<>)2002; (<>)Poon & Merritt, (<>)2004). The changes in shape are quite straightforward to account for in our approach – one needs to regularly update the smooth potential model as the system evolves; however, for the simplicity of interpretation we decided not to explore this possibility, having checked that the systems under study do not noticeably evolve in shape in the absense of relaxation and capture. (Noise can substantially increase the chaotic diffusion rate (e.g. (<>)Kandrup et al., (<>)2000), we leave the impact of noise on the chaotic orbits for a future study). ",
+    "We prepared a number of test models, for three geometries (spherical, axisymmetric and triaxial), constructed by the (<>)Schwarzschild ((<>)1979) orbit superposition method, using the publically available SMILE software ((<>)Vasiliev, (<>)2013). A few modifications were introduced in order to enhance the quality of models. First, to increase the effective “resolution” of the orbit library, we have changed the scheme for generating initial conditions in such a way that it creates more orbits with lower energies (closer to the black hole) and more orbits with low angular momenta. The actual weights of orbits are assigned by the optimization procedure to satisfy the density and kinematic constraints while attaining the most uniform possible distribution of orbit weights; this scheme was modified to correctly account for non-equal priors for orbit weights. Second, to make the non-spherical models as close as possible to spherical in terms of distribution in angular momentum, we binned the distribution function in {E,R} space on a non-uniform grid (with smaller cells closer to loss-cone boundary) and required the distribution in R to be flat in each energy shell. This produces a more isotropic model in the angular momentum space than just a requirement of velocity isotropy. The models were constructed using 105 orbits, 100 × 10 constraints for the spherical-harmonic decomposition of density and 100 × 5 constraints for angular momentum distribution. The increase in effective resolution allowed us to have ∼ factor of 10 more centrophilic orbits compared to a uniform sampling; accordingly, the typical weights of these orbits were also a factor of 10 less than average. ",
+    "To validate the predictions of capture rates given by the Monte-Carlo code, we compared it to a number of direct N-body simulations, in the regime where the latter are feasible. As in our previous studies, we used the efficient direct N-body code φGRAPE-chain ((<>)Harfst et al., (<>)2008). It combines direct summation, using hardware acceleration of force computation provided by the SAPPORO library ((<>)Gaburov et al., ",
+    "(<>)2009), with chain regularization algorithm for accurate treatment of close encounters of stars with the black hole. The accuracy parameter of Hermite integrator was η = 0.01 and the softening length was set to zero. ",
+    "As explained in the previous section, it is very difficult if not impossible to construct even a scaled N-body model for a realistic galactic nucleus. Furthermore, for the difference between three geometries to be most prominent, we need to have a situation when the transition between empty and full loss cone regimes occurs well outside influence radius, and the draining time of saucer orbits at rm is much less than the simulation time (otherwise we don’t expect to have a substantial difference between axisymmetric and triaxial cases – both would have almost full loss cone draining rates at rm). An extensive search through the parameter space has led us to adopt the following parameters for the comparison between N-body and Monte-Calso simulations: γ = 1.5 (<>)Dehnen ((<>)1993) model with total mass of unity and M• = 0.1 (this gives rm ≈ 0.53 and P (rm) ≈ 1.7), capture radius r• = 2 × 10−4 , and simulation time of 20 N-body time units. The non-spherical models had axis ratios 1 : 1 : 0.75 and 1 : 0.9 : 0.75 for the axisymmetric and triaxial case, correspondingly, while having the same average M(r) profile as the spherical one. We stress again that these models do not correspond to any realistic galactic nuclei, but allow us to test the code. We have set up three N-body simulations with N = 5×105 particles using φGRAPE, and ran the Monte-Carlo code on the same initial snapshots, using the value of Coulomb logarithm ln Λ = 11 (calibrated against the energy diffusion rate measured in the N-body simulation). ",
+    "Figure (<>)2 shows the comparison between N-body and Monte-Carlo codes for the three geometries. We considered the time dependence of the number of captured particles and their distribution in semimajor axis a. The agreement between two codes is fairly good, with the N-body simulation giving slightly larger number of captured stars for a  0.2rm; this enhancement may be a result of resonant relaxation, which is not accounted for in the Monte-Carlo code, or large-angle deflections, which are also neglected. We also show the change in L2 during one radial period just before capture; as expected, this change is larger for non-spherical models, and the transition between empty and full loss cone regimes occurs well within rm for most realistic parameters ((<>)Vasiliev & Merritt, (<>)2013). We note that relativistic precession starts playing role for radii smaller than roughly the radius of transition to the full loss cone regime ((<>)Merritt (<>)& Vasiliev, (<>)2011), and therefore our neglect of relativity does not lead to noticeable errors in the overall capture rate. As a final remark, the Monte-Carlo simulation of this scale takes only half an hour on a typical multi-core workstation, while the N-body simulation takes approximately 10 days with a modern GPU. "
+  ],
+  "6. Results ": [
+    "Having tested the Monte-Carlo code on a “toy” model, we now apply it for the models describing realistic galactic nuclei. We take the Dehnen density profile with γ = 1, a black hole mass of either 10−2 or 10−3 of the galaxy mass, and axis ratios of 1 : 1 : 0.8 and 1 : 0.9 : 0.8, corresponding to  ≈ 0.27. The orbit composition of models is shown on Figure (<>)3. The fraction of “orbits of interest” – saucers, pyramids and chaotic orbits – is ∼ 10 − 20% of mass near rm, but their total mass is lower: the mass of chaotic orbits is ∼ 1.5 (5)% of the total galaxy mass and the mass of saucers (pyramids) is ∼ 16 (5)%M• for the axisymmetric (triaxial) models. Thanks to the improved mass sampling scheme, the number fraction of these orbits is much larger ",
+    "Figure 2. Comparison between N-body (solid lines) and Monte-Carlo (dashed lines) simulations of a N = 5 × 105 , γ = 3/2 Dehnen model with M• = 0.1, for three cases: spherical (red, bottom lines), axisymmetric (green, middle lines) and triaxial (blue, top lines). Other parameters of the simulations are given in the text. ",
+    "Top left: cumulative mass of captured particles as a function of time. Top right: distribution of captured particles in semimajor axis a, normalized by the influence radius (rm = 0.53 in model units). Bottom row: change in squared angular momentum L2 in one radial period before capture, for the spherical (left) and triaxial (right) case; axisymmetric case is similar to triaxial. The transition between empty and full loss cone boundary conditions occurs when ΔL2 ≈ L•2 , and is shifted to smaller radii in non-spherical potentials. Red crosses are from N-body simulations, blue dots – from Monte-Carlo models, green lines are the analytic trends (see (<>)Vasiliev & Merritt, (<>)2013, Fig.8). ",
+    "than their mass fraction. The models are scaled to physical scale using three values of M• = 107 , 108 and 109 M, capture radius r• = 4 × 10−5(M•/108 M) pc and the influence radius rm = 45 (M•/108 M)0.56 pc. The simulation time is 1010 yr and the dynamical time at the radius of influence is ∼ 106 (M•/108 M)0.34 yr. We do not include physical collisions in our treatment, since for our models the collision timescale is much longer than the Hubble time at all radii of interest, although the situation could well be different for less massive black holes in dense nuclei ((<>)Duncan & Shapiro, (<>)1983; (<>)Murphy et al., (<>)1991; (<>)Freitag & Benz, (<>)2002). Likewise, the relaxation time is also long enough to neglect the changes in density profile. We consider a population of equal-mass main-sequence stars with solar mass and radius; this is surely a crude simplification, as the red giants have much larger physical radii and are more readily torn apart by tidal forces ((<>)Syer & Ulmer, (<>)1999). Nevertheless, the basic model should ",
+    "Figure 4. Left panel: The total mass of captured stars after 1010 years (left axis), and the present-day capture rate (right axis), as functions of black hole mass M•. The crosses show the total captured mass in Monte-Carlo simulations for three geometries; solid lines show the same quantity computed using time-dependent Fokker-Planck models from (<>)Vasiliev & Merritt ((<>)2013), which include the contribution of draining; and dotted lines show the present-day capture rates derived from the same models. For the triaxial case, the capture rate is almost entirely due to draining of centrophilic orbits (Equation (<>)12). ",
+    "Right panel: Various timescales as functions of radius (normalized to the influence radius rm). Shown is the local relaxation time (red, top), draining time of centrophilic orbits in the triaxial case (blue, middle, Eq. (<>)6) and in the axisymmetric case (green, bottom, Eq. (<>)7). Solid lines – M• = 107 M, rm = 13 pc, dashed – M• = 108 M, rm = 45 pc, dot-dashed – M• = 109 M, rm = 160 pc. ",
+    "capture qualitatively the main features of more realistic galactic nuclei. ",
+    "The results of Monte-Carlo simulations agree well with the qualitative picture described above. The difference between three geometries is modest at low M•, when even the spherical system is largely in the full loss cone regime, but becomes more pronounced for M•  108 M (Figure (<>)4). The peak of distribution of captured stars in energy corresponds to semimajor axis a ∼ rm/2 (as the orbits of captured stars are almost radial, one may say that these stars come from radii ∼ 2a ∼ rm). At this energy, the draining time of loss region is ∼ 4 × 1010 yr for the triaxial model and ∼ 3×108 yr for the axisymmetric one, in both cases weakly depending on M•. Thus in spherical and axisymmetric systems the flux at present time is mostly determined by relaxation, while for triaxial systems it is dominated by draining of centrophilic orbits (mostly pyramids within rm). The difference between the first two comes from the larger size of the effective capture boundary in the axisymmetric case, which enhances the flux by a logarithmic factor of few (∼ ln(R•−1)/ ln(−1), (<>)Vasiliev & Merritt ((<>)2013)), but only in the case when most of the flux in the spherical case occurs in the empty loss cone regime. Again, one should keep in mind that this refers to the steady-state flux, while in the above figure we plot the solution of the time-dependent Fokker-Planck equation, in which the difference between spherical and axisymmetric systems is much larger if the evolution time is shorter than ∼ 0.1Trel(rm) (i.e., for M•  107 M). ",
+    "Figure (<>)5 shows the properties of captured stars for a 108 M black hole in three geometries. In this case the difference in the total captured mass between ",
+    "Figure 5. Properties of captured stars for a M• = 108 black hole. ",
+    "Top left: cumulative mass as a function of time, for three models (from top to bottom: triaxial, axisymmetric, spherical). Top right: distribution of captured stars in semimajor axis a, normalized by the influence radius rm. In addition to the same three models, the full loss cone rate ((<>)4) is plotted as dot-dashed line, and the “draining radius”, at which the draining time ((<>)6) equals 1010 yr, is marked by a vertical line. Bottom panels: distribution of captured stars in a/rm for each orbit type. ",
+    "spherical and axisymmetric cases is already an order of magnitude, while the triaxial system adds another factor of two. The figure also shows that, contrary to a naive expectation, the flux at almost all energies is substantially lower than the full loss cone flux; nevertheless, the crude estimate based on a full loss cone rate above the “draining” energy ((<>)12) is remarkably close to the more refined calculation. Chaotic orbits contribute a minor fraction to the captured mass in both axisymmetric and triaxial cases. The figure was plotted for the model with M• = 10−2 of the total galaxy mass; the model with M• = 10−3 has very similar properties (to within 10%) but less reliable statistics, as the number of captured orbits is lower by a factor of 3. ",
+    "An important question about non-spherical models with black holes is whether the scattering of chaotic orbits by the central mass may lead to the elimination or reduction of triaxiality. We do not see any evidence for this, even though the models were evolved for ∼ 104 dynamical times at the radius of influence. The opposite conclusion reached in earlier studies ((<>)Gerhard & Binney, (<>)1985; (<>)Merritt & Quinlan, (<>)1998; (<>)Kalapotharakos, (<>)2008) might have resulted from considering evolutionary rather ",
+    "than steady-state models, in which a black hole grew in a pre-existing triaxial cusp. We have also considered a model with a larger deviation from spherical symmetry, namely with axis ratio 1 : 0.8 : 0.5, same as in (<>)Poon & Merritt ((<>)2004), and the black hole mass of 1% of galaxy mass. However, it turned out to be impossible to create a quasi-isotropic model with these properties: there is no difficulty to arrange for the given shape and density profile, but the region outside a few rm cannot have a uniform distribution of stars in R. Instead a radially anisotropic system is formed with a scarcity of orbits at intermediate R and an excess of them at R = 1 and even more at R = 0. Naturally, such system may have a draining rate larger than the full loss cone rate, which might explain the conclusions reached by (<>)Merritt & Poon ((<>)2004). Instead, we opted for a model with variable triaxiality: the axis ratio y/x increased from 0.8 to 0.9 between 5 and 7 rm, i.e. outside the region that gives the main contribution to the total flux. As expected, this model yielded a larger captured mass, roughly by a factor 1.5. ",
+    "We also confirmed the scaling relations derived in §(<>)4, by performing a simulation with r•, D and tsim −1 all scaled by the same factor of 10. This resulted in a very similar behaviour for axisymmetric and triaxial systems, while somewhat increasing the flux in the spherical case (due to a logarithmic dependence on R•). "
+  ],
+  "7. Conclusions ": [
+    "We have considered the dynamics of stars in galactic nuclei containing supermassive black holes, with the focus on the rates of capture of stars by the black hole, in particular, in non-spherical nuclei. The supply of stars into the loss cone – the region of phase space from where the capture is possible – is driven by changes in angular momentum due to two effects: collisional two-body relaxation, which operates in any geometry, and collisionless torques which arise in the case that the potential is non-spherical. ",
+    "We have reviewed the structure of orbits in galactic nuclei and identified the classes of orbits that are important for the loss cone problem – saucer orbits in axisymmetric systems and pyramid orbits in triaxial systems, as well as chaotic orbits which exist outside the black hole radius of influence rm in both cases. These orbits form the loss region, from which a star may get into the loss cone and be captured by the black hole even in the absence of two-body relaxation, due to collisionless torques only. In a triaxial case, chaotic and pyramid orbits are centrophilic, i.e. they may attain arbitrarily low values of angular momentum; in an axisymmetric case, the loss region is composed of orbits with the conserved component of angular momentum, Lz, being low enough to let them enter the loss cone. In both cases the volume of the loss region is substantially larger than the loss cone proper, thus we expect a higher capture rate due to two factors: (i) the stars in the loss region are drained over a timescale much longer than the dynamical time, and (ii) two-body relaxation is required only to drive a star into the loss region, instead of a much smaller loss cone, for it to be eventually captured. ",
+    "The interplay between collisonless and collisional effects is poorly handled by present-day N-body simulations, due to the necessity of a very large number of particles for the collisional effects to be realistically small. To circumvent this trouble, we have developed a Monte-Carlo method that can simulate these systems with a rather modest number of particles while ensuring a faithful balance between the two effects. It follows the orbits of stars in a smooth potential of any geometry ",
+    "while perturbing them according to the standard two-body relaxation theory. We applied this method to the loss-cone problem in non-spherical galaxies, with the aim of determining the total mass of stars captured by the black hole during the Hubble time. We assumed a one-parameter family of models with a ρ ∝ r−1 density cusp and the scale radius of the model determied by the M• − σ relation. Our main results are the following: ",
+    "These conclusions were confirmed for a limited set of models but are likely to hold for more general cases. The most important assumption in the present study was that the initial distribution of stars was close to isotropic in the angular momentum space, which results in a rather large draining flux, and an increased capture rate due to relaxation, compared to the steady-state value. If a galaxy has an already depleted stellar population at low angular momenta, for instance, due to ejection ",
+    "of these orbits by a binary supermassive black hole ((<>)Merritt & Wang, (<>)2005), then the difference between the three geometries is likely to be reduced, and the overall flux will be lower. Thus our calculations should be taken rather as upper estimates, which nevertheless predict a rather high capture rate (∼ 10−3 M/yr) for the most massive black holes in non-spherical galaxies. On the other hand, the number of detectable tidal disruption flares for these black holes is much smaller, as for black holes more massive than 108 M most of the captured stars are swallowed entirely without producing any flare. Figure 15 in (<>)MacLeod et al. ((<>)2012) suggests that for M• = 109 M the tidal disruption flares of giant stars could constitute less than 5% of total capture events. A more quantitative estimate is beyond the scope of this paper, we only note for more realistic assumptions about stellar structure and evolution there are several other processes that could be important in the context of star–black hole interaction, such as “growth” of a giant star into the loss cone ((<>)Syer & Ulmer, (<>)1999; (<>)MacLeod et al., (<>)2013), or tidal dissipation–induced capture ((<>)Li & Loeb, (<>)2013). It is also worth noting that we considered rather low-density galactic nuclei, in which we could neglect physical collisions between stars and the changes in density profile due to relaxation in energy, both processes occuring on timescales much longer than Hubble time. For less massive black holes in denser nuclei (like the Milky Way) the situation is more complicated, but in these systems we don’t expect non-spherical effects to play a significant role in the capture rate. ",
+    "I am grateful to the referees for their valuable comments which helped to improve the presentation. This work was partly supported by the National Aeronautics and Space Administration under grant no. NNX13AG92G. The software for estimating capture rates from Fokker-Planck models, including draining of the loss region, is available from (<http://td.lpi.ru/~eugvas/losscone/>)http://td.lpi.ru/~eugvas/losscone/. "
+  ]
+}

jsons_folder/2014IAUS..298..130M.json

@@ -0,0 +1,87 @@
+{
+  "Abstract": [
+    "Abstract. Despite the recent advancements in the field of galaxy formation and evolution, fully self-consistent simulations are still unable to make the detailed predictions necessary for the planned and ongoing large spectroscopic and photometry surveys of the Milky Way disc. These diÿculties arise from the very uncertain nature of sub-grid physical energy feedback within models, a ecting both star formation rates and chemical enrichment. To avoid these problems, we have introduced a new approach which consists of fusing disc chemical evolution models with compatible numerical simulations. We demonstrate the power of this method by showing that a range of observational results can be explained by our new model. We show that due to radial migration from mergers at high redshift and the central bar at later times, a sizable fraction of old metal-poor, high-[ /Fe] stars can reach the solar vicinity. This naturally accounts for a number of recent observations related to both the thin and thick discs, despite the fact that we use thin-disc chemistry only. Within the framework of our model, the MW thick disc has emerged naturally from (i) stars born with high velocity dispersions at high redshift, (ii) stars migrating from the inner disc very early on due to strong merger activity, and (iii) further radial migration driven by the bar and spirals at later times. A significant fraction of old stars with thick-disc characteristics could have been born near the solar radius. "
+  ],
+  "keywords": [
+    "Keywords. Galaxy: abundances, Galaxy: disk, Galaxy: evolution, Galaxy: kinematics and dynamics, (Galaxy:) solar neighborhood "
+  ],
+  "1. Introduction ": [
+    "Crucial information regarding the dominant mechanisms responsible for the formation of the Milky Way (MW) disc and other Galactic components is encoded in the chemical and kinematical properties of its stars. This realization is manifested in the number of on-going and planned spectroscopic Milky Way surveys, such as RAVE (Steinmetz et al. 2006; Boeche et al., this volume), SEGUE (Yanny et al. 2009), APOGEE (Majewski et al. 2010; Schultheis et al., this volume), HERMES (Freeman 2010), Gaia-ESO (Gilmore et al. 2012), Gaia (Perryman et al. 2001; Vallenari et al., this volume), LAMOST (Zhao et al. 2006; Deng et al, this volume) and 4MOST (de Jong et al. 2012), which aim at obtaining kinematic and chemical information for a large number of stars. ",
+    "The common aim of these observational campaigns is to constrain the MW assembly history – one of the main goals of the field of Galactic Archaeology. The underlying principle of Galactic Archaeology is that the chemical elements synthesized inside stars, and later ejected back into the interstellar medium (ISM), are incorporated into new generations of stars. As di erent elements are released to the ISM by stars of di erent masses and, therefore, on di erent timescales, stellar abundance ratios provide a cosmic clock, capable of eliciting the past history of star formation and gas accretion of a galaxy. ",
+    "1 ",
+    "In most cases, the stellar surface abundances reflect the composition of the interstellar medium at the time of their birth, which is the reason why stars can be seen as fossil records of the Galaxy evolution. One of the most widely used “chemical-clocks” is the [ /Fe] ratio†(<>). ",
+    "In order to be able to interpret the large amounts of data to come, galaxy formation models tailored to the MW are needed. "
+  ],
+  "2. Diÿculties with fully self-consistent simulations ": [
+    "Producing disc-dominated galaxies has traditionally been challenging for cosmological models. In early simulations, extreme angular momentum loss during mergers gave birth to galaxies with overly-concentrated mass distributions and massive bulges (e.g., Navaro et al. 1991, Abadi et al. 2003). Although an increase in resolution and a better modeling of star formation and feedback have allowed recent simulations to produce MW-mass galaxies with reduced bulge fractions (Agertz et al. 2011, Guedes et al. 2011, Martig et al. 2012), none of these simulations include chemical evolution. Galaxy formation simulations including some treatment of chemical evolution have been performed by several groups (e.g., Raiter et al. 1996, Kawata et al. 2003, Scannapieco et al. 2005, Few et al. 2012). ",
+    "However, although the results are encouraging, and global observed trends seem to be reproduced, such as the mass-metallicity relation (e.g., Kobayashi et al. 2007, Kobayashi et al., this volume) or the metallicity trends between the di erent galactic components (e.g., Tissera et al. 2012), it is still a challenge for these simulations to reproduce the properties of the MW (e.g., the typical metallicities of the di erent components – Tissera et al. 2012, Tissera et al., this volume). Additionally, the fraction of low metallicity stars are often overestimated (Kobayashi et al. 2011, Calura et al. 2012), and reproducing the position of thin-and thick-disc stars in the [O/Fe]-[Fe/H] plane has proved challenging (Brook et al. 2012). While such issues could be due to unresolved metal mixing (Wiersma et al. 2009), it is also worth noting that none of the above-mentioned simulations reproduce simultaneously the mass, the morphology and star formation history (SFH) of the MW. ",
+    "This situation has led us to look for a novel way to approach this complex problem. We will show that this approach works encouragingly well, explaining not only current observations, but also leading to a more clear picture regarding the nature of the MW thick disc (see also Bensby et al., this volume). "
+  ],
+  "3. A new chemo-dynamical model ": [
+    "To properly model the MW, it is crucial to be consistent with some observational constraints at redshift z = 0, for example, a flat rotation curve, a small bulge, a central bar of an intermediate size, gas to total disc mass ratio of ˘ 0.14 at the solar vicinity, and local disc velocity dispersions close to the observed ones. ",
+    "It is clear that cosmological simulations would be the natural framework for a state-of-the-art chemodynamical study of the MW. Unfortunately, as described in Sec. (<>)2, a number of star formation and chemical enrichment problems still exist in fully self-consistent simulations. We, therefore, resort to (in our view) the next best thing – a high-resolution ",
+    "Figure 1. First row: The left panel shows the rotational velocity (dashed blue curve) and circular velocity (solid black curve) at the final simulation time. The middle panel presents the m = 2 Fourier amplitudes, A2/A0, as a function of radius estimated from the stellar density. Curves of di erent colors present the time evolution of A2/A0. To see better the evolution of the bar strength with time, in the right panel we show the amplitude averaged over the bar maximum. Second row: Face-on density maps of the stellar component for di erent times, as indicated. Third row: The corresponding edge-on view. Contour spacing is logarithmic Fourth row: Changes in angular momentum, L, as a function of radius, estimated in a time window of 0.52 Gyr, centered on the times of the snapshots shown above. Both axes are divided by the circular velocity, thus units are kpc (galactic radius). Strong variations are seen with cosmic time due to satellite perturbations and increase in bar strength. ",
+    "simulation in the cosmological context coupled with a pure chemical evolution model (see Minchev et al. 2013), as described below. "
+  ],
+  "3.1. A late-type disc galaxy simulation in the cosmological context ": [
+    "The simulation used in this work is part of a suite of numerical experiments first presented by (<>)Martig et al.(2012), where the authors studied the evolution of 33 simulated galaxies from z = 5 to z = 0 using the zoom-in technique described in Martig et al. (2009). This technique consists of extracting merger and accretion histories (and geometry) for a given halo in a -CDM cosmological simulation, and then re-simulating these histories at much higher resolution (150 pc spatial, and 104−5 M⊙ mass resolution). The interested reader is referred to Martig et al. (2012) for more information on the simulation method. ",
+    "Originally, our galaxy has a rotational velocity at the solar radius of 210 km/s and a scale-length of ˘ 5 kpc. To match the MW in terms of dynamics, at the end of the simulation we downscale the disc radius by a factor of 1.67 and adjust the rotational ",
+    "Figure 2. Properties of our detailed thin-disc chemical evolution model: Top left: SFR in the solar neighborhood resulting from model. Top middle: The total (solid), stellar (dashed) and gas (dotted) density time evolution at the solar neighborhood. The error bars are observational constraints (see Minchev et al. 2013 for references to the data). Bottom left: SFR as a function of time for di erent galactic radii as color-coded. Bottom middle: Total gas density (remaining after stars formation + recycled) as a function of time for di erent galactic radii as color-coded on the left. Top right: [Fe/H] input (solid curves) and final (dotted curves) gradients. Di erent colors correspond to di erent look-back times as indicated. The dotted-red and solid-blue vertical lines indicate the positions of the bar’s CR and OLR at the final simulation time. Bottom right: As on top but for the [O/Fe] gradients. ",
+    "velocity at the solar radius to be 220 km/s, which a ects the mass of each particle according to the relation GM ˘ v2r, where G is the gravitational constant. This places the bar’s corotation resonance (CR) and 2:1 outer Lindblad resonance (OLR) at ˘ 4.7 and ˘ 7.5 kpc, respectively, consistent with a number of studies (e.g., Dehnen 2000, Minchev et al. 2007, 2010; Monari et al., this volume; Antoja et al., this volume). At the same time the disc scale-length, measured from particles of all ages in the range 3 < r < 15 kpc, becomes ˘ 3 kpc, in close agreement with observations. After this change†(<>), our simulated disc satisfies the criteria outlined at the beginning of this Section, required for any dynamical study of the MW, in the following: ",
+    "early on and grows in strength during the disc evolution (see middle and right panels of Fig. (<>)1 and discussion below). ",
+    "In the first row, middle panel of Fig. (<>)1 we plot the Fourier amplitude, Am/A0, of the density of stars as a function of radius, where A0 is the axisymmetric component and m is the multiplicity of the pattern; here we only show the m = 2 component, A2/A0. Di erent colors indicate the evolution of the A2 radial profile in the time period specified by the color bar. The bar is seen to extend to ˘ 3 − 4 kpc, where deviations from zero beyond that radius are due to spiral structure. The brown curve reaching A2/A0 ˘ 0.9 at r ˇ 4.5 kpc results from a merger-induced two-armed spiral. To see better the evolution of the bar strength with time, in the right panel we show the amplitude averaged over 1 kpc at the bar maximum. ",
+    "The second and third rows of Fig. (<>)1 show face-on and edge-on stellar density contours at di erent times of the disc evolution, as indicated in each panel. The redistribution of stellar angular momentum, L, in the disc as a function of time is shown in the fourth row, where L is the change in the specific angular momentum as a function of radius estimated in a time period t = 520 Myr, centered on the time of each snapshot above. Both axes are divided by the rotational velocity at each radius, therefore L is approximately equal to the initial radius (at the beginning of each time interval) and L gives the distance by which guiding radii change during the time interval t. The dotted-red and solid-blue vertical lines indicate the positions of the bar’s CR and OLR. Note that due to the bar’s slowing down, these resonances are shifted outwards in the disc with time. ",
+    "After the initial bulge formation, the largest merger has a 1:5 stellar-mass ratio and an initially prograde orbit, plunging through the center later and dissolving in ˘ 1 Gyr (in the time period 1.5 . t . 2.5 Gyr, first column of Fig. (<>)1). Due to its in-plane orbit (inclination . 45◦), this merger event results in accelerated disc growth by triggering strong spiral structure in the gas-dominated early disc, in addition to its tidal perturbation. One can see the drastic e ect on the changes in angular momentum, L, in the fourth row, right panel of Fig. (<>)1. A number of less violent events are present at that early epoch, with their frequency decreasing with time. The e ect of small satellites, occasionally penetrating the disc at later times, can be seen in the third and fourth columns at L ˇ r & 7 and L ˇ r ˇ 6 kpc, respectively. ",
+    "We note a strong variation of L with cosmic time, where mergers dominate at earlier times (high z) and internal evolution takes over at t = 5 − 6 Gyr (corresponding to a look-back-time of ˘6-7 Gyr, or z ˘ 1). The latter is related to an increase with time in the bar’s length and major-to-minor axes ratio as seen in the face-on plots, indicating the strengthening of this structure. Examining the top right panel of Fig. (<>)1, we find a continuous increase in the bar’s m = 2 Fourier amplitude with time, where the strongest growth occurs between t=4 and 8 Gyr. The e ect of the bar can be found in the changes in angular momentum, L, as the feature of negative slope, centered on the CR (dotted-red vertical line), shifting from L ˇ 3.4 to L ˇ 4.7 kpc. Due to the increase in the bar’s amplitude, the changes in stellar guiding radii (vertical axis values) induced by its ",
+    "presence in the CR-region double in the time period 4.44 < t < 11.2 Gyr (bottom row of Fig. (<>)1). Until recently bars were not considered e ective at disc mixing once they were formed, due to their long-lived nature. We emphasize the importance of the bar in its persistent mixing of the inner disc throughout the galactic evolution (see Minchev et al. 2012a and discussion therein). "
+  ],
+  "3.2. The chemistry ": [
+    "The chemical evolution model we use here is for the thin disc only. The idea behind this is to test, once radial mixing is taken into account, if we can explain the observations of both thin and thick discs without the need of invoking a discrete thick-disc component. A detailed description of the chemical model is given in Minchev et al. (2013) and here we show its properties in Fig. (<>)2. "
+  ],
+  "3.3. Fusing chemistry and dynamics ": [
+    "To combine the dynamics with the chemistry, we start by dividing the simulated disc into 300-pc radial bins in the range 0 < r < 16 kpc. At each time output we randomly select newly born stars, by matching the SFH corresponding to our chemical evolution model at each radial bin. Since our goal is to satisfy the SFH expected for the chemical model (close, but not identical to that of the simulation), at some radial bins and times we may not have enough newly born stars in the simulation. In such a case we randomly select stars currently on the coldest orbits (i.e., with kinematics close to those of newly born stars). This fraction is about 10% at the final time. The particles selected at each time output are assigned the corresponding chemistry for that particular radius and time. This is done recursively at each time-step of 37.5 Myr. For the current work we extract about 40% of the ˇ 2.5x106 stellar particles comprising our dynamical disc at the final time in the range |z| < 4 kpc, r < 16 kpc. We have verified that decreasing or increasing this extracted sample by a factor two has negligible e ects on the results we present in this work. ",
+    "In the just described manner, we follow the self-consistent disc evolution for 11.2 Gyr, selecting a tracer population possessing known SFH and chemistry enrichment. This bypasses all the problems encountered by previous chemodynamical models based on N-body simulations. It also o ers a way to easily test the impact of di erent chemical prescriptions on the chemodynamical results. "
+  ],
+  "3.4. Local chemodynamical relations ": [
+    "Fig. (<>)3 shows how radial migration a ects the simulated solar neighborhood. A detailed discussion can be found in Minchev et al. (2013). Below we concentrate on the comparison of the model to observations. "
+  ],
+  "4. Comparison to recent observational results ": [
+    "To be able to compare our results to di erent MW surveys we need to constrain spatially our model sample. For example the Geneva-Copenhagen Survey (GCS) and high-resolution stellar samples are confined to within 100 pc from the Sun, while the SEGUE and RAVE samples explore much larger regions, but miss the local stars. ",
+    "4.1. Changes in the MDF for samples at di erent distances from the disc plane In the right panel of Fig. (<>)4 we compare our model MDF to recent observations. We consider the high-resolution sample by Adibekyan et al. (2012) (histogram extracted from Fig. 16 by Rix and Bovy 2013), the mass-corrected SEGUE G-dwarf sample by Bovy et ",
+    "Figure 3. Top left: Birth radii of stars ending up in the “solar” radius (green shaded strip) at the final simulation time. The solid black curve plots the total r0-distribution, while the color-coded curves show the distributions of stars in six di erent age groups, as indicated. The dotted-red and solid-blue vertical lines indicate the positions of the bar’s CR and OLR at the final simulation time. A large fraction of old stars comes from the inner disc, including from inside the CR. Bottom left: [Fe/H] distributions for the sample shown in the top panel, binned by birth radius in six groups, as indicated. The total distribution is shown by the solid black curve. The importance of the bar’s CR is seen in the large fraction of stars with 3 < r0 < 5 kpc (blue line) giving rise to the metal-rich tail of the distribution. Top middle: Stellar density contours of the Age-[Fe/H] relation after fusing with dynamics, for the “solar” radius (7 < r < 9 kpc, as in left column). The overlaid curves indicate the input chemistry for certain radii, indicating where stars were born. The pink dashed curve plots the mean, seen to follow closely the input r0 = 8 kpc line (cyan). Bottom middle: Same as top but for the [Fe/H]-[O/Fe] relation. No bimodality is found for this unbiased model sample. Top right: Metallicity distributions for di erent age bins. Bottom right: Same as above but for the [Fe/H]-[O/Fe] relation. ",
+    "al. (2012a) (MDF extracted from their Fig. 1, right panel). The third data set we consider comes from the latest, Data Release (DR) 9, SEGUE G-dwarf sample, which is also mass-corrected in the same way as Bovy et al. (2012a). The main di erences from the data used by Bovy et al. (2012a) are a di erent distance estimation (spectroscopic instead of photometric), a selection of G-dwarfs based on DR9, instead of on DR7 photometry, and a signal-to-noise S/N > 20 instead of S/N > 15. Further details can be found in Brauer et al. (2013, in preparation). The exact cut in r and z as in the simulation is applied to the latter sample only, since the other two data sets are not available to us. ",
+    "The red histogram in each panel of Fig. (<>)4 shows di erent observational data as indicated; the additional curves plot the model data with no error in [Fe/H] (black) and convolved errors of [Fe/H]=±0.2 dex (blue), drawn from a uniform distribution. We have selected a very local sample to compare to the high-resolution nearby data by ",
+    "Figure 4. Comparison of our model metallicity distribution function (MDF) to recent observations. The red histograms shows data from Adibekyan et al. (2012) (left), Bovy et al. (2012a) (middle), and Brauer et al. (2013) (right). In each panel the black and blue curves plot the model data with no error in [Fe/H] and convolved error of [Fe/H]=0.2 dex, respectively. We have selected a very local sample to compare to the high-resolution nearby sample by Adibekyan et al. (2012) (as indicated) and a range in z and r to approximately match the SEGUE data studied by the other two works. A shift in the peak from [Fe/H]˘0 to [Fe/H]˘ −0.3 dex for both observed and simulated data is seen when considering a larger sample depth. ",
+    "(<>)Adibekyan et al.(2012) and a range in z and r to approximately match the SEGUE data studied by the other two works. A remarkable match is found between our model predictions and the data. The expected broadening in the model distributions is seen, with the inclusion of error in [Fe/H]. "
+  ],
+  "4.2. Is the bimodality in the [Fe/H]-[O/Fe] plane due to selection e ects? ": [
+    "Starting with the assumption of two distinct entities – the thin and thick discs – many surveys select stars according to certain kinematical criteria (e.g., Bensby et al. 2003, Reddy et al. 2006). For example, Bensby et al. (2003) defined a (now widely used) method for preferentially selecting thin-and thick-disc stars with a probability function purely based on kinematics. ",
+    "We now employ the same technique as Bensby et al. (2003) and extract a thin- and thick-disc selections from our initially unbiased sample (Fig. (<>)3, bottom middle panel). In order to obtain a similar number of thin-and thick-disc stars, as done in most surveys, we randomly down-sample the thin-disc selection. To mach the spacial distribution of high-resolution samples, usually confined to small distances from the Sun, we impose the constraints 7.8 < r < 8.2 kpc, |z| < 0.2 kpc. Our results do not change to any significant degree when this sample depth is decreased or increased by a factor of two. ",
+    "The resulting thin- and thick-disc distributions of stars in the [Fe/H]-[O/Fe] plane are presented, respectively, in the top and bottom left panels of Fig. (<>)5. To get an idea of where stars originate, we have overlaid the input chemistry curves for stars born at r0 6 2 kpc (black), at r0 = 8 kpc (or in situ, cyan), and at r0 = 14 kpc (red). The thick-disc selection appears to originate almost exclusively inside the solar circle (sample is confined between the cyan and black curves). On the other hand, the thin-disc sample follows the local curve for [Fe/H] > 0.1, covers the region between the inner and outer disc (black and red curves) for −0.4 < [Fe/H] < 0.1. Thin-disc stars with [Fe/H] < −0.4, referred to as “the metal-poor thin disc” (e.g., Haywood et al. 2013), appear to originate mostly from outside the solar radius in agreement with the conclusions by Haywood et al. (2013). ",
+    "The middle, top panel of Fig. (<>)5 displays the overlaid thin- and thick-disc selections, which were showed separately in the left column. A relatively clear bimodality is found ",
+    "Figure 5. Selection e ects can result in a bimodality in the [Fe/H]-[O/Fe] plane. Left column: We have applied the selection criteria used by Bensby et al. (2003) to extract thin-and thick-disc samples from our model, indicated by orange triangles and blue squares, respectively. Middle column: Overlaid thin-and thick-disc model samples, which are shown separately in the left column. The bottom panel shows the same model data but with convolved errors of [Fe/H]=±0.1 and [O/Fe]=±0.05 dex. Right column: Top panel plots the high-resolution data from Ram´ırez (their Fig. 11, b). In the bottom panel we overlay the observed and simulated data samples, presenting a remarkable match. The black dashed horizontal line shows the location of the gap coincidental for both the model and data. ",
+    "at [O/Fe] ˇ 0.2 dex, similarly to what is seen in observational studies. The thick-disc selection follows the upper boundary of the distribution throughout most of the [Fe/H] extent due to the fact that it originates in the inner disc. In the bottom, middle panel we have convolved errors within our model data of [Fe/H]=±0.1 and [O/Fe]=±0.05 dex, drawing from a uniform distribution. ",
+    "In the right, top panel of Fig. (<>)5 we plot the high-resolution data from (<>)Ram´ırez et al.(2013) (same as their Fig. 11, b). The gap separating the thin-and thick-disc selections occurs at a very similar location to what is found for the model on the left, as indicated by the black dashed horizontal line. In the bottom right panel we overlay the observed and simulated data samples, presenting a remarkable match. An overall o set within the error (0.05 − 0.1 dex) toward negative [O/Fe]-values is found for the model. "
+  ],
+  "4.3. Disc scale-heights of mono-abundance subpopulations ": [
+    "Using SEGUE G-dwarf data, Bovy et al. (2012b) (see also Bovy et al., this volume) showed that the vertical density of stars grouped in narrow bins constrained in both [O/Fe] and [Fe/H] (mono-abundance subpopulations) can be well approximated by single exponential disc models. ",
+    "To see whether we can reproduce these results, in the left panel of Fig. (<>)6 we present the vertical scale-heights of di erent mono-abundance subpopulations, resulting from our model, as a function of their position in the [Fe/H]-[O/Fe] plane. We have convolved errors in our model data of 0.1 and 0.05 dex for [Fe/H] and [O/H], respectively. A range in galactic radius of 6 < r < 10 kpc, similar to the SEGUE data, is used. Very good fits are obtained by using single exponentials, excluding the 200 pc closest to the disc plane. ",
+    "This figure can be directly compared to Fig. 4 by Bovy et al. (2012b), bottom left panel. The general trends found in the SEGUE G-dwarf data are readily reproduced by our model: (i) for a given metallicity bin, scale-heights decrease when moving from low-to high-[O/Fe] populations and (ii) for a given [O/Fe] bin, scale-heights increase with increasing metallicity. ",
+    "Note that a reversal is found for trend (i) above, just as in the data (Fig. 4, Bovy et ",
+    "Figure 6. Left: Model vertical scale-heights for di erent mono-abundance subpopulations as a function of position in the [Fe/H]-[O/Fe] plane. Very good fits are obtained by using single exponentials, excluding the 200 pc closest to the disc plane. A radial range of 6 < r < 10 kpc similar to the SEGUE data is used. This figure can be directly compared to Fig. 4 by Bovy et al. (2012b). Our model predicts scale-heights of up to ˘ 1.9 kpc for the oldest, most metal-poor samples; this should be compared to a maximum of ˘ 1 kpc inferred from Bovy et al.’s mass corrected SEGUE G-dwarf data. Right: Mean metallicity as a function of distance from the disc plane, |z|, in the range 6 < r < 10 kpc. Red filled circles and error bars show SEGUE data from Schlesinger et al. (2012), while blue dashed line is Bovy et al.’s model. The solid black curve is our model. A very good agreement between the two models in found for the metallicity variation with |z|, including the flattening at |z| & 1.5 kpc. This can be associated with the predominance of old/high-[O/Fe] stars at large distances from the plane. ",
+    "al. 2012b): for the four most metal-poor bins ([Fe/H] < −0.7 dex) scale-heights decrease with increasing [O/Fe]. This may be a potentially very important observation, that can be linked to the MW merger history as recently described by Minchev et al. (2014). "
+  ],
+  "4.4. The vertical metallicity gradient ": [
+    "We would now like to compare our model to the recent works by Schlesinger et al. (2012) and Rix and Bovy (2013), where SEGUE G-dwarf data were utilized. We have extracted the data points from Fig. 15 by Rix and Bovy (2013), where a comparison was made between the vertical metallicity gradient estimated by Schlesinger et al. (2012) and the one implied by Bovy et al.’s model. ",
+    "The right panel of Fig. (<>)6 presents these data along with our model prediction, as indicated by di erent colors. We find ˘ 0.05 − 1 dex higher metallicity than Bovy et al.’s model systematically as a function of |z|, appearing to match the data better at |z| . 1 kpc. We note that both models and the data are normalized using the solar abundance values by Asplund et al. (2005). It should be kept in mind that while the errors in [Fe/H] are plotted for each data point, distance uncertainties are not shown; however they should be increasing with distance from the disc plane. ",
+    "A very good agreement between the two models is found for the metallicity variation with |z|, including the flattening at |z| & 1.5 kpc. Minchev et al. (2013) associated this with the predominance of old/high-[O/Fe] stars at large distances from the plane. "
+  ],
+  "5. Discussion ": [
+    "Despite the recent advances in the general field of galaxy formation and evolution, there are currently no self-consistent simulations that have the level of chemical implementation required for making detailed predictions for the number of ongoing and planned ",
+    "MW observational campaigns. Even in high-resolution N-body experiments, one particle represents ˘ 104−5 solar masses. Hence, a number of approximations are necessary in order to compute the chemical enrichment self-consistently in a simulation, leading to the several problems briefly discussed in Sec. (<>)2. Here, instead, we have assumed that each particle is one star† (<>)and have implemented the exact SFH and chemical enrichment from a typical chemical evolution model into a state-of-the-art simulation of the formation of a galactic disc. We note that this is the first time that a chemodynamical model has the extra constraint of defining a realistic solar vicinity also in terms of dynamics, as detailed in Sec. (<>)3. ",
+    "According to our model, the MW “thick disc” emerges naturally from (i) stars born with high velocity dispersions at high redshift, (ii) stars migrating from the inner disc very early on due to strong merger activity, and (iii) further radial migration driven by the bar and spirals at later times. Importantly, a significant fraction of old stars with thick-disc characteristics could have been born near and outside the solar radius (Fig. 15 by Minchev et al. 2013). ",
+    "Minchev et al. (2013) showed that for a simulation lacking early mergers the velocity dispersion of the oldest disc stars in the simulated solar neighborhood is underestimated by a factor of ˘ 2, while the model presented here is compatible with the observations (e.g., the vertical age-velocity relation achieves a maximum at ˘ 50 km/s for the oldest stars, see Fig. 6 by Minchev et al. 2013; Smith et al., this volume). It is, therefore, tempting to conclude that the highest velocity dispersion stars observed in the solar neighborhood are a clear indication of an early-on, merger-dominated epoch, or equivalently, scenarios involving stars born with high velocity dispersions. Our results suggest that the MW thick disc cannot be explained by a merger-free disc evolution as proposed previously. This is related to the inability of internally driven radial migration to thicken galactic discs due to the conservation of vertical action (Minchev et al. 2012b). However, an observational test involving both chemical and kinematic information must be devised to ascertain the e ect of early mergers in the MW. ",
+    "The results of this work present an improvement over previous models as we use a state-of-the-art simulation of a disc formation to extract self-consistent dynamics and fuse with a chemical model tailored for the MW. Future work should consider implementing gas flows, Galactic winds, and Galactic fountains (Fraternali et al., this volume) into the model to asses the importance of these processes. A suite of di erent chemical evolution models assigned to di erent disc dynamics (from di erent simulations) should be investigated to make progress in the field of Galactic Archeology. ",
+    "The method presented here is not only applicable to the MW but is also potentially very useful for extragalactic surveys. The same approach can be used for any other galaxy for which both kinematic and chemical information is available. A large such sample is currently becoming available from the ongoing CALIFA survey (Sanchez et al. 2012). Given the SFH and morphology of each galaxy, a chemodynamical evolution model tailored to each individual object can be developed, thus providing a state-of-the-art database for exploring the formation and evolution of galactic discs. "
+  ]
+}

jsons_folder/2014JCAP...03..001S.json

@@ -0,0 +1,136 @@
+{
+  "Abstract": [
+    "Abstract. We investigate cosmological signatures of uncorrelated isocurvature perturbations whose power spectrum is blue-tilted with spectral index 2 . p. 4. Such an isocurvature power spectrum can promote early formation of small-scale structure, notably dark matter halos and galaxies, and may thereby resolve the shortage of ionizing photons suggested by observations of galaxies at high redshifts (z≃7 −8) but that are required to reionize the universe at z∼10.We mainly focus on how the formation of dark matter halos can be modified, and explore the connection between the spectral shape of CMB anisotropies and the reionization optical depth as a powerful probe of a highly blue-tilted isocurvature primordial power spectrum. We also study the consequences for 21cm line fluctuations due to neutral hydrogens in minihalos. Combination of measurements of the reionization optical depth and 21cm line fluctuations will provide complementary probes of a highly blue-tilted isocurvature power spectrum. "
+  ],
+  "Contents ": [],
+  "1 Introduction ": [
+    "The epoch of reionization is a milestone in cosmological structure formation history. Although recent cosmological observations are beginning to reveal the epoch of reionization, the process of cosmological reionization is still one of the most open questions in cosmology. In particular, observations of star-forming galaxies at high redshifts 6 . z. 8, suggest that the density of UV photons emitted from such galaxies may not be suÿcient to keep the universe ionized [(<>)1], if the number density of the galaxies are as predicted by the concordance cosmological model with a nearly scale-invariant curvature power spectrum consistent with current CMB observations [(<>)2, (<>)3], unless very optimistic assumptions are made about ionizing photon escape fractions and other parameters. Indeed this conclusion is further aggravated by the decline in star formation rate density recently found beyond z∼8 [(<>)4]. ",
+    "To enhance the formation of collapsed objects in the high redshift universe, one possible solution is to allow matter fluctuations to have a large amplitude at small scales. However, in the inflationary cosmology, there are few degrees of freedom available to generate large curvature perturbations at small scales since they are found to be nearly-scale invariant on the scales of CMB and galaxy clustering (k. 0.1Mpc−1). On the other hand, isocurvature perturbations can have a highly blue-tilted power spectrum while satisfying CMB constraints on large scales1 (<>). ",
+    "In this study, we consider how such blue-tilted isocurvature power spectra can a ect cosmological observables at high redshifts, and in particular the CMB via the reionization of the universe. Such an isocurvature power spectrum can promote the formation of dark matter halos and enhance the formation of stars and galaxies in the high-redshift universe. While there are several previous studies on various aspects of these issues [(<>)5, (<>)9–(<>)11]2 (<>), we here focus on e ects on reionization and 21cm fluctuations due to nonlinearities triggered by isocurvature power spectra and especially on the complementarity of these probes. Although several authors have discussed e ects of isocurvature power spectra on 21cm fluctuations [(<>)14, (<>)15], they have generally focused on the contribution of a homogeneous IGM well before the epoch of reionization (z& 20). Here we focus on collapsed halos which make dominant contributions at relatively low redshifts (z. 20). ",
+    "Throughout this paper, we focus on matter isocurvature perturbations, where S(x) = δm −43 δ(δi is the initial density perturbation in a component i) that is uncorrelated with curvature fluctuations, ζ(x), i.e. S(x)ζ(x′)= 0. We in addition assume that there are no initial relative perturbations between baryon and CDM or so-called compensated isocur-vature perturbations [(<>)15]3 (<>), i.e. δc = δb. The power spectrum is defined as S(k)S(k′)= Piso(k)(2π)3 k). We assume the power spectrum Piso(k) is in power-law form, so thatδ(3)(k+′it can be parameterized as ",
+    "(1.1) ",
+    "where Aiso and niso are the amplitude and the spectral index of Piso(k) at the pivot scale k0 = 0.002Mpc−1 , which roughly corresponds to ℓ= 10 in the CMB angular power spectrum. We define the ratio of the isocurvature to adiabatic power spectrum, α= Aiso/Aadi, where the adiabatic power spectrum is given by Hereafter we use two parameters αand p= niso to characterize the model with an isocurvature power spectrum. ",
+    "The CMB and matter power spectra are computed using the CAMB code [(<>)17, (<>)18]. We take the concordance flat CDM model with power-law adiabatic power spectrum as the baseline cosmological model and set parameters to the best fit values from the WMAP 9-year result [(<>)2]. ",
+    "This paper is organized as follows. To begin with, we briefly discuss current constraints on the blue-tilted isocurvature power spectrum from the shape of the CMB power spectrum in the next section. In order to see how such an isocurvature power spectrum a ects the late-time universe, we first investigate its e ects on the mass function of dark matter halos in Section (<>)3. For observational signatures, we focus on the reionization optical depth and 21cm line fluctuations, which are discussed in Section (<>)4 and (<>)5, respectively. A final section is devoted to our conclusions. "
+  ],
+  "2 CMB power spectrum and constraints ": [
+    "First, we see to what extent an isocurvature power spectrum is constrained from measured shapes of the CMB power spectrum. In Fig. (<>)1, we plot the CMB power spectrum with several di erent values of the amplitude and spectral indices of the isocurvature power spectrum. Fig. (<>)2 shows 1 and 2σconstraints in the p-αplane from the observed CMB power spectrum. We adopt the likelihood functions from the WMAP 9-year results [(<>)2, (<>)19] and the ACT 2008 results [(<>)20, (<>)21]. From the figure, we can see that for p. 3, WMAP is more sensitive than ACT. On the other hand, as the spectral index becomes larger p& 4, the CMB spectrum at higher multipoles ℓ& 1000, which can be measured by ACT, becomes more sensitive. ",
+    "We however should note that here we have fixed other cosmological parameters and in addition contributions of foregrounds components that include the thermal Sunyaev-Zel’dovich e ect and point-sources. Varying these may non-negligibly loosen the constraints, in particular for ACT, which observes small angular scales where these foregrounds dominate primary anisotropies. In e ect, our constraints are at least an order of magnitude stronger than the constraints presented by Planck [(<>)22], although it is diÿcult to compare these with ",
+    "Figure 1. CMB power spectrum for di erent amplitudes and spectral indices of the isocurvature power spectrum. In order from top to bottom, the temperature, E-mode polarization and their cross-correlation power spectra are plotted. Cases of p= 2, 3, 4 are shown in order from left to right. In each panel, cases of α= 10−1 (red solid), 10−3 (green dashed), 10−5 (blue dotted) are plotted. Thick and thin lines show contributions from the isocurvature power spectrum alone and the sum of the adiabatic and isocurvature spectra, respectively. ",
+    "our constraints in a straightforward way, as the parameterizations for the isocurvature power spectrum are di erent 4 (<>). Our constraints here should be regarded as very optimistic. "
+  ],
+  "3 Mass function ": [
+    "Since the CMB power spectrum can measure primordial perturbations only on large scales, isocurvature perturbations are allowed to have large amplitudes on small scales if the power spectrum is blue-tilted. Such isocurvature perturbations with a blue-tilted spectrum can significantly a ect structure formation on small scales and can increase the number of dark ",
+    "Figure 2. Constraints on the amplitude αand the spectral index pof the isocurvature power spectrum from CMB datasets. Results from WMAP9 (red) ACT2008 (green) and WMAP9+ACT2008 (blue) are shown The contours and shaded regions respectively show parameter regions excluded at 1 and 2σlevels. ",
+    "matter halos in the high-redshift universe. To investigate this e ect, we evaluate the mass function of dark matter halos for di erent isocurvature parameters in this section. ",
+    "According to the Press-Schechter formalism [(<>)23], the mass function of dark matter halos is given by ",
+    "(3.1) ",
+    "where ρ¯m is the mean energy density of matter, f(ν) is the occupation function and we define ν≡(δcr/σ(M))2 with δcr and σ(M) respectively being the critical overdensity and the variance of matter fluctuations in a sphere of radius Rsatisfying M= 43ˇ ρ¯mR3 . ",
+    "Given a matter power spectrum P(k), σ(M) is obtained by ",
+    "(3.2) ",
+    "where W(kR) is a top-hat window function with radius R, ",
+    "(3.3) ",
+    "Regarding the occupation function f(ν), we adopt the one proposed by Sheth and Tor-men [(<>)24], ",
+    "(3.4) ",
+    "where a= 0.3, q= 0.75 and A(a) is the normalization so that occupation function satisfies dνf(ν) = 1 or, equivalently, dMd ln dnM = ρ¯ m. ",
+    "In Figs. (<>)3-(<>)5, we plot the mass function for various isocurvature power spectra specified by parameter sets (α,p). In these figures, pis varied from 2 to 4. In each figure, mass functions at di erent redshifts z= 20,16,12,8,4 are plotted from the top left panel to the bottom right panel. In each panel, di erent lines correspond to di erent amplitudes of the isocurvature power spectrum α. ",
+    "From Fig. (<>)3, we can see that, for moderately blue-tilted isocurvature power spectra with p= 2, the e ects of isocurvature perturbations can be seen only for large amplitude α& 10−1; for smaller αthe mass function can hardly be distinguished from that for the vanilla model (the purely adiabatic case). For α& 10−1 , the presence of the isocurvature power spectrum amplifies the mass function independently of mass in the range [1M⊙,1011M⊙]. On the other hand, from Figs. (<>)4 and (<>)5, which show the e ects of more blue-tilted isocurvature spectra with p= 3 and p= 4, we can see qualitative di erences from those for p= 2. At larger masses M→1011M⊙, we see that the mass function is enhanced monotonically as αincreases, which is also true for p= 2 as already seen above. However, at the lower mass end M→1M⊙, the e ects on the mass function become more complicated: as αincreases from zero, the mass function first increases and, at some point in alpha, it tends to decrease. At smaller redshift and/or with larger p, the mass function at M= 1M⊙can become even smaller than that of the vanilla model with α= 0. ",
+    "This somewhat counterintuitive behavior of the mass function comes from the normalization dMd ln dnM = ρ¯ m. To see this, it is convenient to define a critical mass Mcr as ",
+    "(3.5) ",
+    "From Eq. ((<>)3.4) as well as Figs. (<>)3-(<>)5, one can see that halos with masses up to Mcr or equivalently ν= 1 can be abundantly produced while the number of halos with larger masses are suppressed exponentially. In particular, Figs. (<>)4 and (<>)5 show that the presence of large isocurvature perturbations with blue spectra makes Mcr much larger than in the pure adiabatic vanilla model. Given fixed total mass in the universe ρ¯m = dMd ln dnM , any increase in the number of halos with large masses should be compensated with a decrease in those with small masses. ",
+    "However, the above explanation may not be satisfactory enough as it lacks a physical pictures, which we try to describe below. First, we divide space into cells with comoving volume V1. We also consider the division of space into larger cells with V2 (>V1). The variance of matter fluctuations for V1 and V2 is given by σ(M1) and σ(M2) with the averaged mass M1 = ρ¯mV1 and M2 = ρ¯mV2 for V1 and V2, respectively. ",
+    "Let us consider the case for which, while σ(M1) >δcr, σ(M2) <δcr (low density fluctuation case). When we divide space into cells with V1, the actual density fluctuations in a cell are larger than δcr in some cells, and dark halos are formed in such cells. For the division into larger cells, the actual density fluctuations in a large cell V2 cannot exceed δc. Therefore, large cells cannot collapse to dark halos (as discussed above, the number destiny of halos for M2 are suppressed exponentially). ",
+    "Suppose that both σ(M1) and σ(M2) are larger than δcr (large density fluctuation case). Dividing space into small cells with V1, we still find that actual density fluctuations in a cell are larger than δcr in some cells, and dark matter halos are formed in such cells. We consider a large cell with V2 which includes such small cells. Since σ(M2) >δc, this large cell can have density fluctuations larger than δcr and a large halo is formed in this cell. In the formation of a large halo, small halos in the cell are merged into a large halo. ",
+    "Therefore, as the density fluctuations are amplified, the number density of large halos increases. On the other hand, the number density of small halos decreases because small halos merge to form a large halo (or due to the normalization as discussed above). As we will see in Section (<>)5, this specific response of the mass function to αat relatively small masses M. 107M⊙leads to nontrivial behavior in 21 cm fluctuations. ",
+    "Figure 3. Mass function dn/dln Mfor the case of isocurvature power spectrum with p= 2. In order from top-left to bottom-right, the panels show mass functions at redshifts z=20, 15, 10, 5. Each line corresponds to a di erent value of the amplitude of isocurvature power spectrum α= 0.1 (red solid), 1 ×10−3 (green short-dashed), 1 ×10−5 (blue dotted), 1 ×10−7 (magenta long-dashed), 1 ×10−9 (light blue dot-dashed), 1 ×10−11 (orange two-dot-chain). As a reference, the pure adiabatic case is also plotted (black three-dot-chain). "
+  ],
+  "4 Optical depth ": [
+    "As we have seen in the previous section, the presence of a blue-tilted isocurvature power spectrum significantly alters the number density of halos at high redshifts. In particular, the formation of massive halos is enhanced, which results in an increase in the number density of ionizing sources, or galaxies, at this epoch. This a ects the reionization history of the universe, to be discussed in this section. ",
+    "To see how the isocurvature power spectrum a ects the reionization history, we here follow the analysis of Ref. [(<>)25]. The ionized fraction of IGM, χ, should be given by ",
+    "(4.1) ",
+    "where fs is the fraction of matter in the collapsed objects which can host galaxies emitting ionizing UV photons, fuvpp is the number of UV photons emitted into the IGM per proton in the collapsed objects, and fion is the net eÿciency of ionization by a single UV photon. Noting that a fraction 0.0073 of the rest mass is released in stellar burning of hydrogen to ",
+    "Figure 4. Same as in Fig. (<>)3 but for p= 3. ",
+    "helium, fuvpp can be further decomposed into ",
+    "(4.2) ",
+    "where mp is the proton mass, 1 −Yp ≃0.75 is the mass fraction of hydrogen in IGM, fburn is the mass fraction of hydrogen burned, fuv is the fraction of energy released as UV photons, and fesc is the fraction of UV photons that escape from galaxies. To compile parameters whose values are not precisely known, we define a parameter ",
+    "(4.3) ",
+    "which has a fairly large uncertainty. Then Eq. ((<>)4.1) can be rewritten as ",
+    "(4.4) ",
+    "The fraction of matter in collapsed objects fs should be given by ",
+    "(4.5) ",
+    "where M∗(z) corresponds to the minimum mass of collapsed objects whose virial temperature should be larger than 104K, above which atomic cooling becomes e ective. According to ",
+    "Figure 5. Same as in Fig. (<>)3 but for p= 4. ",
+    "Ref. [(<>)26], M∗(z) can be approximately given as ",
+    "(4.6) ",
+    "We note that similar calculation of reionization history is done in Ref. [(<>)11] for a blue-tilted isocurvature power spectrum. In particular for fnet = 10−4 , the reionization model we adopted here is almost the same as the model for POP II star in the reference. In this case, we indeed confirm that evolution of the reionization fraction in our calculation show a good agreement with Ref. [(<>)11]. ",
+    "The optical depth of reionization is given by ",
+    "(4.7) ",
+    "where n¯ p(t) and σT are the mean number density of protons and the cross-section for Thomson scattering. ",
+    "Fig. (<>)6 shows the contour plot of the optical depth τreion in the p-αplain and constraints on these parameters from the WMAP9 estimate of the optical depth τreion = 0.09±0.04 (95% C.L.) [(<>)2]5 (<>). The lowest value of the reionization eÿciency fnet = 10−6 we take here should be regarded as a case for very ineÿcient reionization following the discussion of Ref. [(<>)25]. ",
+    "Figure 6. Constraints on the isocurvature power spectrum from considerations on reionization. Here we take the eÿciency parameter for reionization fnet to 10−6 (red), 10−5 (green) and 10−4 (blue), and show contours of the reionization optical depth τreion for each fnet. For each value of fnet, shaded region shows parameter regions which give τreion ≥0.13, while thick solid and thin dashed lines respectively show parameter regions which give τreion = 0.09 and 0.05. Note that for fnet = 10−4 , τreion exceeds 0.05 even if the isocurvature power spectrum vanishes (i.e. α= 0), so that the blue thin dashed line does not appear in the plot. As reference, 1 and 2σconstraints from the CMB dataset (WMAP9+ACT2008) shown in Fig. (<>)2 are also plotted (black solid line). ",
+    "From the figure, we can see that optical depth of reionization is sensitive to highly blue-tilted isocurvature spectrum with p& 3. Even if we assume a very low value of fnet = 10−6 , αshould not be large for p& 3. We found that WMAP constraints on τreion <0.13 (95% C.L.) leads to a constraint ",
+    "(4.8) ",
+    "which is valid for 10−6 ≤fnet ≤10−4 . Compared with the constraints directly obtained from the CMB power spectrum from WMAP9+ACT2008, Fig. (<>)6 shows that considerations of reionization history can give strong constraints on blue-tilted isocurvature power spectrum for large spectral indices p& 3 despite the large uncertainties in reionization eÿciency fnet. "
+  ],
+  "5 21cm fluctuations ": [
+    "Here we discuss signatures of a blue-tilted isocurvature power spectrum on redshifted 21cm line fluctuations. As we discussed in the previous section, a blue-tilted isocurvature power spectrum induces small-mass halos. Among them, we mainly focus on “minihalos” whose mass is too small to host a galaxy. Although minihalos are not considered to be luminous objects, a minihalo can make observable 21 cm line signals [(<>)26, (<>)27]. Our analysis is basically the same as those in Refs. [(<>)26, (<>)28]. As assumed in these references, we also assume that minihalos are modeled as a “truncated isothermal sphere” with physical radius rt(M), gas ",
+    "temperature TK(l,M), dark matter velocity dispersion σV(l,M) and density profile ρ(l,M), where lis the distance from the center of a minihalo. We denote the frequency of 21cm line emission in the rest frame as ν0 = 1.4 GHz. We also note that in this section, any parameter dependences of quantities are significantly abbreviated. ",
+    "Let us consider the brightness temperature of photons with frequency ν′at redshift zwhich penetrate a minihalo of mass Mwith an impact parameter r. The brightness temperature is given by ",
+    "(5.1) ",
+    "Here τ21cm(R) is the 21cm optical depth along the photon path at R, which is obtained from6 (<>)",
+    "(5.2) ",
+    "√where l′= R′2 + r2 , A10 = 2.85×10−15 s−1 and kBT∗= hν0 = 5.9×10−6 eV are respectively the spontaneous decay rate and emitted energy of the 21cm hyperfine transition, and nHI is the number density of neutral hydrogen atoms. The function φ(ν′,l′) is the line profile, which can be modeled by a thermal Doppler-broadening with ",
+    "ν= (ν0/c) 2kBTK(l′)/mH , where mH is the hydrogen mass. The optical depth τ21cm in Eq. ((<>)5.1) is given as τ21cm = τ21cm(R→∞). The di erential brightness temperature observed today at frequency ν= ν′/(1 + z) can be written as ",
+    "(5.3) ",
+    "The mean surface brightness temperature for a halo with mass Mat zis provided by ",
+    "(5.4) ",
+    "where A(M,z) is the geometric cross-section of a halo with mass Mat z, A= πrt2 . The di erential line-integrated flux from this halo is given by [(<>)26] ",
+    "(5.5) ",
+    "For an optically thin halo, we can replace the integration with the multiplication by νe (z,b) ≡1 at ν′= ν0.(1+z)°(0,b) ",
+    "Now we consider an observation with a finite bandwidth νand beam width θ. The mean di erential flux per unit frequency is expressed as ",
+    "(5.6) ",
+    "where ( )beam = π(θ/2)2 , and ν/z= ν0/(1 + z)2 , and Mmax(z) and Mmin(z) are respectively the maximum and minimum masses contributing to the 21cm line emission. ",
+    "Table 1. Survey parameters for the SKA survey ",
+    "The maximum mass Mmax(z) is set to the virial mass M∗(z) in Eq. ((<>)4.6) for which a virial temperature is 104K. Above M∗(z), most of the hydrogen in halos is ionized and do not contribute to 21cm line emission (This is also consistent with the discussion we presented in Section (<>)4). On the other hand, the minimum mass is set to the Jeans mass ",
+    "(5.7) ",
+    "Defining the beam-averaged “e ective” di erential antenna temperature δTb by dδF/dν= 2ν2kBδTb( )beam, we obtain ",
+    "(5.8) ",
+    "So far, we have assumed that the halo number density is homogeneous, following dn/dM. However, halos cluster, depending on the density fluctuations, ",
+    "(5.9) ",
+    "where δN (M) is the number density contrast of halos with mass Mand b(M) is bias. This clustering causes fluctuations in δTb(ν). Since the rms density fluctuations in a beam are given by ",
+    "(5.10) ",
+    "where Wis a pencil beam window function at frequency νwith band width νand beam width θ(See e.g. Ref. [(<>)29]), the rms halo number density fluctuations with Min a beam is obtained from ",
+    "(5.11) ",
+    "Therefore, the rms fluctuations of δTb(ν) are provided by ",
+    "(5.12) ",
+    "where β(z) is the e ective bias of the minihalos weighted by their 21cm line fluxes, defined as ",
+    "(5.13) ",
+    "where F(z,M) ≡d2bδTb(z,b,M) ∝Tbrt2σV [(<>)28] is the flux from a minihalo. ",
+    "In Fig. (<>)7, we plot 3σTb as a function of 6 <z= ¯ erent parameterν/ν0 −1 <20 for di values for the isocurvature power spectrum (p,α). The adopted resolution and bandwidth ",
+    "assume a SKA-like survey whose survey parameters are summarized in Table. (<>)1. As a reference, the noise level of the SKA-like survey is also depicted in the figure, and is given by [(<>)30] ",
+    "(5.14) ",
+    "where Ais the antenna collecting area and tis the integration time. From the figure, we first see that, for p= 2, the signal σTb monotonically increases as αdoes (though we cannot distinguish lines for α<10−2). On the other hand, for p= 3 and p= 4, we can see the dependence of σTb on αis more complicated; As αincreases from zero, σTb also grows. When αexceeds some value depending on redshift, increment of αmakes σTb decrease. However, keeping αincreasing, one can find that σTb starts to increase again. In particular, what may be remarkable is that the signal can even be smaller than the vanilla model at low redshifts. As we will show in the following, this complicated behavior arises mainly from the mass function which has a non-trivial dependence on αfor large p& 3 as shown in section (<>)3. We also note that the redshift evolution of σTb becomes quantitatively di erent for large values of α; while σTb increases as the universe ages for small α, it tends to evolve less for large α. ",
+    "To understand the complicated dependence of σTb on αand p, we divide σTb into parts σ(ν,ν,θ), β(z) and δTb(z) and investigate each of them separately. In Fig. (<>)8, we plot the rms of smoothed matter fluctuations σ(ν,ν,θ), the e ective bias β(z) and the mean 21cm brightness temperature δTb(ν) as a function of z= ν0/ν−1 for di erent values of pand α. Here νand θare fixed to the values adopted in Fig. (<>)7. ",
+    "As expected, σ(��,ν,θ) is monotonically enhanced as αincreases. If we fix α, the enhancement is more significant for larger p. However, as long as αis not so large as to be excluded by current observations (See Figs. (<>)2), the enhancement is not significant and at most O(1). We can also see that β(z) is not significantly a ected by the isocurvature power spectrum; for 2 <p<4, β(z) changes at most 30 % as long as α<0.1. ",
+    "On the other hand, as seen in the figure, δTb(ν) has a complex response to αdepending on p. For a moderately blue-tilted isocurvature spectrum with p= 2, δTb(ν) monotonically increases as αincreases. On the other hand, for p= 3 and p= 4, the dependence of δTb(ν) on αdramatically changes. As αincreases from zero, while at first δTb(ν) increases, then it begins to decrease at some value of α, which depends on p. Since the isocurvature power spectrum a ects δTb(ν) only through the mass function, this behavior can be understood by looking at the mass function dn/dln Mwith MJ(z) <M<M∗(z). As we discussed in Section (<>)3, an increase in αdoes not necessarily increase dn/dln Mfor a highly blue-tilted isocurvature power spectrum and, in particular, dn/ln Mfor large αcan be below that for the vanilla model α= 0 at relatively small masses 103M⊙. M. 107M⊙(this roughly corresponds to MJ(z) <M<M∗(z) for z≃10). Since minihalos which contribute to the 21cm brightness temperature are limited to those with these small masses, δTb(ν) reflects this complicated behavior of the mass function. ",
+    "To summarize, the complicated dependence of σTb on αis understood as follows. A blue-tilted isocurvature power spectrum a ects σTb mainly through the rms smoothed mass fluctuations σ(ν,ν,θ) and the mean di erential brightness temperature δTb(ν). For a moderately blue-tilted isocurvature spectrum p= 2, σ(ν,ν,θ) and δTb increase monotonically as αincreases. On the other hand, for a highly blue-tilted spectrum p= 3 or p= 4, while σ(ν,ν,θ) continuously monotonically increases as αincreases, δTb decreases at some α. As long as αis not so large as to be excluded by current observations, σTb first increases ",
+    "Figure 7. Shown are the rms 21cm di erential brightness fluctuations 3σTb for models with blue-tilted isocurvature power spectra as a function of redshift. In order from left to right, the spectral index of isocurvature power spectrum pis varied from 2 to 4. In each panel, cases of di erent values of α= 10−1 (red solid), 10−3 (green short-dashed), 10−5 (blue dotted), 10−7 (magenta long-dashed), 10−9 (green dot-dashed), 10−11 (blue two-dot-chain), and the pure adiabatic case α= 0 (black three-dot-chain) are plotted. For each parameter set (p,α), we indicate the reionization optical depth computed in Section (<>)4 assuming fnet = 10−6 (former) and 10−4 (latter) in the legend with square bracket. As a reference, we also depict the noise level of a SKA-like survey with survey parameters summarized in Table (<>)1 (thin black solid). ",
+    "and then decreases, mainly reflecting the dependence of δTb. When αis significantly large so that it is already excluded by current observations, the influence of σ(ν,ν,θ) dominates and σTb again starts to increase. ",
+    "Finally, we compute χ2 , assuming that SKA can observe 21cm line fluctuations over 5 ≤z≤20. Here we simply assume that each band in the observed frequency range is independent and has the same survey parameters as in Table (<>)1. Then χ2 can be given as ",
+    "(5.15) ",
+    "where σT(fid) b denotes the rms 21cm line emission fluctuations in the case of the fiducial pure adiabatic model. In Fig. (<>)9, we plot the 2σconstraint expected from the SKA survey. As a reference, the 2σconstraints from the reionization optical depth with a conservative eÿciency parameter fnet = 10−6 and the CMB power spectrum are also shown here. In the figure, one can see that the 2σexcluded region from 21cm line fluctuations has a complex geometry and a region with relatively large α∼10−6-10−3 with p& 3.5 is not excluded by 21cm line observations alone. This reflects the complicated dependence of the 21cm line fluctuations on the isocurvature power spectrum. However, the constraint from the reionization optical depth covers the region. This shows that the 21cm line fluctuations and the reionization optical depth can be complementary as probes of a blue-tilted isocurvature power spectrum. Combining the constraint from the WMAP determination of τreion with fnet >10−6 , we found that the SKA is expected to give a constraint ",
+    "(5.16) ",
+    "at the 2σlevel. In the same figure, we also plot bands of regions corresponding to τreion = 0.09 ±0.01 (2σ), which is expected to be achieved by Planck observations of the CMB polar-",
+    "Figure 8. The three components in Eq. ((<>)5.12) are plotted separately. In order from top to bottom, the rms smoothed matter fluctuations σ(¯ν,ν,θ), the e ective bias β(z) and the mean value of the 21cm di erential brightness temperature δTb(¯ν) are shown as a function of redshift z. Cases of the spectral index p= 2, 3 and 4 are shown in order from left to right. In each panel, cases of di erent values of α= 10−1 (red solid), 10−3 (green short-dashed), 10−5 (blue dotted), 10−7 (magenta long-dashed), 10−9 (green dot-dashed), 10−11 (blue two-dot-chain), and the pure adiabatic case α= 0 (black three-dot-chain) are plotted. ",
+    "ization spectrum [(<>)31]7 (<>)for the values of fnet = 10−5 and 10−6 , which correspond to the cases where isocurvature perturbations at small scales are responsible for inducing cosmological reionization. From the figure, one can see that in these bands, 21cm line fluctuations can be detected with significance of more than 2σ, and thus by observing 21cm line emission, we will have a chance to test whether the isocurvature perturbations are responsible for reionization. "
+  ],
+  "6 Conclusions ": [
+    "In this paper, we have studied cosmological signatures of a blue-tilted isocurvature power spectrum with spectral index 2 . p. 4. Such an isocurvature power spectrum modifies the mass function of dark matter halos. This modification in mass function consequently a ects both the reionization history and 21cm line fluctuations from neutral hydrogen in ",
+    "Figure 9. Forecast of constraints on the isocurvature power spectrum from observations of 21cm line fluctuations. The 2σconstraint expected from SKA is shown as red shaded region. The 2σconstraints from WMAP9+ACT2008 (region shaded with blue horizontal stripes) and reionization optical depth τreion >0.13 for fnet = 10−6 (region shaded with green vertical stripes) are also shown. Black and gray bands show the expected Planck measurements τreion = 0.09±0.01 (2σ) for fnet = 10 5 and 10−6 . ",
+    "minihalos at high redshifts. The presence of a blue-tilted isocurvature spectrum enhances the number density of massive halos at high redshifts and hence promotes formation of galaxies and reionization of the universe. Given the reionization optical depth estimated from current CMB observations, we can obtain constraints on the amplitude and spectral index of the isocurvature power spectrum. Although the constraints strongly depend on the eÿciency of reionization, for reasonable parameter values it can surpass those obtained from the spectral shape of the CMB power spectrum. On the other hand, a blue-tilted isocurvature power spectrum changes the mass function at smaller masses in a complicated manner, which results in either an enhancement or even a suppression of 21cm line fluctuations depending on the parameters of the isocurvature power spectrum. Future surveys such as SKA can probe the parameter space of isocurvature power spectra which cannot be explored directly from the CMB power spectrum. We emphasize that the reionization optical depth and 21cm line fluctuations can provide complementary probes of blue-tilted isocurvature power spectra. ",
+    "Note added: While we were finishing the present work, we noticed that Ref. [(<>)33], which appears on arXiv around the similar time as ours, has some overlap with our analysis on 21cm line fluctuations from a blue-tilted power spectrum. "
+  ],
+  "Acknowledgments ": [
+    "We would like to thank Yoshitaka Takeuchi and Sirichai Chongchitnan for helpful discussion. HT is supported by the DOE at ASU. TS is supported by Japan Society for the promotion of Science and the Academy of Finland grant 1263714. NS is supported by the Grant-in-Aid for the Scientific Research Fund under Grant No. 25287057. This work is also supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. The research of JS has been supported at IAP by the ERC project 267117 (DARK) hosted by Universit´e Pierre et Marie Curie - Paris 6 and at JHU by NSF grant OIA-1124403. "
+  ]
+}

jsons_folder/2014JCAP...05..039P.json

@@ -0,0 +1,259 @@
+{
+  "Abstract": [
+    "Abstract. Sunyaev-Zel’dovich (SZ) surveys are promising probes of cosmology -in particular for Dark Energy (DE) -, given their ability to find distant clusters and provide estimates for their mass. However, current SZ catalogs contain tens to hundreds of objects and maximum likelihood estimators may present biases for such sample sizes. In this work we study estimators from cluster abundance for some cosmological parameters, in particular the DE equation of state parameter w0, the amplitude of density fluctuations σ8, and the Dark Matter density parameter Ωc. We begin by deriving an unbinned likelihood for cluster number counts, showing that it is equivalent to the one commonly used in the literature. We use the Monte Carlo approach to determine the presence of bias using this likelihood and study its behavior with both the area and depth of the survey, and the number of cosmological parameters fitted. Our fiducial models are based on the South Pole Telescope (SPT) SZ survey. Assuming perfect knowledge of mass and redshift some estimators have non-negligible biases. For example, the bias of σ8 corresponds to about 40% of its statistical error bar when fitted together with Ωc and w0. Including a SZ mass-observable relation decreases the relevance of the bias, for the typical sizes of current SZ surveys. Considering a joint likelihood for cluster abundance and the so-called “distance priors”, we obtain that the biases are negligible compared to the statistical errors. However, we show that the biases from SZ estimators do not go away with increasing sample sizes and they may become the dominant source of error for an all sky survey at the SPT sensitivity. Finally, we compute the confidence regions for the cosmological parameters using Fisher matrix and profile likelihood approaches, showing that they are compatible with the Monte Carlo ones. The results of this work validate the use of the current maximum likelihood methods for present SZ surveys, but highlight the need for further studies for upcoming experiments. To perform the analyses of this work, we developed fast, accurate, and adaptable codes for cluster counts in the framework of the Numerical Cosmology Library. "
+  ],
+  "Contents ": [],
+  "1 Introduction ": [
+    "The abundance of galaxy clusters and their spatial distribution as functions of redshift and mass provide strong constraints on the matter density parameter Ωm and the amplitude of the matter power spectrum σ8 [(<>)1–(<>)5]. For high redshift surveys (z > 1.0), clusters are also powerful tools to study Dark Energy (DE) since they depend on the linear growth of density perturbations and the comoving volume [(<>)2, (<>)6] (for a review see [(<>)7] and references therein). The coming years are promising for cluster cosmology in view of surveys which will provide deep and large catalogs such as the Dark Energy Survey (DES) [(<>)8] and the forthcoming Large Synoptic Survey Telescope (LSST) [(<>)9] optical surveys. The ongoing Sunyaev-Zel’dovich (SZ) surveys carried by the South Pole Telescope (SPT) [(<>)10–(<>)12], the Atacama Cosmology Telescope (ACT) [(<>)13] and the Planck probe [(<>)14] have already yielded catalogs with massive clusters and redshifts up to 1.5. ",
+    "The number density of Dark Matter (DM) halos as a function of redshift and mass are modeled using a combination of analytical and numerical results. Although the massive DM halos are identified as galaxy clusters, their masses are not directly observable. It is necessary to use observable quantities, such as the X-ray temperature [(<>)15] or SZ flux decrement [(<>)10], to obtain mass-observable scaling relations (for a review, see [(<>)16]). The combination of a mass proxy with a theoretical model can be used to predict the number density of galaxy clusters. Therefore, the success of cluster cosmology relies on a good description of cluster counts and clustering, both based on a cosmological model and high-quality observations. ",
+    "It is known that uncertainties arising from both mass-observable relations and photometric redshifts degrade constraints on cosmological parameters [(<>)17, (<>)18]. These uncertainties comprehend both statistical and systematic errors. Other sources of uncertainties are sample-variance and shot-noise (due to the discreteness of the clusters). Optical surveys provide large catalogs (tens of thousand clusters) and, therefore, the shot-noise contribution is negligible with respect to sample-variance, which dominates along with mass uncertainties. On the other hand, X-ray and SZ catalogs contain only tens to hundreds objects. However, they usually have better mass estimates, higher completeness and purity, for example. In this case the cosmological analyses are shot-noise dominated. ",
+    "Usually the cluster likelihood function is built taking into account the error sources mentioned above. Nevertheless, it is assumed that cosmological parameter estimators do not yield extra uncertainties. The Maximum Likelihood (ML) method is extensively used to estimate the values of parameters given a data set. ML estimators are usually consistent, i.e., the expected value of a parameter tends to its true value when the size of the data sample (n) is suÿciently large, and asymptotically eÿcient, i.e., the variance of the estimator attains the minimum variance bound as n → ∞. However, ML estimators are not necessarily unbiased and, even if they are consistent, in practical cases the data sample sizes may not be large enough to guarantee that the asymptotic limit is reached [(<>)19–(<>)22].1 (<>)",
+    "In this work, we study some cosmological parameter estimators in the context of SZ surveys, specifically from the SPT. For the redshift and mass ranges of SPT catalogs, sample variance is negligible [(<>)15, (<>)23]. Therefore, we build the likelihood only for the cluster number counts and do not include the spatial clustering. We introduce a formalism to build this likelihood and show that it is similar to the one commonly used in the literature, in the limit where there is only one object in each bin of redshift and mass. To study the estimators, we use the Monte Carlo approach which consists on randomly sampling artificial data sets from a distribution numerous times. ",
+    "To perform this work it was necessary to develop fast and accurate codes. These were implemented in the Numerical Cosmology Library (NumCosmo) [(<>)24] framework, which is open source and adaptable to new models and data, including several cosmological observables. ",
+    "This paper is organized as follows. In section (<>)2 we present the model and assumptions used to compute the halo number counts. In section (<>)3, we introduce an unbinned likelihood for this observable and compare it with the standard one used in the literature. Then we describe the methodology to compute the bias of an estimator (section (<>)4) and apply it using the likelihood for DM halo abundance (section (<>)5). In section (<>)6 we study the biases on the cosmological parameter estimators using a SZ mass-observable relation and investigate their dependence on the combination of free parameters fitted and the survey area and depth. We also include the photometric redshift uncertainty. In section (<>)7 we analyse cosmological ",
+    "parameter estimators obtained from a joint likelihood of cluster number counts and cosmic microwave background data. Finally, in section (<>)8, we compare some estimator error bars computed using three di˙erent statistical methods: Monte Carlo, Fisher matrix and profile likelihood. Our concluding remarks are presented in section (<>)9. "
+  ],
+  "2 Cluster number counts ": [
+    "The mean number of dark matter halos with mass in the range [M, M + dM] and in the redshift interval [z, z + dz] is given by ",
+    "(2.1) ",
+    "where is the comoving number density of halos at redshift z with mass M (i.e., the mass function). Assuming a homogeneous and isotropic universe and, as indicated by current observational data, spatially flat, the comoving volume element is ",
+    "(2.2) ",
+    "where ΔΩ is the survey area in square degrees. In this paper, we assume a constant DE equation of state parameter pDE/ρDE = w0, such that the Hubble function is ",
+    "(2.3) ",
+    "where H0 is the Hubble constant. The energy density parameters Ωx are the ratio between the energy density and the critical energy density In eq. ((<>)2.3) Ωr, Ωm, and ΩDE are the radiation, matter, and DE density parameters, respectively. As we are assuming a flat universe, ΩDE = 1 − Ωm − Ωr. ",
+    "The mass function can be written as [(<>)25–(<>)27] ",
+    "(2.4) ",
+    "where ρm(z) is the mean matter density at redshift z, f(σR, z) is the so called multiplicity function, which contains information about the nonlinear regime of halo formation, and σR 2 is the variance of the linear density contrast filtered on the length scale R associated to the mass M:  ",
+    "(2.5) ",
+    "where W(k, R) is the window function and P(k, z) is the linear power spectrum. In particular, we use the spherical top-hat function whose Fourier transform is ",
+    "(2.6) ",
+    "and encloses a mass M = 4πρmR3/3. ",
+    "The linear power spectrum is given by ",
+    "(2.7) ",
+    "where ns is the spectral index, D(z) is the linear growth function, and T (k) is the transfer function. In this paper, we use the Eisenstein-Hu (EH) [(<>)28] fitting function for T (k). 2 (<>)The power spectrum normalization A may be written in terms of the standard deviation of the density contrast at a scale R = 8h−1Mpc, σ8: ",
+    "(2.8) ",
+    "In this work we compute D(z) by numerically solving the di˙erential equation for the growing mode of linear perturbations [(<>)30, (<>)31], ",
+    "(2.9) ",
+    "where we defined the normalized Hubble function as E(z) = H(z)/H0 and D(z) is normalized to unity at z = 0. ",
+    "The first functional form for f(σ) was obtained analytically by Press & Schechter assuming the spherical collapse of initial density peaks [(<>)25]. The multiplicity function was shown to be universal, in the sense that it does not depend on the cosmological parameters nor the initial conditions. A semi-analytic expression for f(σ) was obtained by Sheth & Tormen [(<>)27] considering an ellipsoidal collapse approximation and a statistical treatment using a moving barrier. Their results were shown to be in broad agreement with cosmological N-body simulations. This motivated multiplicity functions to be fitted directly from the simulations [(<>)32–(<>)34], providing more accurate fitting functions. In addition, the universality property was verified to a good approximation in the simulations. In this work, we use the Tinker et al. [(<>)34] multiplicity function given by ",
+    "(2.10) ",
+    "where the values of the parameters A, a, b, and c depend on the redshift and halo mass definition. To allow for a more direct comparison with SZ data, we consider the mass contained in a spherical region 500 times the critical density at z, i.e., RΔ = (3MΔ/4πΔρcrit)1/3 , with Δ = 500. Reference [(<>)34] provides values for the mass function parameters for various values of Δ. Following their recommendation, we use spline interpolation to obtain these parameters for Δ = 500 to a good accuracy. It is worth noting that, in our analyses, we neglect uncertainties related to the determination of the multiplicity function. In particular, we ignore the errors on the fitted parameters A, a, b and c. In reference [(<>)35] the authors show that while errors of the order of 10% in the mass function degrade the constraints on cosmological parameters, this e˙ect is small when compared with that of the mass-observable relation. "
+  ],
+  "3 Likelihood Model ": [
+    "In this section, we review the standard likelihood employed in the literature for halo abundance and introduce one based on the Extended Maximum Likelihood method.3 (<>)We show that these ",
+    "two likelihoods are equivalent under some conditions. The later will be employed to check if the cosmological parameter estimators are biased (for the considered sample sizes). "
+  ],
+  "3.1 Poisson Distribution ": [
+    "The standard likelihood of the mean halo number counts is built assuming a Poisson distribution in bins of redshift and mass [(<>)1, (<>)3, (<>)10, (<>)11, (<>)13, (<>)15, (<>)36, (<>)37], namely, ",
+    "(3.1) ",
+    "where N is the number of bins in the ln M − z space (or in the mass-observable -z space), nk is the observed number of halos (clusters) in the k-th bin and the random variable λk({θj}) is the expected number of halos in the k-th bin for a given model. ",
+    "In the regime where sample variance is negligible, a common practice is to take the limit where there is at most one halo per bin. In this case eq. ((<>)3.1) takes the form ",
+    "(3.2) ",
+    "where now the first product is over the halos in the sample. The log likelihood is thus ",
+    "(3.3) ",
+    "where is the predicted number of halos with redshift and mass values within, respectively, [zmin,zmax] and [Mmin,Mmax], and {θj} represents the set of cosmological parameters (it may also include other parameters such as those from a mass-observable relation). "
+  ],
+  "3.2 Extended Maximum Likelihood ": [
+    "In this work, we introduce an unbinned likelihood [(<>)38] which we build following the extended maximum likelihood (EML) method [(<>)20, (<>)21]. This approach does not require a normalized probability distribution, i.e., the number of events is not fixed. Particularly, the likelihood is the product of two terms. The first is the Poisson probability to find n halos in the whole mass and redshift ranges of the sample. The second term is the product of n terms, each one given by the probability distribution of a halo to have mass in the range [M,M + dM] and to be found in the redshift interval [z,z + dz], namely, ",
+    "(3.4) ",
+    "j",
+    "where N({θ}) is the normalization factor. ",
+    "Thus the likelihood function is ",
+    "(3.5) ",
+    "where zi is the redshift and Mi is the the mass of each halo. Therefore the log likelihood is ",
+    "(3.6) ",
+    "Note that dropping the last term of eq. ((<>)3.6), since it does not depend on {θj}, lead us to eq. ((<>)3.3). In this case the EML and Poisson methods are identical. ",
+    "One advantage of the EML is the possibility to consider di˙erent informations for each cluster (such as mass-observable relations from di˙erent observables), since the likelihood is naturally a product of individual probabilities for each cluster. Also, the likelihood is naturally unbinned, such that it is free from possible bias that could be associated to the choice of the bin size. For this reason we will use the EML throughout this work. It is worth noting that, in ref. [(<>)6], the authors also build an unbinned likelihood using the truncated regression approach. Their likelihood is equivalent to eq. ((<>)3.6) except for a Poisson term of the number of missing objects Nmis, which is equal to unity when the likelihood is marginalized over Nmis. "
+  ],
+  "4 Obtaining the bias of cosmological parameter estimators with the Monte Carlo method ": [
+    "The estimators for a given set of parameters ({θˆj}) are obtained by maximizing the likelihood with respect to these parameters. In order to analyse whether the estimators obtained from a likelihood function are biased, we need to calculate their expected values given a fiducial model {θj0}. The bias of θˆj is defined as ",
+    "(4.1) ",
+    "The expected value of the cosmological parameter estimators cannot be computed analytically from the cluster number counts likelihood. To obtain θˆj we employ the Monte Carlo (MC) method, i.e., we generate a set of realizations of the cluster distribution in mass and redshift from a given input fiducial model and compute the best-fitting value of θˆj for each realization by minimizing the likelihood function (−2 ln L) [eq. ((<>)3.6)] with respect to θj. Assuming the probability distribution given by eq. ((<>)3.4), each realization is a catalog of DM halos containing their redshifts zi and masses Mi (see appendix (<>)B for a detailed description). ",
+    "Then we compute the expected value using as an estimate the arithmetic mean θˆj, i.e., ",
+    "(4.2) ",
+    "where m is the number of realizations and θˆjl is the best-fitting value for the l-th realization. The variance of θˆj is given by ",
+    "(4.3) ",
+    " ",
+    "where is the variance of the estimator In cases where the significance of this bias is ensured by computing eq. ((<>)4.3). For example, if the estimator has a standard deviation of 1% in and is 5% of then we must generate 100 realizations such that ",
+    "is one order smaller than Note that this procedure usually requires a large number of realizations. In particular for our purposes, it is necessary to generate 10,000 realizations for each case, i.e., each choice of the fiducial model. ",
+    "Therefore, to make this work feasible, it was necessary to develop numerical codes not only fast but whose framework could concatenate the di˙erent steps, i.e., generate a realization, build the likelihood, and perform the statistical analysis. Those algorithms are implemented in the NumCosmo library [(<>)24]. "
+  ],
+  "5 Bias from halo abundance likelihood ": [
+    "In this section, we apply the methodology described above to compute the bias of some cosmological parameter estimators in an idealized scenario where both the redshift and mass are perfectly known. For this, we have to adopt a fiducial model, which comprises both cosmological and survey parameters. Our choice is based on SZ surveys, since sample variance is usually negligible for their configurations. First, we assume a constant minimum mass threshold for the entire redshift interval. This is a good approximation for SZ surveys for which the mass limit for detection Mmin is nearly redshift independent and is weakly dependent on cosmology [(<>)2, (<>)39, (<>)40]. Specifically, we set Mmin = 2 × 1014h−1M, which corresponds to the minimum value of the SZ observable that we will describe in section (<>)6. ",
+    "Besides the minimum mass threshold, we define a fiducial model by the redshift interval, the solid angle, and the set of cosmological parameters {θj}. They are, respectively, [0.3,1.1], ΔΩ = 720deg2 and ",
+    "(5.1) ",
+    "where Ωc is the cold dark matter density, Ωb is the baryonic matter density (Ωm = Ωc + Ωb). The reason for choosing these specific values will become clear later in section (<>)6.2. ",
+    "Having defined the methodology to compute the bias of an estimator and the fiducial model, we now use them to determine whether the estimators are biased or not and if the biases obtained are relevant for cosmological studies. Throughout this paper, we focus our analyses on the estimators for Ωc, σ8, and w0, since the first two are the cosmological parameters better constrained by cluster abundance (see, e.g., [(<>)1, (<>)2]) and the later is the parameter used to probe the nature of dark energy, whose understanding is a major goal of ongoing and future surveys. ",
+    "In this section, we study how the estimators’ bias size vary with respect to the number of free parameters fitted. For this sake, we compute their biases fitting the respective estimators in one, two, and three-dimensional parametric spaces, i.e., (Ωc), (σ8), (w0), (Ωc,σ8), (Ωc,w0), (σ8,w0), and (Ωc,σ8,w0). The remaining parameters (cosmological and from the survey configurations) are always kept fixed. ",
+    "Throughout this paper we report the bias on a parameter as a percentage of the 1σ error bar on this parameter. This helps to assess the significance of the bias in each case, i.e., even if the bias is large when compared to the estimated parameter values, it can be irrelevant if the error on this estimate is much larger. We define the following notation for the relative biases Bxˆ ≡ bxˆ/σ(ˆx), i.e., ",
+    "DM halo abundance likelihood, ΔΩ = 720deg2 ",
+    "Table 1. First Column: Number of fitted parameters. Even Columns: Estimated expected value of xˆ and its standard deviation σ(ˆx) obtained fitting simultaneously 1 (first row), 2 (second, third, and forth rows), and 3 (last row) cosmological parameters and keeping the others fixed. Odd Columns: Bias size bxˆ relative to σ(ˆx). ",
+    "where bxˆ is the bias of the estimator xˆ computed using eqs. ((<>)4.1) and ((<>)4.2), and σ(ˆx) is the standard deviation of xˆ. ",
+    "For each of the 7 parametric spaces defined above, we perform a MC with 10,000 realizations for the chosen fiducial model. This configuration provides an expected number about 80 clusters. The results for the mean values of the parameters, their variance, and their bias are shown in table (<>)1. For a single free parameter the three estimators have small relative biases (about 2%). On the other hand, estimators in the bi-dimensional parametric spaces may have larger relative biases. For example, in the plane (Ωc,w0), Ωˆ c has a relative bias of 23%. We also obtain a significant relative bias of 20% for σˆ8 when we fit this parameter together with w0. For (Ωc,σ8), both estimators have small relative biases. In the three-dimensional parametric space, Ωˆ c and wˆ0 have small biases while σˆ8 has a relative bias of 37%. This case evinces the importance of knowing the properties of the cosmological parameter estimators. "
+  ],
+  "6 Biases from cluster counts including a mass-observable relation ": [
+    "So far we presented a likelihood, a methodology, and a first analysis considering only DM halos. The relatively large biases found in the example above, in particular the significant bias obtained for σˆ8 in the case of 3 free parameters, pushes us to consider more realistic situations. A fundamental ingredient for modelling cluster abundance is to consider a mass proxy and associated mass-observable relation. Here we extend the formalism of the preceding sections to consider specifically the mass-observable relation for SZ surveys and take the fiducial values from SZ catalogs. We study how the relative biases change as a function of the number of parameters fitted and the size of the sample (changing both the area of the survey and the redshift depth). "
+  ],
+  "6.1 Sunyaev–Zel’dovich mass-observable relation ": [
+    "One way to detect galaxy clusters and estimate their masses is through the SZ e˙ect, which consists of a distortion in the frequency distribution of the cosmic microwave background photons due to inverse Compton scattering by the hot intracluster medium. The magnitude decrement due to the SZ e˙ect (or increment for photons with frequencies  217 GHz) is a proxy for the mass of the cluster (see [(<>)16] and references therein). ",
+    "In this work, we use the mass-observable relation developed by the SPT team in refs. [(<>)10– (<>)12], where the detection significance ξ is used as a SZ mass proxy [(<>)41]. In ref. [(<>)10] the authors obtained, using simulations, an unbiased significance ζ such that ",
+    "(6.1) ",
+    "and ξ is related to ξ by a Gaussian scatter of unit width, to which we will refer as P(ξ|ζ). The scaling relation between ζ and M500 is given by [(<>)11, (<>)12] ",
+    "(6.2) ",
+    "where ASZ is the normalization, BSZ is the slope, and CSZ is the redshift evolution parameter. Following refs. [(<>)11, (<>)12], we assume that P(ln ζ| ln M) is a Gaussian distribution with scatter given by DSZ . ",
+    "In section (<>)3.2 we built the likelihood for halo abundance. Analogously, given the ξ−M500 relation, we have that the likelihood for cluster number counts is ",
+    "(6.3) ",
+    "where ",
+    "(6.4) ",
+    "Note that the normalization factor N({θj}) is now the expected number of clusters with zmin ≤ z ≤ zmax and ξ ≥ ξmin. We assume that all objects with ξ ≥ ξmin are detected in the entire redshift interval, i.e., the catalog is complete above this threshold. "
+  ],
+  "6.2 Fiducial values from SPT ": [
+    "Now we shall apply the methodology of section (<>)4 extending our analyses to include the SZ mass-observable relation, considering realistic parameters values taken from SZ surveys. The MC approach is performed by minimizing eq. ((<>)6.3) with respect to θj, assuming the probability distribution given by eq. ((<>)3.4) now in terms of ξ and the mass-observable relations P(ξ|ζ) and P(ln ζ| ln M). Each realization is now a catalog of clusters containing their redshifts zi and the detection significance ξi (see appendix (<>)B for a discussion on the sampling). ",
+    "In this case, the fiducial model used to generate the realizations also includes the parameters of the ζ − M500 relation and the minimum value of the detection significance ξmin. Thus, along with the cosmological parameters, we have ",
+    "(6.5) ",
+    "and ξmin = 5.0. The redshift interval, [0.3,1.1], and the threshold significance ξmin are taken from the SPT catalog given in ref. [(<>)11]. The parameters {θj} correspond to the best-fit values obtained in this same reference by combining cluster abundance, Hubble parameter, and Big-Bang nucleosynthesis measurements, assuming a ΛCDM model. ",
+    "Similarly to the analyses carried out in section (<>)5, we compute the relative biases of Ωˆ c, σˆ8, and wˆ0 in one, two, and three-dimensional parametric spaces. In section (<>)5 we fixed ",
+    "Figure 1. Expected values and error bars of the estimators Ωˆ c (upper left panel), σˆ8 (upper right panel) and wˆ0 (lower panel) computed for three di˙erent survey areas and the four parametric spaces probed. The dashed lines show the fiducial values. ",
+    "ΔΩ = 720 deg2 , which is the area covered by the SPT catalog from ref. [(<>)12]. In this section we also consider ΔΩ = 178 [(<>)11] and 2500 deg2 . The later being the total area covered by the SPT Survey [(<>)42]. Therefore, we are able to check how the estimator biases vary with the number of cosmological parameters being fitted simultaneously as well as with the size of the catalogs. As in section (<>)5, all other parameters are kept fixed in the following analyses (including those from the mass-observable relation) and in each case we perform a MC with 10,000 realizations. "
+  ],
+  "6.3 Dependence on the number of parameters fitted ": [
+    "The results for the several combinations of the parameters being fitted and the 3 values of the area discussed in the previous section are displayed in figure (<>)1, which shows that the bias of the estimators are only a relatively small fraction of the size of the error bars. ",
+    "In the one-dimensional parametric spaces the relative biases are generally greater than 10% but smaller than 25%. For both and the biases, and decrease with the increase of the survey area, as expected. Nevertheless, the errors bars σ(Ωˆ c) and σ(ˆσ8) have a ",
+    "steeper decrease, such that relative biases and end up increasing with the area. This shows that even for large samples, where one would expect the biases related to the cluster abundance likelihood to be smaller, this bias could still be a significant fraction of the error bars. ",
+    "The freedom introduced by the increased number of fitted parameters results in larger error bars in almost all estimators, as expected. In general, the absolute biases |bxˆ| also increase with the number of fitted parameters. For the two and three-dimensional parametric spaces the relative biases, and are roughly constant for both 178 and 720 deg2 . Namely, and On the other hand, for the (Ωc, σ8) and (Ωc, σ8, w0) spaces (being < 1% for the former space and 720 deg2), while and 14% in the plane (σ8, w0) for 178 and 720 deg2 , respectively. ",
+    "Only for ΔΩ = 2500 deg2 we note a consistent decrease of the relative biases with the number of parameters fitted. In this case, all estimators present values for Bxˆ of the order of 20%, 10%, and < 10% for one, two and three-dimensional parametric spaces, respectively. "
+  ],
+  "6.4 Dependence on the survey area and depth ": [
+    "For most cases in the upper panels of figure (<>)1 we see that the absolute values of the bias decrease with the area, as expected from the increase of the sample size. However, one may wonder if this trend continues for higher areas and whether the expected values converge to the fiducial values (it is worth mentioning that the sample size corresponding to 2500 deg2 is of order of 250 objects). Therefore, we extend the analysis to larger areas and include also some intermediate values to see the general evolution scaling with area. In particular, in addition to the three areas of the previous section we run the MC simulations for ΔΩ = 450, 1600, 3250, and 4000 deg2 . The later corresponds to the original planned SPT footprint [(<>)43]. This study is carried out only in the three-dimensional parametric space. ",
+    "Figure (<>)2 summarizes the results for the seven areas considered. We note that the three parameters present the larger absolute biases for the 3 smaller areas. The estimators are closer to their true values for 1600 (σˆ8) or 2500 deg2 (Ωˆ c and wˆ0). Nevertheless, all estimators have their biases increased for the larger areas. In addition to displaying the values of the biases and the uncertainties in the parameters being fitted, in this figure we also show the uncertainties associated to the values of bxˆ, i.e., σ xˆ . We see that the biases are being precisely estimated. ",
+    "To better understand the increase of the biases for larger areas, we also compute the estimators of the one- and three-dimensional parametric spaces for 10,000 and 40, 000deg2 , being the last close to the full-sky limit. The results are displayed in table (<>)2. The biases continue to grow with the increase of the area and, therefore, we have that Ωˆ c, σˆ8, and wˆ0 are not consistent in the sense that we are treating the full-sky area as the the asymptotic limit. We also note that the estimate of the expected value of all estimators computed in the one-dimensional parametric space have already converged for 10, 000 deg2 (since xˆ’s are equal for both areas), but not to their fiducial values, i.e., bxˆ = 0. It is worth emphasizing that in the full-sky limit the bias is a dominant error source, being the relative biases about 30% to 50% for (Ωc, σ8, w0) and about 80% for the one-dimensional parametric spaces. ",
+    "In order to identify the cause of the not consistent feature of the cosmological parameter estimators, Ωˆ c, σˆ8, and wˆ0, we carry out the MC analyses considering 40, 000 deg2 and two other likelihoods: the halo abundance [given by eq. ((<>)3.6)] and a cluster abundance likelihood ",
+    "Figure 2. The expected values of the estimators (dots) are displayed with the error bars of the estimators (a) and of their means (b) for di˙erent survey areas. ",
+    "ξ − M500 cluster abundance likelihood, zmax = 1.1 ",
+    "Table 2. First Column: Survey area. Second Column: Number of fitted parameters. Odd Columns: Estimated expected value of xˆ and its standard deviation σ(ˆx) obtained fitting simultaneously 1 (first and third rows) and 3 (second and forth rows) cosmological parameters and keeping the others fixed. Even Columns: Bias size bxˆ relative to σ(ˆx). ",
+    "given by ",
+    "(6.6) ",
+    "where ",
+    "(6.7) ",
+    "and P (ln Mobs| ln M) is a log-normal probability distribution for obtaining an observable mass Mobs given the true mass M, ",
+    "(6.8) ",
+    "with For both likelihoods, we obtain that all estimators are unbiased, i.e., the fiducial values are recovered within σ xˆ , such that the relative biases are less than 1%. Therefore, while the halo abundance likelihood provides biased estimators, when the sample size is small (see section (<>)5), but is consistent, the ξ −M500 cluster abundance likelihood yields biased estimators whose importance grows with the increase of the sample size. It is worth emphasizing that we cross-checked our code with the SPT team’s one and, therefore, we discard the hypothesis that the results obtained with ξ − M500 cluster abundance likelihood are due to bugs in the code.4 (<>)",
+    "Besides the area, another factor that determines the sample size is the redshift depth. We therefore study the behavior of the bias and the statistical uncertainties as a function of the maximum redshift of the survey. In particular, we perform the MC analyses (using the ξ − M500 cluster abundance likelihood) for seven values of the maximum redshift equally spaced in the interval [0.9, 1.5]. The later, zmax = 1.5, corresponds to the highest redshift of the SPT catalog in ref. [(<>)12]. ",
+    "Figure (<>)3 shows the results considering ΔΩ = 720 deg2 and the (Ωc, σ8, w0) parametric space. The bias on decreases systematically with zmax, whereas decreases and then stays roughly constant after z = 1.1. Meanwhile, bwˆ0 presents an almost linear behavior as a function of zmax with its absolute value increasing after z = 1.3. In any case, as in the previous plots, the biases are not significant compared to the statistical error bars. ",
+    "Finally, we study the estimators in the three-dimensional parametric space assuming zmax = 1.5 and ΔΩ = 10, 000 and 40, 000 deg2 . Both absolute biases and the standard deviations are slightly smaller than those shown in table (<>)2, such that Bxˆ are essentially una˙ected by the change in zmax. "
+  ],
+  "6.5 Including photometric redshifts ": [
+    "The analyses carried out on the previous sections assumed perfect knowledge of the redshifts. However, spectroscopic redshifts are often available for only a fraction of the clusters, with many of them having z estimated photometrically. For example, 49 of 100 clusters from ref. [(<>)12] have just photometric measurements. We therefore include the uncertainties related to photometric redshifts in the likelihood for cluster number counts to verify its e˙ect on the cosmological parameter estimators Ωˆ c, σˆ8, and wˆ0. ",
+    "For simplicity we assume that all clusters have the same Gaussian probability distribution for obtaining a photometric redshift zphot given the true value ztrue , ",
+    "(6.9) ",
+    "Figure 3. The expected values of the estimators (dots) are displayed with the error bars for the estimators (a) and for their means (b) as a function of zmax. ",
+    "where σz = σz0(1 + z), σz0 = 0.05 and the normalization factor is obtained assuming zphot > 0. Similarly to eqs. ((<>)6.3) and ((<>)6.4), we have ",
+    "(6.10) ",
+    "where ",
+    "(6.11) ",
+    "and the normalization factor N({θj}) is now the expected number of clusters with and ",
+    "Now the MC approach is performed by minimizing eq. ((<>)6.10) with respect to θj and the sampling is carried out using the probability distribution given by eq. ((<>)6.11), the mass-observable relations, and P (zphot|ztrue). Each realization is now a catalog of clusters contain-",
+    "ing their photometric redshifts, ziphot , and the detection significance, ξi (see appendix (<>)B). We study the three-dimensional parametric space for zmax = 1.1 and ΔΩ = 720 deg2 . ",
+    "The results for the relative biases for the 3 parameters are shown in figure (<>)4, together with other cases discussed in this work. We find that including the photometric redshift uncertainty has a negligible impact on the relative biases. The relative biases are Bσˆc = 17%, and while the outcomes for the likelihood with only the mass-observable uncertainty give and Thought the biases do increase when considering photometry redshifts, the error bars also increase, keeping the ratio almost constant. For example, considering photometric redshifts we have bwˆ0 = 0.055 and σ(wˆ0) = 0.72, whereas considering perfect knowledge of the redshift yields bwˆ0 = 0.037 and σ(wˆ0) = 0.68. "
+  ],
+  "7 Combination with other observables: CMB distance priors ": [
+    "So far we have studied estimators of three cosmological parameters computed using only the cluster abundance. However, in practice cosmological constraints are obtained combining cluster counts with other observables, such as the cosmic microwave background (CMB) radiation. Hence, in order to study more realistic estimators, we repeat the MC procedure including CMB data. ",
+    "We do not consider the full CMB analysis since each case requires 10,000 realizations. Therefore, we build the CMB likelihood using only the so called distance priors (see [(<>)44] and references therein). They are dependent on the cosmological parameters and correspond to the redshift at decoupling z, the location of the first acoustic peak lA, and the shift parameter R. ",
+    "The acoustic scale lA is given by ",
+    "(7.1) ",
+    "where DA(z) is the angular diameter distance and rs(z) is the sound horizon size. The shift parameter is ",
+    "(7.2) ",
+    "and the decoupling redshift is computed using the Hu & Sugiyama fitting formula [(<>)45]. The likelihood is ",
+    "(7.3) ",
+    "where xi = (lA, R, z) and di are the distance prior values for a given realization (see below). In this work we use Wilkinson Microwave Anisotropy Probe 9-year (WMAP9) data, for which the inverse covariance matrix is given in ref. [(<>)46] as ",
+    "We generate a realization for the CMB distance priors di assuming that they follow a Gaussian distribution with inverse covariance matrix (Cij)−1 above and (lA, R, z) calculated ",
+    "from the fiducial model. Therefore, our MC simulations include both the realizations of the cluster distribution and the distance priors, and the likelihood minimized is a combination of eq. ((<>)7.3) and the cluster likelihood. ",
+    "The results from the 10,000 MC realizations for the relative biases Bxˆ for ΔΩ = 720 deg2 , zmax = 1.1, and the tridimensional parametric space (Ωc, σ8, w0) are shown in figure (<>)4, together with the other cases previously considered in this work. In the combination with the WMAP9 distance priors we consider two cases, including or not the photometric redshifts (always including the SZ mass-observable relation). ",
+    "The combined likelihood provides a large improvement on both absolute biases and error bars for the Ωc and w0 estimators. Roughly, the error bars are 4 to 16 times smaller, depending on the parametric space, than those obtained using only the cluster likelihood. Assuming ΔΩ = 720 deg2 and zmax = 1.1, we obtain that the biases for wˆ0 and Ωˆ c are small and compatible with zero within their own statistical error bars for the parametric spaces (w0), (σ8, w0), and (Ωc, σ8). The relative biases also decrease in the (Ωc, w0) plane to and in comparison to 17% and 9%, respectively, obtained with the cluster number counts likelihood only. ",
+    "The MC results for 178, 720 and 2500 deg2 and the three dimensional space (Ωc, σ8, w0) reinforce that Ωc is essentially constrained by CMB distance priors, since σ(Ωˆc) = 0.01 and BΩˆ c = 1% for the first two cluster catalogs. We note a stronger weight of the cluster likelihood when ΔΩ = 2500 deg2 . Besides a decrease in the error bar, there is an increase in the absolute bias such that In the case of the w0 estimators, the relative biases are for all sky areas, although the biases and error bars are now much smaller. ",
+    "Di˙erently from Ωc and w0, we note from figure (<>)4 that σ8 is almost insensitive to the CMB distance priors. The estimators obtained in (σ8), (Ωc, σ8), and (σ8, w0) have the same bias and error bar than that from unidimensional space using the cluster abundance likelihood, namely bσˆ8 = 0.001 and σ(ˆσ8) = 0.008, which gives Bσˆ8  13%. In the bidimensional planes, this occurs because σ8 is weakly correlated to Ωc and w0 (Cor(Ωc, σ8)  −0.25 and Cor(σ8, w0)  0.09). On the other hand, in the tridimensional parametric space, the strong correlations between these parameters increase their respective error bars such that Bσˆ8  10%, 7%, and 3% for 178, 720 and 2500 deg2 , respectively. ",
+    "Including photometric redshift uncertainty in the cluster abundance likelihood produces even smaller changes than those verified in section (<>)6.5. Assuming ΔΩ = 720 deg2 , the error bars of the estimators obtained in (Ωc, σ8, w0) space are basically equal to those without considering photometric uncertainty. The biases bσˆ8 and bwˆ0 are slightly increased such that Bσˆ8 = 9% and Bwˆ0 = 6%, as illustrated in figure (<>)4. "
+  ],
+  "8 A comparison of methods to determine confidence contours ": [
+    "While the bias on cosmological parameter estimators needs to be evaluated with the Monte Carlo approach, the assessment of statistical errors can also be carried out using other methods such as Fisher matrix (FM) and profile likelihood (PL) (see also [(<>)1, (<>)47, (<>)48]). Therefore, it is worth comparing the error bars computed with these 3 di˙erent methodologies. In ref. [(<>)48], for example, the authors compare the confidence regions computed via FM and Markov Chain Monte Carlo (MCMC) using only a cluster abundance likelihood, as well with one combined with other observables. ",
+    "In this section, we briefly review the FM and PL techniques and carry out some examples obtaining error bars and confidence regions for specific realizations. ",
+    "Figure 4. The relative biases of Ωˆ c (left panel), σˆ8 (right panel), and wˆ0 (lower panel), considering ΔΩ = 720 deg2 , zmax = 1.1, and the tridimensional parametric space (Ωc,σ8,w0), obtained with the likelihood (left to right): DM halo abundance, cluster abundance (i.e. including the SZ mass-observable relation), extending the depth to zmax = 1.5, including photometric redshift uncertainty, combining with WMAP9 distance priors, with and without photometric redshifts, respectively. "
+  ],
+  "8.1 Fisher Matrix ": [
+    "The Fisher matrix is defined as ",
+    "(8.1) ",
+    "If the estimators θˆi are unbiased, then the FM is related with the variance of these estimators as (see ref. [(<>)22]) ",
+    "(8.2) ",
+    "where C(θˆi,θˆj) are the elements of the covariance matrix. In practice it is assumed that the data set is suÿciently large and the second derivative of ln L(θ) computed at the best-fit θˆ ",
+    "by the number of parameters to be fitted. Say, for example, that we are fitting n parameters. Thus, the bidimensional contour (ellipse) of the i-th and j-th parameters is computed as [(<>)49] ",
+    "(8.3) ",
+    "(8.4) ",
+    "where, ",
+    "(8.5) ",
+    "(8.6) ",
+    "(8.7) ",
+    "The confidence level is defined by q, namely, q = 2.48 corresponds to 2σ level. Since Cij is the inverse of an n× n matrix, the other n− 2 parameters are marginalized over. ",
+    "This technique is useful to forecast the constraints on cosmological parameters since it has low computational cost. However, the application of the FM method is limited as it provides just an approximation of the lower bound of the covariance matrix. ",
+    "Although this methodology assumes that estimators are unbiased, we use it to reproduce what is usually done in the literature and then compare the results with MC and PL approaches. It is worth emphasizing that FM can also be obtained for biased estimators [(<>)50]. ",
+    "We begin the analyses computing the FM of the bi and tridimensional parametric spaces for 20 di˙erent realizations, considering the fiducial model with ΔΩ = 720 deg2 . In general, the FM errors bars are smaller than the those from MC. Only 2, 3, and 5 realizations resulted in larger error bars of w0 in (σ8,w0), (Ωc,w0) and (Ωc,σ8,w0), respectively. In all these cases, the best-fits were out of the 1σ confidence interval. ",
+    "In order to compare the FM with the confidence region computed from MC approach, i.e., from the 10,000 realizations, we choose two realizations where the best-fit of the parameters are within the 1σ interval in all parametric spaces. The first realization, called seed 125, 5 (<>)provides error bars on the cosmological parameters smaller (roughly half) than the MC errors in all studied parametric spaces. The second realization, seed 131, gives similar error bars to those obtained with MC approach. ",
+    "Figure (<>)5 shows the results for the bidimensional case (Ωc,w0). In both panels, the orange dots represent the best-fits of the 10,000 realizations and the red lines are the 95.45% confidence regions from MC approach. We compute the MC contour using the quantile function from R Project for Statistical Computing.6 (<>)The black lines are the FM 2σ bounds for seed 125 (left panel) and seed 131 (right panel) both computed using eq. ((<>)8.3). The FM contours are consistent with the MC result and, as expected, their sizes vary for each realization. ",
+    "Figure 5. 2σ contour obtained from Monte Carlo approach (red line) and 2σ confidence regions for two specific realizations (left panel: seed 125 and right panel: seed 131) using Fisher matrix (black line) and profile likelihood (blue line) methods. The orange dots are the best-fits of 10000 realizations. "
+  ],
+  "8.2 Profile Likelihood ": [
+    "The profile likelihood method consists in applying the likelihood ratio test [(<>)20, (<>)51] to obtain the error bounds on the parameters. We define two nested models, i.e., a model with parameters {θj} and the same model where the parameters satisfy a set of nr restrictions fa({θj}) = 0. For each model we obtain the maximum likelihood estimators {θˆj} and {θˆjf }, where the last are the constrained ones. Note that, in general, these two sets are di˙erent. For the first we obtain the maximum of the likelihood with respect to all parameters whereas in the second we obtain the maximum enforcing the conditions fa({θj}) = 0. In a simple example f({θj}) = θ1 − θ10 , where θ10 is a constant, the restriction is equivalent to keeping a parameter fixed to a constant value. Then, the likelihood ratio test is ",
+    "(8.8) ",
+    "where {yi} is the data set. Under certain conditions, −2 ln Λ is, asymptotically, a random variable described by a chi-square distribution of nr degrees of freedom theorem) [(<>)20, (<>)51]. ",
+    "Given the best-fit values {θjbf}, we can use the test described above fixing a given parameter θk to a specific value θkf to obtain the p-value associated with such choice. The p-value is defined as  ∞ ",
+    "(8.9) ",
+    "where Pnr (x) is the probability density of a chi-square distribution of nr degrees of freedom and C is the confidence interval percentage, e.g., 68.27% (or 1σ for a Gaussian distribution). ",
+    "Choosing a critical value C, we vary the value θjf to find the interval within which this parameter is accepted for C. Thus, the bidimensional contour of θi and θj (nr = 2) is obtained computing eq. ((<>)8.9), such that ",
+    "(8.10) ",
+    "where the other parameters{θˆkf } can  remain fixed or free. If {θkf } are free, {θˆkf } are the best-fit values computed at θif , θjf . ",
+    "Similarly as done with FM method, we compute some confidence regions using PL. The dashed lines in figure (<>)5 correspond to 2σ contour for seed 125 (left panel) and seed 131 (right panel). It is worth noting the ability of the PL technique in recovering some features, such as the shape, of the real distribution, in contrast to the FM, which, by construction, can only provide an ellipse. The bottom line is that both FM and PL contours are compatible with the MC result. "
+  ],
+  "9 Conclusions ": [
+    "As has long been anticipated, cosmology has turned from a statistics to a systematics dominated field. Many sources of systematics have been considered in the literature, in particular those originated from observational e˙ects and the modeling of the physical systems. In this work, we studied the biases from the properties of the estimator itself. Motivated by recent SZ surveys, for which the sample sizes are at most of the order of hundreds of objects and by the fact that ML methods can be biased for small samples (and even for large samples if the estimators are not consistent), we investigated the biases from an unbinned method for cluster number counts, which was shown to be equivalent to the now standard cluster abundance likelihood. The main aim of this work was to determine whether the biases found on some cosmological parameters were significant, as compared to their error bars. ",
+    "To determine the biases from a given likelihood we have used the MC method, generating a large set of simulated samples and comparing the mean values of the cosmological parameters obtained by maximizing the likelihood to the fiducial models used in the simulations. This is computationally expensive and motivated the development of optimized codes that were incorporated in the NumCosmo library (see appendix (<>)A). The configurations used in the simulations (survey area, redshift range, cosmological parameters, etc.) were inspired by recent SZ surveys, in particular public catalogs from the SPT. ",
+    "We first considered an idealized situation where the mass and redshift of the clusters are perfectly known, i.e. the DM halo abundance (section (<>)5). In this case we found that the biases can be quite large for small samples. In particular we obtained a relatively large bias for σ8, in the case where ΔΩ = 720 deg2 and the likelihood is simultaneously fit for Ωc, σ8, and w0, as compared to the expected (statistical) error bar on this parameter, yielding On the other hand, we verified that and are consistent when assuming the full-sky area. ",
+    "We then considered a mass-observable (SZ) relation from SPT and found that the relative biases are significantly smaller, assuming typical areas of this survey (section (<>)6.3). However, the relative biases can be as large as ∼ 25% of the error bars for some configurations. Although the absolute values of the bias do in general decrease as the size of the sample increases, at ",
+    "least for the smaller area samples, the statistical error bars also shrink. As a consequence, in these cases, the relative biases are less sensitive to the sample size. ",
+    "To take a deeper look at the role of sample size, we obtained the biases as a function of both survey area and redshift depth, varying the 3 parameters, Ωc, σ8, and w0 (section (<>)6.4). The smaller absolute biases were obtained for ΔΩ = 1, 600 and 2, 500 deg2 . For larger areas, we found out that the bias grows with the increase of the area. As the standard deviation of the estimators decreases, the relative biases become more relevant. In the full-sky limit, Bxˆ ∼ 80% and ∼ 50% for one-and three-dimensional parametric spaces, respectively. Therefore, we find that the estimators computed using ξ − M500 cluster abundance likelihood are not consistent, di˙erently from the those obtained with the halo abundance one. In particular, the biases can be a dominant error source as compared to the statistical errors due to shot-noise. However, other sources of error must be considered and it remains to be checked whether the bias found in this work will dominate in this case. ",
+    "The sensitivity to zmax depends on the parameter under consideration. In any case, for all ranges probed, assuming ΔΩ = 720 deg2 , the biases are very small compared to the error bars. The situation is practically unchanged when we include photometric redshifts in the MC realizations and the likelihood (section (<>)6.5). ",
+    "Combining the cluster abundance likelihood with CMB distance priors (section (<>)7) evinces that the later imposes strong constraints on Ωc and w0, significantly reducing the estimators’ error bars in all parametric spaces. The bias is reduced in these cases, specially for Ωc, since the CMB priors have more weight in this case and are assumed unbiased. On the other hand, since σ8 is mostly determined by the cluster abundance, both its bias and statistical error bar are roughly unchanged. ",
+    "Finally, we have compared the confidence regions of the fitted parameters obtained from the Fisher matrix and profile likelihood methods with the ones derived from the MC realizations and found that the former provide error bars that are broadly consistent with those from MC approach (section (<>)8), further validating the use of these methods in the case of cluster abundance. ",
+    "It is worth emphasizing that the results obtained are weakly sensitive to the values of the fiducial cosmological model. For example, we used also Ωc = 0.15, σ8 = 0.85, and w0 = −0.85 and found very similar results. ",
+    "For optical surveys, such as SDSS, DES and LSST, this study must consider sample variance in the cluster likelihood function. Since sample variance dominates the Poisson term for large galaxy clusters samples, we expect that the cosmological parameter estimators would have smaller biases in this context, provided that the sample variance estimator is unbiased. ",
+    "In general, the mass-observable (M-O) relations are sources of systematic errors in the inference of cosmological parameters. A common approach to minimize the e˙ect of these errors while also constraining the M-O relation is to combine other observables and to fit the cosmological parameters along with those of the M-O relation (so-called self-calibration). Therefore, as future work, we plan to extend this study and obtain the estimators of both type of parameters using, for example, cluster, CMB and type Ia supernovae data. As a preliminary analysis, we used the cluster abundance likelihood and computed the estimators of the two-dimensional parametric spaces, (Ωc, DSZ), (σ8, DSZ) and (w0, DSZ), assuming 720 deg2 . Following ref.[(<>)11], we considered a Gaussian prior on DSZ with mean equal to 0.21 and standard deviation 0.16. In this case, the cosmological parameters are moderately correlated (anti-correlated) to DSZ, Cor(ˆx, DSZ)  ±0.5. Except for Ωˆ c and σˆ8, whose relative biases are about 20%, the other estimators have negligible relative biases (< 5%). ",
+    "If on one hand we obtained that in general Bxˆ  10% for the most realistic cases of SZ surveys (considering typical areas of SPT), on the other hand we have shown that the consistent feature of the estimators depends on the modeling of the M-O relation and, when this property is not fulfilled, the bias of the estimators cannot be neglected for very large areas. ",
+    "The results of this work validate the use of the current maximum likelihood methods for present SZ surveys (small catalogs). However, they highlight the need for further studies for upcoming wide-field sensitive surveys, since biases from SZ estimators do not go away with increasing sample sizes and they may become the dominant source of error for an large area survey, as the Planck probe, and sensitive as the SPT and ACT. "
+  ],
+  "Acknowledgments ": [
+    "MPL acknowledges CAPES (grant PRODOC 2712/2010) and CNPq (PCI/MCTI/CBPF and PCI/MCTI/INPE programs) for financial support. MM is partially supported by CNPq (grant 309804/2012-4) and FAPERJ (grant E-26/110.516/2012). MPL is grateful to Sandro Vitenti for valuable discussions and comments. The authors thank Fernando de Simoni, Juan Estrada, and Scott Dodelson for useful suggestions. The authors also thank the anonymous referee for the careful reading of this work and valuable suggestions. This work made use of the CHE cluster, managed and funded by ICRA/CBPF, with financial support from FINEP and FAPERJ. "
+  ],
+  "A Numerical Cosmology Library (NumCosmo) ": [
+    "In this appendix we present a summary and a short description of each object used in this work. The NumCosmo library is a free library written in the C language dedicated to numerical calculations in cosmology [(<>)24]. The documentation and examples are available at the project’s url. ",
+    "In section (<>)2 we introduced the cosmological model to compute the expected halo number counts. This calculation was split in several objects to allow for each step to be modified for di˙erent modeling or optimization. These objects are listed below, ",
+    "The NumCosmo’s object that implements the sampling method, described in appendix (<>)B, is NcDataClusterNCount. This object is also used to calculate the abundance likelihood described in eqs. ((<>)3.6), ((<>)6.3), and ((<>)6.10). The mass-observable relation and photometric redshift distribution objects are implementations of NcClusterMass and NcClusterRedshift, respectively. In this work we used the implementations NcClusterMassBenson and NcClusterPho-tozGaussGlobal. The WMAP distance priors described in section (<>)7 are implemented by the NcDataCMBDistPriors object for both sampling and likelihood evaluation. ",
+    "To obtain the results from Fisher Matrix, Monte Carlo, and profile likelihood approaches (Secs. (<>)8.1 and (<>)8.2, respectively), we used the objects NcmFit for both FM and MC and NcmLHRatio1d for the profile likelihood method. ",
+    "It is worth emphasizing that, di˙erently from most works, we do not make a grid in redshift and observable quantities, such as ξ, to compute eq. ((<>)6.4) [or eq. ((<>)6.11)] and, thus, the confidence regions. We calculate these equations at each point (ξi, zi). "
+  ],
+  "B Sampling ": [
+    "In this appendix we describe the procedure to generate the realizations of the samples {ξi, zi}. First we compute the halo abundance N({θj}) given a fiducial model, ",
+    "(B.1) ",
+    "where ln Mmin is obtained from eqs. ((<>)6.1) and ((<>)6.2). Using N({θj0}) as the mean of a Poisson distribution, we randomly generate the total number of objects n. ",
+    "The second step consists in creating a sample with n redshift values zi from the probability distribution of finding a halo with mass greater than Mmin and in the redshift interval [z, z + dz], i.e.,   ",
+    "(B.2) ",
+    "where N({θj}) is the normalization factor. To generate the set {zi} following this distribution we employ the inverse transform sampling, which we briefly describe below. First we define the cumulative  z ",
+    "(B.3) ",
+    "since f(z) is a monotonically increasing function whose image is [0, 1], there is a one-to-one relation between z and f(z). Given also that f(z) is a random variable with uniform distribution over [0, 1], we generate n random numbers {ui} from a uniform distribution and inverted equation ((<>)B.3) obtaining z(f) and, therefore, the set {zi} = {z(ui)}. ",
+    "For each value of zi generated, we obtain a value Mi from the conditional distribution of obtaining a halo with mass in the range M and M + dM given zi, defined as ",
+    "(B.4) ",
+    "where P (M, zi) is given by eq. ((<>)3.4) and P(zi) by eq. ((<>)B.2). Then we use the cumulative ",
+    "(B.5) ",
+    "to define M(f, zi) and thus we employ the same procedure described above to get {zi}, but now obtaining {Mi, zi}. ",
+    "Finally, to obtain the cluster sample {ξi, zi} (to which we refer as a realization of the cluster distribution), a value ζi is randomly generated from the Gaussian distribution P (ln ζ| ln M) with scatter DSZ and mean given by the logarithm base e of eq. ((<>)6.2), where M500 is the true halo mass Mi. Then we randomly generate ξi using the Gaussian distribution P (ξ|ζ) with ",
+    "scatter equal to one and mean obtained substituting ζi in eq. ((<>)6.1). As the last step, we select the objects which fulfill the condition ξ ≥ ξmin. ",
+    "In section (<>)6.5 we also included the photometric redshift uncertainty. Therefore, the realization {ξi, ziphot} is obtained from the sample {ξi, zi} described above where ziphot is randomly generated from eq. ((<>)6.9). As done for ξi, the generated values are selected such that zmin ≤ zphot ≤ zmax.i "
+  ]
+}

jsons_folder/2014JCAP...07..051L.json

@@ -0,0 +1,96 @@
+{
+  "Abstract": [
+    "Abstract. There is a great interest in measuring the non-electronic component of neutrinos from core collapse supernovae by observing, for the first time, also neutral-current reactions. In order to assess the physics potential of the ultra-pure scintillators in this respect, we study the entire expected energy spectrum in the Borexino, KamLAND and SNO+ detectors. We examine the various sources of uncertainties in the expectations, and in particular, those due to specific detector features and to the relevant cross sections. We discuss the possibility to identify the di˙erent neutrino flavors, and we quantify the e˙ect of confusion, due to other components of the energy spectrum, overlapped with the neutral-current reactions of interest. "
+  ],
+  "Contents ": [],
+  "1 Introduction ": [
+    "A Core Collapse Supernova (SN) releases 99% of its total energy by emitting neutrinos of the six flavors. The capability to observe the electronic antineutrino component of this emission has already been proven by the detection of SN1987A neutrinos [(<>)1–(<>)3]. The very large statistics that we will collect from the next galactic supernova will allow us to study the time dependence of the spectrum, specific features of the ν¯e luminosity and of its average energy [(<>)4, (<>)5]. The detection of the other neutrinos flavors, however, requires specific detectors and interactions, typically with smaller cross sections. This is true, in particular, for the non electronic component of the spectrum, that can be observed only through Neutral Current (NC) interactions. ",
+    "During the last years a new generation of ultra-pure liquid scintillators, Borexino (BRX) [(<>)6] and KamLAND (KAM) [(<>)7], have been operated, obtaining excellent results thanks to the unprecedented low background levels reached and the new sensitivity in the very low energy range, below 1 MeV. They have a particularly good physics potential for the detection supernova NC channels, and quite remarkably, the Elastic Scattering (ES) of (anti)neutrinos on protons [(<>)8]. It has been argued that the high statistics from this reaction should suÿce to constrain the spectra of the non electronic component for a SN emission, already with the existing detectors [(<>)9]. In view of the importance of this conclusion, we would like to reconsider it in this work. ",
+    "The outline of this paper is as follows. First of all, we summarize the available information regarding SN neutrino detection in the existing ultra-pure scintillators, and calculate for each of them the total number of expected events as well as their spectral features. We consider the contributions of all neutrino interaction channels and obtain in this way the spectrum of events for a galactic supernova. In this way, we are in the position to evaluate which are the capabilities of the present generation of ultra-pure scintillators to identify and measure the di˙erent neutrino flavors. "
+  ],
+  "2 Emission from a Standard Core Collapse Supernova ": [
+    "The aim of this work is to discuss an important question: what we can really see with the existing ultra-pure scintillators and to which extent we can distinguish the di˙erent neutrino ",
+    "flavors. With this purpose in mind, we will use very conservative assumptions on the emission model. We suppose that the energy radiated in neutrinos is E = 3×1053 erg, which is a typical theoretical value that does not contradict what is found in the most complete analyses of SN1987A events [(<>)10, (<>)11]. We also assume that the energy is partitioned in equal amount among the six types of neutrinos, that should be true within a factor of 2 [(<>)12]. ",
+    "In agreement with the recent studies, e.g., [(<>)13], we consider quasi-thermal neutrinos, each species being characterized by an average energy Ei and including a mild deviation from a thermal distribution described by the parameter α = 3 for all flavors. Thus, the neutrino fluence di˙erential in the neutrino energy E is ",
+    "where the energy radiated in each specie is Ei = Efi, with fi = 1/6 in the case of equipartition, and the ‘temperature’ is Ti = Ei/(α + 1). In particular, the neutrino and antineutrino fluences relevant to NC interactions ",
+    "since we suppose that the distribution of the 4 non-electronic species is identical. ",
+    "The average energies are fixed by the following considerations: consistent with the simulations in [(<>)13] and with the findings from SN1987A [(<>)10, (<>)11], we set the electron antineutrino average energy to Eν¯e  =12 MeV. For the average energy of the non-electronic species, that cannot be seriously probed with SN1987A [(<>)11], we suppose that the non-electronic temperature is 30% higher than the one of ν¯ e: Ex = 15.6 MeV, this is in the upper range of values, but still compatible with what is found in [(<>)12]. For a comparison we will consider also the worst case in which the energies of the non electronic component is equal to the one of the ν¯e, namely Ex = 12 MeV as showed in very recent simulation [(<>)14]. We calculate the electron neutrino average energy by the condition that the proton (or electron) fraction of the iron core in the neutron star forming is 0.4: this gives Eνe  = 9.5 MeV. ",
+    "Note that the NC reactions are independent from neutrino oscillations, while for the CC interactions also considering only the standard oscillation scenario, the choice of the mass hierarchy has an important impact on the expectations. Thanks to the fact that θ13 is large (say, larger than about 1 degree) this means that, in normal mass hierarchy, the survival probability of electron neutrinos and antineutrinos are |Ue23| and |Ue21| respectively, whereas for inverted mass hierarchy, the two values become |Ue22| and |Ue23|. Thus, the approximate numerical values that we will assume in the calculations are ",
+    "The value of Pν¯e→ν¯e in the case of inverted hierachy means that what we measure as electronic antineutrinos in terrestrial detectors, are non-electronic antineutrinos at the emission in fact; thus, it has a particularly important impact on the interpretation of the data. We note also that these numerical values would imply that there are only little chances to probe the emission of electron neutrinos, which are, from the astrophysical point of view, the most important type of neutrinos emitted by a supernova. ",
+    "In the following we will consider only the case of the normal mass hierarchy for definiteness and adding a bit of theoretical bias; recall however that this hypothesis is immaterial for ",
+    "Figure 1. Fluences expected for the di˙erent neutrinos flavors. The blue dotted line shows ν¯e, the green dot-dashed line νe. We assume standard neutrino oscillations and Normal mass Hierarchy (NH) for the fluences of each flavor. The black thick lines and the red dashed ones show the fluences relevant for the Neutral Current (NC) detection channels of neutrinos and antineutrinos, respectively. ",
+    "the discussion of the neutral current events. The total fluences expected to reach the Earth under these assumptions are shown in Fig.(<>)1 for a Supernova exploding at 10 kpc from us. "
+  ],
+  "3 Interaction Channels ": [
+    "In the scintillators and at SN energies, we need consider the several interaction processes: ",
+    "CC processes. Those involving electronic antineutrinos are ",
+    "Inverse Beta Decay (IBD), i.e. ν¯e + p → n + e+; ",
+    "while those involving electronic neutrinos are "
+  ],
+  "NC processes. We considered the following channels, ": [
+    "Moreover, we consider the ES on electrons, that receives a contribution from both CC and NC. Let us discuss these reactions in detail. "
+  ],
+  "Detailed description of the cross sections ": [
+    "The IBD, i.e., ν¯e + p → n + e+ , represents the main signal not only in water Cherenkov and also in scintillator detectors. It produces a continuous spectrum due to the positrons energy release. The approximated kinematic of this reaction connects the neutrinos energy with the detected energy through Eν = Ed + Q− me where Q  1.3 MeV is the Q value of the reaction ",
+    "and me is the electron mass. For the calculations, the IBD cross section reported in [(<>)15] was used. The delayed neutron capture on a proton is characterized by a monochromatic γ2.2 MeV emission. The coincidence in a typical time window of about 250 µs between the latter and the prompt signal from the e+ gives a clear signature of an IBD event. This means that, in the time integrated events spectrum, there will be a very high peak around 2.2 MeV that integrates the same number of events expected for IBD, reduced by the eÿciency of the tag. The spectral shape of this peak is due to both the energy resolution of the detector and the quenching of the gamma ray energy in the scintillator. In this work, due to lack of information, we neglect the last e˙ect and consider the optimistic case in which the width of this peak is only due to the energy resolution. ",
+    "The superallowed CC reactions νe+12C→ e−+12N and ν¯e+12C→ e++12B present physical thresholds of Eνe >17.3 MeV and Eν¯e >14.4 MeV respectively. They are detectable through the prompt leptons e− (e+), which give a continuous spectrum. Moreover the nucleus of both reactions in the final state, 12N and 12B, are unstable. The former will decay β+ to 12C with a half life of ∼ 11 ms. The latter will decay β− to 12C with a half life of ∼ 20 ms [(<>)16]. The high energy positrons and electrons emitted in these beta decays can be observed, giving the possibility to tag these events. The cross sections used for the evaluation are those reported in [(<>)17]. ",
+    "In the NC channels all neutrino flavors are involved potentially increasing the number of signal events detected. ",
+    "For the ES on protons channel the cross section in [(<>)18, (<>)19] was used, with a proton strangeness of η = 0.12. However it is important to stress that the uncertainty on the number of events expected for this channel is not negligible due to the proton structure and amounts to about 20% [(<>)20]. To understand the spectral shape of this class of events it is necessary to model the quenching factor for protons in the scintillators; this accounts for the proton light output and depends on the liquid scintillator composition. A detailed description of this factor is given in the next section. ",
+    "The cross section for the superallowed NC reaction ν+12C → ν+12C∗ followed by the emission of a monochromatic γ at 15.11 MeV is reasonably well known. It was measured in KARMEN [(<>)21], confirming the correctness of the calculations as reported in [(<>)17] within an accuracy of 20%. Future measurements, most remarkably in OscSNS [(<>)22], claim the possibility of measuring more than 1,000 events in one year with a systematic estimated at 5% level or better. The prominent spectral feature of this channel can permit the identification of these events, as a sharp peak around 15 MeV, standing out from the main signal due to IBD. ",
+    "The total cross section for NC proton knockout ν + 12C → ν + p+11B has been calculated in [(<>)23], as a part of a network of reactions needed to describe the nucleosynthesis of light elements. However, the calculation of [(<>)24] finds a cross section about 30% larger, which suggests an error of at least this order. The neutrino energy has to exceed a pretty high threshold, i.e. E > (MB + mp)2 − MC2 /(2MC )  15.9 MeV (where we use obvious symbols for the masses of the carbon nucleus, of the boron nucleus and of the proton). The initial neutrino energy (minus the activation energy, quantified by the threshold) is shared by the neutrino and the proton in the final state, E + MC ≈ E + Tp + MB + mp so that the maximum kinetic proton energy Tpmax is obtained when the final state neutrino is almost at rest, E ≈ 0. The expression for the maximum of the proton kinetic energy is ",
+    "(3.1) ",
+    "with In view of the smallness of this sample of events, we adopted ",
+    "mp − mB − Tp)2 . We checked that the integral in the proton kinetic energy of this expression agrees at the level of few percent with the theoretical behaviour of the total cross sections as reported in [(<>)23].1 (<>)",
+    "In the CC knockout proton reaction on 12C the outgoing kinetic energy is shared between the electron and the proton. The maximum kinetic proton energy Tpmax is obtained when the final electron is at rest. Similarly to the previous case, this is given by ",
+    "(3.2) ",
+    " ",
+    "where again M∗ = M2 + 2MCE. In this case the phase space is dσ/dTp ∝ dΦ/dTp ∝  C Tp(M∗ − mp − mC11 − Tp)2 . The theoretical cross sections reported in [(<>)23] and the value estimated from pure phase space agree at the level of ∼ 20%. ",
+    "In the Elastic Scattering on electrons all the flavors participate, but the cross section is slightly di˙erent for the di˙erent flavors. The current best measurement of this interaction arises in a sample of 191 events [(<>)25, (<>)26], and quotes 17% of total error. The error that we estimate in the standard model is instead absolutely negligible for our purposes. "
+  ],
+  "Numerical formulae ": [
+    "Let us conclude this section by giving two numerical formulas to evaluate easily the main neutral current cross sections: ",
+    "An easy-to-implement e˙ective formula for the ν +12 C → ν +12 C∗ cross section, that agrees with [(<>)17] results at better than 1% in the region below 100 MeV, is ",
+    "(3.3) ",
+    "with p(E) =  n3 =0 cn (E/100 MeV)n where E is the incoming neutrino energy, and the numerical coeÿcients are c0 = −0.146, c1 = −0.184, c2 = −0.884, c3 = +0.233. ",
+    "A simple parametrization of the cross section for the ES scattering, νp → νp, assuming that the proton strangeness is η = 0.12, is simply ",
+    "(3.4) ",
+    "where q(E) = −0.333 − 0.16(E/100 MeV). "
+  ],
+  "4 Description of the Ultra-pure Scintillating Detectors ": [
+    "We consider the ultrapure liquid scintillators detectors that are running or under construction, namely the following three: Borexino (BRX) [(<>)6] (0.3 kt of C9H12) in Gran Sasso National Laboratory, Italy, KamLAND (KAM) in Kamioka Observatory, Japan [(<>)7] (1 kt of mixture of ",
+    "Table 1. Constants appearing in the parametrized formula of the quenching function here adopted. ",
+    "C12H20(80%) and C9H12(20%)) and SNO+ (0.8 kt of C6H5C12H25) currently under construction in the SNOLAB facility, located approximately 2 km underground in Sudbury, Ontario, Canada [(<>)27]. ",
+    "We assume that theenergy resolution for each detector is a Gaussian with an error described by σ(Ed) = A× Ed/MeV and a di˙erent value of the constant A for each detector. The trigger threshold in Borexino is as low as about 200 keV, reaching full eÿciency at Ed = 250 keV [(<>)28]. The overall light collection in Borexino is  500 photoelectrons (p.e.)/MeV of deposited energy. The resolution is  5% at 1 MeV (namely A = 50 keV). The trigger eÿciency in KamLAND currently reaches 100% at 350 keV. The energy resolution of the KamLAND detector can be expressed in terms of the deposited energy as ∼ 6.9%/ Ed(MeV) (i.e., A = 69 keV) [(<>)9]. The energy threshold expected for SNO+ is the optimistic one of 200 keV and the energy resolution is supposed to be the same as in Borexino. ",
+    "As we mentioned earlier when the detected particle is a proton, the visible energy is only a fraction of the kinetic energy Tp, as described by the ‘quenching function’. Each detector has its own quenching function, that depends on its chemical composition; for Borexino detector we consider the quenching function discussed in [(<>)20], for KamLAND the one recently discussed in [(<>)30] and finally for SNO+ the response to proton in LAB scintillator as measured in [(<>)31]. Following [(<>)29] a simple parametrization of the quenching function is ",
+    "(4.1) ",
+    "The values for the constants a1, a2 and a3 that should be used for the di˙erent detectors are reported in Tab. (<>)4 and the resulting functions are shown in Fig.(<>)2. ",
+    "At this point, we obtain the following important conclusion: ",
+    "in ultrapure scintillators, the observation of protons from the NC elastic scattering reaction allows us to observe only the high energy part of the neutrino spectra. ",
+    "In fact, due to the thresholds and to the quenching, the protons below a minimum kinetic energy cannot be detected; this is 0.9 MeV for SNO+, 1.8 MeV for Kamland and 1.3 MeV for Borexino. Thus, taking into account the kinematical relation between the proton kinetic energy and the one of incoming neutrinos, we find that the elastic scattering on protons is sensitive to neutrino energies above a threshold of 22 MeV in the best situation of SNO+, it becomes 25 MeV for Borexino, and raises to 30 MeV in the case of Kamland. In view of these considerations, one concludes that the exploration of the low energy of the spectrum via neutral currents is not possible with the existing ultrapure scientillators. "
+  ],
+  "5 Results ": [
+    "For each detection channel, we estimate the number of expected events and report them in Table (<>)2. Moreover, we plot the energy distributions of the events, considering the specific features of the ultrapure scintillating detectors in Figure (<>)3. ",
+    "Figure 2. Quenching functions used to convert the proton kinetic energy in the detectable energy Ed for Borexino (red line), KamLAND (black dashed line) and SNO+ (blue dotted line), respectively. ",
+    "The IBD channel (red line) starts to dominate the global signal at 5 MeV and reaches the maximum around 14 MeV. The total number of interactions expected for a supernova located at 10 kpc is of about 54 events for Borexino, 257 for Kamland and 176 for SNO+. These results are reported in the first row of Table (<>)2. The subsequent gamma from neutron capture gives the peak at 2.2 MeV, shown by a purple line. The eÿciency of the neutron tag is (85±1)% in Borexino (see [(<>)39]), (78±2)% in KamLAND (see [(<>)7]) and also in SNO+. The condition for a successful IBD tag [(<>)39] is that no more than one interaction occurs during the time between the IBD interaction and the neutron capture inside a specific volume, namely ",
+    "(5.1) ",
+    "where RIBD is the rate of IBD events per second and per unit mass, Δt is the temporal window of the tag, that we assume to be Δt = 2τ = 512µs, ΔV is the volume of a sphere with 1 meter of radius, ρ is the density of the scintillator. This is related to the detector mass and to the distance of the supernova by ",
+    "(5.2) ",
+    "where M is the mass of the detector, D is the distance of the SN and T is the duration of the emission. For example to allow the IBD tag in a detector with the density of Borexino and 1 kton of mass, considering that 50% of the total emission is expected during the first second [(<>)11], then the minimum distance of a SN is D ≥ 0.16 kpc, that is not a severe limitation.2 (<>)",
+    "Let us discuss now the NC elastic proton scattering. This channel dominates the low energy part of the spectrum, represented with the blue line in Figure (<>)3, even if as discussed previously, this reaction probes only the high energy part of the supernova neutrinos. It is ",
+    "Table 2. Summary table for all the number of events from the various interaction channels. The result are given for the emission model where the energy of non-electronic components is 30% bigger then the one of ν¯e; in brackets, we indicate the corrispondent values assuming that the energies of ν¯e and νx are the same. The color code (2nd colum) refers to the lines of Figure (<>)3. ",
+    "evident from Table (<>)2 and Fig. (<>)3 that the event spectrum depends strongly on the quenching of the proton signal. The detector threshold used in the case of KamLAND is an optimistic value, since we assumed a threshold of 350 keV, lower than the one that can be obtained with the current radioactivity level, i.e., 600 keV [(<>)40]. If this higher threshold is assumed the ES with protons on KamLAND gives only 17 signal events. ",
+    "It is important to remark that the number of events due to this channel is also very sensitive to the SN emission parameters; in fact, as discussed in the end of the previous section, this interaction is sensitive only to the high energy tail of the SN neutrinos spectra. In particular, the average energy of the di˙erent neutrino flavors have gradually been changing in recent years, moving toward lower mean values [(<>)41] and toward minor di˙erences between the average energies of the di˙erent components [(<>)13, (<>)42]. For comparison we have considered the new paradigm of emission, where the average energy of non-electronic flavors is the same as of the electronic antineutrinos, namely Ex = 12 MeV [(<>)13, (<>)41] and have investigated the two di˙erent cases to outline the impact on this and the other NC process. As shown by the values in brackets in Table (<>)2, the expectations in this case are quite meager. ",
+    "The NC neutral current reaction ν +12 C → ν +12 C∗ followed by the emission of a monochromatic γ is shown in orange in Figure (<>)3. This channel does not require the low energy threshold and the eÿciency for its detection is taken 100% for all the detectors considered. However, the possibility of a successful identification is a˙ected by the quality of the energy resolution of the detector and by the e˙ectiveness to tag the IBD signal. These events can be observed if the IBD events are identified through the correlated neutron capture signal, since they are expected to occur in the same energy region. With the assumed energy resolutions we have that this neutral current reaction can be observed in the energy range (14-16) MeV. For Borexino, the number of events due to the IBD signal in the same range is 5.7; thus, more than the 50% of the total signal collected in this energy window is due to the IBD channel, while for KamLAND and SNO+ the IBD signal is 26.9 and 18.4, representing about 60% of the total one. In the case of Borexino, if the tagging eÿciency is of 85% as assumed in the plot, we expect only 1 event due to IBD not identified, so the uncertainty on the γ15.11MeV signal is reduced to 14%. ",
+    "The ESe involves all the flavors of neutrinos and we expect to collect about 4 events for Borexino, 15 for KamLAND and 12 for SNO+. Their spectrum is reported with a dark ",
+    "Figure 3. Theoretical event spectrum in the detectable energy Ed in ultrapure scintillators for a Supernova exploding at 10 kpc. The top panels refer to Borexino detector, the bottom panels to SNO+, those in the middle to KamLAND. On the left panels, the expectations for the emission model where energy of non-electronic component is 30% higher then the one of ν¯e; on the right panels, the corresponding expectations for the case when the non-electronic components and the ν¯e have the same average energy. See Table (<>)2 and the text for the explanation of the individual lines. ",
+    "green line in the spectra of Figure (<>)3, and dominates in the energy region between the ES on protons and the IBD signals. As we mentioned the cross section for the di˙erent flavors are slightly di˙erent; the νe contribution produces half of the events. ",
+    "The rest of the detection channels have a low signal. All of them show a continuos spectrum, being from e− , e+ or protons. The two CC superallowed reactions are indicated by a magenta line for the 12N final state nucleus and by a black thin line for the 12B one. The decay products of the unstable nucleus are not considered in this plot. For both knockout channels, besides the high energy thresholds, the quenching has to be considered, so the total number of events collected for them is pretty small. The one due to NC is shown in yellow, while the one due to CC is shown with the dashed red line. "
+  ],
+  "6 Conclusions ": [
+    "In this paper, we have obtained and discussed the spectrum of supernova neutrino events in ultrapure scintillators for a supernova exploding at 10 kpc from the Earth. We have examined the capability to distinguish the various detection channels and we have quantified the uncertainties in this type of detectors. ",
+    "As discussed in the introduction, a major reason of specific interest for a future supernova is the possibility to observe neutral current interactions of neutrinos. We have investigated the three possible reactions of detection in ultrapure scintillators, namely: 1) the elastic scattering with protons, 2) the 15.11 MeV γ de-excitation line, 3) the proton knockout channel. Our conclusions are as follows: ",
+    "The first reaction is characterized by the larger number of expected events in all the detectors; however the number of detectable events is strongly limited by the energy thresholds. The uncertainty on the total number of elastic scattering on protons, due to the proton structure, amounts to the 20%; moreover in the same energy region where this reaction can be observed there are also the indistinguishable events due to the elastic scattering with electrons and those due to NC and CC proton knockout. In other words, all we can observe is the total number of events collected in the energy region from the detector threshold to the threshold of the IBD signal, about 1.8 MeV. In this detection window, we have found that a fraction of 8% (Borexino), the 7% (KamLAND), the 4% (SNO+) of the signal is due to the other channels and this uncertainty is small but irreducible. We have also seen that, in the case that the the energy of non-electronic neutrinos is low, the number of events due to this reaction is too small to permit the investigation of the νx spectrum at the level discussed in [(<>)9]. ",
+    "The gamma line due to neutrino-induced 12C de-excitation is in principle easier, giving a signal at a high energies; its detection does not require the extreme performances at very low energies are not needed. However, in the same region of the spectrum where this line is visible we will have also positrons due to IBD reaction; thus, the eÿciency to tag the concomitant neutron will be of crucial importance to identify cleanly a sample of this NC reaction. While this concern is not a severe issue for the type of detectors we have considered in this work, it is much more relevant for future scintillators with a much larger mass and limited performances at low energies. ",
+    "Finally, we have shown that the proton knockout will give a comparably small number of NC events. "
+  ]
+}

jsons_folder/2014MNRAS.437...67C.json

@@ -0,0 +1,136 @@
+{
+  "J. Chluba⋆, L. Dai†and M. Kamionkowski‡": [
+    "Department of Physics and Astronomy, Johns Hopkins University, Bloomberg Center, 3400 N. Charles St., Baltimore, MD 21218, USA ",
+    "Accepted 2013 September 30; Received 2013 August 26 "
+  ],
+  "ABSTRACT ": [
+    "Future high-resolution, high-sensitivity Sunyaev-Zeldovich (SZ) observations of individual clusters will allow us to study the dynamical state of the intra cluster medium (ICM). To exploit the full potential of this new observational window, it is crucial to understand the origin of di erent contributions to the total SZ signal. Here, we investigate the signature caused by multiple scatterings at lowest order of the electron temperature. Previous analytic discussions of this problem used the isotropic scattering approximation (ISA), which even for the simplest cluster geometries is rather rough. We take a step forward and consistently treat the anisotropy of the ambient radiation •eld caused by the •rst scattering. We show that the multiple scattering SZ signal directly probes line of sight anisotropies of the ICM, thereby delivering a new set of SZ observables which could be used for 3D cluster-pro•le reconstruction. The multiple scattering signal should furthermore correlate spatially with the cluster•s X-ray and SZ polarization signals, an e ect that could allow enhancing the detectability of this contribution. ",
+    "Key words: Cosmology: cosmic microwave background • theory • galaxy clusters "
+  ],
+  "1 INTRODUCTION ": [
+    "A number of high-resolution Sunyaev-Zeldovich (SZ) experiments, including ALMA1 (<>), CARMA2 (<>), CCAT3 (<>), and MUSTANG4 (<>), are underway or planned, promising a dramatic increase in sensitivities, spatial resolution and spectral coverage over the next few years. These experiments will allow us to directly probe the dynamical state of the intra cluster medium (ICM) of individual clusters, opening a new window to understanding their cosmological formation and evolution. To realize the full potential of these observations, it is important to understand the SZ signal and its dependence on the cluster atmosphere with high precision. ",
+    "Since the •rst considerations of the thermal SZ (thSZ) e ect ((<>)Zeldovich & Sunyaev (<>)1969) and kinetic SZ (kSZ) e ect ((<>)Sunyaev & Zeldovich (<>)1980), several related signatures have been discussed in the literature. For instance, because the electrons residing inside clusters are very hot [kTe ≃5 keV −10 keV (with k denoting the Boltzmann constant and Te the electron temperature)] relativistic temperature corrections need to be included ((<>)Wright (<>)1979; (<>)Rephaeli (<>)1995; (<>)Challinor & Lasenby (<>)1998; (<>)Itoh et al. (<>)1998; (<>)Sazonov & Sunyaev (<>)1998). Also, higher order kSZ terms, both caused by the clusters bulk motion ((<>)Sazonov & Sunyaev (<>)1998; (<>)Nozawa et al. (<>)1998; (<>)Challinor & Lasenby (<>)1999) and the motion ",
+    "of the observer ((<>)Chluba et al. (<>)2005; (<>)Nozawa et al. (<>)2005) arise5 (<>). Furthermore, relativistic electrons can create a non-thermal SZ signature indicative of past AGN activity and merger shocks ((<>)Enßlin & Kaiser (<>)2000; (<>)Colafrancesco et al. (<>)2003). Additional effects are related to details of the cluster•s atmosphere. For example, internal bulk and turbulent gas motions introduce spatially varying SZ signatures (e.g., (<>)Chluba & Mannheim (<>)2002; (<>)Nagai et al. (<>)2003; (<>)Diego et al. (<>)2003). Line-of-sight variations of the electron temperature cause a non-trivial SZ morphology which depends on moments of the cluster temperature and velocity pro•les ((<>)Chluba et al. (<>)2013, CSNN hereafter). Extra pressure support from large-scale magnetic •eld deforms the electron distribution inside clusters ((<>)Koch et al. (<>)2003). And •nally, shocks and substructures in merging clusters leave distinct signatures in the SZ •ux (e.g., (<>)Komatsu et al. (<>)2001; (<>)Kitayama et al. (<>)2004; (<>)Colafrancesco et al. (<>)2011; (<>)Korngut et al. (<>)2011; (<>)Menanteau et al. (<>)2012; (<>)Mroczkowski et al. (<>)2012; (<>)Zemcov et al. (<>)2012; (<>)Prokhorov & Colafrancesco (<>)2012). ",
+    "In this work we consider the e ect of multiple scattering on the SZ signal ((<>)Sunyaev & Zeldovich (<>)1980; (<>)Sazonov & Sunyaev (<>)1999; (<>)Molnar & Birkinshaw (<>)1999; (<>)Dolgov et al. (<>)2001; (<>)Itoh et al. (<>)2001; (<>)Colafrancesco et al. (<>)2003; (<>)Shimon & Rephaeli (<>)2004). As we show here, this signature depends on inhomogeneities in the clus-ter•s electron and temperature distribution. It therefore provides a new set of SZ observables that are valuable for the reconstruction ",
+    "of 3D cluster pro•les6 (<>), potentially allowing geometric degeneracies to be broken. We restrict our analysis to the lowest order in the electron temperature. Higher order corrections will be discussed in (<>)Chluba & Dai ((<>)2013, CD13 hereafter). ",
+    "The main new physical ingredient is that for the second scattering we include the full anisotropy of the singly-scattered radiation •eld. In previous studies (e.g., (<>)Itoh et al. (<>)2001; (<>)Colafrancesco et al. (<>)2003; (<>)Shimon & Rephaeli (<>)2004), this aspect was omitted; however, even for the simplest cluster geometries this approximation is very rough (see Sect. (<>)3). Some discussion of the scattering-induced anisotropy in the radiation •eld can be found in connection with SZ polarization e ects (e.g., (<>)Sunyaev & Zeldovich (<>)1980; (<>)Sazonov & Sunyaev (<>)1999; (<>)Lavaux et al. (<>)2004; (<>)Shimon et al. (<>)2006) and accretion •ows (e.g., (<>)Sunyaev & Titarchuk (<>)1985), but the SZ signature in the frequency dependence of the speci•c intensity that we consider here was previously not studied. We determine a new set of SZ observables related to the second scattering correction (Sect. (<>)3.4) and demonstrate how the signal depends on the cluster•s geometry (see Fig. (<>)5). We also •nd that the spatial pattern of the second scattering SZ signal can be used to enhance its detectability by cross-correlating with X-ray and future SZ polarization data (Sect. (<>)4.1.3). ",
+    "For those readers less interested in the details of the derivation, we note that the central result of the paper is an expression, Eq. ((<>)12), for the total change I(x,\u001a ) to the speci“c intensity induced along a line of sight \u001a through the cluster in the “rst and second scattering as a function of frequency x. The new parameters γT( \u001a ) and γE( \u001a ) that appear in that expression are explicitly given for a spherically symmetric cluster as a function of impact parameter b in Eq. ((<>)15). "
+  ],
+  "2 EQUATION OF RADIATIVE TRANSFER ": [
+    "We begin with the radiative transfer equation in an anisotropic, static medium7 (<>)(e.g., (<>)Mihalas (<>)1978; (<>)Rybicki & Lightman (<>)1979; (<>)Mihalas & Mihalas (<>)1984): ",
+    "(1) ",
+    "Here, n(x,r,\u001a ) denotes the photon occupation number at the location r, in the direction \u001a and at frequency where is the cosmic microwave background (CMB) temperature at redshift z with the present-day monopole T0 = 2.726 K ((<>)Fixsen et al. (<>)1996; (<>)Fixsen & Mather (<>)2002; (<>)Fixsen (<>)2009), and h denotes the Planck constant. The radiative transfer equation is solved along the photon path (parallel to \u001a ) through the ICM, parametrized by the Thomson optical depth, where Ne(r) is the free electron number density. "
+  ],
+  "2.1 Compton collision term at the lowest order in kTe/mec2 ": [
+    "The collision term C[n] in Eq. ((<>)1) accounts for Compton scattering of photons of frequency x and direction \u001a out of the beam and for scattering of photons of other directions and frequencies into the beam. To linear order in the electron-temperature parameter θe ≡kTe/mec2 (where me is the electron mass), the collision operator for anisotropic incoming radiation, as shown in Appendix (<>)A, is ((<>)Chluba et al. (<>)2012a) ",
+    "where µsc = \u001a ·\u001a ′. Stimulated scattering and electron recoil were neglected, because for SZ clusters Tγ≪Te. ",
+    "The •rst integral in Eq. ((<>)2) describes the e ect of Thomson scattering (no energy exchange or equivalently scattering of photons by resting electrons), leaving the photon spectrum of the incoming radiation •eld unaltered. If the incoming photon •eld is isotropic this term vanishes. ",
+    "The second integral in Eq. ((<>)2) accounts for leading order temperature corrections to the total scattering cross-section. These again do not alter the shape of the photon spectrum (no energy exchange), and vanish for cold/resting electrons. For isotropic incoming photon •eld this term cancels [Klein-Nishina corrections, leading to contributions ≃θe(hν/mec2) are neglected here], but for the radiation dipole through octupole a “rst-order temperature correction arises: although for resting electrons the Thomson cross-section only couples to the monopole and quadrupole anisotropy of the incoming photon “eld, once electrons are moving, due to light aberration (see e.g., (<>)Chluba (<>)2011, for related discussion), also photons from the radiation dipole and octupole scatter into the line of sight at O(θe). Higher order multipoles couple at order O(θeℓ−2). ",
+    "The last integral in Eq. ((<>)2) takes the energy exchange between electrons and photons into account. It depends only on the radiation monopole through octupole. If the incoming radiation monopole through octupole have identical energy distribution, then their spectra are all altered in the same way by the scattering event. The di erence is captured by an overall, frequency independent scattering eÿciency factor that depends on the multipole. This is the case relevant to the second scattering SZ correction, for which all multipoles of the singly-scattered radiation •eld have a spectrum ∝Y0(x), which represents the well-known thSZ spectrum ((<>)Zeldovich & Sunyaev (<>)1969) de“ned in Eq. ((<>)7). "
+  ],
+  "2.2 Rewriting the collision term using Legendre polynomials ": [
+    "The collision term can be further simpli•ed by expanding the radiation •eld in terms of Legendre polynomials, Pℓ(x): ",
+    "(3) ",
+    "Here, n(x,r,µsc) denotes the azimuthally averaged occupation number of the photon “eld along the propagation direction \u001a . The Legendre coeÿcients can also be obtained from a spherical harmonic expansion of the radiation “eld with respect to a general system, n(x,r,\u001a ′) = ℓm Yℓm( \u001a ′)nℓm(x,r), using the identity ",
+    "nℓ(x,r) ≡m Yℓm( \u001a ) nℓm(x,r). Carrying out the integrals in Eq. ((<>)2), we “nd (compare Eq. (C15) and (C19) of (<>)Chluba et al. (<>)2012a): ",
+    "This expression captures all the relevant physics of the collision term, Eq. ((<>)2). Like Eq. ((<>)6), it can be directly obtained by computing the •rst and second moments of the frequency shift over the scattering kernel when accounting for the full angular dependence of the incoming photon •eld (see (<>)Chluba et al. ((<>)2012a) and CNSN). Only multipoles with ℓ≤3 really matter for the scattering problem, greatly simplifying the next steps of the calculation. This expressions also clearly shows that only the azimuthally symmetric part of the incoming photon distribution with respect to \u001a really matters, a property that due to symmetries of the scattering problem also holds at higher temperature (see CD13). "
+  ],
+  "2.3 Born approximation for multiple scattering ": [
+    "In the optically thin limit (τ≪1), relevant for galaxy clusters, repeated Compton scattering only introduces a small correction to the radiation “eld. To solve Eq. ((<>)1), we can thus use a perturbative Ansatz (a Born-series), n(x,r,\u001a ) ≈n(0) +ǫn(1) +ǫ2n(2) +...+ǫkn(k) , yielding the iteration scheme ",
+    "(5) ",
+    "The Compton collision term is linear in n(x,r,\u001a ) since induced scattering terms cancel for Tγ≪Te. Without scattering nothing changes (∂τn(0)(x,r,\u001a ) = 0), and the “rst scattering signal is given by ∂τn(1)(x,r,\u001a ) = C[n(0)(x,r,\u001a )]. For higher order scatterings, the local anisotropy of the radiation “eld becomes important, even if the unscattered radiation “eld was isotropic. Since the optical depth of typical clusters is τ. 0.01, we can restrict ourselves to the “rst and second scattering e ect. "
+  ],
+  "3 MULTIPLE SCATTERING SZ CONTRIBUTIONS AT LOWEST ORDER IN ELECTRON TEMPERATURE ": [],
+  "3.1 SZ signal after the •rst scattering ": [
+    "Assuming that the incoming, unscattered radiation •eld is given by the isotropic CMB blackbody, n(0)(x,r,\u001a ) = nPl(x) ≡1/[ex −1], the only non-vanishing incoming-radiation multipole is the monopole (ℓ= 0). The collision term in this case simpli“es to the well-known form (see (<>)Zeldovich & Sunyaev (<>)1969), ",
+    "for an isotropic radiation “eld. The coeÿcients, 4θe and θe, of the derivative terms are simply the “rst and second moments of the scattered photons relative frequency shift, ν≡(ν′−ν)/ν, over the scattering kernel (e.g., see (<>)Sazonov & Sunyaev (<>)2000). ",
+    "This then leads to the well-known thSZ e ect ((<>)Zeldovich & Sunyaev (<>)1969), with spectral shape, ",
+    "Here, the Compton y parameter, for ",
+    "Figure 1. Optical depth anisotropy of the local radiation •eld introduced by the •rst scattering of CMB photons for a constant density, isothermal sphere of free electrons. The dashed lines indicate the lines-of-sight for the two cases, and the dot marks the locus of the second scattering event. At the center (left panel), the total optical depth in any direction is the same because the total path through the medium is identical. Observing the singly-scattered radiation •eld around an o center position (right panel) on the other hand shows anisotropies because of optical depth variations. ",
+    "a distant observer is computed along the line of sight through the ICM, and Io = (2h/c2)(kT0/h)3 ≈270 MJy sr−1 . We also assumed that the cluster is at rest in the CMB rest frame and internal motions are negligible (no kSZ). "
+  ],
+  "3.2 Second scattering correction ": [],
+  "3.2.1 Simple illustration for the scattering-induced anisotropy ": [
+    "While the derivation given in this section applies to general cluster geometry, to illustrate the physics of the multiple scattering problem, let us consider a spherical, isothermal cloud of free electrons at rest in the CMB rest frame with constant density, Ne, and radius R as a simple example. At any location, r, inside the cluster we can compute the singly-scattered radiation •eld in di erent directions using Eq. ((<>)7), with isothermal y parameter, Here, the optical depth, is computed from r in the direction ˆ ′through the ICM, where s parametrizes the length along photon path. At the cluster center, the incident radiation “eld is fully isotropic, even in the limit of in“nite number of scatterings; however, due to variations of the scattering optical depth in di erent directions, after one scattering the local photon “eld becomes anisotropic elsewhere (see Fig. (<>)1). This scattering-induced anisotropy, generally being sourced by both electron temperature and density variations, has to be taken into account when calculating the second scattering correction to the SZ signal. "
+  ],
+  "3.2.2 Explicit form of the second scattering SZ correction ": [
+    "We now give the explicit expression of the second scattering correction to the thSZ e ect. After the •rst scattering, the correction to the radiation •eld at any position r inside the cluster is given by ",
+    "(8) ",
+    "where the spatial dependence is introduced only by the variation of the y parameter in di erent directions ˆ ′, with the scatterer centered at position r. This expression shows that for the second scattering SZ signal, spectral and spatial parts of the radiation “eld separate. Since all multipoles of the singly-scattered radiation have the same ",
+    "Figure 2. Spectral shape of the lowest order •rst and second scattering contributions to the thSZ signal. Note that we scaled Y0∗(x) = x−2∂x x4∂xY0 to make it more comparable in amplitude to Y0. ",
+    "spectrum, they also have the same after the second scattering. When including higher order temperature corrections and variations of the electron temperature along di erent lines-of-sight, this separation becomes slightly more complicated and the spectra of each multi-pole di er after the second scattering (see CD13). ",
+    "Inserting Eq. ((<>)8) into Eq. ((<>)4), and carrying out the line of sight average, we •nd the second scattering correction to the thSZ signal: ",
+    "with G(x) = xex/[ex −1]2 . Here, z parametrizes the photon path along the line of sight \u001a . We also introduced the Legendre coeÿ-cients, yℓ, of y(r,\u001a ′), which are de“ned like in Eq. ((<>)3). ",
+    "Equation ((<>)9) describes the full second scattering correction at lowest order in the electron temperature. The •rst two lines in Eq. ((<>)9b) provide corrections, I(2),T and I(2),σ, to the amplitude of the usual thSZ distortion, Eq. ((<>)7). The second is smaller by a factor θe ≪1 compared with the “rst, and so we neglect it below. The third provides the new frequency dependence, proportional to Y0∗(x), induced in the second scattering. The results indicate that only radiation multipoles up to ℓ= 3 (the octupole) are required to describe the radiation “eld obtained in second scattering. ",
+    "Since the energy-exchange correction, I(2),E , has a frequency dependence that di ers from that of the usual lowest order thSZ effect, measurement of its amplitude can provide information about anisotropies in the electron temperature and density pro“les. As shown in Fig. 2, the function Y0∗(x) numerically reaches values ≃10 ",
+    "times larger than the maximum of Y0(x). This makes this second-scattering correction roughly an order of magnitude larger than would be guessed from its θe ≃10−2 suppression relative to the lowest order SZ signal. ",
+    "To calculate the observable emergent speci•c intensity, we only need to compute the line of sight averages of the y-parameter multipoles, weighted by the Thomson optical depth, ∝yℓ, and the y parameter itself, ∝θeyℓ. These moments and ",
+    "(10) ",
+    "can be obtained directly from cluster simulations. This greatly simpli•es the computation, since spatial and spectral terms have been separated by our method. Below we give some simple examples assuming spherical symmetry. "
+  ],
+  "3.3 Second scattering SZ correction in the isotropic scattering approximation (ISA) ": [
+    "In the ISA (e.g., (<>)Itoh et al. (<>)2001; (<>)Colafrancesco et al. (<>)2003; (<>)Shimon & Rephaeli (<>)2004), the singly-scattered photon •eld is assumed to be isotropic and the same as in the direction along the line of sight de“ned by \u001a . Explicitly this means y(r,\u001a ′) ≈y(r,\u001a ), where \u001a ′is the direction of the incoming photon. Therefore, none of the anisotropies are taken into account and even the variation of the local monopole is neglected, although generally y(r,\u001a ′) d2 \u001a ′, y(r,\u001a ). At lowest order in θe, with Eq. ((<>)9) we therefore have ",
+    "where we used the identity θey(r,\u001a )≡y( \u001a )2/2, which can be deduced using Eq. ((<>)10). This expression neglects geometric form factors. In addition, no Thomson correction, I(2),T(x,\u001a ), is obtained in the ISA, although it usually is comparable to the energy-exchange correction, I(2),E(x,\u001a ), in Eq. ((<>)9) [see Fig. (<>)5]. "
+  ],
+  "3.4 Total SZ signal with second scattering corrections ": [
+    "The second scattering SZ signal gives rise to new observables that depend on the geometry of the cluster. The required line of sight moments scale like yl∝τ( \u001a )y( \u001a )/2, θeyl∝y2( \u001a )/2 and y(r,\u001a )∝τ( \u001a )y( \u001a )/2. With Eq. ((<>)7) and Eq. ((<>)9), it is therefore useful to rewrite the total SZ signal as ",
+    "The correction due to Thomson scattering is determined by γT( \u001a ), while the energy-exchange correction depends on γE( \u001a ). For the ISA, we have γT( \u001a ) = 0 and γE( \u001a ) = 1. ",
+    "Since the total SZ signal depends on two independent spectral functions, Y0(x) and Y0∗(x) [see Fig. (<>)2], from the observational point of view it in principle is possible to directly measure A( \u001a ) = y( \u001a ) 1 + τ( \u001a ) γT( \u001a )/2and B( \u001a ) = γE( \u001a ) y2( \u001a )/2 for different lines-of-sight. These observables depend on both the temperature and density pro“les of the electron distribution, and thus allow probing properties of the cluster atmosphere. "
+  ],
+  "4 SPHERICALLY SYMMETRIC SYSTEMS ": [
+    "For spherically symmetric systems, the computations of the required y-parameter moments can be further simpli•ed. Due to the symmetry of the problem, the y parameter in any direction ˆ ′around location r is given by ",
+    "(13) ",
+    "with r∗(s,µr ) = r2 + 2rsµr + s2 and µr = r\u001a·\u001a ′, where r\u001a de“nes the radial direction. To compute the Legendre coeÿcients of y(r,\u001a ′), we can use the addition theorem for spherical harmonics to simplify the calculation. This gives ",
+    "(14) ",
+    "where we introduced the impact parameter b of the line√of sight \u001a from the cluster center at the position z, so that r = b2 + z2 . The Legendre coeÿcient yℓ∗(r) ≡yℓ(b = 0,z) describes the simplest case, i.e., the line of sight through the center, and the factor Pℓ(z/r) provides the geometric transformation to the case b , 0. From the practical point of view, this means that for spherically symmetric systems we can compute the required line of sight moments yℓand θeyℓin two independent steps, “rst giving y∗ℓ(r) and then averaging over z. Since yℓ(b,−z) = (−1)ℓyℓ(b,z), all odd moments vanish after averaging over the line of sight. For general cluster geometry this is not necessarily true but it greatly simpli“es the calculation for (quasi) spherically systems. ",
+    "Performing the required integrals, the parameters γE(b) and γT(b) in Eq. ((<>)12), as a function of impact parameter b become (see Appendix (<>)B for more details) ",
+    "in terms of yobs(b), the y parameter observed along a line of sight that passes√an impact parameter b from the center. In these expressions, r = z2 + b2 , and κ0 = 1 and κ2 = 1/2. We also assumed that the cluster extends only to a maximal radius R and introduced the pressure pro“le Pe(r) = kTe(r)Ne(r). To simplify the computation, the innermost integrals over dµcan be tabulated as a function of r. "
+  ],
+  "4.1 Optical depth moments for illustrative cases ": [
+    "The second scattering SZ signal, Eq. ((<>)12), directly depends on the geometry of the cluster atmosphere. General cases can be studied ",
+    "Figure 3. Weighted average optical depth multipoles for an isothermal, constant density sphere with radius R as a function of impact parameter. All curves were normalized to their central value with and according to Eq. ((<>)C1). Odd moments vanish. ",
+    "Figure 4. Weighted average optical depth multipoles for isothermal β-pro“le with core radius, rc, as a function of impact parameter. All curves where normalized to their central value with and Odd moments vanish by symmetry. ",
+    "using cluster simulations, but to illustrate the main e ects we consider an isothermal, constant density sphere and an isothermal β-model (see Appendix (<>)C for de“nitions). Since for this case yℓ= θe τℓ, θeyℓ= θe2 τℓand y(r,\u001a )= θeτ( \u001a )2/2, we only have to compute line of sight moments of the optical depth “eld, τℓ. Some details of the calculation for b = 0 are given in Appendix (<>)C, and the general case is obtained by averaging yℓ(b,z) ≡Pℓ(z/r) yℓ∗(r) along the line of sight. ",
+    "The dependence of τℓon impact parameter b for the two cases is illustrated in Fig. (<>)3 and (<>)4. For the constant density sphere, the moments show signi“cant variation with b. They drop rapidly with ℓ, and in all cases the largest values of τℓare found for the line of sight directly through the center. This behavior depends critically on the geometry and density pro“le of the cloud, and for an ",
+    "Figure 5. Total second scattering correction for the constant density, isothermal sphere and the isothermal β-model at zero impact parameter. For comparison, we show the single-scattering thSZ e ect (the same in all cases), and the second scattering signal obtained with the ISA. ",
+    "isothermal β-pro“le the situations is already very di erent. In contrast to the constant density sphere, the pro“les τℓare monotonic, with higher order terms decreasing more gradually. It is evident that the amplitude and spatial morphology of the second scattering SZ correction di ers in the two cases. Consequently, the second scattering correction directly probes the geometry of the scattering medium, an e ect that is not captured by the ISA. "
+  ],
+  "4.1.1 Total second scattering signal and comparison to the ISA ": [
+    "We now compute the total correction caused by second scattering terms. In Fig. (<>)5 we show a comparison of the signal for the constant density, isothermal sphere and the isothermal β-model. The overall signal is very small, in both cases reaching no more than ≃0.2% of I(1) . However, as Fig. (<>)5 illustrates, the second scattering signal directly depends on the geometry of the scattering electron distribution, an e ect that is absent in the ISA. ",
+    "Comparing the di erent contributions in Eq. ((<>)12) also shows that the dominant correction is caused in the Thomson limit, I(2),T . For the isothermal sphere and impact parameter b = 0, we “nd I(2),T(x) ≈−0.06 τc I(1)(x). For some clusters one encounters central optical depth τc ≃0.01, so that this e ect gives rise to a correction ≃−0.06% relative to the singly-scattered SZ signal. For an isothermal β-pro“le (β= 2/3), we obtain a slightly larger e ect, giving I(2),T(x) ≈−0.15 τc I(1)(x) or a correction ≃−0.15% relative to I(1)(x) for τc = 0.01. Comparing the energy-exchange correction with the ISA, we “nd I(2),E,iso ≃1.12I(2),E and I(2),E,iso ≃1.4I(2),E for the isothermal sphere and β-model, respectively. Hence, this part of the correction is overestimated when using the ISA. The total correction (I(2),T ) for the isother-+ I(2),E mal β-model is ≃3 −4 times larger than obtained with the ISA. "
+  ],
+  "4.1.2 E ect on the crossover frequency ": [
+    "Because the frequency dependence of I(2),E di ers from I(1) , the position of the crossover frequency (≡null of the SZ signal at ν≃217 GHz or xc ≃3.83) is a ected by the second scattering ",
+    "Figure 6. Spatial dependence of the di erent contributions to the second scattering signal for an isothermal β-pro“le with β= 2/3. To represent the “rst scattering we show y = τθe, renormalized by its central value. For the ISA, we presented κEiso = (τθe)2/2 again renor-malizing by its central value. The Thomson scattering term is κT = γT (θeτ2/2) = θe τ0+ τ2/10 −τ2/2 and was normalized by X0 = −θeτ2/2 at b = 0. Finally, the energy-exchange term is κE = γE (θe2τ2/2) = θe2 [τ0+ τ2/10] and was normalized by X0 = (θeτ)2/2 at b = 0. ",
+    "contribution. From Eq. ((<>)12), we •nd ",
+    "(16) ",
+    "which for the isothermal β-model (γE ≃0.71 at b = 0) with total y parameter y ≃10−4 means xc ≃2.2 ×10−4 . For the constant density sphere (γE ≃0.89 at b = 0), we “nd xc ≃2.7 ×10−4 , while the ISA gives xc ≃3.1 ×10−4 . ",
+    "For comparison, at Te . 30 keV the shift in the position of the crossover frequency caused by higher order temperature corrections is xc ≃0.0421T\u001ae −3.29 ×10−4T\u001a e2 with T\u001ae = Te/5keV. For θe = 0.01(≡T\u001a e ≃1), this means xc ≃0.0418, which is roughly two orders of magnitudes larger. Similarly, the shift introduced by line of sight variations of the electron temperature is roughly given by xc ≃0.042T\u001ae[1−0.069T\u001ae]ω(1) , where ω(1) parametrizes the line of sight temperature variance (see CSNN). For θe = 0.01 and typical temperature-dispersion ω(1) ≃0.1 this means xc ≃3.9 ×10−3 , which is about one order of magnitude larger than the e ect caused by multiple scattering. Note that at lowest order in Te, Eq. ((<>)16) agrees with the expressions given by (<>)Dolgov et al. ((<>)2001) when setting γE ≡1, i.e., ignoring scattering-induced anisotropies of the radiation. "
+  ],
+  "4.1.3 Spatial dependence of the total second scattering signal ": [
+    "One interesting aspects of the second scattering correction is that it introduces both a new spatial and spectral dependence. At lowest order in temperature, the singly-scattered signal has a spectrum ≃x3Y0(x) and spatial variation y ≃τθe. In the ISA, the second scattering contribution [cf. Eq. ((<>)11)] has spectrum and spatial dependence On the other hand, when including the anisotropy of the singly-scattered radiation “eld, two new contributions arise, each with individual spatial and spectral dependence [see Eq. ((<>)9)]. The Thomson correction term scales like with a spectrum ≃x3Y0(x), while the energy-exchange term has spectrum ",
+    "and spatial dependence κE = γE (θe2τ2/2) ≃θe2 [τ0+ τ2/10] (τ1= τ3= 0 by symmetry). ",
+    "In Fig. (<>)6 we illustrate the spatial dependence of di erent terms for an isothermal β-pro“le with β= 2/3. The second scattering correction is most important at b ≃0, exhibiting a Ne2-scaling like X-rays. Thus, the detectability of the second scattering signal may be enhanced by cross-correlating with X-ray maps, as the X-ray emission also scales with Ne2 . Similarly, part of the SZ polarization signature (e.g., (<>)Sunyaev & Zeldovich (<>)1980; (<>)Sazonov & Sunyaev (<>)1999; (<>)Lavaux et al. (<>)2004; (<>)Shimon et al. (<>)2006) caused by the second scattering should correlate spatially with the SZ intensity signal. "
+  ],
+  "4.2 Angle-averaged SZ signal ": [
+    "For spherical systems with •nite radius R, we can also compute the angle-averaged SZ signal, assuming that the cluster is •lling a circular beam with radius R. It is well known, that the average single-scattering signal depends on the volume integral over the electron pressure pro•le, Pe(r) = kTe(r)Ne(r) ",
+    "For the second scattering signal, geometric form factors appear, which depend on the cluster atmosphere. This can be seen from ",
+    "where we used r∗= r2 + 2r sµ′r + s2 ≡|r + r′|. In the ISA, we have y0ISA = 0 and θey0ISA = y¯2/2. Similar to Eq. ((<>)12), it thus makes sense to de“ne the scattering form factors ",
+    "With Eq. ((<>)7) and ((<>)9), the total average SZ signal thus reads ",
+    "(20) ",
+    "The above expressions show that the average SZ signal just depends on the overall geometry of the electron pressure and density distribution, but local anisotropies, that were visible for a resolved cluster, no longer contribute. ",
+    "The geometric form factors have to be computed on a case-by-case basis. For constant pressure and electron density pro•les, we •nd and where we de•ned and used This implies Assuming that the pressure and electron density pro•les scale like 1/r, we similarly •nd ",
+    "and θey0= [ln(2)/R2] y2c = ln(2) y¯2 ≡y0/θe, or form factors γ¯ T + 1 = γ¯ E = 2 ln(2) ≈1.4. This shows that depending on the geometry of the cluster pro“le the ISA scattering approximation only provides a rough approximation for the second scattering signal. In particular it underestimates the average SZ signal related to Y0∗(x). Although the ISA overestimated the second scattering SZ signal for small impact parameters, at larger radii, which contribute strongly to the averaged signal, it underestimates the signal, explaining this net total e ect. "
+  ],
+  "5 CONCLUSION ": [
+    "We analyzed the e ect of multiple scattering on the SZ signal demonstrating how this small correction (order ≃0.1%) depends on the geometry of the ICM. Previous studies applied the ISA which does not capture the e ects discussed here, giving very di erent results for the second scattering correction (see Fig. (<>)5). The di er-ence has two main sources: (i) due to the anisotropy of the singly-scattered radiation “eld, the second scattering already introduces a modi“cation in the Thomson limit which is absent in the ISA; (ii) the e ective monopole of the radiation “eld along the line of sight di ers from the one used in ISA. ",
+    "Although, very small in comparison to the singly-scattered signal, our analysis shows that the second scattering SZ signal delivers a new set of observables (see Sect. (<>)3.4) which in the future might be useful for 3D cluster-pro•le reconstruction, allowing us to break geometric degeneracies. Since at lowest order in kTe/mec2 , the second scattering correction for isothermal clusters roughly scales as τ2 ∝Ne2 , it introduces an additional spatial dependence of the SZ signal, similar to the one of X-rays. Cross-correlating high-resolution X-ray maps with future SZ maps might thus allow enhancing the detectability of the second scattering signal. Similarly, combining with high-resolution SZ polarization measurements should allow extracting this contribution, potentially opening a path for more detailed studies of the clumpiness of the ICM. ",
+    "The method developed here can in principle be directly applied to simulated clusters. This can be used to give more realistic estimates for the signi•cance of the second scattering signal. The computation is greatly simpli•ed with our approach, since spatial averages over the ICM can be performed independently of the spectral integrals, accelerating the calculation. ",
+    "For the examples discussed here, we assumed spherical symmetry. In this case, all odd moments of the optical depth •eld vanish; however, in general this is an oversimpli•cation. More realistic cluster atmospheres might exhibit larger di erences in the second scattering signal and could thus provide a way to directly probe the asphericity and clumpiness of the ICM along the line of sight. From the observational point of view this is very intriguing, but given the low amplitude of the e ect this certainly remains challenging. For our estimates we also assumed isothermality. Variations of the electron temperature cause additional anisotropies in the singly-scattered radiation which might even exceed those introduced by optical depth e ects. The second scattering SZ contribution therefore could be used to directly probe the cluster•s temperature •eld. These aspects should, however, be addressed using realistic cluster simulations. ",
+    "We mention that a similar analysis can be carried out for SZ polarization e ects. In particular, the scattering-induced quadrupole anisotropy of the radiation •eld sources a SZ polarization e ect, which is directly related to line of sight average of the Compton y parameter•s quadrupole components. In this case, the ",
+    "projections perpendicular to the line of sight are most important (i.e., moments like y2,±2 ), de“ning both amplitude and direction of the polarization signature. Our separation of spatial and spectral dependence should again allow simplifying the calculation of the SZ polarization signature from cluster simulations. Similarly, our techniques can be applied to other scattering media at small and intermediate optical depth, providing a starting point for eÿcient numerical schemes, e.g., for cosmological simulations with Lyman-αradiative transfer (e.g., (<>)Maselli et al. (<>)2003; (<>)Zheng et al. (<>)2010). We plan to explore these possibilities in the future. "
+  ],
+  "ACKNOWLEDGEMENTS ": [
+    "JC thanks Donghui Jeong for stimulating discussions on the problem. The authors are also grateful to Anthony Challinor, Daisuke Nagai and Rashid Sunyaev for useful comments on the manuscript. This work was supported by the grants DoE SC-0008108 and NASA NNX12AE86G. "
+  ]
+}

jsons_folder/2014MNRAS.437.2652M.json

@@ -0,0 +1,185 @@
+{
+  "arXiv:1307.1705v3  [astro-ph.CO]  6 Jul 2017 ": [],
+  "ABSTRACT ": [
+    "There are several issues to do with dwarf galaxy predictions in the standard ΛCDM cosmology that have suscitated much recent debate about the possible modification of the nature of dark matter as providing a solution. We explore a novel solution involving ultra-light axions that can potentially resolve the missing satellites problem, the cusp-core problem, and the ‘too big to fail’ problem. We discuss approximations to non-linear structure formation in dark matter models containing a component of ultra-light axions across four orders of magnitude in mass, 10−24 eV  ma  10−20 eV, a range too heavy to be well constrained by linear cosmological probes such as the CMB and matter power spectrum, and too light/non-interacting for other astrophysical or terrestrial axion searches. We find that an axion of mass ma ≈ 10−21 eV contributing approximately 85% of the total dark matter can introduce a significant kpc scale core in a typical Milky Way satellite galaxy in sharp contrast to a thermal relic with a transfer function cut off at the same scale, while still allowing such galaxies to form in significant number. Therefore ultra-light axions do not suffer from the Catch 22 that applies to using a warm dark matter as a solution to the small scale problems of cold dark matter. Our model simultaneously allows formation of enough high redshift galaxies to allow reconciliation with observational constraints, and also reduces the maximum circular velocities of massive dwarfs so that baryonic feedback may more plausibly resolve the predicted overproduction of massive MWG dwarf satellites. ",
+    "Key words: cosmology: theory, dark matter, elementary particles, galaxies: dwarf, galaxies: halo "
+  ],
+  "1 INTRODUCTION ": [
+    "There are three outstanding problems in the dwarf galaxy astrophysics of the standard ΛCDM cosmology. The controversies on small scales may be summarised as a) the Missing Satellites problem (MSP), b) the Cusp-Core problem (CCP), and c) the ‘too big to fail’ problem (which we refer to here as the Massive Failures Problem, MFP), all reviewed in (<>)Weinberg et al. ((<>)2013). ",
+    "The MSP and CCP with CDM structure formation can both be solved by introducing a length scale ",
+    "into the DM. This can be thermal, coming from free-streaming of warm dark matter (WDM), or, as we will discuss below, non-thermal, coming from coherent oscillations of a light scalar field. The thermal solution may suffer from a Catch 22 issue, whereby galaxy formation occurs too late ((<>)Macci`o et al. (<>)2012). We show here that the non-thermal solution both avoids this dilemma and also augurs well for a particle-orientated solution of MFP, a problem for which a feedback solution seems questionable ((<>)Garrison-Kimmel et al. (<>)2013; (<>)Boylan-Kolchin, Bullock & Kaplinghat (<>)2012), although not all agree ((<>)Brooks et al. (<>)2013). ",
+    "ultra-light scalar dark matter and compare the linear theory to WDM in Section (<>)2. In Section (<>)3 we compute the halo mass function and model a cut-off in it. In Section (<>)4 we discuss the halo-density profile and core formation. In Section (<>)5 we discuss the relevance of our model for MFP, and in Section (<>)6 we discuss implications for high-redshift galaxy formation. The casual reader can skip to Section (<>)7 where we summarise and discuss our main results, and provide a guide to the relevant figures. Appendix (<>)A provides details of our two-component density profile model. "
+  ],
+  "2 ULTRA-LIGHT SCALAR DARK MATTER ": [
+    "A coherently oscillating scalar field, φ, in a quadratic potential V = ma2 φ2/2, has an energy density that scales as a−3 and thus can behave in cosmology as DM ((<>)Turner (<>)1983, (<>)1986)1 (<>). The relic density contains a non-thermal component produced by vacuum realignment, which depends on the initial field displacement φi. The Klein-Gordon equation is: ",
+    "(1) ",
+    "where the Hubble rate H = a/a˙ . When H  ma the field is frozen by Hubble friction and behaves as a contribution to the cosmological constant (which is negligible for sub-Planckian field values). Therefore, in order to contribute to DM we must have ma  H0 ∼ 10−33 eV. Once the mass overcomes the Hubble friction at ma ≈ 3H(aosc) the field begins to coherently oscillate. The relic density is then an environmental variable set by the initial field displacement: Ωa = Ωa(ma, φi) ≈ (8πG/3H02)aosc(ma)3m2aφ2i /2. ",
+    "As we will discuss below there is a length scale, which depends on the inverse mass, below which perturbations in the scalar field energy density will not cluster. Therefore the clustering of light scalar DM is observationally analogous to that of thermal relic dark matter. In the range 10−33 eV  ma  10−28 eV the clustering scale is analogous to hot (H)DM, for example composed of thermal relic neutrinos of mass mν  1 eV ((<>)Amendola & Barbieri (<>)2006; (<>)Marsh et al. (<>)2012). In this section we will discuss how scalar masses in the range 10−24 eV  ma  10−20 eV lead to structure formation that is analogous to WDM in an observationally relevant mass range. Related aspects of structure formation for axion/scalar dark matter in this mass range have been studied in, e.g. (<>)Hu, Barkana & Gruzinov ((<>)2000); (<>)Matos & Urena-Lopez ((<>)2000); (<>)Arbey, Lesgourgues & (<>)Salati ((<>)2001, (<>)2003); (<>)Bernal & Guzman ((<>)2006); (<>)Lee & (<>)Lim ((<>)2009); (<>)Park, Hwang & Noh ((<>)2012). ",
+    "While the signatures of thermal relics and ultralight scalars are similar in large scale structure, there are distinct signatures in the adiabatic and isocurvature CMB spectra ((<>)Marsh et al. (<>)2012, (<>)2013), and future measurements of weak lensing tomography can further break degeneracies ((<>)Amendola et al. (<>)2012). For the range of axion masses we consider aosc ∝ (ma/eV)−1/2 and the redshift zosc is in the range 105  zosc  107 . If the axion field is coupled to photons, the rolling field from φ = φi to φ = 0 at zosc can further affect the CMB. For axions with mass ma  10−28 eV that roll after recombination this leads to rotation of CMB polarisation (see e.g. (<>)Komatsu et al. ((<>)2009)). For heavier axions rolling at z ∼ 106 , photon production in primordial magnetic fields may lead to CMB spectral distortions ((<>)Mirizzi, (<>)Redondo & Sigl (<>)2009). It is necessary to understand the observational signatures of the parameters ma and Ωa if we are to make inferences about the nature of the DM from cosmological constraints, and in particular if hints from the CMB and large scale structure are pointing to a hot, warm, or ultra-light scalar component to the DM. In the rest of this article we will explore in detail structure formation with ultra-light scalars, and similarities and differences with thermal DM. ",
+    "Such ultra-light scalars might arise in a string theory context. It is well known that string theory compact-ified on sufficiently complicated six-dimensional manifolds contains many axion like particles (ALPs) ((<>)Wit-(<>)ten (<>)1984; (<>)Svrcek & Witten (<>)2006). In (<>)Arvanitaki et al. ((<>)2010) it was pointed out that since the masses of such axions depend exponentially on the areas of the cycles in the compact manifold, one should expect a uniform distribution of axion masses on a logarithmic scale spanning many orders of magnitude. This phenomenon was dubbed the “String Axiverse”. Explicit constructions of the axiverse have been made in M-theory ((<>)Acharya, (<>)Bobkov & Kumar (<>)2010) and Type IIB theory ((<>)Cicoli, (<>)Goodsell & Ringwald (<>)2012). ",
+    "The string axiverse has the potential to provide an elegant solution to the MSP, CCP, and possibly MFP, by leading us to expect as natural an axion mixed DM (aMDM) model with many axionic components populating hierarchically different mass regimes. Since the relic density produced via vacuum misalignment is environmental it can be taken as a free parameter to be constrained observationally, although theoretical priors can be considered (e.g. (<>)Aguirre & Tegmark (<>)2005; (<>)Tegmark et al. (<>)2006). A component of CDM in the aMDM model from the axiverse arises naturally in the form of the QCD axion ((<>)Peccei & Quinn (<>)1977; (<>)Wein-(<>)berg (<>)1978; (<>)Wilczek (<>)1978; (<>)Wise, Georgi & Glashow (<>)1981; (<>)Preskill, Wise & Wilczek (<>)1983; (<>)Berezhiani, Sakharov & (<>)Khlopov (<>)1992). The mass of the QCD axion is fixed by the pion mass and decay constant, and the axion decay constant fa. For stringy values of fa ∼ 1016GeV the QCD axion has a mass around 10−10eV. This is light, but not so light that the sound speed (see below) plays a cosmological role. The requirement that the QCD axion remains light enough, barring accidents, ",
+    "coincidences or fine-tuning, to solve the strong CP problem is what guarantees the lightness of the other axions, and as such one should always expect some CDM component alongside the ultra-light ALPs (ULAs). Axion mixed dark matter with a QCD axion and supersym-metric neutralino is also expected in many models of beyond the standard model particle physics (see, e.g. (<>)Bae, Baer & Lessa (<>)2013). "
+  ],
+  "2.1 Transfer Functions ": [
+    "The ULA perturbations, δφ, do not behave as CDM: they have a non-zero sound speed 2 (<>)ca2 = δP/δρ, which is scale-dependent and given by ((<>)Hu, Barkana & Gruzinov (<>)2000; Hwang & Noh (<>)2009; (<>)Marsh & Ferreira (<>)2010): ",
+    "(2) ",
+    "One finds that in a cosmology where axions make up a fraction of the DM, fax = Ωa/Ωd, that this causes suppression of the matter power spectrum relative to the case where the DM is pure CDM. Suppression occurs for those modes k that entered the horizon when the sound speed was large. The suppression is centred around a scale km, which depends on the mass, and takes the power spectrum down to some value S, which depends on Ωa, times its value in the CDM case. ",
+    "We compute the transfer functions and matter power spectrum in cosmologies containing CDM plus a ULA component using a modified version of the publicly available Boltzmann code CAMB ((<>)Lewis, Challinor (<>)& Lasenby (<>)2000; (<>)Lewis (<>)2000). The modification, which makes use of the fluid treatment of axion perturbations, is described in ?. The transfer function is defined as ",
+    "(3) ",
+    "We compare to the WDM transfer function (in the case where all the DM is warm) ",
+    "(4) ",
+    "where µ = 1.12 ((<>)Bode, Ostriker & Turok (<>)2001). The mixed C+WDM case is discussed in more detail in e.g. (<>)Anderhalden et al. ((<>)2012). A well-defined characteristic scale to assign to any such step-like transfer function is the ‘half-mode’ ",
+    "(5) ",
+    "where T (k → ∞)  0 is the constant plateau value of the transfer function on small scales. This is not the Jeans scale where all structure is suppressed. The Jeans scale is found analytically to be ((<>)Hu, Barkana & Gruzi-(<>)nov (<>)2000) ",
+    "(6) ",
+    "2 This is in the cosmological frame, e.g. synchronous or Newtonian gauge, where δφ = 0. ",
+    "Figure 1. The transfer function, Eq. ((<>)3) for aMDM with ma = 10−22 eV and varying axion fractions to total DM. For comparison, we also plot the FCDM transfer function of (<>)Hu, Barkana & Gruzinov ((<>)2000) and the WDM transfer function (Eq. ((<>)4)) with mW ≈ 0.84 keV chosen to match the transfer function half mode, km (Eq. ((<>)5)). With this choice and Ωa/Ωd = 1 the axion transfer function at km is much steeper than its WDM counterpart. ",
+    "The ρ1/4 scaling follows from balancing the growing and oscillating modes in eΓt where Γ2 = 4πGρ − (k 2/2m)2 , with k 2/2m coming from the oscillation frequency of the free field. ",
+    "In Fig. (<>)1 we plot the linear theory aMDM transfer function for a variety of aMDM models, all with ma = 10−22 eV which gives km(10−22 eV) = 6.7 h Mpc−1 . We compare to Eq. ((<>)4) with α ≈ 0.065 h−1Mpc chosen to give the same km. Taking Ωdh 2 = 0.112, Ωbh 2 = 0.0226, h = 0.7 as our benchmark cosmology, (<>)Angulo, Hahn & (<>)Abel ((<>)2013) gives α in terms of the WDM mass as: ",
+    "(7) ",
+    "Therefore, the matching of half-mode scales gives mW ≈ 0.83 keV as equivalent to ma = 10−22 eV. ",
+    "The logarithmic slope, d ln T (k)/d ln k, evaluated at k = km is much steeper for the pure axion model than for the pure WDM model, in agreement with the transfer function of (<>)Hu, Barkana & Gruzinov ((<>)2000) for ‘Fuzzy’ (F)CDM, also shown in Fig. (<>)1. ",
+    "With decreasing fraction of DM in ULAs the slope becomes shallower, and km moves out to larger values. The steeper slope for ULAs compared to WDM means that models with the same half-mode will not have kJ = kF S (where kF S is the WDM free-streaming scale, which some authors define differently), and vice versa. Matching Jeans and free-streaming scales, axions will have more power on larger scales relative to WDM; matching the half-mode, axions will have less power on small scales relative to WDM. We choose always to match the transfer function half-mode, since it is well-defined for both models. "
+  ],
+  "2.2 Mass Scales ": [
+    "We associate characteristic masses to scales k through the mass enclosed within a sphere of radius the half wavelength λ/2 = π/k: ",
+    "(8) ",
+    "where ρ0 is the matter density. ",
+    "In particular, using k = km we can expect suppression of the formation of halos below Mm caused by the decrease in linear power on these scales. We have shown the effects in the transfer function with low axion fraction for illustration, but as we will see in Section (<>)4 the only axion fractions relevant for producing cored density profiles are large, Ωa/Ωm  0.85, and so the characteristic scales will be very close to their values for the pure ULA DM case. Mass scales relevant for halo formation cover axions in the range 10−24 eV  ma  10−20eV. Axions lighter than this are well probed by the CMB and the linear matter power spectrum ((<>)Amendola & (<>)Barbieri (<>)2006; ?), while those heavier are probed by su-permassive black holes ((<>)Arvanitaki & Dubovsky (<>)2011; (<>)Pani et al. (<>)2012) and terrestrial experiments ((<>)Jaeckel (<>)& Ringwald (<>)2010; (<>)Ringwald (<>)2012a,(<>)b). In Fig. (<>)2 we plot Mm(ma) for the pure ULA cosmology and find it to be fit well by a power law Mm ∝ m−a γ with γ ≈ 1.35 by least squares over the range of interest. This is very close to the value γ = 4/3 using the fit of (<>)Hu, Barkana (<>)& Gruzinov ((<>)2000). ",
+    "In Fig. (<>)2 we also show the Jeans mass, MJ , which is lower by more than two orders of magnitude than Mm. The axion Jeans scale is analogous to the WDM free-streaming scale, where Mfs is also some orders of magnitude lower than Mm ((<>)Angulo, Hahn & Abel (<>)2013). ",
+    "Solving Eq. ((<>)4) for the half-mode with WDM and using the fit with γ = 1.35 to match Mm(mW ) to Mm(ma), we plot mW (ma) in Fig. (<>)3. The power law relating them is mW ∝ ma0.39 . Our matching to WDM mass applies to thermal relics like gravitinos, and on Fig. (<>)3 we show the constraint on thermal relics of mW > 0.55 keV from Lyman-α forest data reported in (<>)Viel (<>)et al. ((<>)2005). This translates to a constraint on axion mass of ma > 5 × 10−23eV, which is consistent with the Lyman-α constraints on ULAs reported in (<>)Amendola & (<>)Barbieri ((<>)2006). The more recent Lyman-α constraints to WDM, such as (<>)Viel et al. ((<>)2013) (mW  3.3keV) are much stronger, but there is no corresponding constraint to axions using this data to compare to. ",
+    "Lyman-α constraints are sensitive to the exact shape of the transfer function: since mass goes as radius cubed, small differences between the transfer functions of ULA and WDM models will be amplified to larger differences in the associated mass scales. Lyman-α constraints also require careful calibration with hydrodynamical simulations (as done in e.g. (<>)Viel et al. (<>)2013). Such simulations are available for CDM and WDM models, but not for ULAs, making the simple comparison of constraints by mass scale perhaps too naive. ",
+    "Figure 2. The characteristic mass associated to the half-mode, km, of the transfer function as a function of axion mass, Mm(ma), found from Eqs. ((<>)5) and ((<>)8). It is well fit by a power law Mm ∝ m −a γ with γ ≈ 1.35. We also show the mass associated to the Jeans scale of Eq. ((<>)6), which is lower by two to three orders of magnitude. ",
+    "Figure 3. Thermal relic warm dark matter mass in keV chosen to give the same transfer function half-mode, km (Eq. ((<>)5)), as a ULA, as a function of ULA mass in eV. We also show the Lyman-α forest constraints mW > 0.55 keV of (<>)Viel et al. ((<>)2005) corresponding to ma > 5 × 10−23 eV, consistent with (<>)Amendola & Barbieri ((<>)2006). ",
+    "The variance of the power spectrum, σ(M), is computed by smoothing the power spectrum using a spherical top-hat window function of size R, and is done within CAMB: ",
+    "(9) ",
+    "(10) ",
+    "In Fig. (<>)4 we show the variance associated to the same models as in Fig. (<>)1. The variance for the aMDM models varies little when the fraction is changed between Ωa/Ωd = 1 and Ωa/Ωd = 0.5, and is comparable to the associated WDM variance. ",
+    "Figure 4. Variance σ(M) for ΛCDM, and aMDM with various Ωah2 at fixed total Ωdh2 = 0.112 and axion mass ma = 10−22 eV. ",
+    "In the sections that follow we investigate the suppression of halo formation at and below Mm in axion models in more detail. "
+  ],
+  "3 THE HALO MASS FUNCTION ": [
+    "The MSP arises with CDM due to a larger expected number of low mass haloes than the number of low mass satellites observed in the Local Group (see e.g. (<>)Primack ((<>)2009) for a review). ",
+    "To quantify this problem in various models we adopt the Press-Schechter (PS) approach ((<>)Press & (<>)Schechter (<>)1974) to compute the abundance of halos of a given mass: the halo mass function (HMF). In the usual formalism this gives ",
+    "(11) ",
+    "(12) ",
+    "where dn = n(M)dM is the abundance of halos within a mass interval dM. For the function f(ν) we use the model of (<>)Sheth & Tormen ((<>)1999) (ST): ",
+    "with parameters {A = 0.3222, p = 0.3, q = 0.707}. The remaining ingredient in this approach is the critical overdensity, δc, and what to do on mass scales M < Mm, both of which we now discuss. "
+  ],
+  "3.1 Mass Dependent Critical Density from Scale Dependent Growth ": [
+    "In the case where all of the DM is made up of ULAs, as we saw in Fig. (<>)1, there is no structure formed below ",
+    "kJ , and so we should expect no peaks in the density field, and thus no halos, below the mass scale MJ . However, applying the PS formalism described above with a constant barrier δc leads to a non-zero mass function for M < MJ . In the case of WDM this discrepancy is modelled in (<>)Smith & Markovic ((<>)2011) by the addition of a smooth step in dn/d log M at M = Mf s. In the analytical results of (<>)Benson et al. ((<>)2012) a much sharper cut-off was seen, and was attributed in part to a strong mass dependence in δc, which was seen to increase rapidly below Mf s. A shallower cut-off was seen in the numerical results of (<>)Angulo, Hahn & Abel ((<>)2013). In the recent work of (<>)Schneider, Smith & Reed ((<>)2013) the cut-off due to free-streaming in WDM was investigated, and also found to be shallower than (<>)Benson (<>)et al. ((<>)2012). (<>)Schneider, Smith & Reed ((<>)2013) advocate a sharp k-space window function to match simulations and remove spurious structure thus providing the source of the cut-off: investigating different cut-offs and mass functions in aMDM will be the subject of a future work. ",
+    "In the absence of numerical simulations for ULA DM, or an existing treatment of the excursion set and spherical collapse in these models, one does not know what form the cut-off in the HMF near MJ should take. In addition, for mixed dark matter models where the small-scale power is not entirely erased but only suppressed, one does not know how much (additional, ad hoc) suppression to introduce. In this subsection we make a physically motivated argument for a mass dependent increase in δc at low M that should account in some way for additional suppression in the HMF for M < Mm. ",
+    "Since we use results from CAMB, we take the over-density δ to evolve with redshift, and in an Einstein-de Sitter (EdS) universe, take the critical overdensity to be fixed, δc = δEdS ≈ 1.686. Alternatively, one can view the overdensity as being fixed, and take δc to evolve with redshift as δc(z) = D0δEdS/D(z) ((<>)Percival, Miller (<>)& Peacock (<>)2000; (<>)Percival (<>)2005), which accounts for the growth between z and z = 0. The growth factor D(z) is given by ",
+    "In the aMDM model, there is scale-dependent growth (see e.g. (<>)Acquaviva & Gawiser (<>)2010; (<>)Marsh et al. (<>)2012), and we use this to model the change in δc with scale. For the relatively heavy axions we consider here the growth at the pivot scale k0 = 0.002 h Mpc−1 is the same as in ΛCDM, while it is much smaller at k > km. We take δc(k) at z = 0 to be altered by an amount D(k0)/D(k), and normalise by the same ratio in ΛCDM (to take account of the small amount of scale-dependent growth there). In the interests of simplicity, we will only be concerned with examples of the HMF at z = 0 and take δc(z = 0, k = k0) = δEdS, which is good to within a few percent for ΛCDM ((<>)Percival (<>)2005)3 (<>). At redshift ",
+    "z = 0 our model takes ",
+    "Two, not entirely unrelated, issues arise with model when trying to extract the growth from a Boltzmann code. The first is that to use this model we must disentangle growth from transfer function, which is definition somewhat problematic in the case of scale-dependent growth. Defining the transfer function the piece which depends solely on k this can only done with the logarithmic derivative d log δ/d log d log D/ log a, which does not give us the absolute value at z = 0 that we seek. We take a more practical nition suited to numerical computation. In ΛCDM, transfer function freezes in somewhere around the coupling epoch ((<>)Eisenstein & Hu (<>)1997), when matter domination is total. This provides a definition of the scale-dependent growth at z = 0 which is easily accessible from a numerical solution for δ(k, z), normalised such that D(k = k0) = 1: ",
+    "(17) ",
+    "where zh is chosen so that in ΛCDM the transfer function has frozen in, and k0  km is the pivot scale. Using CAMB, we find zh ≈ 300 works well. We then use exactly the same definition to set the scale of D(k) in the aMDM case. ",
+    "Scale dependent growth causes the mass dependent critical density to increase below M ≈ Mm. Fig. (<>)5 shows G(M) for these models. There is the obvious trend that G(M) decreases with increasing CDM fraction. ",
+    "The second issue is that if the axions completely dominate the matter density then the overdensity will become vanishingly small for k  km even at high redshift, and so we are faced with the problem of dividing zero by zero to set the scale of D(k). This is a numerical precision problem and, when combined with BAO distortions, leads to the spikey/oscillatory behaviour of G(M) for Ωc/Ωd  0.01 in Fig. (<>)5. "
+  ],
+  "3.2 HMF Results ": [
+    "In Fig. (<>)6 we plot the HMF with a fixed axion mass of ma = 10−22eV for a variety of values of the axion density, with fixed total Ωdh2 = 0.112. We see suppression of the mass function beginning at Mm, with the amount of suppression increasing and the asymptotic slope of the mass function decreasing as we raise the axion density. We show results taking δc fixed, and those with mass dependent δc(M), modelled for as above. ",
+    "The introduction of scale-dependent growth via ",
+    "quintessence cosmologies in (<>)Tarrant et al. ((<>)2012) found that even in ΛCDM δc(z = 0) can differ from δEdS by more than this amount. ",
+    "Figure 5. The mass dependent critical density from scale-dependent growth, Eq. ((<>)16), is given by δc(M) = G(M)δEdS. We show G(M) for aMDM with various Ωc/Ωd at fixed total Ωdh2 = 0.112 and axion mass ma = 10−22 eV. The spikes at low fraction are due to BAO distortions and numerical instability defining scale-dependent growth via a ratio. ",
+    "G(M) in Fig. (<>)6 causes the HMF to be sharply cut off at around M ≈ 108 h−1M ≈ 0.01Mm with large axion fraction. This is in agreement with the cut-off of (<>)Smith (<>)& Markovic ((<>)2011) and the numerical results of (<>)Angulo, (<>)Hahn & Abel ((<>)2013) for WDM: the HMF falls below its ΛCDM value at the half-mode mass, but only cuts off completely at a lower mass, intermediate between the Jeans (free-streaming for WDM) mass and the half-mode mass. By considering fragmentation of proto-halo objects formed in WDM cosmologies (<>)Angulo, Hahn & (<>)Abel ((<>)2013) found a smoother cut-off in the HMF than the sharp cut-off of (<>)Benson et al. ((<>)2012) coming from analytic results. By the time we reach the Jeans scale of MJ ≈ 1.1×107 h−1M the mass function for Ωa/Ωd = 1 is vanishingly small, more than eight orders of magnitude below its ΛCDM value. ",
+    "In Fig. (<>)7 we plot the HMF evaluated at various masses near M = 0.01Mm as a function of fc = Ωc/Ωa at low fc to investigate the effect of a small admixture of CDM on the value of the mass function at the cut-off. Varying fc between 1 and 15% can change the value of the HMF near the cut-off by two orders of magnitude. The small admixture of CDM can help an aMDM model form dwarf halos near the HMF cut-off. ",
+    "The low values of fc  0.13, as we will see in Section (<>)4.3, are those relevant for core formation with aMDM. At larger values of fc approaching the equally mixed DM fc = 0.5 the sharp cut-off in the HMF has vanished, although it is still significantly reduced compared to ΛCDM. The large admixture of CDM, if the need for cores is foregone, still remains relevant to the MSP and introduces no potentially problematic cut-off in the HMF. ",
+    "Figure 6. Halo mass function computed directly from CAMB for ΛCDM, and aMDM with various fc = Ωc/Ωd at fixed total Ωdh2 = 0.112 and axion mass ma = 10−22 eV. Solid lines have δc(M) while dashed lines have δc = δEdS. At fc = 0.5 the cut-off is no longer present in the mass range shown, the difference between δEdS and δc(M) having largely vanished. The spikes at low fraction are due to BAO distortions and numerical instability defining scale-dependent growth via a ratio. ",
+    "Figure 7. The HMF evaluated at M = 1 × 108 h−1M ≈ 0.01Mm and M = 0.8× 108 h−1M for aMDM as a function of fc = Ωc/Ωd at fixed total Ωdh2 = 0.112 and axion mass ma = 10−22 eV. The HMF decreases rapidly below the cut-off, at around 1% of the half-mode mass. Varying the CDM fraction between 1 and 15% can change the value of the HMF at the cut-off by two orders of magnitude. ",
+    "Scale dependent growth in aMDM induces a cut-off in the HMF similar to the cut-off observed in numerical simulations of WDM. In (<>)Angulo, Hahn & Abel ((<>)2013) the cut-off in WDM simulations could be fit by introducing non-spherical filtering to compute σ(R). By assigning masses to radii differently for WDM compared to CDM after accounting for formation of halos by fragmentation this cut-off was made less severe. In order to discuss the assignment of masses to halos in aMDM we now move on to model the halo density profile and its normalisation. "
+  ],
+  "4 HALO DENSITY PROFILE ": [
+    "The Catch 22 ((<>)Maccio’ et al. (<>)2012a) of solving the CCP with WDM is that the WDM particle mass required to introduce a core of sufficient size in a dwarf galaxy serves to cut off the HMF at exactly the mass of the dwarf, so that it is never formed. At the same time, WDM allowed by constraints from LSS does not form cores of relevant (kiloparsec) size. In order to ascertain whether the Catch 22 applies to aMDM, or indeed to the case of pure axion DM, we must must model the expected core size. ",
+    "We follow (<>)Hu, Barkana & Gruzinov ((<>)2000) and associate a core size to the Jeans scale within the halo, rJ,h, below which the density will be assumed constant 4 (<>). The Jeans scale within the halo is related to the linear Jeans scale, rJ , by scaling the energy density in Eq. ((<>)6) ",
+    "(18) ",
+    "Thus we can determine the linear Jeans scale (and so the ULA mass) necessary to provide a given core size inside a dwarf halo, if we know the external profile ρ(r). The assumption inherent in Eq. ((<>)18) is that the coherent effects in the scalar field giving rise to the Jeans scale survive in the non-linear regime when mode mixing becomes important and the linear derivation of the sound speed in Eq. ((<>)2) may break down. N-body/lattice simulations of the axion field are needed to test this assumption. ",
+    "Assuming that collapse occurs as in ΛCDM, (<>)Hu, (<>)Barkana & Gruzinov ((<>)2000) computed ρ0/ρ(rJ,h) and found that a core of size rJ,h ∼ 3.4 kpc is obtained in a dwarf halo of mass 10 10 M for an axion of mass ma = 10−22 eV. As we have seen, the HMF for such a ULA is only cut off for M  108h−1M suggesting that axions do not suffer the Catch 22 of WDM. ",
+    "In the following section we address this is in a more ",
+    "detailed model of aMDM. Firstly, we compute halo parameters with the pure ULA variance, normalise our cored halo profile, and find the relationship between ULA mass and core size in a representative Milky Way satellite. The picture that emerges is qualitatively the same as (<>)Hu, Barkana & Gruzinov ((<>)2000), but quantitatively different. Secondly, we extend this picture to a two-component profile and ask whether cores can be maintained as a small admixture of CDM is added. ",
+    "The definition of zcoll in Eq. ((<>)20), and hence the concentration defined from it will go to zero for a variance that flattens out at low masses, as is the case for aMDM with small CDM fraction. The lower concentration of low mass halos in comparison to ΛCDM will be relevant for MFP, which we discuss in Section (<>)5. Since zcoll is also lower, in Section (<>)6 we discuss the collapsed mass fraction and potential conflicts with observations of high-redshift galaxies. "
+  ],
+  "4.1 The NFW Profile ": [
+    "For the external profile, ρ(r), outside of the Jeans scale where the ULA behaves as CDM, we use the universal radial density profile of (<>)Navarro, Frenk & White ((<>)1997) (hereafter, NFW): ",
+    "(19) "
+  ],
+  "4.2 Halo Jeans Scale For Pure Axion DM ": [
+    "In this subsection we consider the core size, and nor-malisation of halos in a pure ULA dark matter model. We assume collapse occurs as in ΛCDM, with D(z), but use the axion variance, σ(M). ",
+    "For definiteness, we consider halos with the simplest possible cored profile ",
+    "where the scale radius rs = r200/c, with r200 the virial radius, c the concentration parameter, and δchar the characteristic density. ",
+    "The characteristic density is assumed to be proportional to the density of matter in the universe at the collapse redshift of the halo, zcoll. The definition of zcoll(M) is fixed for NFW and follows from Press-Schechter (see also (<>)Lacey & Cole (<>)1993) : ",
+    "(20) ",
+    "The NFW profile is fit with f = 0.01. As above we work in the convention where δc is constant but the overden-sities themselves evolve with linear growth factor D(z). The characteristic density is then ",
+    "(21) ",
+    "where C = 3.4 × 103 is fit by NFW to simulations of CDM, which should match axion DM above the Jeans scale. ",
+    "The virial radius is defined as the radius at which the average enclosed density is 200 times the mean density, in terms of the halo mass M at redshift z = 0 it is given by: ",
+    "For the NFW profile the concentration and scale radius, with the correct choice of C, are defined such that M = M200. For the cored profile that we discuss below the scale radius of the external NFW profile does not have the same relationship with the true virial radius, and we normalise separately for M200. ",
+    "Finally, the concentration is defined from the characteristic density, δchar, by ",
+    "where θ(x) is the Heaviside function, although much of what we say below will apply to any cored profile with core radius rc = rJ,h fixed by Eq. ((<>)18)5 (<>). In particular, the choice of a Heaviside function introduces sharp transitions into the density profile, and as such is only for illustration. The external NFW profile is consistent with what is observed in the WDM simulations of (<>)Mac-(<>)cio’ et al. ((<>)2012a). ",
+    "In order to find the Jeans scale within a halo we must solve Eq. ((<>)18) for an NFW profile with external profile normalisation fixed at Ms (the ‘scale mass’), and shape fixed by scale radius rs(Ms) = r200(Ms)/c(Ms) to find rJ,h(Ms). This is not the Jeans scale within a halo of mass M = Ms: the mass Ms is the mass that an equivalent NFW profile would have. We will discuss normalisation of M shortly. ",
+    "We use the variance for the axion model to compute our NFW halo parameters: using the ΛCDM variance, the halo Jeans scales with fixed Ms will be differ-ent. With low Ms relative to Mm the concentration is lower when the correct variance is used, which causes the Jeans scale to be smaller by the increase in scale radius relative to r200. On the other hand the Jeans scale within intermediate and high mass objects is found to be larger with the correct variance. For example, with ma = 10−21 eV the shift in halo Jeans scale inside dwarf galaxies can be of order 0.1 h−1kpc. ",
+    "The Jeans scale decreases in higher density environments and therefore the positive real solution of Eq. ((<>)18) is a monotonically decreasing function of Ms. At low enough Ms, then, one finds rJ,h > rJ . This cannot be a physical solution. Solutions to Eq. ((<>)18) giving rJ,h > rJ can only occur when ρ/ρ0 < 1, which represents a void ",
+    "Figure 8. Halo profiles of Eq. ((<>)24) (solid lines) with various M200 compared to their parent NFW profiles of mass Ms ≈ M200 (dot-dashed lines). The axion mass is ma = 10−22 eV and we show the linear Jeans scale, rJ = 31.2 h−1 kpc (vertical dashed line). As long as halo becomes overdense outside of rJ it can continue to be overdense inside until it reaches the halo Jeans scale, rJ,h satisfying Eq. ((<>)18). More massive halos are more dense at rJ and the halo Jeans scale is smaller. No profiles form with Ms < Mlow when the NFW parent has not become overdense outside of rJ (although they may form by fragmentation). ",
+    "and not a halo 6 (<>). This break at rJ = rJ,h will occur at a certain mass, Mlow(M, rJ ), which is a function of the linear Jeans scale. It is found by solving ",
+    "(25) ",
+    "This tells us that no cored halos with normalisation Ms < Mlow exist for fixed rJ . Cored halo profiles of various masses are shown in Fig. (<>)8 and compared to their parent NFW profiles, with the linear Jeans scale shown for scale. It is clear that no halos should form that do not already become overdense outside rJ . In the example, with rJ = 31.2 h−1 kpc, this implies that halos with Ms = 4 × 108h−1M only just form. ",
+    "Given that no halos form with external scale Ms < Mlow, what is the minimum halo mass in this model? A halo is normalised to mass M200 by the integral out to the virial radius, r200 ",
+    "This defines M200(Ms). Since the Jeans scale within halos is a monotonically decreasing function of Ms, at ",
+    "some scale mass Mnon−vir the solution for r200 will occur when ρNFW(Mnon−vir, rJ,h(Mnon−vir)) = 200ρ0. Halos with scale mass Ms < Mnon−vir will not be virialised in the sense that their average density never exceeds 200 times the background density. In order to assign mass to these halos one cannot use M200. The total enclosed mass is found by integrating out to ρ(r1) = ρ0. With this alternative definition of mass it is clear that the lowest mass object formed at Ms = Mlow is at exactly the Jeans mass, MJ . ",
+    "Halos with M < M200(Mnon−vir) will also need to have masses assigned to radii coming form the linear filtering in σ(M|R) in the HMF in a different manner than is applicable to CDM. This is accounted for by fits to simulations in (<>)Angulo, Hahn & Abel ((<>)2013) and is partly responsible for the less severe cut-off in the HMF found in that work. By comparison, if we made the same assignment in the HMF with pure axion DM, the cut-off found by introducing scale-dependent growth might also become less severe. ",
+    "We typically find that, for Ms > Mnon−vir, r200 for the cored profile is approximately the same as for the parent NFW, and that M200 ≈ Ms. Approaching Mnon−vir, M200 drops below Ms. ",
+    "Finally, having normalised our halos, we show in Fig. (<>)9 the core size expected in the typical Milky Way dwarf galaxy of mass M200 = 5 × 108 h−1M as a function of axion mass for the heavier axions ma  10−22 eV allowed by the relevant Lyman-α constraints. The core size is well fit by a single power law in axion mass. The best fit power law has rJ,h ∼ m−a 0.87 , while the power law given in (<>)Hu, Barkana & Gruzinov ((<>)2000) is rJ,h ∼ ma−2/3 . (<>)Hu, Barkana & Gruzinov ((<>)2000) used approximate formulae to solve Eq. ((<>)18) and do not give the dependence of the concentration on axion mass. The dependence of the concentration on axions mass comes from computing NFW parameters with the correct variance and leads to the different power law. ",
+    "We find that there is a considerable core size for all masses considered. In particular, even our heaviest axion with ma = 10−20 eV has a core size of rJ,h = 0.1 h−1 kpc. This heaviest axion has a characteristic mass scale of Mm = 108 h−1M and would not affect the formation rate of these dwarf galaxies in any dramatic way. This demonstrates that pure ULA dark matter does not suffer from the Catch 22 of WDM: ULAs allowed by even the most stringent large scale structure constraints, which would barely affect the HMF at Milky Way satellite masses, can still give significant cores to dwarf galaxies. "
+  ],
+  "4.3 A Mixed Dark Matter Halo Profile ": [
+    "Having understood the simple cored profile in pure axion DM, we now move on to consider the two-component dark matter subclass of aMDM (see (<>)Medvedev ((<>)2013) and references therein for recent work on two-component DM halos). In this subsection we continue to assume ΛCDM growth. We study axion mass ",
+    "Figure 9. The expected core size in a typical Milky Way satellite of mass M200 = 5 × 108 h−1M as a function of axion mass, ma. The relationship is well fit by a simple power law, shown as m−a 0.87 , but due to the dependence of the concentration on ma this is not the scaling of rJ with ma. The core size is fairly significant,  0.1 h−1 kpc, across the entire mass range, which demonstrates that axions satisfying all large scale structure constraints can provide a potentially viable resolution of the cusp-core problem in CDM halos. ",
+    "Figure 10. The mixed dark matter halo profile Eq. ((<>)A1) with 13% CDM, fc = 0.13. The outer region is an NFW profile of mixed axions and CDM. The halo mass is M200 = 5 × 108h−1M and the halo Jeans scale rJ,h = 5.4 h−1 kpc (outer vertical dashed line) corresponds to axion mass ma = 10−22 eV with this particular DM composition. At the halo Jeans scale the axions stop clustering and form a uniform component, while the CDM forms an NFW cusp. There is a core down to rcore = 2.1 h−1 kpc where the cusp takes over from the uniform piece (inner vertical dashed line). ",
+    "ma = 10−22 eV and a benchmark halo with M200 5 × 108 h−1M. ",
+    "Again, we take the halo density profile to be NFW outside of the halo Jeans scale, while inside the Jeans scale we take the axion component to be smooth. Inside this smooth background we then assume CDM component of the DM collapses as usual and forms its own NFW halo. Because the axion component smooth inside this radius, we superpose the profiles therefore below the Jeans scale the ratio of axions CDM is not constant but decreases at small radius. This is in agreement with the simulations of mixed cold warm DM in (<>)Anderhalden et al. ((<>)2012). The assumed 2-component profile is given in Appendix (<>)A. ",
+    "The size of the cored region depends on the fraction of DM that is cold: fc = Ωc/Ωd. For r < rcore Eq. ((<>)A3)) there is a cusp while for rcore(fc,Ms) < rJ,h(Ms) there is a core. We plot the halo profile fc = 0.13 in our benchmark halo in Fig. (<>)10, while we plot rcore(fc) for our benchmark halo in Fig. (<>)11. We judge the core to be of significant size if it persists down to < 50% of the halo Jeans scale. With fc = 0.13 the benchmark axion mass and halo corresponds to a core in the range 2.1 h−1 kpc  r  5.4 h−1 kpc. ",
+    "Although this benchmark core is significant, it is actually not present on sub-kiloparsec scales, which suggests that while introducing a fraction of CDM with an axion of mass 10−22 eV may raise the HMF for low mass dwarf galaxies to acceptable levels, it may not provide a totally adequate solution to the CCP. As we will see below, a more preferable solution to all the problems outlined may be given instead by a higher axion mass. ",
+    "Figure 11. Core radius and halo Jeans scale as a function of CDM fraction, fc = Ωc/Ωd, in the two component halo (Eq. ((<>)A1)). There is a core for rcore < r < rJ,h, while there is a cusp for r < rcore, so that increasing fc makes halo profiles more cuspy, as expected. The halo mass M200 = 5 × 108h−1M and the axion mass ma = 10−22 eV. "
+  ],
+  "5 TOO BIG TO FAIL? ": [
+    "The so-called ‘Too Big To Fail’ problem (here ‘Massive Failures Problem’, MFP) was introduced by (<>)Boylan-(<>)Kolchin, Bullock & Kaplinghat ((<>)2011). In ΛCDM there are predicted to be massive subhaloes of the milky way of high concentration and circular velocity that cannot ",
+    "Figure 12. Halo concentration parameter, c(M) for ΛCDM and various axion masses. The flattening of the variance near Mm causes a later formation time for low mass halos, and due to the presence of f = 0.01 in Eq. ((<>)20) leads to a lower concentration for halos below fMm. The lowered concentration can help alleviate the ‘Too Big To Fail’ problem. ",
+    "host bright satellites, and are not observed. One astrophysical solutions to this problem is feedback ((<>)Garrison-(<>)Kimmel et al. (<>)2013). WDM ((<>)Lovell et al. (<>)2012) and C+WDM ((<>)Maccio’ et al. (<>)2012b; (<>)Medvedev (<>)2013) are also known to help this problem, since the flattened variance leads to later formation times and lower concentration for these most massive subhaloes. ",
+    "Since the variance, σ(M) in aMDM also flattens at low masses, just like WDM it will lead to a lower concentration for Milky Way sub-haloes compared to ΛCDM if the subhalo mass is lower than fMm (see Eq. ((<>)20)). In Fig. (<>)12 we plot c(M200) for three representative axion masses, ma = 10−22 ,10−2110−20 eV and compare to ΛCDM, confirming that this is the case. ",
+    "MFP can also be expressed as the non-observation of large numbers of satellites with maximum circular velocity vmax  40 km s−1 . The circular velocity as a function of r is given by ",
+    "(27) ",
+    "In Fig. (<>)13 we plot v(r) for a halo of mass M200 = 2 × 1010 h−1M. In ΛCDM this halo has vmax > 40 km s−1 . We compare this to v(r) where the DM is made up of an axion of mass ma = 10−22 eV, and to WDM. The axion and WDM halos are chosen to have the same rmax as ΛCDM, having M200 = 1010 h−1M. Both the axion and WDM models reduce the maximum circular velocity considerably: vmax ≈ 30 km s−1 . ",
+    "For WDM we do not model the effect of a possible core, and so for fair comparison we show the axion model with both a cored and NFW profile. The effect of the core in the axion model is small, so that the assumption of core formation does not affect an axion solution to MFP. ",
+    "Figure 13. The circular velocity profile for a one component DM halo in various models, derived from the NFW profile. For ΛCDM we have chosen a halo with M200 = 2 × 1010 h−1M which has a maximum circular velocity vmax > 40 km s−1 , demonstrating that CDM suffers from the ‘Too Big To Fail’ problem. We compare to axion and WDM models with M200 = 1010 h−1M chosen such that they have the same rmax as ΛCDM. Both axions and WDM suppress vmax by a factor of about 1.5 relative to ΛCDM, demonstrating their relevance for the solution to MFP. The core in the axion density profile does not affect the suppression of vmax. We choose axion mass ma = 10−22 eV and equivalent WDM mass of mW ≈ 0.84 keV. "
+  ],
+  "6 HIGH REDSHIFT OBJECTS ": [
+    "We now move on to discuss the collapse redshift of objects to see whether ULAs can accommodate observations of high-redshift galaxies. We consider collapse with ΛCDM growth given by D(z), ignoring for the moment the scale-dependent growth, which will only serve to amplify effects below the characteristic mass. All the effects of axions therefore come in the variance, σ(M). For the large axion fractions relevant for core formation in the two-component halo of Section (<>)4.3 the effects of CDM on the variance are virtually negligible, so in our examples we take Ωa/Ωd = 1 and investigate only the effects of varying axion mass. ",
+    "The total fraction of objects collapsed with M > Mmin at redshift z is ",
+    "We plot this assuming ΛCDM growth for Mmin = 106 h−1M in Fig. (<>)14. For our benchmark mass ma = 10−22 eV the collapsed mass fraction F(z  6)  0.01 putting such a light axion in considerable tension with observations of high redshift galaxies. ",
+    "Using the scale-dependent growth to assign a mass-dependent critical density for collapse as in Eq. ((<>)16) provided a good working model for the cut-off in the HMF, however we cannot naively apply such a prescription for δc into Eq. ((<>)28): such a cut-off would make the collapsed ",
+    "Figure 14. Total collapsed mass fraction, Eq. ((<>)28), with Mmin = 106 h−1M with varying axion mass. We ignore scale-dependent growth and take the axions to make up all of the DM. ",
+    "mass fraction non-monotonic. The ansatz of Eq. ((<>)16) applies only in the HMF and takes the HMF as fundamental, so the analog of Eq. ((<>)28) is properly defined in this framework as the integral of the HMF. The redshift dependence of such an integral requires us to know the full function D(k,z). Alternatively one could make a fit for the HMF with the ansatz that the cut-off remains always a fixed geometric distance between Mm and MJ as they evolve with redshift. We do not explore this effect of the cut-off on the collapsed mass fraction as a function of redshift, but the qualitative effects are obvious: scale-dependent growth should amplify the effects we have seen already in Fig. (<>)14. ",
+    "Knowing the HMF at z = 10 allowed the authors of (<>)Pacucci, Mesinger & Haiman ((<>)2013) to place constraints on a WDM thermal relic of mW > 0.9 keV using high redshift observations. Using our mass scale conversions of Section (<>)2.2 we might expect such observations to constrain ma  few × 10−22eV, as the simple argument based on collapsed mass fraction with ΛCDM growth given above anticipates. ",
+    "Suppression of galaxy formation at high redshift has been invoked as a possible solution to another problem of structure formation in ΛCDM: the discrepancy in the evolution of the stellar mass function between observations and models, highlighted in (<>)Wein-(<>)mann et al. ((<>)2012). ULAs were invoked, along with WDM, by these authors as a solution. Again, as with Lyman-α constraints, access to hydrodynamical simulations with WDM allowed for a detailed comparison of models to observations, and showed a WDM solution to most likely be unviable. Do ULAs remain a viable solution? We have shown in previous sections that there are enough differences between ULAs and WDM that this is possible, but without simulations one cannot quantify ",
+    "this. However, in this section we have confirmed the suppression of halo formation at high redshift necessary for ULAs to be an interesting candidate for further study in this regard. "
+  ],
+  "7 SUMMARY AND DISCUSSION ": [
+    "By studying large scale structure we have probed ultralight axion-like-particles (ULAs) with masses in the range 10−24 eV  ma  10−20 eV. Across a fair portion of this range such ultra-light fields can evade large-scale structure constraints while still being different enough from standard CDM on scales relevant to three main problems of structure formation: the missing satellites problem (MSP), the cusp-core problem (CCP), and the massive failures problem (MFP). We have primarily studied a benchmark ULA of mass ma = 10−22 eV and shown that it is able to solve the MSP, CCP and MFP, avoiding the so-called Catch 22 of a WDM solution. If this axion constitutes all of the DM, however, then it may come into tension with observations of the Lyman-α flux power spectrum (which constrains WDM at masses mW  3.3 keV), high-redshift galaxies (at z  6) and the existence of very low mass dwarf galaxies (M  5 × 107 h−1M). These tensions can be relieved in two ways: by introducing a fraction of CDM or increasing the axion mass. Introducing a fraction of CDM retains adequate solutions to all problems, but cores may yield to cusps at unacceptably large radii. We advocate a higher mass axion of ma  10−21 eV as potentially the best solution. ",
+    "If all the DM is constituted of an axion or other light scalar of mass ma = 10−22 eV then in the linear power spectrum structure formation is suppressed below some characteristic scale (Fig. (<>)1). The half-mode for this suppression is the same as the half-mode for a WDM particle of mass mW ≈ 0.84 keV, just on the edge of the bounds coming from Lyman-α forest flux power spectrum constraints (Fig. (<>)3). By considering scale-dependent growth it has been shown that such an axion will cut off the halo mass function for M  108 h−1M. Introducing a fraction of CDM, fc = Ωc/Ωd, the cut-off is made less severe, disappearing completely and leaving only a small suppression to dwarf galaxy formation when fc ≈ 0.5 (Fig. (<>)6). This mixed dark matter model, aMDM, may therefore be relevant to the MSP. Such a mix of DM may be natural given certain theoretical priors ((<>)Aguirre & Tegmark (<>)2005; (<>)Wilczek (<>)2004; (<>)Tegmark (<>)et al. (<>)2006; (<>)Bousso & Hall (<>)2013; (<>)Wilczek (<>)2013), or in non-thermal cosmologies expected after moduli stabili-sation (e.g. (<>)Acharya, Bobkov & Kumar (<>)2010; (<>)Acharya, (<>)Kane & Kuflik (<>)2010). ",
+    "If the axion linear Jeans scale can be considered to scale into non-linear environments as the fourth root of the relative density contrast (Eqs. ((<>)6), ((<>)18)), requiring coherence of field oscillations to be maintained, then ultra-light axions can give cores to dwarf galaxy density profiles ((<>)Hu, Barkana & Gruzinov (<>)2000). By considering ",
+    "a simple cored profile given by an external NFW pro-file outside the Jeans scale, it was shown that in such a scenario no halos are formed below the linear Jeans mass, MJ . Axions in the mass range 10−22 eV  ma  10−20 eV can give kiloparsec scale cores to dwarf galaxies of mass M = 5 × 108 h−1M, and are thus relevant to the CCP of CDM halo density profiles (Figs. (<>)8, (<>)9). Since the halo mass function is only cut off below the dwarf mass, and axions in this mass range are allowed by large-scale structure constraints, we can conclude that in this simple model ultra-light axions, or other ‘Fuzzy’ CDM candidates, do not suffer from the Catch 22 that might affect WDM ((<>)Maccio’ et al. (<>)2012a). ",
+    "For an axion mass at the low end of the range allowed by large-scale structure constraints, ma ≈ 10−22 eV, to form lighter dwarf galaxies of M  5 × 107 h−1M, however, the mixed aMDM is necessary. By considering a two-component density profile below the axion Jeans scale it was shown that an admixture of fc ≈ 13% will significantly increase the mass function for light dwarves (Fig. (<>)7), while still allowing for a core on scales greater than a kiloparsec (Fig. (<>)10, (<>)11), although such a core may in fact be too large. ",
+    "The flattened variance in aMDM (Fig. (<>)4) in the NFW formalism leads to later formation times and consequently lower concentrations for low mass halos compared to CDM (Fig. (<>)12). This, combined with maximum circular velocity remaining low, vmax < 40km s−1 , in typical dwarves (Fig. (<>)13), also suggests that ULAs may, just like WDM, play a role in the resolution of the MFP ((<>)Boylan-Kolchin, Bullock & Kaplinghat (<>)2011). ",
+    "While avoiding the Catch 22 in an axion cusp-core and missing satellites resolution an axion mass as low as ma = 10−22 eV comes into tension with high-redshift observations since the collapsed mass fraction becomes very small at z  6 (Fig. (<>)14). A heavier axion of mass ma  10−21 eV would be in less tension with observations of high-redshift galaxies (and more recent Lymanα forest constraints to WDM) and could still introduce a kiloparsec scale core to dwarf galaxies and significantly lower the concentration of these galaxies. The formation of dwarves would still be significant, yet also reduced relative to ΛCDM, so that such heavier axions remain relevant to the cusp-core, missing satellites, and ‘too big to fail’ problems of CDM. Suppression of galaxy formation at high redshift relative to ΛCDM may also be a factor in resolving conflicts between models and observations of the stellar mass function ((<>)Weinmann et al. (<>)2012). ",
+    "With large axion fractions (<>)Marsh et al. ((<>)2013) showed that isocurvature constraints imply such a model would be falsified by any detection of tensor modes at the percent level in the CMB by Planck. Axions lighter than those we study are well constrained as components of the DM by observations of the CMB and the linear matter power spectrum ((<>)Amendola & Bar-(<>)bieri (<>)2006; ?), while heavier axions are probed, and in some cases ruled, out by the spins of supermassive black holes ((<>)Arvanitaki & Dubovsky (<>)2011; (<>)Pani et al. (<>)2012), ",
+    "and terrestrial axion searches ((<>)Jaeckel & Ringwald (<>)2010; (<>)Ringwald (<>)2012a). ",
+    "We have not discussed the role of baryons in this model, the knowledge of this role being incomplete in even the most state of the art simulations. We have preferred to focus on simple and idealised DM only models where the relevant physics is well understood. The baryonic disk has only a modest effect on the rotation curve, with DM halos still necessary. Adiabatic contraction of baryons may lead to the enhancement of DM cusps, and thus more need for a core forming component (<>)Zemp et al. ((<>)2012). On the other hand, baryonic feedback is a process driven by supernova explosions driving outflows of gas, which can remove DM cusps in dwarf galaxies while leaving a thick stellar disk (<>)Gover-(<>)nato et al. ((<>)2012). Baryons may also transfer angular momentum to the halo and modestly effect the spin-up of a massive halo. In massive galaxies it is unlikely that baryons have a significant effect on the DM halo profile. None of these effects, most notably feedback, solve the excess baryon problems of the MSP and MFP. ",
+    "It will be important to investigate this model further in the future with numerical N-body and other nonlinear studies in order to verify whether our simple predictions stand up to detailed scrutiny both theoretically and observationally. It is possible that non-linear effects such as oscillons (see e.g. (<>)Gleiser & Sicilia ((<>)2009)) may play a role. Also, at non-linear order additional terms in the effective fluid description of the axion will be generated, such as anisotropic stresses (<>)Hertzberg ((<>)2012), which could alter the simple picture of structure formation with a sound speed and Jeans scale dominating effects at short distances. ",
+    "Furthermore, Lyman-α constraints play a key role in determining the validity of WDM models to resolve small scale crises in CDM, the constraints of (<>)Viel et al. ((<>)2013) appearing to all but rule out WDM in this regard. Applying such constraints reliably to ULAs will require developing hydrodynamical simulations with them. Finally, a thorough development of the halo model with ULAs building on the groundwork laid here (as was done for WDM by (<>)Smith & Markovic ((<>)2011)) will be invaluable in understanding weak lensing constraints to ULAs obtainable with future surveys ((<>)Marsh et al. (<>)2012; (<>)Amendola et al. (<>)2012). "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. The research of JS has been supported at IAP by the ERC project 267117 (DARK) hosted by Universit´e Pierre et Marie Curie -Paris 6 and at JHU by NSF grant OIA-1124403. "
+  ]
+}

jsons_folder/2014MNRAS.438.1038R.json

@@ -0,0 +1,167 @@
+{
+  "Bruno Rodríguez Del Pino, 1⋆Steven P. Bamford, 1 Alfonso Aragón-Salamanca, 1 Bo Milvang-Jensen2 , Michael R. Merrifield1 and Marc Balcells3,4,5 ": [],
+  "(<http://arxiv.org/abs/1311.2842v1>)arXiv:1311.2842v1  [astro-ph.GA]  12 Nov 2013": [],
+  "ABSTRACT ": [
+    "We use integral field spectroscopy of 13 disk galaxies in the cluster AC114 at z˘ 0.31 in an attempt to disentangle the physical processes responsible for the transformation of spiral galaxies in clusters. Our sample is selected to display a dominant young stellar population, as indicated by strong Hδabsorption lines in their integrated spectra. Most of our galaxies lack the [OII]λ3727 emission line, and hence ongoing star formation. They therefore possess ‘k+a’ spectra, indicative of a recent truncation of star formation, possibly preceded by a starburst. Disky ‘k+a’ galaxies are a promising candidate for the intermediate stage of the transformation from star-forming spiral galaxies to passive S0s. ",
+    "Our observations allow us to study the spatial distributions and the kinematics of the di˙erent stellar populations within the galaxies. We used three di˙erent indicators to evaluate the presence of a young population: the equivalent width of Hδ, the luminosity-weighted fraction of A stars, and the fraction of the galaxy light attributable to simple stellar populations with ages between 0.5 and 1.5 Gyr. We find a mixture of behaviours, but are able to show that in most of galaxies the last episode of star-formation occured in an extended disk, similar to preceeding generations of stars, though somewhat more centrally concentrated. We thus exclude nuclear starbursts and violent gravitational interactions as causes of the star formation truncation. Gentler mechanisms, such as ram-pressure stripping or weak galaxy-galaxy interactions, appear to be responsible for ending star-formation in these intermediate-redshift cluster disk galaxies. ",
+    "Key words: galaxies:clusters:individual: AC114-galaxies:evolution-galaxies: interactions. "
+  ],
+  "1 INTRODUCTION ": [
+    "Thepropertiesofgalaxies–suchasmorphology,colour,sizeandmass–varyaccordingtotheenvironmentwheretheyreside.Inparticular,galaxymorphologieshavebeenshowntochangewithlocalprojecteddensity(e.g.,(<>)Dressler(<>)1980;(<>)Bamfordetal.(<>)2009),withlate-typespiralandirregulargalaxiesshowingmorepreferenceforregionswithlowerdensities,whileearly-typeS0andellipticalgalaxiesaremoreabundantindenserregions.Althoughinadiffer-enttimescale,specificstarformationrates,SSFR,arealsoaffectedbytheenvironment((<>)Baloghetal.(<>)2004a;(<>)Vogtetal.",
+    "(<>)2004a)andhasbeenshowntobethegalaxypropertymostaffectedbythedensityoftheenvironment((<>)Kauffmannetal.(<>)2004;(<>)Wolfetal.(<>)2009).Theconcentrationofthestarformationinclusterdiskgalaxiesisalsofoundtobe˘ 25percentsmallerthancomparablegalaxiesinthefield((<>)Bamford,Milvang-Jensen&Aragón-Salamanca(<>)2007).",
+    "Thereisalsoachangeinthemorphologicalmake-upofthegalaxypopulationwithredshift,particularlyinclusters.Spiralgalaxiesshowhighfractionsinclustersatintermediateredshift(z˘ 0.5),wherethefractionofS0sislow,butwhilethefractionofspiralsdecreasesforlocalclusters,S0sbecomemoredominant,being2–3timesmoreabundanttodaythanatintermediateredshift((<>)Dressleretal.(<>)1997).Ontheotherhand,ellipticalsdonotshowasub-",
+    "stantialvariation,comprisingasignificantfractionofclustergalaxiessinceatleastz ˘ 1 ((<>)Dressleretal.(<>)1997;(<>)Fasanoetal.(<>)2000;(<>)Desaietal.(<>)2007).Correspondingly,thefractionofstar-formingbluegalaxiesinclustershasbeenshowntoincreasewithredshift((<>)Butcher&Oemler(<>)1978,(<>)1984;(<>)Margonineretal.(<>)2001),knownastheButcher-Oemlereffect,andthesehavebeenfoundtocomprisenormallate-typespirals((<>)Dressleretal.(<>)1994;(<>)Couchetal.(<>)1994).",
+    "AllthesedifferentfindingspointtoatransformationofgalaxiesfromspiralintoS0withintheclusterenvironment,assuggestedinmanystudies(e.g.,(<>)Larson,Tinsley&Caldwell(<>)1980;(<>)Shioyaetal.(<>)2002;(<>)Bekki,Couch&Shioya(<>)2002;(<>)Aragón-Salamanca,Bedregal&Merrifield(<>)2006).Thistransformationwouldstartwithblue,star-forming,spiralgalaxiesatintermediateredshiftfallingintoregionsofhigherdensitysuchasgroupsandclusters,experiencingthelossoftheirgasandsubsequentsuppressionofstarformation,butretainingtheirdisks,resultinginred,passive,S0galaxies.",
+    "Avarietyofmechanismshavebeensuggestedtoberesponsibleforsuchtransformations:interactionwiththehotintraclustermedium(ICM)viathermalevaporation((<>)Nipoti&Binney(<>)2007)andram-pressurestrip-ping((<>)Gunn&Gott(<>)1972;(<>)Abadi,Moore&Bower(<>)1999;(<>)Bekki,Couch&Shioya(<>)2002),interactionswiththeclustertidalfield((<>)Larson,Tinsley&Caldwell(<>)1980),galaxyharassment((<>)Mooreetal.(<>)1996)andminormergers((<>)Bekkietal.(<>)2005;(<>)Eliche-Moraletal.(<>)2012,(<>)2013).Alltheseprocessesmaybeexpectedtoremoveordisturbthegascontentsofgalaxies,whileleavingthestellardistributionsrelativelyunscathed.Majormergerscanalsotriggerstarburstswhichmayconsumegasreservoirsandultimatelysupressstar-formation((<>)Mihos&Hernquist(<>)1996),althoughunlesstheyaregas-rich((<>)Hopkinsetal.(<>)2009),theirstellardisksmaybedisrupted.Importantly,noneofthesemechanismsisthoughttooperateequallyfromlow-massgroupstorichclusters.ThehighfractionofS0spresentinallthesedenseenvironmentsthereforesuggeststhatacombinationofthesemechanismsmaybeinvolved,withvaryingdegreesofimportance.",
+    "Galaxiesinwhichstarformationhasbeenrecentlysuppressed,˘ 0.5–1.5 Gyrago,shouldbewelldescribedbythecompositeofanA-typestellarpopulation(whosemain-sequencelifetimerangesfrom0.5–1.5 Gyr)andanoldpopulation,whichwaspresentinthegalaxybeforethelastepisodeofstarformation.Thistypeofgalaxieswasfoundforthefirsttimeby(<>)Dressler&Gunn((<>)1983),andtheyareconspicuousbythepresenceofstrongBalmerabsorptionlinesintheirspectra,characteristicoftheAstars,superimposedontoaspectrumofanolder(severalGyr)stellarpopulation,andwithnoemissionlines(indicatingnoongoingstarformation).Thesegalaxiesarecalledeither‘k+a’,aftertheirdominantstellartypes(old‘k’andyoung‘a’),or‘E+A’,indicatingtheirspectracorrespondtothatofatypicalearly-type(‘E’)galaxywithadditionalA-stars.Wewillrefertothemas‘k+a’galaxieshereafter.",
+    "Duetotheimportanceof‘k+a’galaxiesasobservableinstancesofrapidevolution,theyhavebeenthesubjectofmanystudies((<>)Dressler&Gunn(<>)1983;(<>)Zabludoffetal.(<>)1996;(<>)Nortonetal.(<>)2001;(<>)Pracyetal.(<>)2009;(<>)Poggiantietal.(<>)2009;(<>)Pracyetal.(<>)2012;(<>)Pracyetal.(<>)2013).Althoughfirstdiscoveredintheclusterenvironment((<>)Dressler&Gunn(<>)1983),",
+    "theyhavealsobeenfoundinthefield((<>)Zabludoffetal.(<>)1996;(<>)Blakeetal.(<>)2004)andingroups((<>)Poggiantietal.(<>)2009).Few‘k+a’galaxiesarefoundinthelocaluniverse,buttheirprevalenceincreasessignificantlywithredshift,suchthatinintermediate-redshiftclusterstheycanrepresentupto10percentofthetotalgalaxypopulation((<>)Poggiantietal.(<>)2009).Inthoseintermediate-redshiftclusters,‘k+a’galaxiestendtoavoidthecentralregions,implyingthatthesuppressionofstarformationdoesnotrequiretheextremeconditionsofclustercores,andmaybegininlessdenseenvironmentssuchasgroups((<>)Dressleretal.(<>)1999).While‘k+a’galaxiesingeneraloftenshowearly-typemorphologies(sometimesdisturbed;(<>)Yangetal.(<>)2008),inclusterstheyaregenerallyassociatedwithdisk-likesystems((<>)Caldwell,Rose&Dendy(<>)1999;(<>)Tranetal.(<>)2003),andinmanycasestheyalsoshowspiralsignatures,implyingthatthetimescaleforthespectralevolutionisshorterthanthatforanymorphologicaltransformation((<>)Poggiantietal.(<>)1999).",
+    "Analysingtheinternalspatialdistributions,andideallykinematics,ofthedifferentstellarpopulationsinhabitingthesegalaxiesiscrucialtounderstandingthemechanismsresponsibleforthesuppressionofstarformation.Ifthelastepisodeofstarformationtookplaceinthecentralregions,itwouldbeconsistentwithprocessessuchasgalaxy-galaxyinteractionsandminormergers((<>)Mihos&Hernquist(<>)1996;(<>)Bekkietal.(<>)2005,butsee,e.g.,(<>)Teyssier,Chapon&Bournaud(<>)2010,andthediscussioninSection(<>)4inthispaper).Incontrast,amoreextendedyoungpopulationcouldimplydepletionofagalaxy’sgasreservoirthroughinteractionwiththehotICM((<>)Roseetal.(<>)2001;(<>)Bekkietal.(<>)2005;(<>)Bekki(<>)2009).",
+    "Toperformsuchananalysis,wehaveusedintegralfieldspectroscopy,obtainedusingtheFLAMES-GIRAFFEmulti-objectspectrographattheVLT((<>)Pasquinietal.(<>)2002),toanalyse13galaxieswithdiskmorphologiesandstrongH absorptionintheclusterAC114(alsoknownasAbellS1077;(<>)Abell,Corwin&Olowin((<>)1989))atz ˘ 0.3.AC114hasbeenshowntocontainasignificantpopulationofbluestar-forminggalaxiesby(<>)Couch&Sharples((<>)1987,hereafterCS87),butalsotohaveasubstantialgeneralsuppressionofthestarformation(asinferredfromHemission;(<>)Couchetal.(<>)2001),whichmakesitanideallaboratoryforstudyinghowclustergalaxiesaretransformed.Apreviousstudyof‘k+a’galaxiesinthisclusterhasbeencarriedoutby(<>)Pracyetal.((<>)2005,hereafterP05).TheyobtainedobservationsusingFLAMESwithaverysimilarconfiguration,althoughtheydidnotfocusspecificallyongalaxieswithdiskmorphology.Wewerenotawarethattheirobservationsexistedwhenourswerescheduled,butsuchrepeatedobservationsenableustocheckthereproducibilityofourmeasurements.CombiningtheP05datasetwithourownalsoaddssomeadditionalgalaxiestothesampleweconsiderinthispaper.Intheirstudy,P05onlyconsiderthespatialdistributionoftheH equivalentwidth.Weexpandonthis,measuringthestellarpopulationsinmoredetailandconsideringtheresolvedgalaxykinematics.",
+    "Throughoutthispaperweassumeacosmologywithm = 0.3, = 0.7,H0 = 70 km s−1Mpc−1 ."
+  ],
+  "2 DATA ": [],
+  "2.1 Sample ": [
+    "Thecurrentsampleconsistsof13galaxies,observedandidentifiedbyCS87asmembersoftheclusterAC114atz ˘ 0.31.TheCS87catalogueprovidesredshiftsandspectrallinemeasurements,asmeasuredon8hourintegrationswiththe3.9 mAAT,usingaspectrographwithaspectralresolutionR ˘ 1400 andfedby2.6 ′′diameterfibres.AC114alsohaswide-fieldarchiveHST WFPC2imaging,whichisusedtocataloguethemorphologicalmake-upofAC114in(<>)Couchetal.((<>)1998,hereafterC98).BasedonthecombinedCS87/C98catalogue,thesamplegalaxieswereselectedtohaveH rest-frameequivalentwidthEW(H) > 3Å(thesignconventionhereisthatapositiveEWforH meansabsorption),whichisthecommoncriteriontobeconsidered‘k+a’((<>)Poggiantietal.(<>)1999),diskmorphologyandmagnitudeRF 6 20.5.Somefurthersamplelimitationswereimposedbythespectrograph’sfield-of-viewandrestrictionsontheplacementofeachintegralfieldunit(IFU)inordertoavoidbuttoncollisionsandcrossedfibres.",
+    "Nineoftheobjectsselectedtobeobservedshowno[OII]3727 emissionintheCS87catalogue,andhencecorrespondtoatrue‘k+a’selection.Theremainingfourshowsome[OII]3727 emission,indicatingthattheyhaveongoingstarformation,thoughpossiblydeclininggiventheirH EW,orhostanAGN.",
+    "Inadditiontothesegalaxies,weinclude��inouranalysistheobjectsobservedbyP05.Thissamplewasselectedfromthesameclusterinasimilarmannertothatdescribedabove,exceptthatnorestrictionwasplacedonmorphologyandnoneoftheirgalaxieshaddetected[OII]3727 emission.SixgalaxiesfromourselectionwerealsoobservedbyP05,aswellastwoadditionaldiskgalaxies,fourellipticalsandonepeculiargalaxy.Thecombinedsamplethereforecomprisestwentygalaxies,ofwhichfifteenpossessdiskmorphology.",
+    "Notethat,forgalaxyCN849,thefluxpresentinourobservationswasverylow.Thiswasfoundtobeduetoanincorrecttargetposition.Fortunately,thisgalaxywasalsoincludedintheP05datasampleandcouldbeanalysedusingthatdata.Also,whencomparingtheredshiftsmeasuredforthegalaxiesobservedbybothP05andourselveswediscoveredaninconsistencyforCN254.InspectingthecoordinateswediscoveredthatthegalaxylabelledCN254inP05isactuallyCN229,anotherdiskgalaxyatz = 0.319.Thecross-comparisonsub-samplewithmultipleobservationsthereforecomprisesfourobjects.",
+    "InTable(<>)1welistalloftheobjectsconsideredinthispaper,withtheircoordinates,morphologies,colour(BJ-RF,correctedforGalacticreddening)andprojecteddistancetotheclustercentre."
+  ],
+  "2.2 Observations ": [
+    "TheobservationswereobtainedattheVLT-UT2usingtheFibreLargeArrayMultiElementSpectrograph(FLAMES)inGIRAFFEmodeataresolutionofR˘ 9600.Withthissetup,15individualIFUsweredeployedoverthewholefieldofview,withtwoofthembeingdedicatedtotheskytoensureareliableskysubtraction.EachIFUconsistsof20squaredmicrolensesof0.52 arcseconaside,makingupa",
+    "surfaceof3 × 2 arcsec2 perIFU,whichcorrespondsto˘ 14.0 × 9.3 kpc2 atthedistanceofAC114(˘ 2.3 × 2.3 kpc2 perspaxel).",
+    "Thetotalexposuretimewas˘ 13 hours,distributedin14exposuresindifferentnightsofJune,AugustandDecemberof2004.Observationsweretakenwithseeingconditionswithintherequestedservicemodeconstrain(6 0.8arcsec),andDIMMseeingrangedfrom0.49to1.06arcsec.Theobservedwavelengthrangewas5015–5831Å,whichataredshiftofz ˘ 0.3 correspondsto3850–4394Åinrestframe,coveringtheKandHcalciumfeatures(3934Åand3969Å),theBalmerlinesH (4102Å)andH(4341Å)andtheG-band(4305Å).Atthatwavelengthrange,theinstrumentalresolutionis0.57Åsampledwith0.2Åpixels,yieldingavelocityresolutionof˙ = 10 km s−1 atz ˘ 0.3.Sinceweexpect˙ > 50 km s−1 ,thisresolutionisenoughtocomfortablyresolvethelines.",
+    "Inordertoensureanaccuratecalibrationofthedataset,weobtainedarclampandNasmythflatfieldimagesimmediatelyaftereachscienceexposure.",
+    "TheobservationsbyP05wereobtainedwithanidenticalsetup,thoughwithslightlylowerintegrationtimes.Theseeingvaluesfortheseobservationsrangedfrom0.54to0.84arcsec.Theirindependentspectraforthefourgalaxieswehaveincommonprovideausefulcheckoftherobustnessofourresults."
+  ],
+  "2.3 Data reduction ": [
+    "ThedatawerereducedusingtheGIRAFFEpipelineprovidedbyESO((<>)Izzoetal.(<>)2004).Thepipelinefirstsubtractsthebiasandtheoverscanregions.Then,usingthecorrespondingNasmythflatfieldimage,itdeterminesthepositionandwidthofthespectraontheCCDandsimultaneouslyproducesanormalisedflatfieldtoaccountforthevariationsintransmissionfromfibretofibre.BecausetheobservationsweretakenwiththeoriginalCCD,whichwasonlychangedinMay2008,removalofthedarkwasnecessaryduetothepresenceofaprominentglowintheCCD.AdispersionsolutionwascreatedusingthecorrespondingThArarclampframe,andthespectrarebinnedtoaconstantdispersion.Nofluxcalibrationwasrequiredfortheanalysisofthedata.",
+    "Thepipelinedidnotincludearecipeforthesubtractionofthesky.Therefore,thesubtractionwasdonecombiningallfibresfromthetwoIFUsdedicatedtothesky,togetherwiththesingleskyfibreassociatedwitheachIFU,givingatotalof52fibres.WenoticedthatoneoftheskyIFUswassystematicallytoobright,perhapsduetocontaminationbyalowsurfacebrightnessobject,resultinginanoversubtrac-tionoftheskyinourobjectfibres.WedecidedtoexcludethisIFUandusetheremaining32skyfibresfortheskysubtraction.",
+    "Forconsistency,weobtainedtherawdatafortheP05observationsfromtheESOarchiveandreducedtheminthesamemannerasourownobservations."
+  ],
+  "2.4 Stellar population and kinematic analysis ": [
+    "Toextractinformationaboutthekinematicsandstellarpopulationsofthegalaxies,weusedthepenalizedpixelfittingpPXF softwaredescribedin(<>)Cappellari&Emsellem((<>)2004).",
+    "Table 1. Identity number of the galaxy from (<>)Couch & Newell ((<>)1984), coordinates, morphologies, Galactic reddening corrected colours and distance to the cluster centre for the galaxies in our sample (top) and the P05 sample (bottom). At z = 0.3 one arc second corresponds to 4.454 kpc. Galaxies labeled with * have detected emission in [OII]3727. Galaxies labeled with \"P05\" are present in both samples. ",
+    "Thisalgorithmusesamaximum-likelihoodapproachtofitthespectrainpixelspace,simultaneouslydeterminingboththestellarkinematicsandtheoptimallinearcombinationofspectraltemplatesrequiredtomatchtheinputspectrum.Weemployedtwoseparatecollectionsoftemplates,onedrawnfromtheELODIE3.1stellarlibrary((<>)Prugnieletal.(<>)2007)andtheothercontainingPEGASE-HRsimplestellarpopulation(SSP)models((<>)LeBorgneetal.(<>)2004).ThelatterspectraareconstructedusingtheELODIElibrary,andhencebothhavethehighresolutionandwavelengthcoveragerequiredtofitourspectra(0.5ÅFWHMand4000–6000Å,respectively).Internally,pPXF convolvedthetemplatespectrawithaGaussianinordertomatchthespectralresolutionofourobservations.Werestrictedthetemplatestotwoclasses(II-IIIandV)foreachstellartypeOBAFGKM,andtoSSPswith12differentageslogarithmicallydistributedbetween1Myrand15Gyrand5differentmetallicities[Fe/H]rangingfrom-1.7to0.4.",
+    "Foreachspectrum,theprogramoutputsthevelocity,V ,andvelocitydispersion,˙,togetherwitharefinedestimateoftheredshift.ThevaluesobtainedforthekinematicswhenusingthestellarlibrarytemplatesandthoseobtainedusingtheSSPmodelswere,ingeneral,verysimilar.However,forsomeofthegalaxyspectra,occasionalnoisefeaturespresentinthestellarlibrarytemplatesspectraresultedinobviouslydiscrepantfitsandwrongvaluesforthekinematics.Inthesecases,weonlyusetheresultsobtainedusingtheSSPmodels.ErrorsinthekinematicparametersobtainedwithpPXF wereestimatedintherecommendedmanner,byperformingMonteCarlosimulationsontheoriginalspectrawithaddednoise.",
+    "Inadditiontothekinematics,pPXF alsoprovidestheweightsofthetemplateswhichprovidethebestfittotheobservedspectrum.Theseweights,afternormalisation,representthefractionalcontributionofeachtemplatetothetotalluminosity.Belowweusetheweightsobtainedusing",
+    "thestellarlibraryandtheSSPmodelsseparately,inordertostudythedistributionofdifferentstellartypesandstellarpopulationsthroughoutoursamplegalaxies."
+  ],
+  "3 ANALYSIS ": [
+    "Webeginbystudyingtheglobalpropertiesofthesample,byintegratingthefibresfromeachIFUtoproduceasinglespectrumpergalaxy.Formostofthesamplewecombinedallthefibres.However,inafewcasesthisresultedinanexcessively-noisyspectrum,andthereforeonlyfibreswithsignal-to-noiseratio(S/N)& 5Å−1 (definedinselectedregionsofthecontinuum)werethencombined.Therejectedfibreswerealwaysfarfromthebrightestpixel,intheoutskirtsofthetargetgalaxy.",
+    "InFigure(<>)1weplottheintegratedspectraforarepresentativesubsampleofthegalaxies:CN191,CN232,CN143andCN74.Thesignal-to-noiseratios(S/N)oftheintegratedspectrawererelativelyhigh,reachingvaluesof˘ 22Å−1 (CN146).AllofthespectradisplaytheKandHCalciumlinesandtheG-band,whicharecharacteristicofanoldpopulation.However,theH andHabsorptionlines,producedbytheyoung,A-starpopulationareonlystrongintwoofthespectra.ThelackofstrongBalmerabsorptionintheremaindercontrastswiththeirselectionas‘k+a’galaxies.BelowwemeasuretheH indexofthegalaxiesinordertoquantifythestrengthofthisfeature.",
+    "Wearealsointerestedinconsideringspatially-resolvedinformationfromthedifferentregionsofthegalaxiescoveredbytheIFUs.InthemajorityofthegalaxiesatleastsomeofthecentralfibreshadsufficientS/N(reachingvaluesof˘ 15Å−1)tobeanalysedindividually,althoughthedegreetowhichthisispossiblevariesbetweengalaxies.Forthisreason,inadditiontoperformingtheanalysisfortheindividualfibres,ineachgalaxywecombinedallthepixelsimmediatelyadjacenttothebrightestone,whichwerefertoasthe‘surroundings’(coveringfrom˘1.6to3.2kpc),andthoseplacedfurtheraway,whichwedefineasthe‘outskirts’(˘3.2to4.8kpc).Insomecases,duetothelowS/Ninthepixelsfarawayfromthecentre,wecouldnotobtainreasonablequalityspectraforthe‘outskirts’.",
+    "TofindthecentreofeachgalaxywebuiltimagesofthelightdistributioninthecontinuumregionbetweentheH featureandtheskylineat5577foreachIFU.Thecentreofthegalaxywasassociatedwiththebrightest(andhenceusuallyhighestS/N)pixel.SomelargeandinclinedgalaxieswerepurposefullyoffsettoincludetheirouterregionsintheIFU.However,manyoftheothergalaxiesalsodisplayoffsetsfromtheIFUcentre.Theseoffsets,whicharealsopresentintheobservationscarriedoutbyP05,arelikelyaresultofinaccuraciesintheastrometryandIFUpositioningerrors.Theyare,however,significantlysmallerthanthefieldofviewsodonotcompromisetheanalysis."
+  ],
+  "3.1 Indicators of a young population in the ‘k+a’ galaxies ": [],
+  "3.1.1 Line index measurements ": [
+    "Asexplainedabove,‘k+a’spectralfeaturesarisefromthetruncationofstarformationinagalaxy,whichmaybepre-",
+    "Figure 1. Integrated spectra for a representative sample of our galaxies, from left to right and top to bottom: CN191, CN232, CN143 and CN74. We provide two examples of targets with prominent Balmer absorption (left) and two targets without (right). The spectra have been smoothed with a Gaussian of FWHM 1Å to improve their presentation. Note that the spectra have not been flux calibrated. ",
+    "cededbyastarburst,andreflectthecompositeofayoungandanoldstellarpopulation.ThesegalaxiesareusuallyidentifiedbythestrongBalmerabsorptionlinesintheirspectra.Sincethehigher-orderBalmerlinesarelessaffectedbyemissionfromionizedgas((<>)Osterbrock(<>)1989),themostcommonlyusedindicatoristheH lineat4102Å,whichisalsoconvenientlylocatedintheopticalpartofthespectrumatlowandintermediateredshift.Althoughtheselectioncriteriadoesvarydependingonthestudy,‘k+a’galaxiesaregenerallyselectedtohaveEW(H) > 3Åandnodetectedemissionlines.",
+    "ThestrengthoftheH absorptionlineisrelatedtothemechanismresponsibleforthe‘k+a’feature.(<>)Poggiantietal.((<>)1999)showedthatstrongH absorptionlines(EW(H) > 4–5Å)canonlybecausedbytheabrupttruncationofstarformationafter���astarburst.Lowervaluesof[EW(H)]canalsobeachievedbyasimpletruncationofacontinuousandregularstarformationinthegalaxy.However,thestrengthoftheH linesubsideswithtime,soitisdifficulttodistinguishbetweenrecenttruncationandanolderonethatwasprecededbyastarburst.",
+    "Althoughweconsidermoresophisticatedindicatorsofthestellarpopulationlaterinthispaper,giventheimportanceandsimplicityoftheH absorptionfeature,wefirstmeasuretheequivalentwidthofthislineforthesamplegalaxies.WeutilisedtheredshiftsobtainedfromthetemplatefitswithpPXF (Section(<>)2.4),aslistedinTable(<>)2.EquivalentwidthsweremeasuredusingthesoftwareINDEXF ",
+    "((<>)Cardiel(<>)2010),whichusestheLick/IDSindexdefinitionsof(<>)Worthey&Ottaviani((<>)1997)tomeasurethesignalwithinthelinewithrespecttotheneighbouringcontinuum.TomakeourresultscomparablewiththoseobtainedbyP05,weusetheindexHF,whichtakesthecontinuumintervals4057.25–4088.5Åand4114.75–4137.25Åaroundthecentral4091.00–4112.25Åbandpass.Errorsareestimatedfromthepropagationofuncertaintiesinthespectraandthemeasuredradialvelocities.",
+    "Fourofthegalaxiesinoursampledisplayemissionlines,whichwouldaffectthelineindexmeasurementduetothefillingoftheabsorptionlines.Toavoidthis,forthesefourgalaxiesinsteadofusingtheoriginalspectrumwemeasuredthelineindexonthebestfitspectrumconstructedbypPXF.Thisprocedurehasbeenshowntoproduceverygoodresultsby(<>)Johnstonetal.((<>)2013b).",
+    "ThevaluesofHF forallthegalaxiesinoursamplearelistedinTable(<>)2.WealsolistthevaluesobtainedforthegalaxiesfromtheP05sample.Forgalaxiesthatarepresentinbothsamplesweobtainedverysimilarvalues,consistentwithinthegivenuncertainties.Hereafterweusedthevaluesmeasuredinourdata,becausetheypossesshigherS/Nratios.",
+    "ThefirstsurprisingfindingisthenumberofgalaxiesforwhichwemeasureHF lowerthan3Å.ThiswasalreadysuggestedfromtheweakBalmerabsorptionlinesapparentinsomeofthespectrauponvisualinspection,see(Figure(<>)1).Theselowvaluescontrastwiththoseexpectedfromthespec-",
+    "troscopicstudybyCS87,inwhichallofoursampleshowedEW(H) higherthan3Å.ThisdiscrepancywasalsofoundbyP05.ItappearsthattheuncertaintiesintheCS87H EWsareratherlarge,andhencetheirspectralclassificationsareonlyreliableforthemostextreme‘k+a’cases.",
+    "Fromouranalysis,onlysevenofthetwentygalaxiesdisplayEW(H) > 3Å,withthreeofthemalsohavingdetected[OII]3727emission.IfweconsideralsothosewithEW(H) > 2 Å,threemoregalaxiesareincluded,givingatotaloften.ThevaluesobtainedinouranalysisoftheP05sampleareinreasonablegoodagreementwithwhattheyfound,consideringthateachstudyappliedadiffer-entmethod.Weonlyfoundonegalaxy,CN849,wherewemeasuredalowervalueofHF (2.3± 0.4)thanwhattheyobtained(3.6± 0.3),whichinthiscaseissignificantbecauseitchangesthegalaxy’s‘k+a’classification.",
+    "Asmentionedabove,fourofthegalaxiesweobservedarelistedashaving[OII]3727emissioninCS87andthereforedonotmeetthestandard‘k+a’criteria.TheirEW([OII])valuesrangefrom7.6Åto39.6Å.Thesearelikelyreliableemissionlineidentifications.ThreeofthemarefoundtohaveHF > 3 Å(CN146,CN155andCN243)andtheyalsoshowsignsofemissioninHandH inourdata.However,itisnotclearwhethertheseemissionlinesresultfromresidualstarformationorAGNactivity.",
+    "2",
+    "OnewouldexpectthatifstarformationhasbeenrecentlytruncatedinthosegalaxieswithstrongH absorption,theyshouldhavebluercolorsduetothepresenceoftheyoungpopulation.Totestthis,inFig.weplotHF versusBJ− RFforallthesamplegalaxies.ObjectswithstrongH absorptionareconspicuouslybluerthanthosewithweakerH absorption.CS87alsopresentthisplot,findingaconsistenttrend,thoughsomewhatweaker,presumablyduetothelargeruncertaintiesontheirEW(H) estimates.ThistrendgivescompellingsupportthatthegalaxiesinoursamplewithstrongerH absorption,andparticularlyEW(H) & 2,containyoungerstellarpopulations.",
+    "InFig.(<>)2wealsoindicatethegalaxieswhichhaveobserved[OII]emission.Recallthat,forthesegalaxies,EW(H) wasmeasuredonthetemplatefitsproducedbypPXF,ratherthanthedataitself,toavoidtheeffectofline-filling.Itispossiblethatinthecaseofthebluestgalaxytheline-fillinghasaffectedthepPXF fititself,resultinginanunderestimateofEW(H).Thesefourgalaxiesarenotstrictly‘k+a’systems,theymaysimplybenormalstar-forminggalaxies,althoughtheirhighEW(H) mightindicatesomerecentsuppressionoftheirstar-formation.Nevertheless,weretainthemintheanalysisbecausetheyprobablyliejustoutsidetheboundariesofthe‘k+a’class,andmayprovideusefulcluesontheprocessbywhichgalaxiesbecome‘k+a’systems."
+  ],
+  "3.1.2 A/(AFGKM) and fyoung measurement ": [
+    "AlthoughstrongH absorptionisthestandardindicatorofayoungpopulationin‘k+a’galaxies,thissimplyreflectsthepresenceofasubstantialstellarpopulationwithagesbetween0.5 and1.5 Gyr,whoselightisdominatedbyAstars,butanabsenceofyoungerpopulationscontainingOBstars,poweringnebularemissionfromHIIregions.Thepresenceofthisintemediate-agestellarpopulationmayalsobeinferredusingother,morequantitative,methods.Oneap-",
+    "Figure 2. HF versus BJ− RFcolour for our entire galaxy sample. In the case of objects that were observed by both P05 and ourselves, we only plot our values. Galaxies with detected emission in [OII] by CS87 are indicated by a red cross. ",
+    "proachistemplatefitting,whichusesthefullwavelengthrangeavailableandaccountsforthefactthatpopulationsofallagescontributetoEW(H) (andotherspectralfeatures).WeusetheresultsoftemplatefitsperformedusingpPXF,asdescribedinSection(<>)2.4.",
+    "Toestimatetherelativeproportionofeachstellarpopulation,weusethenormalizedlight-weightedproportionsassignedtothevarioustemplatesinthebest-fittingmodel.",
+    "Fromtheweightsobtainedusingthestellarlibrarytemplateswedeterminethefractionsofeachstellartype(OBAFGKM)contributingtothegalaxyspectrum.ForthefitsusingtheSSPmodels,wegroupthetemplatesintofouragebins:‘Age < 0.5 Gyr’,‘0.5 < Age < 1.5 Gyr’,‘1.5 < Age < 7 Gyr’and‘Age > 7 Gyr’.OneexpectsanapproximatecorrespondencebetweenthestellartypesandSSPages:starsformedveryrecently(OB)willdominatetheAge < 0.5 Gyrbin,starswithlifetimes˘ 1 Gyr(mainsequenceAandFstars)willdominatethe‘0.5 < Age < 1.5 Gyr’bin,andlonger-livedstars(GKM)willcorrespondtothetwoolderagebins.However,thestellarpopulationtemplatescontaincontributionsfromstarsofalltypeswithlifetimeslongerthattheSSPage.",
+    "ToevaluatethefractionofA-typestarsweusetheratioA/(AFGKM).OBstarsareexcludedfromthisfractionbecausetheirpresenceisill-constrainedbyourfits,duetotheirfeaturelessspectratogetherwiththeuncertainfluxcalibrationandlimitedwavelengthrangeofourdata.Also,OBstarsdonotcontributesignificantlytothestellarmassofagalaxy.Forthestellarpopulations,ourprimaryquantityisthefractionalcontributionofSSPswith0.5 < Age < 1.5 Gyroverthetotal,hereafterfyoung.ThevaluesofA/(AFGKM)andfyoung,determinedwiththeintegratedspectraforeachgalaxy,arelistedinTable(<>)2.",
+    "3",
+    "Thusnowwehavethreedifferentindicatorsofthepresenceofayoungpopulationsinthesegalaxies,HF,A/(AFGKM)andfyoung.Comparingtheseparametersprovidesausefulindicationoftheirrobustness,andthereforethereliabilityofusingonlyoneofthemincaseswhentheotheronescannotbeobtained.ThiscomparisonisdoneinFig.,whereweplotA/(AFGKM)andfyoung againstHF forourentiregalaxysample.UncertaintiesontheHF mea-",
+    "Figure 3. Values of A/(AFGKM), fyoung and HF plotted against each other for our sample (green circles) and measured by us on spectra obtained by P05 (blue squares). For galaxies that are present in both samples we only plot values measured in our data because they have higher S/N. We only plot error bars in HF, as pPXF does not provide uncertainties on the weights in the best-fitting combination of templates. Galaxies with detected emission in [OII] by CS87 are indicated by a red cross. In the plot of fyoung vs A/(AFGKM) there are fewer visible points because they are superimposed onto each other. ",
+    "surementsareindicated,butpPXF doesnotprovideerrorestimatesforthetemplateweights.WethereforeestimateaverageuncertaintiesforA/(AFGKM)andfyoung fromthestandarddeviationofthescatterfromalinearcorrelationwithrespecttoHF aftersubtractingthecontributiontotheirerrorbyHF.Weobtainanuncertaintyinbothquantitiesof0.2.whichisalsonotedinTable(<>)2.",
+    "Asexpected,thereisagoodcorrelationbetweenthese",
+    "Figure 4. Maps of the individual fibre values of A/(AFGKM), fyoung and HF index (top) and the corresponding values for the integrated regions ‘centre’ and ‘surroundings’ (bottom) in CN228. Errors of the HF index are printed over the regions. Each spatial pixel (or spaxel) has a size of 0.52 x 0.52 arcsec2 which corresponds to ∼ 2.3 x 2.3 kpc2 at the redshift of AC114. ",
+    "quantities.GalaxieswithstrongBalmerabsorptionlinesalsoshowhighfractionsofA/(AFGKM)andfyoung,whilethosewithweakHF showverylowvaluesofA/(AFGKM)andfyoung.ThefractionsofA/(AFGKM)andfyoung alsopresentgoodcorrelationbetweenthem.Morequantitatively,forA/(AFGKM)andHF weobtainaSpearman’scorrelationcoefficientˆ = 0.65,whileforfyoung andHF,ˆ = 0.56.InthecaseofA/(AFGKM)andfyoung,ˆ = 0.76.Thechanceofanyofthesecorrelationsbeingspuriousis. 1 percent."
+  ],
+  "3.2 Spatial distributions ": [
+    "Asmentionedpreviously,inadditiontoprovidingglobalinformationaboutagalaxy,integralfieldspectroscopyallowsustostudypropertiesatsmallerspatialscalesandhenceconsiderdifferentregionswithinagalaxy.Weexploitthispossibilitybyperformingthesameanalysisdescribedabove,butnowappliedbothtothespectrafromindividualIFUelementsandtocombinedspectrafromthe‘centre’,‘surroundings’and‘outskirts’regionsofeachgalaxy.",
+    "Wehaveusedtheseresultstoconstructmapsofthethreedifferentageindicators,HF,A/(AFGKM)andfyoung,foreachgalaxy.Inmanygalaxies,duetotheS/Nbeingtoolowinthe‘outskirts’,onlythe‘centre’and‘surroundings’couldbeanalysed.CaseswherethethreeintegratedregionscouldbeanalysedcanbefoundintheAppendix(CN74andCN849).AnexampleofthisanalysisisshowninFig.(<>)4forthegalaxyCN228,wherethethreeindicatorsshowahighconcentrationoftheyoungpopulationinthecentreofthegalaxy.Thisisparticularlyclearwhenconsideringthe‘centre‘versus‘surroundings‘regions.ThevaluesoftheindividualfibresforA/(AFGKM)andfyoung alsoshowahighconcentrationtowardsthecentre,whiletheindividualHF arelessconclusive.",
+    "Toexaminethestellarpopulationinmoredetail,inFig.(<>)5weshowthenormalizeddistributionsofthedifferentspectraltypesandSSPagesobtainedfordifferentregionsofthesamegalaxy.Thetwoapproachesarebroadlyconsistent:aprominentfractionofA-starsisassociatedwithasignificantyoung-agepopulation.",
+    "ThemapsofHF,A/(AFGKM)andfyoung foreachgalaxyareourprimarysourceofinformationregardingthespatialdistributionsoftheyoungandoldstellarpopulations.However,themapsaredifficulttodealwithquantitatively,andthereissomesubjectivityinidentifyingthe",
+    "Figure 5. Histograms of stellar type and stellar population age obtained with pPXF for the integrated spectra, ‘centre’ and ‘surroundings’ of CN228. ",
+    "trendstheyreveal.Wehaveexaminedthesemapsindetail,andintheAppendixwepresentqualitativedescriptionsofeachgalaxy,inadditiontothemapsthemselves.",
+    "Inanattempttoquantifythedifferencesinthespatialdistributionsoftheyoungandoldstellarpopulationswehaveusedthesemapstoestimatetheluminosity-weightedfractionoftheyoungstellarpopulationcontainedwithinthehalf-lightradiusoftheoldpopulation.Wehaveassumedexponentialintensityprofilesforbothpopulations.Avalueofthisfractionlargerthan0.5 indicatesthattheyoungpopulationismoreconcentratedthantheoldone.Figure(<>)6showsthisfractionplottedagainsttheglobalHF values.Thereisalargescatter,indicatingsignificantdifferencesinthecurrentpropertiesandformationhistoriesofthegalaxies.Nevertheless,galaxieswiththestrongestHF seemtoshowsometendencytohavemorecentrally-concentratedyoungpopulations.Thissuggeststhatthelastepisodeofstarformationoftentookplaceinthecentralregionsofthesegalaxies.Thesamplesize,spatialresolutionanduncertaintiesofthisstudypreventusfromreachingaveryrobustconclusioninthisrespect,butitisreassuringthatourfindingsareconsistentwithindependentevidencefromrecentstudiesoflocalS0galaxies((<>)Bedregaletal.(<>)2011;(<>)Johnstonetal.(<>)2012;(<>)Johnstonetal.(<>)2013a)."
+  ],
+  "3.3 Kinematics ": [
+    "IfspiralgalaxiesarebeingtransformedintoS0sbyanyoftheprocessesdiscussedintheintroduction,inadditiontothechangesinstellarpopulationsconsideredabove,theirkinematicsmayalsobeaffected.Thekinematicsofthe‘k+a’galaxiesinoursamplecanthereforeindicatewhatmechanismsareresponsibleforthetruncationoftheirstarformation.Iftheprocessactsprimarilytostarveaspiralgalaxyofitsgassupply,thediskrotationshouldbepreservedintheresultinggalaxy.However,ifamergerisinvolved,theremnantwouldbeexpectedtoshowmorerandommotions.",
+    "ThekinematicsofthegalaxiesanalysedherewereextractedusingthesoftwarepPXF,asexplainedinSection(<>)2.4.Firstofall,weobtainedavalueoftheoverallvelocitydispersion˙int fortheintegratedspectrumofeachgalaxy,which",
+    "Figure 6. The luminosity-weighted fraction of the young stellar population contained within the half-light radius of the old population plotted against the global HF. A value of this fraction larger than 0.5 indicates that the young population is more concentrated than the old one (see text for details). ",
+    "arelistedin(<>)2.ItshouldbeborneinmindthatforthegalaxieswithdetectedemissionbyCS87,themeasurementof˙int mightbeaffectedbythefillingoftheabsorptionlinesduetoemission.Awiderangeofvaluesof˙int arefound,from˘ 60 to˘ 280 km s−1 .Theseoverall˙int includecontributionsfrombothrotationalandrandommotions,whichwewillattempttoseparatebelow.",
+    "Ifthegasandthekinematicsofthegalaxiesarebeingaffectedbytheclusterenvironment,onewouldexpectgalaxiesclosertotheclustercentretoshowdifferentbehaviourtothosethatarefurtherout,asfoundby(<>)Jafféetal.((<>)2011).Totestthis,weconsider˙int asafunctionoftheprojecteddistancefromtheclustercentre(Table(<>)1),whichisplottedinFigure(<>)7.Forthefullsampletheredoesnotappeartobeanycleartrend.However,ifweseparategalaxieswithhigh(> 3Å)andlow(< 3Å)HF,weseethatthosewithhighHF (bluesquares)presentastrongtrend.HighHF galaxieshavehigher˙int thefurthertheyarefromtheclustercentre,whilethosewithlowHF (greencircles)showlittlechangewithposition.Someofthehigh-HF andhigh-˙int galaxiesdisplayemission-lines(redcrosses),whichmaymaketheestimationof˙int unreliable.However,ifweremovethemfromtheplot,weseethatthetrendremains.",
+    "Wenowturnourattentiontothekinematicsofthegalaxiesonsmallerscales,whichcanbestudiedusingtheoutputsoffitsperformedtotheindividualIFUfibres.Weconstructline-of-sightvelocity,Vobs,andvelocitydispersion,˙,mapsofthegalaxies,inasimilarmannertothosefortheyoungpopulationindicators.AnexampleisshowninFigure(<>)8forthegalaxyCN228.",
+    "Wehavestudiedthesemapsforsignsofrotationanddifferencesinvelocitydispersionbetweenthecentralandsurroundingpixels.Oneproblemwehadtofaceherewasthatthe‘good’fibreswerenotalwaysdistributedaroundthebrightestpixelintheIFU,anditwassometimesdiffi-culttoidentifypatternsofrotationorvelocitydispersion.SincetheobservedvelocityisVobs = Vrotsini,whereVrot istherotationalvelocityandi theinclinationofthegalaxy,weneedtoknowthegalaxyinclinationinordertoobtaintheactualrotationalvelocity.Theinclinationwasthereforedeterminedbytheapparentellipticityobtainedbyfitting",
+    "Table 2. Galaxy ID, redshifts, young population indicators, velocity dispersions, Vrot/˙ and state of interaction for the galaxies in our sample (top) and the P05 sample (bottom). Note that morphology and colour are listed in Table (<>)1. Galaxies labeled with * have [OII]3727 detected emission by CS87. ",
+    "Figure 7. Velocity dispersion ˙ vs projected distance to the cen-tre of the cluster for galaxies with HF > 3Å (blue squares) and HF < 3Å (green circles). For those galaxies that are observed by both P05 and ourselves we plot the mean value. Galaxies with detected emission in [OII] by CS87 have a red cross overplotted. ",
+    "anellipsetotheHST/WFPC2imagesusingtheIRAF taskELLIPSE.InthecasepresentedinFig.(<>)8,wecanseeaclearpatterntypicalofrotation,withVrot = 177±38 km s−1 .Thedistributionof˙ isroughlyflat.",
+    "Previousstudiesofthekinematicsof‘k+a’galaxieshavefoundsignificantrotationinmanyofthem((<>)Franx(<>)1993;(<>)Caldwelletal.(<>)1996;(<>)Pracyetal.(<>)2009;(<>)Swinbanketal.(<>)2012;(<>)Pracyetal.(<>)2013),althoughsomearefoundtobemainlypressure-supported((<>)Nortonetal.(<>)2001).Weattemptedourkinematicanalysisinallthegalaxies,includingtheobservationsofP05,andfoundthatatleast8galaxiesdisplayrotation,withvaluesofVrot ˘ 85–180 km s−1 .",
+    "2",
+    "Themeasuredvaluesof˙int andVrot arelistedinTable,alongwiththeirratio(Vrot/˙int),whichindicateswhetheragalaxyisarotationally(> 1)orpressure(< 1)supported",
+    "Figure 8. Example of the radial velocity and velocity dispersion maps, with errors plotted below. The plus (‘+’) and minus (‘-’) symbols indicate the direction of rotation. In this image we show the example of CN228, showing a clear pattern of rotation and with similar values of ˙ along the galaxy. ",
+    "system.Usingthislastparameter,weseethat2ofthesystemsdisplayingrotationareclearlyrotationallysupported,typicalofdisk-likesystems,while5showVrot/˙int < 1 indicatingtheyaredominatedbyrandommotions.ComingbacktoFigure(<>)7,nowweareabletoestablishifthehighvaluesof˙int foundforsomegalaxiesareduetorotationortorandommotions.Fromthe10galaxieswithHF > 2Å,rotationisdetectedin6ofthemanddominantin2ofthese.However,theamountofrotationingalaxiesfarfromthecen-tre,inparticularCN254andCN228isconspicuouslyhigher(> 160 km s−1)thaninthoseclosertothecentresuchasCN143andCN191(< 140 km s−1).Theobservedtrendtolowerinternalvelocitieswithdecreasingdistancefromtheclustercoremaythereforeindicateatrendtolessregularkinematics,andhenceenvironmentallyinduceddisturbancesinthecentreofthecluster."
+  ],
+  "3.4 Kinematic decomposition ": [
+    "Thekinematicsstudiedintheprevioussectionarederivedassumingthatallstellarpopulationscontributingtoaspectrumhavethesamekinematics.However,ourdataaffordsthepossibilityofmeasuringthekinematicsoftheyoungandoldpopulationsin‘k+a’galaxiesseparately(e.g.,(<>)Franx(<>)1993;(<>)Nortonetal.(<>)2001).Separatedkinematicsofferafurthermethodofdistinguishingbetweenthemechanismsresponsiblefor‘k+a’signature.Rotationintheyoungcomponentsimpliesitisinadiskandthatthegalaxyhasnotbeensubjecttoaviolentprocess,particularlyiftheyoungpopulationkinematicsanddistributionareconsistentwiththeolderpopulation.Ontheotherhand,apressure-supportedyoungpopulationimpliesthatasignificantinteractionhasoccurred.Thedegreeofrotationalsupportintheoldpopulationmaythenindicatethestrengthofthisinteraction.",
+    "Inordertostudythekinematicsofthetwodifferentpopulations,wemodifiedthepPXF algorithminsuchawaythatitcouldfittwodifferentstellartemplatestoonespectrumsimultaneously,convolvingeachonewithdifferentradialvelocitiesandvelocitydispersions.Thesamemodifiedalgorithmhasbeenusedtostudyagalaxywithtwocounter-rotatingdisksby(<>)Johnstonetal.((<>)2013b),withgoodresults.Inourcase,weusedasetoftemplatescontainingA-starsandK-starswithdifferentmetallicitiessothatpPXF couldclearlydistinguishbetweenthetwopopulations.",
+    "Decomposingthekinematicsisverychallenging,andrequireshighersignal-to-noisethanavailableinmostoftheindividualIFUelements.Thedecompositionwasthereforeattemptedoncoaddedspectracorrespondingtothreeregionsforeachgalaxy,thecentreandbothsides,wheretheorientationofeachgalaxyisjudgedfromthekinematicmapsfromSection(<>)3.3.WefoundthatthealgorithmwassometimessensitivetotheinitialvaluesofV and˙ used.Wethereforevariedtheseinputvaluesand,inordertobeconsideredrobust,theoutputsofthefitswererequiredtoremainconstantforawiderangeofinitialvalues.",
+    "TheresultsarepresentedintermsofV and˙ mapsinasimilarmannertotheprevioussection.Asanexample,thekinematicdecompositionofCN228isshowninFigure(<>)9.Inthiscase,thegalaxyisacompositeoftwopopulationswithsimilarpatternsofrotation,whiletheyoungpopulationdisplayshighervaluesof˙ thantheoldpopulation,throughoutthegalaxy.AsshownpreviouslyinFigure(<>)4,CN228showscentralconcentrationoftheyoungpopulationinthedistributionofthethreeindicatorsHF,A/(AFGKM)andfyoung,impliyingaconcentrationoftheyoungpopulationinthecentreofthegalaxy.Now,addingtheinformationprovidedbythekinematicdecomposition,thefactthatthisgalaxyandothersshowsimilarrotationbetweentheyoungandoldpopulationseemstoindicatethatthesewerefairlynormaldiskgalaxieswhichhavenotexperiencedamajormergerordominantcentralstarburst.However,thehigher˙ suggeststhattheyhaveexperiencedaninteractionwhichincreasedtherandommotionsinthegasfromwhichthelastpopulationofstarswasformed.",
+    "Intotal,threediskgalaxieswithHF > 3Å(CN228,CN146andCN191)andtwowithHF > 2Å(CN254,CN849)couldbekinematicallydecomposedintotwopopulations.Infourofthesecasesboththeyoungandoldpopulationswerefoundtohavesimilarpatternsofrotation,",
+    "Figure 9. Kinematic decomposition of the young and old stellar populations in CN228, obtained using our two-component fitting method. Mean velocity and velocity dispersion values are presented in the IFU image. The plus (‘+’) and minus (‘-’) symbols indicate the direction of rotation. Errors in the fits are plotted over the corresponding regions. ",
+    "whereasnoclearpatternwasfoundintheremainingone(CN146).",
+    "The˙ valuesobtainedforthetwopopulationsdisplayavarietyofbehaviours,bothintermsoftheirrelativestrengthandtheirradialgradients.InthecaseofCN228discussedabove,the˙ oftheyoungstarsishigherthanthatoftheoldpopulation,whichsuggeststhatthisdisky‘k+a’galaxymayhaveexperiencedarecentinteraction,whichhasincreasedtherandommotionsoftheircoldgas,fromwhichthelatestgenerationofstarshaveformed,buthadlesseffectontheirpreviouslyexistingstellarpopulations.Thus,theprocesscannotbepurelygravitational,sincetheoldpopulationisnotperturbed,anditmustbeaffectingonlythegas((<>)Jafféetal.(<>)2011).AmoredetailedanalysisofthekinematicdecompositionforeachgalaxyispresentedintheAppendix."
+  ],
+  "3.5 Influence of interactions ": [
+    "Dynamicallyinteractinggalaxiesareoftenobservedtobeexperiencingastarburst(e.g.(<>)Keeletal.(<>)1985).Simulationshavelongsuggestedthatmergersandinteractionscancausegasinagalaxydisktoloseangularmomentumandfalltowardthecentreofthegalaxy,poten-tiallyfuelingacentralstarburst((<>)Barnes&Hernquist(<>)1991;(<>)Mihos&Hernquist(<>)1996;(<>)Bekkietal.(<>)2005).However,observationsoftenfindthatinteractionspromotestarformationthroughoutthegalaxiesinvolved(e.g.(<>)Kennicuttetal.(<>)1987;(<>)Elmegreenetal.(<>)2006),notjustinthenuclearregion.Thiscannowbereproducedbymodelswhichpaycloserattentiontotheroleofshock-inducedstar-formation(e.g.(<>)Chien&Barnes(<>)2010;(<>)Teyssier,Chapon&Bournaud(<>)2010).",
+    "Assumingthatthestarburstprocessoccursfasterthanthereplenishmentofthegasdiskviainfall,oralternativelythatsuchinfallissuppressed,thenfollowingthestarburstthegalaxywillceasestarformation.Theresultinggalaxywillthereforedisplayak+aspectrumforatime.",
+    "Theimportanceofmergersandinteractionsastheoriginofthe‘k+a’featureissupportedbystudieswhichfindthat‘k+a’galaxies(ofallmorphologies)aremorelikelytobefoundwithacompaniongalaxy,whencomparedtonormalgalaxies((<>)Goto(<>)2003,(<>)2005;(<>)Yamauchi,Yagi&Goto",
+    "(<>)2008;(<>)Pracyetal.(<>)2012).Forexample,intheircatalogueofk+aandtheircompaniongalaxies,(<>)Yamauchi,Yagi&Goto((<>)2008)foundthatk+agalaxieswere54percentmorelikelythannormalgalaxiestohaveasignificantcompanion.Similarly,thetwo‘k+a’galaxieswithlate-typemorphologyandwithacentralconcentrationoftheyoungpopulationstudiedby(<>)Pracyetal.((<>)2012)havenearbycompanionsandcouldbeexperiencingtidalinteractions.However,notethatalloftheseresultsarebasedonthegeneral‘k+a’population,andthusmaydifferfromthedisky,cluster‘k+a’populationconsideredinthispaper.Wehavethereforelookedforevidenceofinteractionsinthesample.",
+    "InTable(<>)2wehaveincludedacolumnspecifyingwhethereachgalaxydisplaysindicationsofinteractingwithotherobjects.ThiswasevaluatedbyvisualinspectionoftheHST/WFPC2imagesoftheAC114cluster.Ofthetwentygalaxiesinoursample,sevenhaveaclosecompanionandshowclearsignsofamergerorinteraction.Theremainderappearfairlyisolatedandundistorted.However,thefactthatagalaxydoesnotappeartobecurrentlyinteractingdoesnotruleoutsuchaprocessasthecauseofa‘k+a’feature.Thespectral‘k+a’signaturecanlastforupto1.5 Gyr,whichisenoughtimeforaninteractinggalaxytohavemovedtoacompletelydifferentregionoftheclusterandanydistortionfeaturemighthavefaded.",
+    "Totestifinteractionshaveanyinfluenceinthepropertiesofthegalaxies,welookedforanykindofcorrelationwithanyoftheresultsobtainedsofarinthisstudy.OfthetengalaxieswithH > 2Å,fiveshowsignsofinteraction.OfthesevenH > 2Ågalaxieswithdiskymorphologyandusablespatialinformation,threehavecentrallyconcentratedyoungpopulations(CN155,CN228and849)andalloftheseshowevidenceforinteractions.Incontrast,thefourdiskgalaxieswiththeiryoungpopulationextendedthroughoutthegalaxydonotshowanysignofmergersorinteractions.",
+    "Thisfindingstronglysupportsalinkbetweendynamicalinteractionsandacentrallyconcentratedstarburstindisky,clusterk+agalaxies.Theremainder,withanapparentlylessconcentratedyoungstellarpopulationmaysimplybetheresultofweakerorolderinteractions,orcausedbyanalternativemechanism.However,thestrengthofHF fortheinteractingandnon-interactinggalaxiesdoesnotdiffersignificantly."
+  ],
+  "4 DISCUSSION ": [
+    "Ouranalysisrevealsthatdisky‘k+a’galaxiesinintermediate-redshiftclustersareamixedpopulation.However,despitethesmallsamplesize,wedoseesomeconsistentbehaviourinanumberofimportantrespects.Theseresultsarerobusttochangesinthewaywequantifythepresenceandkinematicsoftheyoungandoldstellarpopulations.",
+    "Theyoungstellarpopulationswithinoursamplegalaxiesarealwayseitherdistributedsimilarlyto,ormorecompactlythan,theolderpopulation.Importantly,however,theyarerarelyconsistentwithbeingpurelyconfinedtothegalaxynucleus.Furthermore,theyoungstarsoftendisplayrotationalkinematicscorrespondingtotherestofthegalaxy,implyingtheyarelocatedinthedisk.However,therearesomeindicationsthattheirvelocitydispersionsaresomewhatgreaterthaninnormalspiralgalaxies.",
+    "Togethertheseresultssuggestthattheyoungstellarcomponentformedinanextendeddisk,inamannersimilartopreviousgenerationsofstarsinthesegalaxies.Itisnotassociatedwiththeaftermathofanuclearstarburst,norstarformationintidallyaccretedmaterial.Howeverthegasfromwhichthelateststarsformedwastypicallymorecentrallyconcentratedthanthatfromwhichtheirpredecessorswereborn.",
+    "Thescenariopresentedbyourdatacanbebroughttogetherwithmanyotherpiecesofobservationalevidencetosupportaconsistentpicturedescribingtheevolutionofthemajorityofdiskgalaxiesinintermediate-redshiftclustersandgroups.",
+    "Firstly,wenotethatanysatellitegalaxywithinalargerhalo,particularlyonemassiveenoughtohavedevelopedaquasi-statichotatmosphere((<>)Rees&Ostriker(<>)1977),isverylikelytohaveitsowngashalorapidlyremovedbyinteractionswiththehosthalo’sintergalacticmediumandtidalfield,viathemechanismsdiscussedintheintroduction.TheenvironmentalremovalofHIgasreservoirsisobservedbothlocally(e.g.,(<>)Vogtetal.(<>)2004a)andatintermediateredshift(e.g.,(<>)Jafféetal.(<>)2012).Star-forminggalaxiesenteringadenseenvironment(i.e.becomingsatellites:lowmassgalaxiesingroupsandhighermassgalaxiesinclusters),wouldthereforebeexpectedtograduallydecreasetheirstar-formationrateastheyconsumetheirremainingsupplyofdensegas.",
+    "However,agradualdeclineinthestarformationratesofstar-forminggalaxiesindenseenvironmentsisatoddswithresultsfromlargesurveys.ThecoloursandHequivalentwidthsofstar-forminggalaxiesareinvariantwithenvironment(e.g.,(<>)Baloghetal.(<>)2004a,(<>)b;(<>)Baldryetal.(<>)2006;(<>)Bamfordetal.(<>)2008),althoughtherelativeproportionsofblueversusredorstar-formingversuspassivegalaxiesvarysubstantially.Thisstronglyimpliesthatgalaxiesmustrapidlytransformfromstar-formingtopassive,suchthatatransitionpopulationisnotseen.Thetransformationmechanismcannotbeparticularlyviolent,asmanygalaxiesbecomepassivewhilstmaintainingtheirdiskmorphology,firstasredspirals,andthenaslenticulars(e.g.,(<>)Laneetal.(<>)2007;(<>)Bamfordetal.(<>)2009;(<>)Maltbyetal.(<>)2012).Wemustthereforereconciletheneedforarapidtransformationintermsofobservedcolourandemission-lineproperties,withtherequirementthatthemechanismonlyactrelativelygentlyongalaxystructure.",
+    "Star-forminggalaxiesareobservedinenvironmentsofalldensities,thoughtheybecomemuchrarerindenseregions.However,itisnotyetclearwhetherthosestar-forminggalaxieswhichappeartoinhabitdenseregionsaresimplytheresultofprojectioneffects,orwhethersomegalaxiesareabletomaintaintheirstarformation,atleastforawhile,insuchextremeenvironments.Theformerwouldimplythatthetransitionfromstar-formingtopassiveisdrivenbyadeterministicmechanism,specifictoparticularenvironments,whereasthelattercouldwouldpermitsomethingmorestochasticinnature,inwhichtheeffectofenvironmentissimplytoincreasethelikelihoodofsuchatransition((<>)Pengetal.(<>)2010).",
+    "Astochasticmechanism,whichisnotdirectlyrelatedtoagalaxy’sbroad-scaleenvironment,issupportedbytheobservationthattheproportionsofredorpassivegalaxiesshowtrendsacrossawiderangeofenvironmentaldensity,and",
+    "thatgalaxieswithtruncatedstar-formationareoftenassociatedwithgroups((<>)Moranetal.(<>)2007;(<>)Poggiantietal.(<>)2009;(<>)Wilmanetal.(<>)2009;(<>)Lackner&Gunn(<>)2013),whichalsohostnormalstar-forminggalaxies.",
+    "Therealityisprobablyacombinationofthedeterministicandstochasticpictures,forexampleamechanismwhoseeffectivenessdependssensitivelyonthedetailedsmall-scalesubstructureoftheenvironmentandagalaxy’sorbitthroughit(e.g.,(<>)Fontetal.(<>)2008;(<>)Pengetal.(<>)2012).Inanycase,thedeterministicremovalofagalaxy’sgashalosoonafteritbecomesasatellitemakesthegalaxymorevulnerable,helpingtoreducethetimescaleofanytranforma-tioninstigatedbyasubsequentmechanism.",
+    "Aninitialenhancementofstar-formationefficiencyearlyinthestar-forming-to-passivetransformationprocesswilleffectivelyreducetheobservabilityofthetransition.Theincreasedstarformationefficiencywouldbalancetheeffectofthedecliningfuelsupply,maintainingtheappearanceofnormality,untilthefuelsupplyisentirelydepleted.Thegalaxywouldthenimmediatelyceasestar-formationandrapidlyappearpassive.",
+    "Brieflyenhancedorextendedstar-formationinthecentralregionsofclusterspiralsissupportedbyourresults,aswellastheprevelanceofclustergalaxieswith‘k+a’spectraltypes((<>)Poggiantietal.(<>)2009)andmorecentrallyconcentratedyoungpopulationsinspi-rals((<>)Caldwelletal.(<>)1996;(<>)Koopmann&Kenney(<>)2004b,(<>)a;(<>)Vogtetal.(<>)2004a,(<>)b;(<>)Crowl&Kenney(<>)2008;(<>)Roseetal.(<>)2010;(<>)Bamford,Milvang-Jensen&Aragón-Salamanca(<>)2007;(<>)Jafféetal.(<>)2011;(<>)Böschetal.(<>)2013a)andS0s((<>)Bedregaletal.(<>)2011;(<>)Johnstonetal.(<>)2012;contrarytoearlierresults,e.g.,(<>)Fisher,Franx&Illingworth(<>)1996),aswellashintsofabrightenedpopulationintheTully-Fisherrelation((<>)Bamfordetal.(<>)2005;(<>)Böschetal.(<>)2013b).Simulationsdemonstratesimilarbehaviour(e.g.,(<>)Kronbergeretal.(<>)2008).Theprocessresponsibleofamorecentrallyconcentratedyoungpopulationcouldbeeitherfadingoftheexternalpartsofthegalaxiesorpushingthe��gasinwards.",
+    "Recentstudieshavefounddisturbedkinematicsintheemission-linegasinclusterspirals,fromwhichtheirfinalgenerationofstarswouldbeexpectedtoform((<>)Jafféetal.(<>)2011;(<>)Böschetal.(<>)2013a).Theincreasedcentralconcentrationoftheyoungpopulationinmanyofourgalaxiesiscertainlyconsistentwithadecreaseinthedegreeofrotationalsupport.Unfortunately,thequalityofourdatamakeithardtodirectlydeterminewhethertherelativevelocitydispersionoftheyoungstarsintheclusterspiralsishigherthanthatoftheoldstellarpopulations.However,togethertheseresultssuggestthatfuturestudiesofclusterS0smayexpecttofindthatthemostrecentdiskstellarpopulationhasasmallerscalelength(andpossiblygreaterscaleheight)comparedtopreviousgenerations,implyingthepresenceofayoung,small,thickdisk.Suchafeaturemayalsobeinterpretedasalenseoradditionalexponentialbulge.",
+    "Dustmayalsoplayaroleinacceleratingtheprogressionoftheobservationalsignaturesthatwouldbeassociatedwithatransition.Thecentralconcentrationofstar-formation,asdescribedabove,tothedustierinnerregionsofgalaxies((<>)Driveretal.(<>)2007)resultsinagreaterfractionofthatstarformationbeingobscuredfromopticalindicators((<>)Wolfetal.(<>)2009).Thetransitionstagemaythusbehiddenfromopticalstudies,butapopulationofdusty,red",
+    "galaxiesformingstarsatasignificant,thoughpossiblysuppressed,rateisrevealedbyobservationsatlongerwavelengths((<>)Gallazzietal.(<>)2009;(<>)Geachetal.(<>)2009).",
+    "Ourresultsindicatethatgalaxy–galaxyinteractionsmaybeassociatedwithstrongerormorerecenttruncatedstarbursts,andhencemaybeasignificanttransitionmechanism.Wethereforesupporttheconclusionsof(<>)Moranetal.((<>)2007),thatacombinationofgalaxy–galaxyinteractions,ram-pressurestripping,andothermoreminormechanismsareresponsibleforspiraltoS0transformation.",
+    "Galaxy–galaxyinteractionshavelongbeentheoreticallyassociatedwithstrongbarformationandnuclearstarbursts(e.g.,(<>)Mihos&Hernquist(<>)1996).However,duetothehighrelativevelocitiesofgalaxiesinadenseenvironment,tidalinteractionscanalsohavearelativelygentleeffect((<>)Mooreetal.(<>)1996).Thereisgrowingobservationalevidencethatevenpairinteractionsmaynotcausenuclearstarburstsasreadilyasanticipated,enhancingstar-formationinspiralarmsinstead(e.g.,(<>)Casteelsetal.(<>)2013).Furthermore,barsarefoundtobeprevalentingas-poor,redspirals(e.g.,(<>)Mastersetal.(<>)2011,(<>)2012),andsomaybemoreassociatedwiththesuppressionofstar-formation,ratherthanitsenhancement.",
+    "Thefinalargumentforaspiraltolenticulartranformationisthepropertiesofthefinalgalaxies.LenticularsareconsistentwithbeingformedfromfadedspiralsintermsoftheirTully-Fisherrelation((<>)Bedregal,Aragón-Salamanca&Merrifield(<>)2006),globularclusterspecificfrequencies((<>)Aragón-Salamanca,Bedregal&Merrifield(<>)2006).However,theydotendtobemorebulgedominated((<>)Christlein&Zabludoff(<>)2004)andhavehotterdisksthanspiralgalaxies((<>)Cortesietal.(<>)2013).Thiscanbeachievedbyanenhancementofcentralstar-formationpriortotransformation,andamarginalincreaseinpressuresupport,perhapsthroughanaccumulationofgalaxy-galaxyinteractions.Bothoftheseprocessesaresuggestedbyourresultsandmanyoftheotherstudiesdiscussedabove.TheclearingofdustinthecentralregionsduringthetransitionfromspiraltoS0mayalsoenhancethebulge-to-diskratio((<>)Driveretal.(<>)2007).SeparatelymeasuringthestellarpopulationpropertiesofbulgesanddisksforlargesamplesofspiralandS0galaxies,inbothspectroscopic(e.g.,(<>)Johnstonetal.(<>)2012)andmulti-bandphotometricdata(e.g.,(<>)Simardetal.(<>)2011;(<>)Lackner&Gunn(<>)2012;(<>)Bamfordetal.(<>)2012;(<>)Häuleretal.(<>)2013),willhelptofillinmanyofthemissingdetails."
+  ],
+  "5 CONCLUSIONS ": [
+    "ThetransformationfromspiralgalaxiesintoS0s,ifitactuallyoccurs,mustcompriseaspectraltransformation,resultingfromthesuppressionofstarformationinthediskofthegalaxy;amorphologicaltransformation,intermsoftheremovalofspiralfeaturesfromthediskandgrowthofthebulge;andamodestdynamicaltransformation,withasmallincreaseintheratioofpressureversusrotationalsupport.",
+    "Wehavestudiedthesignificanceofdisky‘k+a’galaxies,indicativeofaspiralgalaxyinwhichstarformationwastruncated˘ 0.5–1.5 Gyrago,asthepossibleintermediate",
+    "stepinthetransformationofstar-formingspiralsintopassiveS0sintheintermediate-redshiftclusterenvironment.",
+    "ThesegalaxiesaretypicallyidentifiedbytheirstrongBalmerabsorptionlineequivalentwidths,anexpectedsignatureofadominant˘ 1 Gyroldstellarpopulation.WehaveusedspectraltemplatefittingtoshowthatgalaxiesselectedviatheHF indexdo,indeed,containsignificantfractionsofA-typestarsandstellarpopulationswithagesbetween0.5 and1.5 Gyr.Westudythespatialdistributionoftheyoungpopulationusingthesedifferentindicators,findinggenerallyconsistentresults.Whilethedisky‘k+a’galaxiesappeartobearathermixedpopulation,theirfinalepisodeofstar-formationisalwaysdistributedoveraregionofsizesimilarto,orsomewhatsmallerthan,theolderstars.",
+    "Wehavecoarselymeasuredthevelocityfieldofthesegalaxies,bothintermsofthefullstellarpopulationand,inalimitednumberofcases,theseparateyoungandoldpopulations.Theresultssupportthepicturethat,inthemajorityofoursample,thelastgenerationofstarsformedinadisk,inaverysimilarmannertopreviousgenerations.",
+    "Noneofthedisky‘k+a’galaxiesinthisintermediateredshiftclusterappeartohaveexperiencedaviolentevent,suchasamergerorsignificantnuclearstarburst,priortothetruncationoftheirstar-formation.Instead,theirregulardiskstar-formationhassimplyceasedwithonly,insomecases,asmallincreaseincentralconcentrationbeforehand.",
+    "Arelativelygentlemechanismmustthusberesponsibleforthecessationofstar-formation.Gas-relatedmechanisms,suchasrampressurestripping,arethereforefavoured.However,thereisalsoanindicationthatmanyofourgalaxieswithmorecentrallyconcentratedyoungpopulationshaveexperiencedrecentgalaxy-galaxyinteractions.Thisraisesthepossibilitythat,thankstopriorremovalofthegashalo,stochasticgravitationalinteractionsmayprovidethenecessaryimpetustohaltstar-formation,perhapsviaabriefperiodofcentralenhancement."
+  ],
+  "6 ACKNOWLEDGMENTS ": [
+    "WethankEvelynJohnstonforherinvaluablehelpmodifyingthecodeandforveryusefuldiscussions.Wealsothanktheanonymousrefereeforveryusefulcommentsthathavehelpedimprovingthemanuscript.BRDPacknowledgessupportfromIACandSTFC.BMJacknowledgessupportfromtheERC-StGgrantEGGS-278202.TheDarkCosmologyCentreisfundedbytheDanishNationalResearchFoundation.BasedonobservationsmadewithESOtelescopesattheLaSillaParanalObservatoryunderprogrammeID073.A-0362A."
+  ]
+}

jsons_folder/2014MNRAS.438.2732D.json

@@ -0,0 +1,178 @@
+{
+  "ABSTRACT ": [
+    "Identifying galaxy clustering at high redshift (i.e. z > 1) is essential to our understanding of the current cosmological model. However, at increasing redshift, clusters evolve considerably in star-formation activity and so are less likely to be identified using the widely-used red sequence method. Here we assess the viability of instead identifying high redshift clustering using actively star-forming galaxies (SMGs associated with over-densities of BzKs/LBGs). We perform both a 2-and 3-D clustering analysis to determine whether or not true (3D) clustering can be identified where only 2D data are available. As expected, we find that 2D clustering signals are weak at best and inferred results are method dependant. In our 3D analysis, we identify 12 SMGs associated with an over-density of galaxies coincident both spatially and in redshift - just 8% of SMGs with known redshifts in our sample. Where an SMG in our target fields lacks a known redshift, their sightline is no more likely to display clustering than blank sky fields; prior redshift information for the SMG is required to identify a true clustering signal. We find that the strength of clustering in the volume around typical SMGs, while identifiable, is not exceptional. However, we identify a small number of highly clustered regions, all associated with an SMG. The most notable of these, surrounding LESSJ033336.8-274401, potentially contains an SMG, a QSO and 36 star-forming galaxies (a > 20σ over-density) all at z ∼ 1.8. This region is highly likely to represent an actively star-forming cluster and illustrates the success of using star-forming galaxies to select sites of early clustering. Given the increasing number of deep fields with large volumes of spectroscopy, or high quality and reliable photometric redshifts, this opens a new avenue for cluster identification in the young Universe. ",
+    "Key words: galaxies: clusters: general -galaxies: high-redshift -galaxies: starburst "
+  ],
+  "1 INTRODUCTION ": [
+    "High redshift (z > 1) galaxy clusters and groups are sensitive probes of cosmology and the dependance of galaxy evolution on environment. According to current paradigms, today’s galaxy clusters form in the early Universe (z > 3) and grow hierarchically over cosmological timescales. ",
+    "Both the exceptionally tight colour-magnitude relation in local clusters (e.g. (<>)Bower, Kodama, & Terlevich (<>)1998) and stellar population models ((<>)Thomas et al. (<>)2010), suggest that today’s massive cluster galaxies formed in a brief (per-",
+    "haps as little as 1 Gyr) period at z > 2. Assuming a typical cluster core of a few ×1012 M at z = 0 forms in this interval, it would host a few ×1000 M yr−1 of star-formation in a comparatively small volume at z  2. Recent observations have supported the interpretation that at increasing redshifts (z > 2), galaxy clusters become increasingly populated with star-forming galaxies ((<>)Tran et al. (<>)2010; (<>)Tanaka (<>)et al. (<>)2013), but whether these systems formed in a monolithic collapse scenario (see, (<>)Davies et al. (<>)2013b, for discussion), through mergers of many small starburst galaxies (e.g. Lyman Break galaxies, LBGs, with SFRs < 200 M yr−1 , (<>)Davies et al. (<>)2013) or as a region of small star-forming systems (such as LBGs or sBzKs, (<>)Daddi et al. (<>)2004) sur-",
+    "rounding a more massive obscured star-forming galaxy (a submillimeter galaxy, or SMG, with SFR 1000 M yr−1 , (<>)Casey et al. (<>)2013) is unclear. While (<>)van Dokkum et al. ((<>)2008) and (<>)Cimatti et al. ((<>)2008) find evidence in favour of the merger scenarios, others such as (<>)Nipoti et al. ((<>)2009), (<>)Nipoti et al. ((<>)2012) and (<>)Newman et al. ((<>)2012) predict that mergers alone cannot account for the rapid structure evolution observed at z > 1.3. (<>)Huang et al. ((<>)2013) take a middle ground, finding that local elliptical galaxies have a three-component structure that implies the central core of such systems formed from major (wet) mergers at high redshift, while the outer regions formed through minor (dry) mergers at a later epoch. ",
+    "Evidence for formation processes from galaxy cluster morphology is similarly ambiguous. (<>)Bassett et al. ((<>)2013), studying a z ∼ 1.6 cluster, and (<>)Bauer et al. ((<>)2011), (<>)Gr¨utzbauch et al. ((<>)2012) and (<>)Santos et al. ((<>)2013), all targeting the same z ∼ 1.4 cluster, find that star-forming galaxies do not reside in the cluster core but are confined to large radii (>200 kpc), consistent with the SFR-radius relation found in low redshift clusters ((<>)Treu et al. (<>)2003; (<>)Haines et al. (<>)2007). Conversely, other studies (e.g. (<>)Hilton et al. (<>)2010; (<>)Tran (<>)et al. (<>)2010; (<>)Strazzullo et al. (<>)2013) suggest that high redshift clusters display an inverse SFR-radius relation, with star-forming galaxies residing in the cluster core, or even no SFR-radius relation at all ((<>)Ziparo et al. (<>)2013)! Clearly a fuller understanding and consensus on the structure and hence formation mechanism of distant galaxy clusters requires further study. ",
+    "Of course, investigation of these early stages of structure growth requires the identification of clusters in their infancy at high redshift. One successful method for doing this is the galaxy red-sequence technique (first discussed in (<>)Gladders & Yee (<>)2000, and used in many studies since). This searches for a population of mature, passively evolving galaxies occupying a well-defined region in colour-magnitude space, inferring their near-coeval formation and hence likely association as cluster members. While this technique has proved successful in identifying some clusters at z > 1 (e.g. using the Spitzer Adaptation of the Red-Sequence Cluster Survey, (<>)Wilson et al. (<>)2006), it is biased towards systems which formed at a much earlier epoch, and hence have a significant number of old, passively evolving members. It is insensitive to less evolved structures dominated by active star-forming galaxies. ",
+    "An alternative is to consider other tracers. It has long been thought that massive high-z galaxies (such as SMGs) trace the most significant over-densities of mass at any epoch (e.g. (<>)Mo & White (<>)2002; (<>)Springel et al. (<>)2006), and the recent simulations of (<>)Gonz´alez et al. ((<>)2011) suggest that the majority of Abell-richness clusters contain at least one bright and distant (z > 1.5, S850µm > 5 mJy) SMG in their merger tree. If so, the volumes surrounding such systems should also contain an excess of other, more numerous, galaxy populations relative to the mean for the given epoch: high redshift SMGs should act as signposts for sites of cluster formation at early times. This premise has been explored at very high redshift with the identification of proto-cluster regions surrounding both SMGs and QSO/SMGs at z ∼ 5 ((<>)Capak et al. (<>)2011; (<>)Husband et al. (<>)2013), and would seem to be supported by (<>)Huang et al. ((<>)2013)’s suggestion that the environs of form-",
+    "ing, massive ellipticals must host a supply of relatively small, gas poor, post-starburst systems for later accretion. ",
+    "So, if the red sequence technique misses forming clusters, but the most massive galaxies signpost the most massive regions, do we observe clustering around those we know about? And are our methods sufficient to be sure of our answer to that question? ",
+    "Some studies have suggested that these questions merit further study. Using deep multi-wavelength coverage of the Cosmic Evolution Survey (COSMOS) field, (<>)Aravena et (<>)al. ((<>)2010, hereafter A10) identified candidate star-forming galaxies at 1.4 < z < 2.5 (sBzKs). Using a two dimensional analysis (i.e. projected distribution of sources in the plane of the sky), they compared regions of high sBzK number density with the positions of SMGs across a small ∼ 0.135 deg2 region with millimeter data. They identified three over-densities of systems surrounding 1.1 mm (MAMBO-2) detected sources at z = 1.42.5, suggesting that ∼30% of bright SMGs at this redshift are embedded in a galaxy over density. However their analysis was limited by the small field area and their use of two-dimensional clustering data. ",
+    "In this work, we extend the analysis of Aravena et al to the bulk (∼0.75 deg2) of the COSMOS region, using SMG catalogues taken from the AzTEC observations of the field ((<>)Aretxaga et al. (<>)2011). This area encompasses the region discussed in A10 -allowing a comparison between our methods. We also select star-forming galaxies over a much larger range of epochs than that covered by A10 (1.4 < z < 4.5, targeting the bulk of the SMG redshift distribution, (<>)Chapman et al. (<>)2005), ensuring that we do not miss clustered regions around SMGs at an earlier time. We also perform a similar analysis over the 0.25 deg2 of the Extended Chandra Deep Field South (ECDF-S) using the deep LABOCA observations of the field ((<>)Weiß et al. (<>)2009). In these fields, we have the ben-efit of deep many-band photometric and spectroscopic data which we can use to verify or refute any clustering observed in 2D through a 3D analysis (i.e. incorporating redshift information). ",
+    "We consider an analysis of spatial clustering in these two fields and address the following primary questions: ",
+    "In sections 2 through 6 we discuss our methods and observations, while in sections 7 to 10 we discuss the implications of our work and also present two strong candidates for z > 1.4 galaxy clusters, marked out through star formation rather than passively evolving cluster members. We propose these (and other similar regions) as key sites in the ",
+    "Figure 1. The colour selection of LBGs at z ∼ 3 (left) and z ∼ 4 (right) in the COSMOS field. Black points show a representative sample of all sources in the field. The red line indicates the colours of a young, metal poor galaxy at various redshifts, taken from the stellar population models of (<>)Maraston ((<>)2005). Green points show sources with photometric redshifts within our desired colour selection range (2.8 < z < 3.5 in the left panel and 3.5 < z < 4.5 in the right panel). Our colour selection regions are highlighted by the grey filled box. ",
+    "formation of today’s massive structures. Finally, in section 11 we present our conclusions. ",
+    "Throughout this paper all optical magnitudes are quoted in the AB system ((<>)Oke & Gunn (<>)1983), and we use a standard ΛCDM cosmology with H0 = 70 kms−1 Mpc−1 , ΩΛ = 0.7 and ΩM = 0.3. "
+  ],
+  "2 DATA SETS AND SOURCE SELECTION ": [],
+  "2.1 Star-forming galaxies and passive galaxies ": [
+    "In order to evaluate the clustering in our two target fields, we must first select samples of star forming galaxies for analysis. Both the COSMOS field (e.g. (<>)Guillaume et al. (<>)2006; (<>)Capak et al. (<>)2008) and the ECDF-S ((<>)Gawiser et al. (<>)2006a, e.g.) are abundantly supplied with publicly-available, multi-wavelength archival data across a broad wavelength range although the use of different filter sets in the two fields requires some adjustment of galaxy selection criteria to ensure that like-for-like comparisons are undertaken. Bearing this in mind, we use public catalogue data and well-established colour selection methods to identify star-forming systems at 1.4  z  4.5 -using three separate colour/magnitude cuts. Initially, we select sources at 2.8  z  4.5 using the ",
+    "Lyman break colour selection criteria (hereafter LBGs, e.g. (<>)Steidel et al. (<>)1995). This method essentially performs a crude photometric redshift estimate, selecting sources with a large spectral break and relatively flat continuum long-ward of the break. This selection is aimed at identifying the Lyman-α continuum break produced via intervening neutral hydrogen in relatively unobscured star-forming galaxies at high redshift (for further details of the well documented Ly-",
+    "man Break Technique, see (<>)Steidel et al. (<>)1995; (<>)Lehnert & Bre-(<>)mer (<>)2003; (<>)Stanway et al. (<>)2003; (<>)Verma et al. (<>)2007; (<>)Douglas (<>)et al. (<>)2009, etc and references therein). We apply two sets of colour selection criteria to identify sources at 2.8 < z < 4.5, outlined in Figure (<>)1 and Table (<>)1. These colour cuts are designed to select potential high redshift sources while limiting the contamination fraction in our sample. ",
+    "Colour selection of similar LBG sources at z  2.8 proves much more problematic as the Lyman break moves from optical wavelengths to the UV - and is therefore only observable by space based instruments. However, many ground based studies have been successful in identifying large numbers of z  2.8 star-forming galaxies through other colour selection techniques. Although these sources vary in intrinsic properties to LBGs at higher redshift, they are typical of the general population at z < 2.8. The most notable of these is the BzK colour selection outlined in (<>)Daddi et al. ((<>)2004). This method essentially selects sources with greater z-K than B-z colour and targets the 4000˚A/Balmer breaks in systems at z ∼ 2. While these systems appear more massive and reddened than true LBG selected sources at this epoch (see (<>)Haberzettl et al. (<>)2012), and comprise both passive and starforming subclasses, they represent typical star-forming galaxies at z ∼ 2 and are easily selected in the publicly available data covering the COSMOS field. We therefore use the BzK method as a third selection criterion in this study. ",
+    "It is well documented that simple colour selections such as these still contain significant numbers of contaminating sources such as lower-redshift passively evolving galaxies and (at higher redshifts) cool stars (e.g. (<>)Stanway et al. (<>)2008). In order to mitigate the effects of such contaminants, we also ",
+    "make use of the many-band photometric redshift catalogues that have been published for sources in both fields. ",
+    "In the ECDF-S we use the deep multi-wavelength data taken from the MUSYC survey ((<>)Gawiser et al. (<>)2006a), which provides deep coverage in 32 (broad and intermediate) bands in the optical and near-IR. Such detailed photometric coverage allows the determination of accurate photometric redshifts over a large redshift range (see (<>)Cardamone et al. (<>)2010, for further details). Our ECDF-S LBG sample is identical to that described in (<>)Davies et al. ((<>)2013). Hence we refer the reader to that work for the details of our selection. ",
+    "In the COSMOS field, we use the photometric redshift catalogues of (<>)Ilbert et al. ((<>)2008). We only select sources with a best fit photometric redshift within our selection redshift range (for photometric redshift calculations, see (<>)Ilbert (<>)et al. (<>)2008). We also remove objects whose 68% confidence (1σ) error range extends below the lower boundary of our selection redshifts to eliminate sources with poorly-fit photometric redshifts. Therefore, we essentially treat the well-constrained and reliable photometric redshifts of (<>)Ilbert et (<>)al. ((<>)2008) as a redshift confirmation. To avoid any additional stellar contaminants we remove all ACS point sources with a stellar or AGN type spectral energy distribution (see (<>)Robin et al. (<>)2007) and sources which display BzK colours which are consistent with stars at KAB < 22 ((<>)Daddi et (<>)al. (<>)2004). In Section (<>)4 we shall briefly discuss the affects of using a simple colour cut with no photometric classifica-tion applied. This removes any bias applied by selecting only those sources with good photometric redshifts (effectively a magnitude cut) but uses a more highly contaminated sample. ",
+    "For BzK galaxies, we apply the same selection as that outlined in (<>)Greve et al. ((<>)2010) in the ECDF-S, with colour selections for these samples given in Table (<>)1. In COSMOS we produce a sample of BzK selected galaxies (both star-forming and passive) using similar colour selections to those outlined in (<>)Daddi et al. ((<>)2004), supplementing the published catalogues by the K-band magnitudes from the year 1 Ul-traVISTA data set (KAB < 23.4, (<>)McCracken et al. (<>)2012). To be consistent with our higher redshift samples, we also apply a photometric redshift cut restricting the sample to sources with 1.4 < zphoto < 2.5. Figure (<>)2 and Table (<>)1 illustrate the BzK colour selection of sources at 1.4 < z < 2.5 in the COSMOS field. "
+  ],
+  "2.2 Sub-mm bright sources ": [
+    "As discussed in the introduction, submillimeter bright galaxies are believed to be more massive than the systems identi-fied above, and to be forming stars at a significantly higher rate. In order to evaluate the presence or absence of these sources in early structures, we use available surveys at (sub)-millimeter wavelengths in each field. ",
+    "The COSMOS field has been surveyed at 1.1mm using the 144-pixel AzTEC camera. The AzTEC observations cover a 0.72 deg2 region in the centre of the COSMOS field obtaining a uniform noise of ∼ 1.26 mJy/beam (see (<>)Aretx-(<>)aga et al. (<>)2011, for details). We use the catalogue produced in (<>)Aretxaga et al. ((<>)2011) which contains 189 sources detected at S/N > 3.5. As the region with uniform noise properties is smaller than the area covered by the UV and optically selected sources, we limit all our samples to this region (which ",
+    "Figure 2. The BzK colour selection of galaxies at z > 1.4. Objects with a clear z-and K-band detection, and a reliable photometric redshift are plotted as points. The colour of the points represent a photometric redshift estimation of z > 1.4 (red), z < 1.4 (orange) and star (green). We select z > 1.4 star-forming galaxies as sources with (z-K) >(B-z)-0.2 (grey shaded region) and passive galaxies a sources with (z-K) <(B-z)-0.2 and (z-k) > 2.5. ",
+    "incorporates that considered in earlier, similar studies, e.g. A10). In order to identify 3D clustering of sources surrounding the SMGs, we use both the spectroscopically-confirmed (43 sources at z > 1.4, (<>)Smolcic et al. (<>)2012; (<>)Casey et al. (<>)2012a,(<>)b) and photometrically-derived (21 sources with best-fit zphoto > 1.4, (<>)Smolcic et al. (<>)2012) redshifts for the sample. We exclude any SMG from our analysis which has a redshift z < 1.4. Combined with the AzTEC sources without redshifts this gives a total of 234 SMGs in the field (hereafter the COSMOS-SMG sample). A brief summary of the surveys used in this work can be found in Table (<>)2. ",
+    "The ECDF-S has been surveyed at 870µm using the 295-element Bolometer camera LABOCA (the Large APEX Bolometer Camera, (<>)Siringo et al. (<>)2009). We used data from the Large APEX Bolometer Camera Survey of the Extended Chandra Deep Field South (LESS) (for full details see (<>)Weiß (<>)et al. (<>)2009). The LESS map comprises of 200 h of integration time, covering the 0.25 deg2 of the ECDF-S with a uniform coverage of rms=1.2 mJy/beam and a beam FWHM of 19 arcsec. The LESS survey identifies 126 submm bright sources at > 3.7σ in the ECDF-S. We glean redshift data and a small number of additional sources from the data, of which 17 sources have spectroscopic redshifts (Casey et al. 2011, 2012b) and 67 sources have best-fit photometrically derived redshifts of zphoto > 1.4 ((<>)Biggs et al. (<>)2011; (<>)Wardlow (<>)et al. (<>)2011), forming a total sample of 136 unique submil-limeter sources. We note that this ‘ECDFS-SMG’ sample contains ∼ 60% of the number of SMGs in the COSMOS field while covering only ∼ 35% of the area. The number density of SMGs in the ECDF-S remains much higher than that in COSMOS even when considering sources to comparable 1.1mm depth (see Table (<>)2) and will be discussed further in Section (<>)5.5. ",
+    "Table 1. The colour selection criteria used to identify star-forming galaxies at z ∼ 2, 3 and 4. An additional I-J colour selection is applied at z ∼ 4 in order to reduce contamination from low redshift sources (see (<>)Stanway et al. (<>)2008). ",
+    "Table 2. Summary of survey data used in this work. (1) Field covered, (2) survey name, + denotes that the survey in supplemented with additional sources, (3) wavelength of survey, (4) area of survey region in deg2 , (5) survey depth -for optical-NIR surveys this is the limit for reliable photometric redshift estimation, (6) number of source identified in the region -for optical-NIR surveys this is for sources with R<25.5, (7) number of sources with photometric redshifts at z > 1.4, (8) number of spectroscopically confirmed SMGs at z > 1.4, (9) depth of the survey at 1.1mm, assuming source flux scaling of f ∝ λ−2 for LESS -in order to compare depths of submm surveys directly, (10) number of galaxies which would be detected as 3.5σ sources to the 1.1mm flux limit of the AzTEC/COSMOS survey. Note the high number density of SMGs in the ECDF-S relative to COSMOS, even after adjusting for observed wavelength. "
+  ],
+  "3 ANALYSIS ": [],
+  "3.1 2D Correlations ": [
+    "We first consider the projected number density of star-forming galaxies in the plane of the sky, using only the crude colour selections and no additional redshift information. We produce number density maps using the method outlined in (<>)Dressler ((<>)1980) and also in A10. For each of our high redshift samples, and each field, we grid the region into equally spaced positions separated by 7 . Each grid position is then assigned a value ρn, defined as: ",
+    "where dn is the distance to the nth nearest object. We scale the derived number density values for a given value of n with respect to the mean and standard deviation of the density distribution over the entire field, in order to assess the significance of any over-dense regions 1 (<>). For consistency with earlier work by A10, we consider the case n = 7 for the sBzK samples. A ∼ 3× standard deviation galaxy over-density (relative to the mean of our sBzK sample, d7=0.43 Mpc) occurs when 7 source occupy a region defined by d=0.375 Mpc or less. For our other photometric samples, at z ∼ 3 and 4 and in our pBzK sample, we use n = 3 to produce our density maps -selected such that an over-density of the same significance occurs on the same scale as that defined above for sBzKs. In selecting these values of n, we are sensitive to structures on small projected ",
+    "angular scales, and also study the density with a reasonably large sample of data points. In the Section (<>)4.3 we shall also discuss how varying the choice of n affects the over-densities which are identified. "
+  ],
+  "3.2 3D Correlations ": [
+    "We also undertake a clustering analysis in three dimensions, using the accurate photometric redshifts of (<>)Ilbert et (<>)al. ((<>)2008) in COSMOS, and (<>)Cardamone et al. ((<>)2010) in the ECDF-S. Where either an SMG or a peak in the projected number density has been identified, we generate redshift distributions surrounding that location in Δz = 0.1 bins (similar to the typical photometric redshift error on the star-forming galaxies). For SMGs with known redshifts we centre the redshift bins on the precise SMG redshift. We investigate these redshift distributions on 0.375, 0.75, 1.5, and 6 Mpc scales (co-moving). In this manner we aim to identify clustered sources on a broad spectrum of scales, ranging from nascent galaxy clusters right down to the formation locations of individual galaxies. We also consider both Δz = 0.2 and Δz = 0.3 binning. We find that -as expected -any clustering signal is reduced by averaging over a larger redshift interval, and so do not present detailed results for these cases. In the following, we discuss results derived from the Δz = 0.1 binning. ",
+    "We consider four different types of regions: ",
+    "• Volumes centred on SMGs and also associated with a region of high-projected number density in the 2D analysis, are examined for peaks in the galaxy photometric redshift distribution coincident with the SMG redshift, assessing the validity of the 2D analysis (Section (<>)5.1.1). ",
+    "We define the significance of any redshift spike in terms of the standard deviation, σ, of number counts in regions on the same angular scale and redshift bin size, measured across the full field under examination. We define > 3σ peaks as significant if these occur either at the SMG redshift (if known) or at z > 1.4 (if unknown). We consider a number of angular scale griddings and so are sensitive to both over-densities with a small number of galaxies on small scales, and more populated structures on larger scales. This method also selects systems of varying number density and size as a function of redshift -an identical number of clustered galaxies on a fixed scale becomes more significant as redshift increases. As such, while the structures identified in this work vary dramatically in absolute numbers of galaxies and scale, they are all significant over-densities for their redshift and physical size. ",
+    "We summarise the structures identified using this method in Table (<>)3 which compiles the number of clustered regions identified at each stage of our analysis. A more detailed discussion of individual sources, including estimated stellar mass of individual systems and comments on their counterparts in simulations, is given in Appendix A, while our main results consider the sample as a statistical whole. "
+  ],
+  "4 TWO DIMENSIONAL OVER-DENSITY ANALYSIS ": [],
+  "4.1 Over-densities in the Projected Number Density ": [
+    "An example of the projected number density maps produced by the method described in section (<>)3 is shown in Figure (<>)3. Regions over-dense relative to the field are shown in dark greyscale while under-dense regions are relatively pale. The locations of SMGs are circled, and comparisons of the two distributions allow us to evaluate the correlation between these. "
+  ],
+  "4.1.1 COSMOS ": [
+    "sBzKs: As Figure (<>)3 shows, we identify a total of 15 regions of high projected number density (>6 times the mean) in sBzK galaxies in the COSMOS field that are within 30 of the position of a sub-mm bright source. We recover three of the four over-dense regions discussed in the A10 work (which considered a similar redshift range in a subset of this field). These are shown on the figure as purple triangles 2, 3 and 4. A10’s Source 5 is not identified in our COSMOS-SMG sample but is associated with an over-density of sBzKs and we add it to our list. Outside of the subfield considered by A10, we locate 11 additional regions where an over-density of ",
+    "sBzK selected galaxies are found within 30 of the position of a sub-mm bright source. However, of these 15 regions (across the full field), just 4 are coincident with an SMG with a known redshift at 1.4 < z < 2.5 (red circles with red crosses). ",
+    "pBzKs: Similar maps (not shown here) are produced for each galaxy selection, in each field. Only one SMG is associated with an over-density of more passive galaxies pBzK at 1.4 < z < 2.5. This region is not associated with any of the over-densities identified in the sBzK sample. Hence for pBzK sources with photometric redshifts, we find no strong evidence for clustering associated with SMGs. However, only a small fraction of the sources colour-selected as pBzKs have photometric redshifts and make our cuts. We shall investigate clustering of pBzKs without photometric redshifts later. ",
+    "LBGs: Moving to higher redshifts, we find find 13 (8) coincident positions between a submillimeter source and LBGs selected to lie at z ∼ 3 (4). None of these are coincident with an overdensity in the sBzK (z < 2.5) sample. However none of the SMGs in these regions have a known redshift, and -as in sBzK cases without SMG redshifts -we must consider the possibility that the small projected separations represents chance alignments. We do so in section (<>)4.2 "
+  ],
+  "4.1.2 ECDF-S ": [
+    "We repeat the above analysis for systems in the ECDF-S region. Due to the smaller field coverage (and therefore number of significant over-densities), we relax our criteria for correlations between submm bright sources and regions of high-projected number density, to include all positions with a > 4.5× the mean over-density of sources (previously > 6× the mean). ",
+    "We find just 6, 1, and 0 such correlations in our sBzK, z ∼ 3 LBGs and z ∼ 4 LBGs sample respectively. As the ECDF-S covers 1/3 of the area of the COSMOS field discussed in this work, the number density of 2D correlations is roughly consistent between both fields. Of the 6 regions identified in the sBzK sample, 4 have SMGs with a redshift consistent with the star-forming galaxies. This matches the number in the COSMOS field. However, as noted previously, the ECDF-S contains much higher number density of submm bright sources than COSMOS (136 compared to 234 while only covering ∼ 1/3 of the area, to the same depth). This is even more apparent when only considering SMGs with either spectroscopic or photometric redshifts at 1.4 < z < 2.5 (the range covered by the sBzK selection), where the ECDF-S contains 53 SMGs in comparison to just 37 in COSMOS. This suggests that the number of 2D correlations in the ECDF-S is less than might be expected, if the results in the COSMOS field are representative (see Section (<>)5.5), even before the probability of chance alignments (which is obviously higher for ECDF-S) is taken into account. "
+  ],
+  "4.2 Likelihood of Chance Alignment ": [
+    "In order to estimate the incidence of chance alignments between SMGs and star forming galaxy over-densities, we randomly reposition all SMGs in each field and repeat our analysis. We note that produces a crude estimate since the real ",
+    "Figure 3. The projected number density map of sources in the sBzK in the COSMOS field. Dark colours represent regions of high projected number density. The circles represent the COSMOS-SMG sources in the field. The region covered by the MAMBO-2 map used by A10 is bounded by the dashed line. The red circles represent COSMOS-SMG sources which are within 30 of a > 6× standard deviation over-density of star-forming galaxies (these are labeled with red numbers and referenced in Section (<>)4.1). The purple triangles are MAMBO-2 submm sources which are within 30 of a > 6× standard deviation over-density of BzK galaxies and are discussed in A10 (labeled with purple numbers and also referenced in Section (<>)4.1). Crosses denote SMGs with either a spectroscopic redshift or best fit photometric redshift taken from (<>)Smolcic et al. ((<>)2012); (<>)Casey et al. ((<>)2012a,(<>)b) and references therein. Red crosses highlight sources where the SMG falls within the redshift range of the colour selection for star-forming galaxies (1.4 < z < 2.5), while green crosses mark all other sources which have a known redshift. ",
+    "Figure 4. The distribution of the number of sub-mm sources with a chance association with a random distribution of star-forming galaxies for the sBzK (left), z ∼ 3 (middle) and z ∼ 4 (right) samples. We produce 10,000 realisations of a random distribution of points of the same number as the sources in each of our samples. We then identify the number of sub-mm sources that have a > 6× the standard deviation over-density within 30 in each sample. The distribution of the number of sub-mm sources with a chance > 6× the standard deviation association is plotted as the solid histogram. The dashed line represents the number of sub-mm sources with a > 6× the standard deviation association in our data sample. Clearly, in all samples the number of sub-mm sources with an association is consistent with a random distribution of points. ",
+    "galaxy population is not drawn from a random distribution, but is spatially correlated, even when projected on the sky. Furthermore, this method does not account for the effect of over-densities of galaxies on background SMGs (which are at a much higher redshift). Over-densities in the mass distribution of the cosmic web may cause lensing of background SMGs, increasing their observed flux and allowing them to be identified in submm surveys. As such, any lensing will cause background SMGs in the line of sight of galaxy over-densities to be preferentially identified and enhance any 2D clustering signal. While this effect is likely to be small, it can be removed by only considering SMGs with known redshifts. In addition, the above analysis does not take into account that only a fraction of the SMGs are likely to fall at the same redshift as the star-forming galaxies in each of our redshift samples -the SMGs themselves will have a broad range of redshifts. Including sources which are not at the same redshift as the star-forming galaxies will wash out any true 2D clustering signal. ",
+    "Nonetheless, producing 10,000 Monte Carlo realisations of this randomisation process allows some indication of the probability of chance alignment to be assessed. We undertake the analysis in the COSMOS data (the larger of our two fields). Figure (<>)4 presents the incidence of chance alignments of an SMG within 30 of an over-density in the COSMOS field. We find that in each sample the number of high density regions which are coincident with an SMG in our COSMOS sample is consistent with a random distribution. However, the number of correlations in our sBzK sample is somewhat above average for the random distribution (∼ 2σ from the mean predicted number, assuming a Gaussian distribution). This suggests that there is a weak correlation between SMGs and sBzK star-forming galaxies when considering a 2D analysis alone (with no redshift information on the SMG), although the caveats mentioned above hold for any 2D analysis. As already noted, the ECDF-S region is both sparser in observed SMG-overdensity coincidences, and has a higher probability of chance alignments -thus it ",
+    "seems unlikely that SMGs are significantly correlated with sBzK density in this field. "
+  ],
+  "4.3 Affects of changes to our method: choice of n and colour selections without zphoto ": [
+    "The above results suggest that at best there is a very weak correlation between star-forming galaxy density and SMGs when only the crudest redshift information (i.e. zphoto > 1.4) is taken into account. However, it is interesting to consider how this is affected by our method. How does varying our choice of the density scale parameter n affect the number and distribution of correlations we find? And does removing zphoto cuts in our selection improve our clustering signal? If our 2D approach, and that used by A10, is strongly sensitive to our method, then we can not draw reliable conclusions from the analysis above. ",
+    "To investigate this, we vary our choice of n by ±5. We find that varying n has a reasonably significant affect on the number of potential clustered regions we find. For example, in our COSMOS sBzK sample, fluctuating our choice of n by just ±1 varies the number of regions identified by +2 −3, with the lower n value producing a higher number of correlations. This is unsurprising, as at lower values of n fewer individual galaxies are required for a region to be classified as over-dense. This result is true for our samples at all redshifts and in both COSMOS and the ECDF-S. Hence, any statistical correlations derived from our 2D analysis are largely depen-dant on our choice of n and as such, can not be deemed reliable. However, while this affects our number statistics, it does not rule out diminish the importance of individual clustered regions identified using this method, which may still be significantly over-dense structures by any definition. ",
+    "We find a different but equally significant uncertainty is generated when considering the effects of omitting a photometric redshift cut. In both ECDFS and COSMOS we find that the same selection method identifies different regions than in samples with photometric redshift cuts applied. This "
+  ],
+  "4.4 Summary ": [
+    "Figure 5. Same as Figure (<>)4 but for the sample of pBzk galaxies in COSMOS, with no photometric redshift cut applied to the sample. ",
+    "In summary, while a 2D analysis identifies potential weak clustering of high redshift sources, the individual regions which are identified and their number density is extremely sensitive to the method used (both in choice of n and in the use of photometric redshifts). As a result, we can not perform a statistical analysis on the number and distribution of sources identified in 2D, and a full 3D approach (utilis-ing the maximum possible redshift information in addition to projected alignment) is required. Despite this we do see a potential weak 2D correlation between SMGs and more typical galaxies at z ∼ 2 in the COSMOS field. This is most evident in the passive BzK sample when a photometric redshift cut is omitted from the procedure. However, we can not currently confirm any of the structures identified through pBzKs in 3D, as only a small fraction of pBzK sources have a photometric redshift. The regions identified using the pBzK sample are different to those found using sBzKs and as such, this validates an approach that uses star-forming galaxies for cluster searches - as by using passive galaxies we may be missing a large fraction of high redshift galaxy clusters. ",
+    "is compounded by changes in the number of regions selected due to varying our choice of n in this sample. ",
+    "Hence both the number and distribution of clustered regions is dependant on details of our method. As a result we conclude that a 2D analysis is a valid method primarily for identifying regions with which to follow up with a 3D investigation, rather than to generate statstical samples. ",
+    "However, we do note one interesting corrollary that arises from this analysis. The relatively smooth spectral energy distributions of passive pBzK selected sources mean that only a small fraction of those selected based on colour have accurate photometric redshifts -only ∼ 10% of pBzK sources in the COSMOS field have a known photometric redshift, compared to ∼ 35% of sBzK sources in the MUSYC sample. When the cut on photometric redshift quality is removed, our estimate of the clustering strength of passive BzK sources dramatically changes. Using n=3, as in the analysis discussed above, we would now find 14 spatial coincidences between over-densities of pBzK sources and an SMG in COSMOS. This is significantly higher than the mean expected from a random distribution (∼ 6, Figure (<>)5), and suggests that pBzK systems are potentially the most effect method for identifying clustering at these redshifts in the absence of detailed 3D redshift information. However, it is difficult confirm any of these clustered structures without detailed spectroscopic follow up. ",
+    "Comparing the potential pBzK over-densities to those identified using actively star-forming galaxies at the same redshift (our sBzK sample), we find that only one structure is identified in both samples. As such, using both passive and actively star-forming galaxies identifies different systems at z ∼ 2. This strengthens the motivation for searching for actively star-forming clusters at high redshift, as we are likely to identify different structures to those found using passive galaxies alone. "
+  ],
+  "5 THREE DIMENSIONAL OVER-DENSITY ANALYSIS ": [],
+  "5.1 SMGs with known redshifts ": [],
+  "5.1.1 SMGs identified with two-dimensional over-densities ": [
+    "Four SMGs with known redshifts were found to be spatially coincident with a 2D over-density of galaxies in the COSMOS field, and a further four in the ECDF-S (see Section (<>)4.1). ",
+    "Now exploiting the full redshift information available for each source, we probe clustering on a number of scales by identifying > 3σ excesses in the redshift distribution, relative to that over the entire field in the relevant survey. We also apply the constraint that there must be at least three sources in a Δz = 0.1 peak for it to be selected (removing shot noise of single sources at high redshifts and on small scales). For spectroscopically confirmed sources we only identify peaks which are within Δz = ±0.1 of the SMG redshift, while for SMGs with photometric redshifts we select over-densities within a window defined by combining the photometric uncertainty on the SMG with the typical, Δzphoto = 0.1, uncertainty on the star-forming galaxies. ",
+    "We find two of the four SMGs with known redshifts in COSMOS, and just one of the four in the ECDF-S (that of LESSJ033336.8-274401), show an over-density of galaxies in redshift as well as projected space in their surrounding volume (see the appendix and Figure (<>)A1 for more details). ",
+    "As such, only ∼ 40% of regions identified in our 2D analysis (with the caveat of effects due to our choice of n and galaxy selection method) are confirmed in a fuller analysis. Once a three dimensional over-density has been identified we refine the size of the surrounding region for which we measure the photometric redshift distribution, rather than allowing this to vary, but restrict this region to a square to avoid complex clustering selection (as shown by the dashed region in the bottom panels of Figure (<>)A1). "
+  ],
+  "5.1.2 SMGs with over-densities identified only in three dimensions ": [
+    "In addition to the structures identified above, we also consider the volume surrounding all SMGs in the COSMOS field with known redshifts (irrespective of the previous determination of a 2D galaxy over-density). We find a further five regions in COSMOS where an SMG is coincident with a redshift peak (Figure (<>)A2), and three such regions in the ECDF-S. ",
+    "The over-densities we identify around SMGs with known redshifts in COSMOS (both in this and the previous subsection) constitute either a small number of sources over a small volume producing a highly significant over-density (as in the case of AzTEC/C8 and 1HERMESX24J100023.75+021029) or less significant over-densities on larger scales (as in 1HERMESX24J100024.00+024201 and 1HERMESX24J100038.88+024129). The former of these are likely to represent individual massive galaxies in formation, while the latter are potential forming clusters and groups. The most intriguing of these regions is 1HERMESX24J100046.31+024132 which contains a significant over-density of 10 sources spanning Δz = 0.2 at z ∼ 1.9 over a 0.5 × 0.5 Mpc region. We note that the region surrounding AzTEC/C6 is the same as that identified around COSBO-3 in the previous work of A10. COSBO-3 is the only SMG in an over-density from A10 which has a known redshift at z > 1.4 and is also detected in the AzTEC maps (and so is used in our analysis). Hence, this detection is in agreement with the A10 results and displays consistency between our methods. Properties of all of the over-dense regions selected in the paper are given in Table A1 of the Appendix. ",
+    "This number density of SMG + over-densities in ECDFS is consistent with that which is found in the COSMOS field. The ECDF-S contains around half the number of clustered regions showing a three dimensional excess around SMGs with known redshifts (4 compared to 7), while also containing roughly half the number of SMGs. We find that two of the regions in the ECDF-S are exceptionally interesting, those surrounding LESSJ033136.9-275456 and LESSJ033336.8-274401, the former of the two is discussed further in Section (<>)A of the Appendix, while the latter is discussed in Section (<>)7. The other two regions contain SMGs with poorly constrained redshifts, and only moderate over-densities of sources. Hence, we consider these less secure identifications of early clusters. ",
+    "In total, only ∼ 30% (3/11) of over-densities identified around SMGs with known redshifts, using full three dimensional information, were selected in our 2D analysis. As such, in addition to being dependant on method, the 2D analysis misses a significant fraction of clustered regions which can be selected using detailed redshift data. "
+  ],
+  "5.1.3 Population-averaged 3D results ": [
+    "In Section (<>)4.1 we identified a potential weak 2D spatial correlation between SMGs and star-forming galaxies, however it would appear that only a small fraction of SMGs show clear (> 3σ) 3D clustering in their surrounding volume. This suggests that any clustering associated with SMGs may be weak, and may be missed when investigating individual ",
+    "sources. To investigate this, we consider all 63 SMGs in COSMOS (the larger of our target) with known redshifts and assess the statistical significance (which varies with redshift) of the number of lower mass sources in their surrounding volume. ",
+    "Figure (<>)6 shows the number of sources predicted from random regions of 4 arcmin diameter, as a function of redshift (black and red lines, Δz = 0.1 binning). We over-plot the number of galaxies in the volume surrounding COSMOS SMGs with known redshifts (on the same scale). For SMGs with only photometric redshifts (10 of the 63) we take the volume surrounding the best fit photometric redshift. A sub-millimeter galaxy with a significant excess for its redshift would be expected to lie more than three standard deviations above the mean of the random fields. We find that only one SMG is significantly over-dense for its redshift on 4 arcmin scales -the SMG at z ∼ 2.3 (this is in fact AZTEC 7 identified in Section (<>)5.1.1). This suggests that there is no strong clustering around the bulk of SMGs on these scales (as we showed found in Sections (<>)5.1.1 and (<>)5.1.2). ",
+    "However, Figure (<>)6 also indicates that the majority (81%) of the SMGs have a galaxy density in their surrounding volumes that exceeds the mean of the random distribution. This echoes the results found in our two-dimensional analysis -that SMGs and typical galaxy over-densities correlate, but only weakly. As such, it is likely that SMGs reside in over-dense regions relative to the field, but generally not suf-ficiently so to be individually detected as clustered regions. This result is consistent with that found for the surrounding environments of other massive galaxies (QSO hosts) at much higher redshifts ((<>)Husband et al. (<>)2013). ",
+    "We repeat this analysis on 0.25, 0.5, 1 arcmin scales but do not see a clear signal -potentially due to low number statistics -in small projected regions, very few star-forming galaxies occupy each redshift bin. "
+  ],
+  "5.2 SMGs with unknown redshifts ": [
+    "In addition to the SMGs with known redshifts, there are also 171 SMGs in the COSMOS region, and 53 in the ECDF-S, which have neither a spectroscopic nor photometric redshift. While we cannot confirm that these SMGs and any redshift spike in their vicinity are coincident in three dimensions, it is interesting to consider the fraction of SMG fields which contain a spike in their line of sight, relative to blank sky fields. Are redshift over-densities of star-forming galaxies more frequently identified in sight-lines which contain an SMG than those without? In addition, could a line of sight correlation between an SMG and over-density be used to constrain the SMG redshift where no other diagnostic is available? ",
+    "We find 20 regions in COSMOS with a > 3σ galaxy excess in a Δz = 0.1 bin at 1.4 < z < 4.5, coincident with an SMG, and a single additional region in the ECDF-S. (examples are shown in Figure (<>)A3 -for full list of regions identified see Table A1). ",
+    "As we have no redshift information about the SMGs in these regions, it is possible that any number of these structures may be chance superpositions of sources. In order to test this further, we take 1000 realisations of 171 random pointing in the COSMOS region and identify the fraction of these pointings which contain a > 3σ over-density in a Δz = 0.1 bin at 1.4 < z < 4.5 (Figure (<>)7). We only se-",
+    "Figure 6. The predicted number of COSMOS galaxies in a 4 × 4 ×Δz = 0.1 volume, as a function of redshift, in comparison to a similarly sized volume in regions surrounding SMGs with known redshifts. The black line displays the mean predicted number of sources, while the red line shows the 3σ excess beyond which an overdensity might be considered significant as a function of redshift. Stars show the number of sources surrounding individual SMGs, similarly divided by redshift. ",
+    "lect random pointings which are centred at least 2 away from an SMG, to exclude reselecting over-densities associated with the SMGs. Figure (<>)7 clearly shows that the number of correlations around SMGs with unknown redshifts is completely consistent with a random distribution. Similarly, the equivalent analysis on the ECDF-S predicts two such chance alignments (where we found one). ",
+    "We conclude that all of these regions are potentially chance projections of a galaxy over-density with an SMG. Without further spectroscopic information or SMG redshifts, we can not confirm any of the potential cluster candidates identified here, and also cannot use line of sight correlations between SMG and galaxy over-densities to constrain the SMG redshifts, as they are highly likely to be chance superpositions. ",
+    "The potential lack of line of sight correlations between SMGs and galaxy over-densities is surprising. Given that 7 of 63 SMGs with redshifts in COSMOS display an over-density, we may expect ∼ 20 COSMOS SMGs without redshifts to be associated with a true over-density. While this is identical to the number of line of sight matches we find, the bulk of these are likely to be chance superpositions and not truly clustered regions. As such, the number of true line of sight associations is lower than that predicted from the SMGs with known redshifts. ",
+    "Of course, sources with either spectroscopic or photometric redshifts are likely to have either strong emission line features (e.g. (<>)Casey et al. (<>)2012a,(<>)b) or bright rest-frame UV-optical fluxes (e.g. (<>)Smolcic et al. (<>)2012). Therefore, they are likely to form a subsample of the most UV-optically bright SMGs and as such, may display different clustering statis-",
+    "Figure 7. The distribution of the number of pointings that contain a > 3σ over-density of galaxies at 1.4 < z < 4.5 when taking 1000 realisations of 171 pointings (see text for details). The number of SMG fields which contains an over-density is plotted as the dashed vertical line. Clearly this is consistent with a random distribution. ",
+    "tics to the UV-optically faint SMGs without redshifts. Our results may suggest that the SMGs with redshifts and those without may not form a single population. It may also suggest that background SMGs are not significantly lensed by clustered regions at z ∼ 2. If background SMGs were lensed, we may expect sight-lines containing an SMG to preferentially have an over-density of star-forming galaxies (in fact, it would be the over-density that preferentially causes the detection of an SMG through lensing, but the effect should be apparent when targeting either SMGs or over-densities). As we find no excess of over-densities in SMG sight-lines in comparison to random fields, it is likely that any lensing effect from z > 1.4 is minimal. "
+  ],
+  "5.3 Regions of high projected number density and no SMG ": [
+    "We have identified a certain degree of clustering around SMGs, but it is also interesting to investigate whether similar structures exist which are not associated with an SMG but can be targeted simply by galaxy number density. These regions will potentially contain less stellar material (the SMGs are likely to dominate the stellar budget in their surrounding volume) but may be equally likely to form a massive cluster at low redshift. The assumption of lower mass is not clear cut, however: the relatively short SMG duty cycle (< 500 Myr, (<>)Hayward et al. (<>)2011) means that such structures may potentially be associated with an SMG-mass galaxy, detectable either in the past or future. ",
+    "To investigate this further we repeat the process outlined in Section (<>)5.1.1, but target the regions surrounding peaks in the projected number density which are not associated with an SMG (from Figure (<>)3). We once again identify > 3σ peaks in the photometric redshift distribution between ",
+    "1.4 < z < 4.5 on a number of angular scales. We find 32 regions in COSMOS and 3 in the ECDF-S which meet our selection criteria. Figure (<>)A4 displays a selection of these regions (further discussion of individual regions can be found in Section (<>)A of the Appendix, while properties of the full sample can be found in Table A1). The ECDFS BzK 1 region is particularly interesting as it contains a Lyman-alpha blob (LAB, e.g. (<>)Fynbo et al. (<>)1999) falling at the exact same redshift ((<>)Yang et al. (<>)2010) as the over-density of galaxies (for further discussion see Section (<>)8). However the structures identified using this method show a wide variety of properties from large over-densities at moderate redshift containing a relatively large number of sources (such as COSMOS BzK 6) to highly significant over-densities of a small number of sources in a small volume at high redshift (such as COSMOS z3 13/14). Once again, the former of these are likely to form a massive structure at low redshift, while the latter, given the timescales involved, are likely to represent massive galaxies in formation. "
+  ],
+  "5.4 Summary of three dimensional over-densities ": [
+    "In total, we identify 59 regions clustered both spatially and in redshift in the COSMOS field at 1.4 < z < 4.5. Of these, 27 are spatially coincident with an SMG (7 with redshifts), while the other 32 are simply identified as 3D over-densities in the star-forming galaxy population. We identify 8 such regions in the ECDF-S, 5 spatially coincident with SMGs and 3 not associated with SMGs. For a breakdown of the numbers of over-densities identified using each method see summary Table (<>)3. ",
+    "The number of lines of sight which contain both a redshift spike and an SMG is slightly lower than those which just display a redshift spike (even assuming that the SMG and galaxy over-density are associated where there is no redshift information about the SMG -hence an upper limit, see Section (<>)5.2). This suggests that SMGs are not necessarily the most reliable tracers of distant structure. Potentially we are equally likely to identify clustering by targeting regions of high projected number density of star-forming galaxies selected using colour methods (without any detailed redshift information). However, these numbers place no weight on the strength of the over-densities found using each tracer. However, we note that the two most interesting over-dense regions (those around LESSJ033136.9-275456 and LESSJ033336.8-274401 in the ECDFS), potentially the most extreme clusters/proto-clusters in our sample, are both associated with an SMG in 3D. This implies that while the majority of SMGs are found in typical to moderately over-dense environments, a small number of SMGs are found in the most over-dense structures. The region surrounding LESSJ033336.8-274401 is the most extreme example in our study and this is discussed further in Section (<>)7. However a second LESS region, LESSJ033136.9-275456, is the second strongest potential protocluster and thus itself of significant interest. It is discussed in detail in the Appendix. ",
+    "If it is assumed that the SMGs and over-densities discussed are correlated in all cases with spatial coincidence, we find that at best only ∼ 12% of SMGs in the field show any evidence, even loosely, of potential 3D clustering. As a significant fraction of these are likely to be chance superpo-",
+    "sitions of sources, this represents an upper limit to the true number of clustered regions around SMGs. ",
+    "Considering the entire volume probed by this work (at 1.4 < z < 4.5) we find that the number density of volumes with evidence for 3D clustering is a few ×10−7 Mpc−3 . This is comparable to the number density of the most massive (> 1014.5 M) galaxy clusters at z = 0 (e.g. (<>)Wen et (<>)al. (<>)2010). While this does not necessarily mean that we have identified all regions which will eventually form a massive cluster at z = 0 or that all of the structures iden-tified in this work are massive clusters in formation (this has been shown to be extremely unlikely as potentially all of the regions identified without SMG redshifts are likely to be chance superpositions). It is interesting to note that we do not find significantly higher number densities than those of > 1014.5 M clusters at low redshift -if we had, it would be unlikely that these regions represent the progenitors of massive clusters. Simply considering the volume over which the majority of clustered regions surrounding SMGs are found (1.4 < z < 2.6 -assuming we are less sensitive to over-dense regions at z > 2.6) we find a number density of ∼ 10−6 Mpc−3 -comparable to that of ∼ 1014.3 M clusters at z = 0 and once again consistent with the most massive structures. "
+  ],
+  "5.5 Comparisons between COSMOS and ECDF-S ": [
+    "In our 2D analysis, we find 5 times as many projected galaxy over-densities around SMGs in COSMOS than in the ECDFS, while the ECDF-S covers a third of the COSMOS area (see Table (<>)3 for details). As shown previously, the ECDFS region contains a higher number density of SMGs, even when considering sources to a similar flux limit (Table (<>)2). Hence, the discrepancy between the number of 2D clustered regions is even more problematic (with a higher number density of SMGs, we would expect more correlations). Both fields have a similar number density of colour-selected star-forming galaxies satisfying our selection at zphoto > 1.4 and hence it is unlikely that the fidelity of the photometric redshifts of star-forming galaxies is a significant factor in this discrepancy. In combination with the significant effects of varying our method, this discrepency in the number of 2D over-densities identified continues to suggest that a 2D analysis alone is not a reliable method for identifying high redshift clustering. ",
+    "Considering the number of 3D over-densities around SMGs with known redshifts (7 in COSMOS and 4 in ECDFS), we find these to be much more consistent with the number density of SMGs. COSMOS contains roughly twice as many SMGs, when considering the surveys to the same depth, and roughly twice as many spectroscopically con-firmed SMGs. Therefore, the number of 3D over-densities identified around spectroscopically confirmed SMGs is consistent with the total number density of SMGs. "
+  ],
+  "6 IDENTIFICATION WITH PREVIOUSLY KNOWN CLUSTERS ": [],
+  "6.1 Regions in COSMOS ": [
+    "Three regions in our COSMOS sample have previously been identified in the H-band selected HIROCS survey ((<>)Zatloukal et al. (<>)2007). The region surrounding 1HERMESX24J100023.75+021029 is at an identical position and estimated redshift to HIROCS 100023.9+024158, COSMOS BzK 6 is identical to HIROCS 095954.2+022924 and COSMOS BzK 9 to HIROCS 095957.9+024125. As mentioned previously, the region surrounding AzTEC/6 (COSBO-3) was also identified in A10. The re-identification of the HIROCS clusters using a completely different cluster finding technique once again validates our method. ",
+    "Despite these reconfirmations it is nonetheless interesting to investigate why other known high redshift clusters in the field were not selected by our cluster finding method. We select all z > 1.3 (clusters at z > 1.4 should be identified in our sample, however the typical photometric redshift error is ∼ 0.1) known clusters in the field from the literature, all taken from the HIROCS survey, and all at z < 2.0. Of the ten z > 1.3 clusters, only six are coincident with high projected number density region of sBzKs in our maps. We investigate the photometric redshift distribution around these regions on a number of angular scales and find that only three sources (those already identified in our sample and discussed above) display a significant (> 3σ) redshift over-density on any scale. Therefore, the other systems are unlikely to be identified as actively star-forming clusters. The HIROCS clusters are primarily selected as over-densities of NIR-bright sources and as such, they target older, more passively evolving systems than the method described in this work. However, it is interesting to note that the HIROCS clusters not identified through star-forming galaxies are also not coincident with with a 2D over-density of pBzK sources in our analysis. This suggests that these HIROCS clusters would not be identified by a purely 2D analysis alone, even when considering passive galaxies. ",
+    "We note that HIROCS 095954.2+022924 and HIROCS 095957.9+024125 (those identified here as COSMOS BzK 6 and COSMOS BzK 9) are actually among the weakest over-densities identified in the HIROCS survey. However, in our current analysis we identify almost twice as many potential cluster sources as those discussed in (<>)Zatloukal et al. ((<>)2007). Hence, previous work may be missing a significant fraction of the cluster population. We also note that the region surrounding 1HERMESX24J100023.75+021029 (HIROCS 100023.9+024158) was rejected from the final cata-logues of (<>)Zatloukal et al. ((<>)2007) as they found no clear redshift spike in their data, and their colour-magnitude plots suggested it was a chance projection of two structures. The re-confirmation of this region using our analysis, and the spectroscopic confirmation of an SMG at a similar redshift to the over-density spike, suggest that this is in fact a true forming cluster at high redshift and should not have been dismissed. "
+  ],
+  "6.2 Regions in the ECDF-S ": [
+    "We compare the positions of our clustered regions in the ECDF-S with those of known clusters in the region. There ",
+    "are just two known high redshift clusters in the field; [TCF2007] 3, an over-density of sources at z ∼ 1.55 iden-tified in the photometric redshift distribution of the field ((<>)Trevese et al. (<>)2007) and CL J0332-2742, a spectroscopically confirmed forming cluster at z ∼ 1.6 ((<>)Castellano et al. (<>)2007; (<>)Kurk et al. (<>)2009). Both of these clusters correspond to regions of high projected number densities of sBzKs in our 2D maps. While [TCF2007] 3 displays some evidence of a peak in its photometric redshift distribution, it is not significant enough (> 3σ) to be selected using the analysis outlined in this paper. However, the region around CL J0332-2742 is re-identified it as a > 4σ over-density in our analysis. [TCF2007] 3 was selected through its passively evolving galaxy population and, if it contains relatively few star-forming galaxies, it is unsurprising that it remains undetected in our sample. "
+  ],
+  "7 THE LESSJ033336.8-274401 REGION ": [
+    "The region surrounding LESSJ033336.8-274401 is by far the strongest outlier in galaxy density identified in this study and is likely to be an actively star-forming cluster at z ∼ 1.8. The structure contains a highly significant over-density of 23 sources (∼ 27σ) spanning Δz = 0.2 and is consistent both spatially and in redshift with both an SMG and a QSO at z = 1.764 ((<>)Treister et al. (<>)2009). We note that the LESSJ033336.8-274401 region does not fall in the extensively well studied Great Observatories Origins Deep Survey South (GOODS-S) field region of the ECDF-S. While it is covered by the XMM observations of the field, it is situated in an off-axis position and is not obviously associated with any x-ray emission. In addition, given the depths of the sub-millimetre and optical-NIR data in the COSMOS field, if a system such as LESSJ033336.8-274401 were in the COSMOS region, it would have been identified in our analysis as a similar significance over-density. ",
+    "If we search for similarly over-dense regions in the Millennium Run (MR) Simulations (see Appendix A for details) we fail to identify any volumes which are comparable in number density to the LESSJ033336.8-274401 region. This may suggest that the Millennium Run semi-analytic models do not accurately reproduce the most over-dense structures. A potential explanation for this is that the MR does not model a sufficient volume to produce the most extreme structures at high redshift. Our cluster finding search covers ∼ 1 deg2 in total and probes 1.4 < z < 4.5, which equates to a volume of ∼ 0.377 Gpc−3 . In comparison, the MR simulates a volume of ∼ 0.125 Gpc−3 , a third of the volume probed in this work. Therefore, it is unsurprising that we do not find a LESSJ033336.8-274401 type region in the simulation volume. ",
+    "Regions such as LESSJ033336.8-274401 are likely to be key sites in testing the validity of our current paradigm and therefore are highly attractive candidates for spectroscopic follow-up observations which would confirm their nature. Comparisons of such structures with the next generation of large scale cosmological simulations (which should cover sufficient volume to detect these low number density outliers, e.g. the Millennium-XXL, (<>)Angulo et al. (<>)2012), will be paramount to demonstrating the validity of structure formation models. ",
+    "While this region is highly significant as it stands, the restriction of out analysis to square selection regions may be limiting the number of cluster members we have iden-tified. Figure (<>)A5 clearly shows an excess of sources at the cluster redshift falling South of our box-selected region. In addition, the LESSJ033336.8-274401 region lies at the edge of the ECDF-S and we may be missing further clustering which falls out of the MUSYC field 2 (<>). To explore this further, we repeat the analysis discussed in Section (<>)5.1.1 but apply a rectangular selection region, covering the full extent of the over-dense structure (Figure (<>)8). We find that the redshift spike extends over Δz = 0.3 in redshift and spans ∼ 1.5 (∼ 770 kpc at z = 1.8). It contains 36 galaxies (predominantly sBzK sources), an SMG and a QSO essentially at the same redshift (the mean 1σ photometric redshift error on each of the star-forming galaxies is +0−0..04 1 ). Follow up observations of this region are currently being undertaken (Davies et al, in prep). "
+  ],
+  "8 THE ECDFS BZK 1 REGION ": [
+    "As noted previously, the ECDFS BzK 1 region is also of particular (Figure (<>)A6). The structure contains a strong galaxy over-density of 7 sources at z ∼ 2.3 in a very small ∼ 22 (∼ 170 kpc at z = 2.3) region, surrounding a Lyman-alpha blob (LAB, e.g. (<>)Fynbo et al. (<>)1999) at an identical redshift ((<>)Yang et al. (<>)2010). Given the extent of this structure we are likely to be witnessing either a cluster core or massive galaxy in formation. If the former, then we may be witnessing a new mode of star formation in high redshift cluster cores -with actively star-forming systems surrounding what may be a central region of intense, unconstrained star-formation (traced by the LAB). While extended line emission is observed in radio galaxies at these redshifts, and these can can exist in forming clusters (e.g. (<>)Hatch et al. (<>)2011), this system has no strong radio source to power the nebulosity. At low redshifts extended emission line regions exist at the centres of clusters with cooling cores. Given the similarity of the physics of cooling cores and that expected to control the formation of stars out of cooling gas at high redshift, the presence of the ionised gas here may not be surprising. ",
+    "If the system is instead a single massive galaxy in formation, most of the SF appears to be occurring in plain sight -with no submillimeter bright source associated with it in the LESS map. Summing the total K-band estimated stellar mass of the constituent galaxies in this system (see Appendix A for details), we already observe  1011 M. While systems of this mass are found at this redshift, they are typically submm-bright ULIRGS or old passively evolving systems. "
+  ],
+  "9 SUMMARY AND CONCLUSIONS ": [
+    "We have identified clustering of star-forming galaxies at z > 1.4 in both the COSMOS field and ECDF-S using a variety of different methods. Firstly, we compared the 2D distribution of the general population of high redshift galaxies with submm bright sources at the same epoch and find a weak correlation at best. This correlation is most apparent at z ∼ 2, near the peak of the SMG redshift distribution and at the latest epoch probed in this work (where clusters have had more time to coalesce). However, we find that when applying a 3D analysis to the same fields we only confirm a small fraction (30%) of over-densities identified in 2D. In addition, we find that the 2D analysis misses the majority of 3D galaxy overdensities surrounding SMGs with known redshifts. Thus using a 2D analysis alone (with no redshift information beyond simple colour selection) suggests a weak general correlation between SMGs and star-forming galaxies but is an inefficient and unreliable method for selecting individual clustered regions. In addition to this, the significant affects of varying our method renders our 2D approach unsuccessfully in robustly identifying high redshift clustering. ",
+    "We also perform a full 3D analysis of clustering in the volumes surrounding SMGs (using well-calibrated photometric redshift information) and identify eleven regions where an over-density in the general galaxy population is coincident in both spatial position and redshift with the submm bright source. These regions are likely to represent a broad range of clustered regions, from actively star-forming clusters to massive galaxies in formation. Further to this, we investigate the typical environment of the volumes surrounding SMGs with known redshifts and demonstrate that, while only a small number of SMGs display a significant over-density, the majority (∼ 80%) are associated with an above average number of sources for their redshift. This is consistent with the premise that the progenitors of massive ",
+    "Figure 8. The clustered region surrounding LESSJ033336.8-274401. The selected region is expanded to a rectangular shape to encompass all of the cluster members. Left: The photometric redshift distribution of sources surrounding LESSJ033336.8-274401. Right: The spatial position of sources surrounding the SMG. In the left panel, the redshift distribution (black line) is taken from the region bounded by the dashed box in the right panel. The green line shows the mean number of sources (with 3σ error) in a region of this size over the entire ECDF-S. Orange stars mark LESSJ033336.8-27440, while pink squares indicate QSOs. In the right panel, red diamonds indicate galaxies with a photometric redshift which is consistent with the peak in the redshift distribution (bounded by dashed vertical lines in the top panel). Green diamonds are sources within zSMG ± 0.3. In total we find 38 potential cluster members spanning Δz = 0.3 on a ∼ 1.5 scale (∼ 770 kpc at z = 1.8). The region contains 36 high redshift galaxies, an SMG and a QSO. As such, this region is highly likely to be an actively star-forming cluster at z ∼ 1.8. ",
+    "early type cluster galaxies at low redshift, require their seeds to form in over-dense environments where they can grow slowly via minor mergers (e.g. (<>)van de Sande et al. (<>)2013). If SMGs are such progenitors, then the consistently above average number of sources in their surrounding volume may provide a constant supply of these minor merger systems. ",
+    "We identify a further 21 regions where an SMG (without a redshift) and over-density of star-forming galaxies are coincident in the line of sight. The number of over-densities in random pointings selected in an identical manner, is 21 ± 4. As such, it is likely that all regions where an SMG and over-density are coincident in the line of sight are chance superpositions. ",
+    "In comparison, we also identify 35 regions where a 3D over-density is suggested by a region of high projected number density of star-forming galaxies, but does not have an SMG. This suggests that we are equally likely to identify 3D clustering by targeting such regions as targeting SMGs. However, the significance of the 3D over-densities identified does show a bias, as the most interesting over-densities identified in our analysis (LESSJ033136.9-275456 and LESSJ033336.8-274401) are both associated with SMGs in three dimensions. ",
+    "In conclusion we find that: ",
+    "Using star-forming galaxies we can identify individual clustered regions at high redshift. This is highlighted by regions such as LESSJ033336.8-274401 and the reconfirmation of ",
+    "known clusters in the COSMOS field, and opens up a new channel for cluster identification at redshifts where the red sequence method fails. ",
+    "significant found in this study and is highly likely to represent an actively star-forming cluster at z ∼ 1.8. The structure contains 36 galaxies, an SMG and a QSO all at essentially the same redshift. This region is therefore a highly attractive candidate as, not only one of the highest redshift clusters yet identified, but also as one of the first high redshift clusters to be identified through its actively star-forming galaxy population. We do not identify similar volumes to that surrounding LESSJ033336.8-274401 in the Millennium Run simulation. This suggests that either the simulations do not probe a large enough volume to produce the most massive structures or the LESSJ033336.8-274401 region serendipitously falls in the well studied ECDF-S. Either way, if confirmed, regions such a LESSJ033336.8-274401 are likely to be key sites in testing our current cosmological model. ",
+    "• The region of ECDFS BzK 1 is also intriguing, containing a significant over-density of sources surrounding a Lyman-α blob at the same redshift. In this system we may be witnessing a new mode of star formation in high redshift cluster cores -with actively star-forming galaxies surrounding a central region of intense, unconstrained star-formation. "
+  ],
+  "ACKNOWLEDGEMENTS ": [
+    "We would like to thank the anonymous referee for their extremely helpful comments which have improved this paper. LJMD, KH and EJAM acknowledge funding from the UK science technologies and facilities council. This paper makes use of data obtained for APEX program IDs 078.F-9028(A), 079.F-9500(A), 080.A-3023(A), and 081.F-9500(A). APEX is operated by the Max Planck-Institut fur Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory. "
+  ]
+}

jsons_folder/2014MNRAS.439..623G.json

@@ -0,0 +1,169 @@
+{
+  "Robert J.J. Grand ⋆ , Daisuke Kawata, Mark Cropper ": [],
+  "Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT ": [],
+  "ABSTRACT ": [
+    "Recent numerical N-body simulations of spiral galaxies have shown that spiral arms in N-body simulations do not rotate rigidly as expected in classic density wave theory, but instead seem to rotate at a similar speed to the local rotation speed of the stellar disc material. This in turn yields winding, transient and recurrent spiral structure, whose co-rotating nature gives rise to changes in the angular momentum (radial migration) of star particles close to the spiral arm at many radii. From high resolution N-body simulations, we highlight the evolution of strongly migrating star particles (migrators) and star particles that do not migrate (non-migrators) around a spiral arm. We investigate the individual orbit histories of migrators and non-migrators and find that there are several types of migrator and non-migrator, each with unique radial evolution. We find the important quantities that a˙ect the orbital evolution to be the radial and tangential velocity components in combination with the azimuthal distance to the spiral arm at the time the star particle begins to feel tangential force. We contrast each type of orbit to compare how these factors combine for migrators and non-migrators. We find that the positive (negative) migrators sustain a position behind (in front of) the spiral arm, and feel continuous tangential force as long as the spiral arm persists. This is because the positive (negative) migrators are close to the apocentre (pericentre) epicycle phase during their migration, and rotate slower (faster) than the co-rotating spiral arm. On the other hand, non-migrators stay close to the spiral arm, and pass or are passed by the spiral arm one or two times. Although they gain or lose the angular momentum when they are behind or in front of the spiral arm, their net angular momentum change becomes close to zero. We discuss also the long term e˙ects of radial migration on the radial metallicity distribution and radial angular momentum and mass profiles. ",
+    "Key words: galaxies: evolution -galaxies: kinematics and dynamics -galaxies: spiral -galaxies: structure "
+  ],
+  "1 INTRODUCTION ": [
+    "Radialmigrationreferstoachangeintheguidingcentreofastarasitorbitsthegalacticcentre.Theprincipalphenomenonthatcausesradialmigrationistheinteractionwithnon-axisymmetricstructuresuchasspiralarms,especiallyaroundtheco-rotationradius(e.g.(<>)Goldreich&Lynden-Bell(<>)1965;(<>)Lynden-Bell&Kalnajs(<>)1972;(<>)Sellwood&Binney(<>)2002).Unlikeothermechanismssuchasmolecularcloudscattering((<>)Spitzer&Schwarzschild(<>)1951,(<>)1953)anddiffusionthroughphasespace((<>)Binney&Lacey(<>)1988;(<>)Brunettietal.(<>)2011),radialmigrationbyspiralarmsdoesnotnecessarilyincreasetheorbitaleccentricityofthestars((<>)Lynden-Bell&Kalnajs(<>)1972).",
+    "Thephenomenonwasfirstdiscoveredby(<>)Goldreich&Lynden-Bell((<>)1965)and(<>)Lynden-Bell&Kalnajs((<>)1972).Forastanding,long-liveddensitywavepattern,theangularrotationspeedofthespiralarms,thepatternspeedp,isconstantovertheentireradialrangeofthespiralstructure.Thereisasingleradialpointinthediscwherethespiralarmsrotateatthesamespeedasthediscmaterial.Astarnearthespiralarmatthisradiusmaythereforebeacceleratedordeceleratedsuchthatthestarguidingcentremovesawayfromortowardsthegalacticcentrerespectively.Thisco-rotationradiuswasfoundtobetheonlyradiusinthediscaroundwhichradialmigrationfromspiralarmswithoutheatingcanoccur((<>)Lynden-Bell&Kalnajs(<>)1972;(<>)Lépineetal.(<>)2003).",
+    "(<>)Sellwood&Binney((<>)2002)showedthattheradialmi-",
+    "grationprocesscanhavelongtermeffectsontheentirestellardisc(whichtheytermradialmixing)ifthediscdevelopssuccessivetransientspiralarms.Transientspiralarmsareseeninallsimulationsandtheirexistencerepresentsadeparturefromclassicdensitywavetheory((<>)Lin&Shu(<>)1964),inwhichthespiralarmsarelong-livedandstandingwavefeatures.Instead,whilethereductionofnumericalnoiseasaresultofimprovedresolution(N > 106 ,asdescribedin(<>)Fujiietal.(<>)2011)enablesthespiralmorphologyofgalaxiestopersistformanyrotationperiods,simulationsrepeatedlyshowthatindividualspiralarmsdisappearandreappearonthetimescaleofagalacticrotation.",
+    "Radialmigrationproducedfromtransientspiralarmshasbeenhighlightedinmanyrecentnumericalstudies((<>)Roškaretal.(<>)2008;(<>)Minchev&Famaey(<>)2010;(<>)Fujiietal.(<>)2011;(<>)Grandetal.(<>)2012a,(<>)b;(<>)Minchevetal.(<>)2011,(<>)2012;(<>)Fujii&Baba(<>)2012;(<>)Roškaretal.(<>)2012;(<>)Solwayetal.(<>)2012),althoughtheprecisemechanismoftheradialmigrationprocessisstilldebated,whichstemsmainlyfromuncertaintiesinourunderstandingofthespiralarmnature.Forexample,(<>)Minchev&Quillen((<>)2006);(<>)Minchev&Famaey((<>)2010);(<>)Comparetta&Quillen((<>)2012);(<>)Chamandyetal.((<>)2013)explainthetransientspiralarmsasasuperpositionofmultipledensitywavemodepatternsthatspanseparateradialrangesthatoverlap.Becauseinnerpatternsrotatefasterthanouterpatterns,theyaresaidtoconstructivelyinterfereperiodicallywhichcausesthegrowthanddecayofaspiralarmonthetimescaleofaninterference.Ontheotherhand,otherstudies(e.g(<>)Wadaetal.(<>)2011;(<>)Grandetal.(<>)2012a,(<>)b;(<>)Fujiietal.(<>)2011;(<>)Fujii&Baba(<>)2012)reportthespiralarmtobeanamplifiedover-densitywhoserotationspeedmatchesthatofthediscmaterialatallradii.Suchspiralarmsarenaturallywindingandtransientasshownby(<>)Wadaetal.((<>)2011)whoreportstransientspiralarmsthatexhibitaverysmoothlydecreasingpatternspeedasafunctionofradius.Theco-rotatingspiralarmissupportedby(<>)Grandetal.((<>)2012a,(<>)2013),whoperformedN-bodysimulationsofnon-barredgalaxiesembeddedinastaticdarkmatterhalopotentialandtracedthespiralarmpeakdensitydirectlyfromthedensitydistribution.Thisisfurtherbacked-upby(<>)Roca-Fàbregaetal.((<>)2013),whoperformedhighresolutionN-bodysimulationswithalivedarkmatterhalo.",
+    "Theorbitalevolutionofparticlesthatradiallymigratehastodatebeendiscussedinfewstudies.(<>)Roškaretal.((<>)2012)explainthatinaspiraldiscofmultipleco-existingdensitywavepatterns,radialmigrationoccursonlyattheco-rotationradiusofeachpattern.Fromasampleofstarparticleschosenfromthetop10% ofmigrators,theyinterpretradialmigrationoveralargeradialrangeastwosuccessivediscreteparticle-patterninteractions,whereaparticlemaybetransportedfromtheco-rotationradiusofonepatternclosetothelocationoftheotherpattern.Inourpreviouswork,(<>)Grandetal.((<>)2012a,(<>)b),weshowedthatradialmigrationcanoccurcontinuouslyoveralargeradialrangeuntilthespiralarmdisappears.WeexaminedindividualN-bodystarparticlesandfoundthattheorbitaleccentricitywaslargelyconserved.(<>)Babaetal.((<>)2013)studytheorbitevolutionofstarparticlesintheirhighresolutionN-bodysimulation.However,theyfocusonarandomsampleofstarparticlesassociatedwiththe“non-steady”spiralarmsinordertolinktheformationanddisruptionofspiralarmsto",
+    "themotionsofitsconstituentstars,withlessfocusonradialmigration.",
+    "Inthispaper,wecomplementthesestudiesandbuilduponourownworkbyrunningahighresolutionsimulationofagalacticdisctoexploreindetailtheinteractionofstarparticleswiththespiralarm.Inparticularwefocusonstarparticlesthatshowsignificantradialmigration(migra-tors),andstarparticlesthatshowalmostnomigration(non-migrators)betweenthebirthanddeathofaspiralarm.Wepresentdetailedstep-by-stepevolutionofeachgroupofparticle,whichrevealsseveraltypesofmigratorsaswellasnon-migratorseachwithdifferentorbitalcharacteristics,noneofwhich(toourknowledge)havebeenreportedinliterature(includingourpreviousworks,(<>)Grandetal.(<>)2012a,(<>)b).Individualorbitsaretrackedextensivelytocoverthetimebefore,duringandafterasinglespiral-particleinteraction.Ourspiralarmpeaktracingmethod((<>)Grandetal.(<>)2012b)enablesustofollowtheevolutionoftheparticlepositionwithrespecttothespiralarm,whichisaquantitycurrentlyunexploredintheliterature.Thisisanimportantdiagnosticthatallowsustoidentifyandexplainthepropertiesofthemigrating/non-migratingstarparticlesinourMilkyWaysizedsimulation.Therefore,thesetypesoforbitsmaybeobservablefortheGalaxyinGalacticsurveyssuchasRAVE(e.g.(<>)Steinmetzetal.(<>)2006;(<>)Pasettoetal.(<>)2012a,(<>)b;(<>)Siebertetal.(<>)2012;(<>)Williamsetal.(<>)2013),Gaia (e.g.(<>)Lindegrenetal.(<>)2008),Gaia-ESO((<>)Gilmoreetal.(<>)2012),APOGEE(e.g.(<>)AllendePrietoetal.(<>)2008;(<>)Bovyetal.(<>)2012),SEGUE(e.g.(<>)Yannyetal.(<>)2009;(<>)Leeetal.(<>)2011),LAMOST(e.g.(<>)Chenetal.(<>)2012)and4MOST((<>)deJong(<>)2012).",
+    "Themainresultsofthispapercomefromthedetailedanalysisofmanyindividualstarparticleorbits,henceforbrevityweshowtheresultsfromonehighresolutionsimulation.Howeverwebrieflydiscusstheapplicabilityoftheseresultstoothersimulationsofdifferentspiralstructure,anddiscusstheeffectsofradialmigrationontheglobalproperties,suchasthemetallicityandangularmomentumdistribution.",
+    "Thispaperisorganisedasfollows.InSection2,wedescribethesimulation.InSection3,wedescribeourparticleselection.InSection4weanalysethegroupevolutionofthesamplesinvariousphasespaceprojectionsanddescribeoverallmacroscopicbehaviour.Wethenexaminetheorbitsofindividualparticlesandcategoriseseveraltypesofmigra-torsandnon-migratorsinSection5.Theorbitalcharacteristicsofeachtyperevealdeterminingfactors,whichwhencombinedtogetherdistinguishthemigratorsfromthenon-migrators.Insection6,wediscusstheapplicabilityoftheresultstoothersimulations,andbrieflyshowtheevolutionoftheglobalmassandmetallicitydistributionsasaconsequenceoftheradialmigration.Insection7,wesummariseourconclusions."
+  ],
+  "2 SIMULATION ": [
+    "ThesimulationinthispaperisperformedwithaTreeN-bodycode((<>)Kawata&Gibson(<>)2003;(<>)Kawataetal.(<>)2013),andsimulatesagalaxycomprisedofasphericalstaticdarkmatterhaloandalivestellardisconly(foramoredetaileddescriptionofthesimulationset-up,see(<>)Grandetal.(<>)2012a).",
+    "Alivedarkmatterhalocanrespondtothe",
+    "self-gravitatingstellardiscbyexchangingangularmomentum.Thisisprominentonlongtimescalesforlong-livednon-axisymmetricstructuressuchasabar((<>)Debattista&Sellwood(<>)2000;(<>)Athanassoula(<>)2002,(<>)2012).However,theeffectofthelivedarkmatterhaloisexpectedtobesmallfortransientspiralarms,whichjustifiestheuseofastaticdarkmatterhaloforourinvestigation.Furthermore,forpracticalreasonsalivedarkmatterhaloisoftenmod-elledwithparticlesmoremassivethandiscparticles,whichmayintroducesomescatteringandheatingthatdependsonthescaleofthemassdifferencebetweentheparticlespecies.Therefore,intheinterestofcomputationalspeedandamorecontrolledexperiment,weuseastaticdarkmatterhalo.",
+    "Thedarkmatterhalodensityprofilefollowsthatof(<>)Navarroetal.((<>)1997)withtheadditionofanexponentialtruncationterm((<>)Rodionov&Athanassoula(<>)2011):",
+    "(1)",
+    "whereˆc isthecharacteristicdensitydescribedby(<>)Navarroetal.((<>)1997),theconcentrationparameter,c = r200/rs = 20,andx = r/r200.Thetruncationterm,exp(−x2),isneededtoensurethatthetotalmassisconvergent.Itdoesnotchangethedarkmatterdensityprofileintheinnerregionofthedisc,whichisthefocusofthispaper.Thescalelengthisrs,andr200 istheradiusinsidewhichthemeandensityofthedarkmattersphereisequalto200ˆcrit (whereˆcrit= 3H02/8ˇG;thecriticaldensityforclosure):",
+    "(2)",
+    "whereM200 = 1.5 × 1012 M⊙,h = H0/100 km s−1 Mpc−1 .Weassume0 = 0.266,b= 0.0044 andH0 = 71 km s−1 Mpc−1 .",
+    "Thestellardiscisassumedtofollowanexponentialsurfacedensityprofile:",
+    "(3)",
+    "whereMd,∗ = 5 × 1010 M⊙ isthediscmass,Rd,∗ = 3.5 kpcisthediscscalelengthandzd,∗ = 350 pcisthediscscaleheight.ThesimulationpresentedinthispaperhasN = 1×107 particlesinthestellardisc,sothateachstarparticleis5000 M⊙.ThisissufficienttominimisenumericalheatingfromPoissonnoise((<>)Fujiietal.(<>)2011;(<>)Sellwood(<>)2013).Weapplyafixedsofteninglengthof160 pc(Plummerequivalentsofteninglengthof53 pc)forstarparticleswiththesplinesofteningsuggestedby(<>)Price&Monaghan((<>)2007)."
+  ],
+  "3 PARTICLE SELECTION OF STRONG MIGRATORS AND NON-MIGRATORS ": [
+    "Inthisstudy,wefocusonsinglespiralarm-starparticleinteractionsonthetimescaleofthespiralarmlifetime,whichwefindtobe˘ 100 Myr.Wescrutinizetheevolutionofasampleofstarparticlesinordertoobtaindetailedinformationontheseinteractions.",
+    "Thefirststepistoidentifycoherentspiralarmsforwhichwecanreliablytracethespiralarmpeakposition.Areliabletraceisdefinedasaradialrangeforwhicheachradialpointshowsasmoothsingledensitypeakinazimuth.Asnapshotinwhichthespiralarmexhibitsadoublepeakstructureanywherewithinthedefinedradialrangefortracingisrejected.Doublepeakfeaturesareusuallyassociatedwiththeformationanddestructionstagesofspiralarmevolution,andarenotsuitableforanunambiguoustrace(see(<>)Grandetal.(<>)2012b,formoredetails).Fig.(<>)1showstheface-ondensitysnapshotsofourselectedspiralarm.Thereisatimewindowoverwhichthespiralarmcanbereliablytraced,andawidertimewindowwhichwillbeusedtoexaminethepriorandsubsequentstarparticlebehaviour.Wecouldtracethespiralarmreliablyattheradiibetween6and10kpcinthetraceabletimewindowspanningt = 1.968 to2.024 Gyr(highlightedwiththewhitelineinFig.(<>)1).Outsideofthistimewindow,weextrapolatethespiralarmpositionbyrotatingtheR = 7, 8 and9 kpcpeakpositionsofthet = 2.0 Gyrsnapshotwiththecircularvelocity(anchorsmarkedwithwhitecrosses)toguidetheeyetothespiralarmwhenitformsanddisrupts.Thepatternspeediscalculatedbysimplesubtractionofthepeaklinebetweensnapshots.Fig.(<>)2showstheradialprofileofthetime-averagedpatternspeed(dashedredline)andtheangularrotationalvelocityofthedisc(solidblackline).Thelatteriscalculatedfromtheradialforceaveragedoverazimuthforeachradius.Fig.(<>)2confirmsthatthespiralarmisco-rotatingwiththerotationalvelocityofthedisc(asshownin(<>)Grandetal.(<>)2012a;(<>)Roca-Fàbregaetal.(<>)2013).Fortherestoftheanalysis,wefocusonparticleinteractionswiththisspiralarm.",
+    "Wechooseasnapshotatatimewhenthespiralarmisfullyformedandadoptt = 2.0 Gyr(Fig.(<>)1)asthetimeofparticleselection.Fromthetracedspiralarmatthistime,wedefinearegionwithinarangeof4 kpceithersideofthedensitypeakofthespiralarmintheazimuthaldirection.Theregionisboundedbyaradialrangeof6 -10 kpcandaverticalheightof|z| < 0.1 kpc.Thesampleisconstitutedofparticlesfoundinsidethisspatiallydefinedregionatt = 2.0 Gyr.Thisprobesawiderangeinradiusandazimuthalpositionwithrespecttothespiralarm,andrestrictsthemajorityofparticlestobeintheplaneofthediscbecausemoremigrationtakesplaceintheplaneofthedisc.Notethatovertime,theverticaloscillationscausesomeparticlestomovetoheightsthatexceedtheselectioncutof|z| < 0.1 kpc.Wefoundthatabout15% ofthestarparticlesselectedreachzmax> 0.35 kpc(oneinitialgalacticscaleheight).However,wefindthatthereisnosignificantdifferencebetweenthetrendsdiscussedinthispaperforparticlesofdifferentmaximumheights.",
+    "Thetimeatwhichthestarparticlesareselectedisde-finedasthecentraltimestep,Tc= 2 Gyr,andatimewindowisthendefinedasT = Tfin−Tini,whereTini= Tc−48 MyrandTfin= Tc+ 48 Myr.Thistimewindowspansthe˘ 100 Myrlifetimeofthespiralarm.Notethatthistimewindowislongerthanthetimewindowforwhichwecouldtracethespiralarm.However,asseeninFig.(<>)1,thespiralarmbeginstoformataroundt = 1.952 Gyranddisruptsataroundt = 2.048 Gyr.Themotionofnearbystarparticlescanbeaffectedatthesetimes.Infact,wewilldemonstrateinSection.5thatthemotionofsomestarparticlescanbeaffectedasearlyast ˘ 1.9 Gyrandlastuntilt ˘ 2.2 Gyr.",
+    "Figure 1. The face-on density snapshots showing the sequence of the traceable spiral arm. The white line indicates the traced spiral arm of interest. The spiral peak position for R = 7, 8 and 9 kpc radii at the t = 2.0 Gyr snapshot are rotated with the corresponding circular velocity and marked as anchors (white crosses) on the t = 1.952, 2.032 and 2.048 Gyr snapshots, to guide the eye to the forming and disrupting stages of the spiral arm respectively. ",
+    "Hencethistimewindowissetbyconvenienceandnotastrictdefinitionoftheformationanddestructiontime.ThestarparticlesampleisthenplottedintheLz,ini− Lzplane,whereLz,iniisthez−componentofangularmomentumofthestarparticlesatthebeginningofthetimewindow,Tini,andLzisthechangeinangularmomentumfromtheinitialtime,Tini,tothefinaltime,Tfin.ThisisplottedinFig.(<>)3.FromFig.(<>)3,weseethatthereisawiderangeofinitialangularmomentumvaluesoverwhichtheangularmomentumi.e.theguidingcentre,ischanged,whichisconsistentwithourpreviousstudies((<>)Grandetal.(<>)2012a,(<>)b).",
+    "FromthestarparticledistributioninFig.(<>)3,weselectasampleintherange1.86 × 103 < Lz,ini< 1.97 × 103 kpc km s−1 (particlesamplesatotherLz,iniexhibitsimilarbe-haviour,sowefocusononesample),whichcorrespondstoaguidingcentreradiusofabout8kpc.Thesampleisfurthercutintosubgroups:strongmigrators(bothnegativeandpositive)andnon-migrators.Thestrongpositive(negative)migratorsconsistofthoseparticlesthathavethelargestpositive(negative)Lz,andthenon-migratorsarethosethathavethelowestchangesinangularmomentum.Thesestarparticlesareselectedsuchthatthereare˘ 200 − 300 particlesineachstarparticlegroup,andarehighlightedinFig.(<>)3."
+  ],
+  "4 EVOLUTION OF SAMPLE IN PHASE SPACE ": [
+    "Weploteachparticleinthesampleinvariousprojectionsinphasespace,andhighlightthepositivemigrator(blue",
+    "Figure 2. The pattern speed (red dashed line) of the traced spiral arm highlighted above. The angular speed of the stellar disc is also plotted (solid black line). The pattern speed matches the angular speed of the disc material well. ",
+    "circles),negativemigrator(redsquares)andnon-migrator(blackdiamonds)groupsinFig.(<>)4.Eachcolumncorrespondstoadifferenttime:theleftcolumnshowsthesampleattheearliesttimethatthespiralarmcouldbereliablytraced(followingcriteriain(<>)Grandetal.(<>)2012b),themiddlecolumn",
+    "Figure 4. Top row: The negative migrators (red squares), positive migrators (blue circles) and non-migrators (black diamonds) of the sample in vθ− vRspace. Middle row: Shows the azimuthal distance between the star particles and the spiral arm peak position, R, as a function of azimuthal velocity, vθ. Bottom row: Plots the radius of the same star particles with vθ. Each column shows these projections at three time epochs, increasing from left to right. The circular velocity at the 8 kpc radius, vc= 243.5 km s−1 , is marked in each panel by the vertical dashed green line. ",
+    "isthetimeofselection,Tc,andtherightcolumnisthelatesttimethatthespiralarmcouldbereliablytraced.",
+    "ThetoprowofFig.(<>)4showsthesampleplottedintheradialvelocity,vR-azimuthalvelocity,vθ,plane.Positiveradialvelocity,vR> 0,isinthedirectionofthegalacticcen-tre.ThecircularvelocityatR = 8 kpcisvc(R = 8) = 243.5 kms−1 ,whichismarkedbythedashedgreenlinesinFig.(<>)4.Thepositiveandnegativemigratorsappeartooccupyseparateregionsofvelocityspace,whereasthenon-migrators(blackdiamonds)aremoreevenlydistributedandoverlapthemigratorgroups.Thepositivemigratorshaveoutwardfacingvelocities(vR< 0)duringtheiroutwardmigration.ItisinterestingtoseethattheirazimuthalvelocitytendstobeslowerthanthecircularvelocityatR = 8 kpc.Theoppositeisappliedtothenegativemigrators,whichmoveinward(vR> 0)androtatefasterthanthecircularvelocityatR = 8 kpc.",
+    "Theazimuthaldistanceofastarparticlewithrespecttothespiralarm,R,isdefinedasthelengthofanarcthatjoinsthestarparticleazimuthpositiontothespiralarmpeakazimuthpositionatthatradius.ThesecondrowofFig.(<>)4showsthisquantityasafunctionofazimuthalvelocityfor",
+    "thesample.Inthisplane,eachgroupofparticles(includingnon-migrators)isveryclearlyseparated.Thepositivemi-gratorsalwaysstaybehindthespiralarm(R < 0),andthenegativemigratorsalwaysstayinfrontofthespiralarm(R > 0),throughoutthetraceablespiralarmlifetime.Thenon-migratorsareclusteredaroundthespiralarm.Atthet = 1.968 Gyr(leftpanel),thearrangementofeachparticlegroupishighlyordered.Thenon-migratorgroupinparticularisspreadoveralargerangeofazimuthalvelocity,whichappearstightlycorrelatedwiththeazimuthaldistancebetweenstarparticleandspiralarm.Forexample,att = 1.968 Gyr,atvθ= 220 km s−1 thepositivemigratorshaveanegativeR,i.e.theyarebehindthespiralarm,whilethenon-migratorshaveapositiveR,i.e.theyareinthefrontofthespiralarm.Conversely,atvθ˘ 265 km s−1 ,thenegativemigratorshaveapositiveR,i.e.theyareinthefrontofthespiralarm,whilethenon-migratorshaveanegativeR,i.e.theyarebehindthespiralarm.InSection.5.3,wedemonstratethatnon-migratorsmustpassorbepassedbythespiralarmatsomepointduringthespiralarmlifetime.Roughlyspeaking,thestarparticlewillcrossthespiralarmif:|R| < | R tt01 vθ,subdt|,wheret1 −t0 < T ,",
+    "Figure 3. The change in angular momentum of the sample of particles over the time window Tfin− Tini, as a function of their initial angular momentum. Over-plotted are the strong positive migrators (white with black outline symbols), strong negative mi-grators (white symbols) and non-migrator particles (black symbols) selected. The units are kpc km s−1 . ",
+    "andvθ,sub= vθ− vc,wherevθistheazimuthalvelocityofthestarparticleandvcisthecircularvelocityattheparticleradius.Althoughthesestarparticleswereselectedatt = 2.0 Gyr,theyaremoreorderedatt = 1.968 Gyr.ThisindicatesthattheR−vθphasespacecanbediagnosticattheearlystagesofspiralarmformation(middle-leftpanelofFig.(<>)4)inpre-determiningwhetherastarparticlewillbeamigratororanon-migrator.Atlatertimes,thegroupsbecomelessclearlyseparated,butstillmaintainthetrend.",
+    "ThebottomrowofFig.(<>)4showsthesampleintheR − vθplane.Att = 1.968 Gyr(leftpanel),migratorandnon-migratorparticlegroupsoccupythesameregionofthisspace,andbecomemoreseparatedatthelatertimes(middleandrightpanelsofFig.(<>)4)owingtothemigrationtakingplace.Thedistributionofnon-migratorsinthisplanehighlightstheepicyclicmotionofthestarparticles.Starparticlesthatareataradiusgreaterthantheguidingcentreofthesample,R > Rg˘ 8 kpc,possessazimuthalvelocitieslowerthanthecircularvelocityattheguidingcentre,vθ< vc(Rg),whereasstarparticlesataradiussmallerthantheguidingcentrepossessazimuthalvelocitieslargerthanthecircularvelocityattheguidingcentre.Positivemigra-torsobviouslymovetowardlargerradii,andareoutsideoftheirguidingcentreowingtotheirrelativelylowrotationvelocitywithrespecttothecircularvelocityatthatradius.Inotherwords,thepositivemigratorsarealwaysclosetotheapocentrephaseduringtheirmigration,andthenegativemigratorsarealwaysclosetothepericentrephase.",
+    "Fig.(<>)5showstheevolutionofbothpositivemigrators(bluestars)andnegativemigrators(redstars)plottedontheface-ondensitymapsofthediscintheR − fsplane.Theevolutionisshowninarotatingframethatco-rotateswiththecircularvelocityatR = 8 kpc.The coordinateofallstarparticleshasbeensubtractedbyanamountcorrespondingtotherotatingframesuchthatthespiralarmandsampleparticlesremainwithinthe120-280degreeazimuthwindowi.e.fs= true− frt,wheret = Tini−t.Herefristheangularrotationspeedoftheframe.Thedirectionofmotionisfromrighttoleft.Eachmigratorparticleisoutlinedinwhite(black)toindicatetheoutward,",
+    "Figure 5. Time sequence of a close up of the density map in the R−fsplane. The rotation is from right to left in a rotating frame that co-rotates with the circular velocity at R = 8 kpc. Positive migrators are marked as blue stars, and negative migrators are marked as red stars. The radial velocity direction is indicated by the white and black outline of the symbols, which represent outward and inward moving radial velocities respectively. The white line (present in some panels) highlights the peak position of spiral arm at each radius. ",
+    "vR< 0 (inward,vR> 0)directionoftheradialvelocityvector,inordertoindicatetheepicyclephasei.e.vR< 0 meansthatthestarparticleismovingfrompericentretoapocentre,whilevR> 0 indicatesthatthestarparticleismovingfromapocentretopericentre.Bothgroupsexhibitarangeofradialvelocitiesateachsnapshot,whichindicatesthereissomespreadintheepicyclephasewithinthegroups.Forthepositivemigrators,particlesclosertothespiralarmatt = 1.928 and2.024 Gyrhavenegativeradialvelocities",
+    "Figure 6. The same as Fig. (<>)5 but showing non-migrator particles. The red line indicates the spiral arm peak position. ",
+    "(approachingapocentre)andparticlesfurtherfromthespiralarmhavepositiveradialvelocities(movingawayfromapocentre).Theoppositetrendisseeninthenegativemi-gratorgroup.Despitethedifferentepicyclephasesofthesemigratorgroups,allstarparticlesinthepositiveandnegativemigratorgroupsradiallymigrateeventually,asweshowbelow.",
+    "Fig.(<>)6showstheevolutionofthenon-migratorsintheR − fsdensityplaneintherotatingframedescribedaboveforFig.(<>)5.Thesymbolsareoutlinedinblackandwhitecorrespondingtoinwardandoutwardradialvelocityunitvectorsrespectively.Mostofthenon-migratorsareclusteredclosearoundthespiralarm(peakpositionmarkedinred),andappearspatiallyseparatedaccordingtothedirectionofradialmotion.Forexample,att = 1.992 and2.008 Gyr,most",
+    "starparticlesbehind(infrontof)thespiralarmaremovingtowardspericentre(apocentre).Thisisaclearcontrastfromthemigrators.Att = 1.976 Gyr,thepositivemigratorsbehindthespiralarmaremovingtowardapocentre,i.e.outward,whilethenegativemigratorsinthefrontofthespiralarmaremovingtowardpericentre,i.e.inward."
+  ],
+  "5 INDIVIDUAL PARTICLE ORBITS ": [
+    "Inthissection,weanalysetheorbitsofthepositive,negativeandnon-migratorparticlesofthesampleindividually.Wetook˘ 100 randomsamplesofeachstarparticlegroup,andfollowedtheevolutionofeachorbitindividually.Wescru-tinisedtheorbitsoverthecourseoftheparticle-spiralarminteraction,andcategoriseseveraltypesofmigratorsandnon-migrators.Belowweshowanexampleofeachtypeandoutlinetheirdefiningfeatures.Werefertopositivemigra-torswithasuffix‘g’becausetheygainangularmomentum,negativemigratorswithasuffix‘l’becausetheyloseangularmomentumandnon-migratorswithasuffix‘n’.InTable.(<>)1,welisttheorbitalpropertiesofeachorbitaltypementionedbelow."
+  ],
+  "5.1 Orbits of positive migrators ": [
+    "Fig.(<>)7showsanexampleofthreedifferenttypesofpositivemigrator.Intheleftpanels,weshowaselectionofsnapshotsfromthetimesequenceevolutionoftheseparticlesinthesamerotatingframeadoptedinFig.(<>)5.Thesymbolineachsnapshotindicatesthepositionoftheparticleatthetimegiveninthebottom-rightcornerofthepanel,andthelinesshowthehistoryoftheorbitintheco-rotatingframe.Becausethespiralarmrotateswiththecircularvelocity(Fig.2),thespiralarmintheleftpanelsofFig.(<>)7movesrelativetotherotatingframeintime:forR < 8 kpc,thespiralarmmovestolowerfs,whereasforR > 8 kpcthespiralarmmovestohigherfs.Weremovetherelativemotionbetweenthespiralarmandstarparticleorbithistoriesbymakingafurtheradjustmenttotheorbithistory.Wecalculatethedifferencebetweenthevelocityoftherotatingframeandthecircularvelocityattheradiusofthelinepoint.Ateachsubsequenttimestepafterthelinepointappearsthepositionofthelinepointisshiftedbytheamountcorrespondingtothisvelocitydifference.Thepurposeofthisadjustmentistogiveanideaofwherethepastparticlepositionswererelative to the spiral arm atprevioustimes,althoughitisnotexactbecauseitisimpossibletoplacethepastorbitaroundthedynamicallychangingspiralarm.",
+    "The1st-and2nd-rightpanelsofFig.(<>)7showstheevolutionofparticleangularmomentum,Lz,andthetangentialforceperunitmass,Fθ,wherethepositivedirectionisoppositetothedirectionofrotation,i.e.fromlefttorightintheleftpanelsofFig.(<>)7.Bluesolid,blackdashedandgreendot-dashedlinescorrespondtotheblue,blackandgreenlinesintheleftpanelsofFig.(<>)7.",
+    "Wedefineradialmigrationtobeachangeinangularmomentumovertime,suchasthechangeseeninthetop-rightpanelofFig.(<>)7,e.g.theblackdashedlinefromt ˘ 1.89 to2.08 GyrwhenLzincreases.NotethatthetangentialforceisalwaysnegativeduringtheincreaseinLz.Themagnitude",
+    "Figure 7. The evolution of three types of positive migrator. Left panels: The time evolution of the particles in the close up R − fsdensity map in a rotating frame equal to the circular velocity at R = 8 kpc. Rotation is from right to left. The symbols depict the current position of each star particle, and the lines show the history of each star particle orbit relative to the spiral arm (see text for more details). Top-right panel: The evolution of the angular momentum of the star particles. Second-right panel: The evolution of the tangential force per unit mass, Fθ, acting upon the star particles. Third-right panel: The radial evolution of the star particles. Bottom-right panel: The azimuthal angle of the star particles in the rotating frame of the left panels, fs, (lines) and spiral arm azimuthal angle at the particle radius (symbols). The latter can only be calculated in the traceable spiral arm time window defined in Section. 3. In all right-hand panels, the time at which each particle first feels the tangential force is indicated by a vertical line of corresponding line style. ",
+    "ofthetangentialforceindicatestherateofchangeofangularmomentum,whichallowsustoseemoreclearlywhenandwherethestarparticlesmigrateintheleftpanelsofFig.(<>)7.Thethird-rightandbottom-rightpanelsofFig.(<>)7showtheevolutionoftheparticleradius,R,andazimuthangleintherotatingframe,fs,respectively.Inthebottompanel,thebluestar,blacktriangleandgreensquareindicatetheazimuthangleofthespiralarmthatweidentifiedinFig.(<>)1atthestarparticleradiusatthecorrespondingtime.Notethatwecouldtracethespiralarmforonlypartoftheperiodwhenthespiralarmisclearlyseen.However,thisdemonstratesthatthespiralarmaffectstheorbitofthestarparticleswellbeforethearmisclearlyseenandevenafteritbeginstodisrupt.Atleastinthisshortperiodwhenwecanclearlytracethespiralarm,wecanshowtheparticle",
+    "positionwithrespecttothespiralarmasseeninthebottompanelofFig.(<>)7.TheevolutionofeachquantityshownintherightpanelsofFig.(<>)7willdeterminethetypeofeachpositivemigrator."
+  ],
+  "5.1.1 Type 1g positive migrator ": [
+    "Thefirsttype(Type1g)ofpositivemigrator(bluestarandsolidbluelineintheleftpanelsandbluesolidlineintherightpanelsofFig.(<>)7)isquiteclosetothespiralarmwhenitbeginstofeelanegativetangentialforceataroundt ˘ 1.9 Gyr(2nd-rightpanelofFig.(<>)7).ThetopleftpanelofFig.(<>)7showsthatthespiralarmbeginstobuildupatt ˘ 1.9 Gyr.Itappearsthatthedensityenhancementsaroundfs= 180 andfs= 220 atR ˘ 8 kpcatt = 1.912 Gyrmergeandform",
+    "thesinglespiralarmaroundt ˘ 1.976 Gyr.Att = 1.912 Gyrthebluestarislocatedbehindthedensityenhancementatfs= 220,andthereforethedirectionoftangentialforceisnegative(Fθ< 0)andthestarparticleisaccelerated.",
+    "Att ˘ 1.9 Gyr,theparticleisapproachingtheapocen-trephaseoforbit(3rd-rightpanelofFig.(<>)7).However,asaresultofstrongnegativetangentialforceatthisphase(2ndrightpanelofFig.(<>)7),theradiusofthestarparticledoesnotdecreaseagainaccordingtonormalepicyclemotion.Thisisbecauseofthecompetitionbetweenmainlytheradialgravitationalforceandtheincreaseincentrifugalforcecausedbythegaininangularmomentum.Inthiscase,theradialforceisbalancedbytheincreasedcentrifugalforce.Asaresult,thestarparticlepausesataradiusofR ˘ 7.9 kpcfor˘ 20 − 30 Myrataroundt ˘ 1.94 Gyr,thenincreasesagainoncetheangularmomentumhasincreasedsuchthatthecentrifugalforceislargeenoughtoovercometheradialgravitationalforce.",
+    "Notethatirrespectiveoftheevolutionofradius,theincreaseinangularmomentumissustainedastheparticlecontinuestobeacceleratedbythenegativetangentialforce,becausetheparticleisalwaysbehindthespiralarm.Thebottom-rightpanelofFig.(<>)7showsthattheazimuthangleoftheparticleisalwayslargerthanthatofthespiralarm(starparticleisbehindthespiralarm)duringtheepochatwhichthespiralarmisclearlytraced.Thestrongmigratorsareabletostayononesideofthespiralarm,becausethespiralarmco-rotateswiththediscmaterial((<>)Grandetal.(<>)2012a).Asaresult,positivemigratorsmaintaintheirpositionbehindthespiralarmandcontinuetobeacceleratedandmigratealongthespiralarm.Ataroundt ˘ 2.08 Gyrwhenthespiralarmisdisrupted,theparticlestopsgainingangularmomentumandthestarparticleresumesepicyclemotion."
+  ],
+  "5.1.2 Type 2g positive migrator ": [
+    "Thesecondtype(Type2g)ofpositivemigrator(blacktriangleandsolidblacklineintheleftpanelsandblackdashedlineintherightpanelsofFig.(<>)7)beginstofeelanegativetangentialforceataboutthesametimeastheType1gpositivemigratormentionedabove(t ˘ 1.89 Gyr),andisaccelerated.Again,thereisacompetitionbetweentheradialgravitationalforceandtheincreaseinangularmomentum.However,atthistimetheparticlehasjustpassedtheapoc-entrephaseoftheepicyclemotion(3rd-rightpanelofFig.(<>)7)whentheangularmomentumbeginstoincrease.Therefore,thestarparticlebeginstomoveinwardforawhile,untiltheangularmomentumincreasessufficientlytoovercomethegravitationalforce.Asaresult,theamplitudeoftheepicyclemotionisshortened.Thisshorteninginamplitudeisshownbythechangedpericentreradiibetweent ˘ 1.83 and1.93 Gyrinthe3rd-rightpanelofFig.(<>)7.Thepericen-treradiusislargeratthelatertimeowingtotheincreaseinguidingcentre.NotethatalthoughtheradialevolutionoftheorbitlooksdifferenttothatoftheType1gpositivemigratorshownabove,theangularmomentumsteadilyincreasesirrespectiveoftheirradialevolutionbecausethestarparticleisalwayslocatedbehindthespiralarmandaccelerated(bottom-rightpanelofFig.(<>)7).",
+    "Thisisthemostcommontypeofpositivemigratorinthissample.Theshortenedepicyclemotionpresentin",
+    "theradialevolutionoftheType2gpositivemigratorisalsoreportedin(<>)Roškaretal.((<>)2012).Thestrongestmigra-torsintheirsimulationareshowntoexhibitseveralshortenedepicyclemotions,whichtheyinterpretaseffectsofco-rotationresonancesoftwospiralwaves:oneinner,fasterrotatingspiralpatternandoneouter,slowerrotatingspiralpattern.Forexample,inthetoppanelsofFig.11of(<>)Roškaretal.((<>)2012),theorbitofthemigratorshows˘ 6 epicyclemotionsfromt ˘ 5.4 to5.9 Gyr.Inourstudy,wefocuson1-2epicycleperiodswhichcorrespondstothelifetimeofthespiralarminoursimulation.TheType2gmigratordemonstratesthatduringtheshortenedepicyclemotiontheguidingcentreofthestarparticlecontinuouslyincreasesowingtotheangularmomentumincreaseateveryradius.Therefore,wethinkthatitisdifficulttoattribute6shortenedepicyclemotionsseenin(<>)Roškaretal.((<>)2012)toonlytwoco-rotationresonances.Instead,wethinkthatthespiralarmfeatureco-rotateswiththediscmaterialateveryradius((<>)Grandetal.(<>)2012a),andinducesacontinuousgaininangularmomentumofmigratorsaslongasthefeaturepersists.Wesuspectthattheirspiralarmisshort-lived,andthatthe6epicyclemotionsseenover˘ 0.5 Gyrareaffectedbyseveraltransientspiralarmfeaturesthatco-rotateandacceleratestarparticlesbehindthespiralarmatallradii."
+  ],
+  "5.1.3 Type 3g positive migrators ": [
+    "Thethirdtype(Type3g)ofpositivemigrator(greensquareandgreensolidlineintheleftpanelsandgreendot-dashedlineintherightpanelsofFig.(<>)7)originatesmuchfartherfromthespiralarmasitbeginstobuildupataroundt ˘ 1.9 Gyr(top-leftpanelofFig.(<>)7),andconsequentlybeginstofeelanegativetangentialforceatthelatertimeoft ˘ 1.93 GyrwithrespecttoTypes1gand2g.Atthistime,thestarparticleapproachesthepericentrephaseoftheepicycle(3rdrightpanelofFig.(<>)7),andthereforeitmovesclosertothespiralarmatt ˘ 1.976 Gyrintheleftpanelsandbottom-rightpanelofFig.(<>)7.Inthiscase,boththeoutwardepicyclemotionandtheangularmomentumincreasefacilitatetheoutwardmotionofthestarparticle.Asaresult,theparticleradiusincreasesveryrapidly(third-rightpanelofFig.(<>)7).",
+    "Notethatthestarparticlereachestheapocentreatt ˘ 2.02 Gyr,wellbeforetheangularmomentumgainendsatt ˘ 2.06 Gyr.Thismeansthataroundt ˘ 2.02 Gyr,theradialgravitationalforcebecomesgreaterthantheenhancedcentrifugalforceprovidedbytheboostinangularmomentum.Theradialevolutionofthestarparticlethenproceedsinwardswhiletheparticlecontinuestogainangularmomentumuntilepicyclemotionresumesatt ˘ 2.06 Gyr."
+  ],
+  "5.2 Orbits of negative migrators ": [
+    "Fig.(<>)8showstheevolutionofanexampleofeachtypeofnegativemigratorfoundintheparticlesample.EachpanelisthesameasinFig.(<>)7."
+  ],
+  "5.2.1 Type 1l negative migrator ": [
+    "Thefirsttype(Type1l)ofnegativemigrator(bluestarandsolidbluelineintheleftpanelsandbluesolidlineinthe",
+    "Figure 8. The same as Fig. (<>)7 but for types of negative migrator. ",
+    "rightpanelsofFig.(<>)8)isthecounterpartoftheType1gpositivemigratorshowninFig.(<>)7.The2nd-rightpanelofFig.(<>)8showsthatthestarparticlebeginstofeelapositivetangentialforceatatimeofaroundt ˘ 1.91 Gyr,whentheparticleismovingtowardsthepericentrephaseoforbit(3rdrightand1st-leftpanelofFig.(<>)8).Asthespiralarmgrowsindensity,e.g.t = 1.944 and1.976 Gyr(2nd-and3rd-leftpanelsofFig.(<>)8),thestarparticlecontinuestofeelastrongpositivetangentialforceaccompaniedbyasteepnegativeslopeintheangularmomentumevolution(1st-rightpanelofFig.(<>)8).Att ˘ 1.98 Gyr,theradialgravitationalforceandcentrifugalforcearetemporarilybalancedandthestarparticlestaysatR ˘ 7.2 kpcfor˘ 30 − 40 Myr-asimilarradialpausetothatoftheType1gmigratordescribedintheprevioussection.Att ˘ 2.02 Gyr,theradialgravitationalforceplusthelossinangularmomentumovercomethecentrifugalforce,hencethestarparticlemovesradiallyinwardagain.Asthespiralarmbeginstofadeataroundt ˘ 2.06 Gyr,thetangentialforcediminishes,andthestarparticleresumesnormalepicyclemotion.Again,thestarparticlehas",
+    "remainedinfrontofthespiralarmandcontinuallymigratedalongthespiralarm."
+  ],
+  "5.2.2 Type 3l negative migrator ": [
+    "TheotherexamplestarparticleshowninFig.(<>)8isthenegativemigratorcounterpartoftheType3gpositivemigrator,andthereforewedesignateitasType3l(blacktriangleandblacksolidlineintheleftpanelsandblackdashedlineintherightpanelsofFig.(<>)8).ThisstarparticleoriginatesfartherfromthespiralarmthanType1lasthespiralarmbeginstobuildupatt = 1.912 Gyr(top-leftpanelofFig.(<>)8).Therefore,thestarparticlebeginstofeelthepositivetangentialforce(deceleration)atatimeoft ˘ 1.93 Gyr,whichislaterthanthetimeatwhichtheType1lnegativemigratorbeginstoloseangularmomentum(2nd-leftand2nd-rightpanelsofFig.(<>)8).Atthistime,thestarparticleisclosetotheapocentrephaseoforbit(3rd-rightpanelofFig.(<>)8),andconsequentlymovesclosertothespiralarmatt ˘ 1.976 Gyr(3rd-leftpanelofFig.(<>)8).SimilartotheType3gpositivemigrator,theinwarddirectionoftheangular",
+    "momentumchangeandepicyclemotionmeansthatthestarparticlemovesrapidlytowardsthecentreofthegalaxy(leftpanelsofFig.(<>)8).Again,thestarparticlereachestheperi-centreatt ˘ 2.01 Gyr,beforetheangularmomentumlosshasceased.Thismeansthatthecentrifugalforcebecomesgreaterthantheradialgravitationalpotentialeventhoughthestarparticlecontinuestoloseangularmomentum.Thetangentialforcediminishesatt ˘ 2.07 Gyr,whentheparticleresumesepicyclemotion."
+  ],
+  "5.2.3 No Type 2l negative migrator ": [
+    "WecouldnotfindanegativemigratorcounterparttotheType2gpositivemigrator.Thismaybeattributedtothepresenceofanotherspiralarme.g.theoneseenonthefrontsideofthemainspiralarmataround(R kpc,fs)= (8, 130) at1.976 Gyr(3rd-leftpanelofFig.(<>)8)relativetothemainspiralarmonwhichwefocus(R, fs)= (8, 185).Thisiscloserthanthespiralarmbehindthemainspiralarmat(R, fs)= (8, 265).Thecloserproximitytothemainspiralofthedensityenhancementonthefront-sideofthespiralarmincomparisontothedensityenhancementonthebacksideofthespiralmaycausethemotionsofstarparticlesinfrontofthespiraltobemoreinfluencedbyneighbour-ingdensityenhancementsthanthosebehindthemainspiralarm.",
+    "TomirrortheType2gpositivemigrator,theType2lnegativemigratorswouldhavebeguntoloseangularmomentumjustaftertheypassedpericentre.Inthisepicyclephase,theType2lstarparticlewouldtemporarilymoveawayfromthespiralarm(becauseithasahigherrotationvelocityinthisphasethanthespiralarm),anditispossiblethattheover-densityinfrontofthespiralarm“moppedup”thesestarparticles,whichwouldeitherreduceorchangesignofthepositivetangentialforceactinguponthestarparticle.Thiswouldmeanthatthesestarparticlesgainedsomeangularmomentumfromthisover-densityduringthetimewindowexamined.Therefore,thesestarparticleswouldnotbestrongmigrators,becausetheywouldpopulatearegionoflower|Lz| inFig.(<>)3.Inthiscase,theywillnotbeselectedinourstrongmigratorsample."
+  ],
+  "5.3 Orbits of non-migrators ": [
+    "Inthissection,weanalysetheorbitalevolutionofthosestarparticlesthatexperienceverylittleornonetchangeinangularmomentumoverthetimewindow(non-migrators).Fig.(<>)9showsanexampleofeachofthethreetypesofnon-migratorinthesample."
+  ],
+  "5.3.1 Type 1n non-migrator ": [
+    "Thefirsttypeofnon-migrator(Type1n,representedbythebluestarandsolidbluelineintheleftpanelsandthesolidbluelineintherightpanelsofFig.(<>)9),isveryclosetowherethespiralarmbeginstobuildupatt ˘ 1.912 Gyr(1st-leftpanelofFig.(<>)9),anditbeginstofeelanegativetangentialforceearlyatt ˘ 1.86 Gyr(2nd-rightpanelofFig.(<>)9).Att = 1.944 Gyr(2nd-leftpanelFig.(<>)9),thestarparticleislocatedinbetweenthemainspiralarmat(R, fs)= (8, 185) andtheweakerspiralarmbehinditat(R, fs)= (8, 205) -",
+    "incontrasttothepositivemigratorswhichwerebehindbothdensityenhancementsatthistime.Thestarparticlemovestowardspericentre(3rd-rightpanelofFig.(<>)9),whileitgainsangularmomentum(top-rightpanelofFig.(<>)9).Becausethestarparticleisaroundpericentreandlocatedclosebehindthearm(3rd-leftpanelofFig.(<>)9),thestarparticlemovestowardsthespiralarmuntilt ˘ 1.99 Gyrwhenitpassesthespiralarm,asseeninthebottom-rightpanelandthe3rdand4th-leftpanelsofFig.(<>)9.Theparticleisnowlocatedonthefrontsideofthespiralandasaresultthetangentialforceactinguponthestarparticlehasbecomepositive,whichcausesthestarparticletobegintoloseangularmomentum.Thestarparticlethenresumesepicyclemotionasthespiralarmfadesatt ˘ 2.05 Gyr.",
+    "Thegeneralpropertiesofthesenon-migratorsisthattheyoriginateveryclosetothespiralarm,andorbitthespiralarmuntilitdisappears,continuallygainingandlosingangularmomentumsuchthatthenetangularmomentumgainisLz˘ 0,attheendofthetimewindow.Itisworthnotingthatwhenthestarparticleiscirclingaroundthespiralarm,theamplitudeoftheepicyclemotionissmaller.Thisisbecausethetangentialforcefromthespiralarmactsalwaystochangetheguidingcentreinthedirectionoppositetothatofepicyclemotion.Therefore,asthestarparticlemovestowardspericentre,itisaccelerated(Fθ< 0),whichincreasestheguidingcentreandinturnincreasestheperi-centreradius.Forexample,thepericentreradiusislargeratt ˘ 1.96 Gyrthanatt = 1.84 Gyr,andatt ˘ 2.09 Gyrthepericentreisreturnedtothatatt ˘ 1.84 Gyr.Thisindicatestheamplitudeoftheepicyclemotionisshortened,becausethetangentialforcefromthespiralarmactsagainsttheepicyclemotion.TheType1norbitisfoundtooriginatealsoinfrontofthespiralarmwhenitfirstfeelsthetangentialforce."
+  ],
+  "5.3.2 Type 2n non-migrator ": [
+    "Thesecondtype(Type2n)ofnon-migrator(blacktriangleandsolidblacklineinleftpanelsanddashedblacklineinrightpanelsofFig.(<>)9)islocatedinfrontofthespiralarmasitformsatt ˘ 1.944 Gyr(1st-and2nd-leftpanelsofFig.(<>)9).Itbeginstofeelapositivetangentialforceandmigratesinwardatt ˘ 1.91 Gyr.Thisoccursjustbeforethestarparticlereachestheapocentreoftheorbit,andatt ˘ 1.95 − 1.97 Gyrthelossofangularmomentumandtheinwardepicyclemotion(1st-and3rd-rightpanelsofFig.(<>)9)causetheradiusofthestarparticletodecreaserapidlyinamannersimilartoType3lnegativemigrator.Thiscausesadecreaseinpericentreradius(seetheradiusatt ˘ 1.87 andt ˘ 2.0 Gyrin3rd-rightpanelofFig.(<>)9).However,unliketheType3lnegativemigrator,thisnon-migratoristooclosetothespiralarmwhenitreachesapocentreatt = 1.94 Gyrandasaresultispassedbythespiralarmatt ˘ 1.98 Gyr(bottom-rightpanelofFig.(<>)9).Thiscausesthechangeoftangentialforcefrompositivetonegative,andthestarparticlethengainsbacktheangularmomentumlostpreviously(top-rightpanelofFig.(<>)9).Thisonceagainensuresthatthisnon-migratorhasanetangularmomentumchangeofLz˘ 0 attheendofthetimewindow.",
+    "ThedifferenceinradialevolutionbetweenthisType2nandtheType1nnon-migratorsisthattheType2nnon-migratorshowsanincreaseinepicycleamplitudebecause",
+    "Figure 9. The same as Fig. (<>)7 but for types of non-migrator. ",
+    "thepericentreatt ˘ 2.0 Gyrislowerwithrespecttotheearliertime,t ˘ 1.86 Gyr,i.e.theamplitudeofepicyclemotionisincreasedinsteadofdecreasedasinthecaseoftheType1nnon-migrator.",
+    "Itisinterestingtonotethatthistypeofnon-migratorisnotfoundtooriginatefrombehindthespiralarm.Thismayberelatedtothedifferencesbetweenthefront-andback-sideofthespiralarmasdiscussedinSection.5.2.3.Inaddition,asdiscussedinSection5.1.1and5.3.1,thereisasmalldensityenhancementthatmergeswiththeback-sideofthespiralarmatt ˘ 1.976 Gyr.Thereforetheback-sideofthespiralarmseemstobuilduplaterthanthefront-side,andthislikelycausesthedifferenceinthevarietyintheorbitsofstarparticlesthatoriginatefromthefront-andback-sideofthespiralarm."
+  ],
+  "5.3.3 Type 3n non-migrator ": [
+    "Thethirdtype(Type3n)ofnon-migratorparticlefoundinthissample(thegreensquareandsolidgreenlineinleftpanelsandgreendot-dashedlineintherightpanelsofFig.",
+    "9",
+    "(<>)9)beginstofeelanegativetangentialforceatt ˘ 1.88 Gyr(2nd-rightpanelofFig.(<>)9)justasitreachestheapocen-treoftheorbitatt ˘ 1.912 Gyr(top-leftandthird-rightpanelsofFig.(<>)9).Thisisaccompaniedbyanincreaseinangularmomentum(top-rightpanelofFig.(<>)9)fromaboutt ˘ 1.88 − 1.99 Gyr.Duringthistime,theradiusofthestarparticleproceedstoapocentreandexhibitsasmalldipinradiusatt ˘ 1.96 Gyr(3rd-rightpanelofFig.(<>)9).Thisisobviouslythefeatureofanincreasedpericentreradiusowingtotheimbalancebetweentheradialgravitationalforceandcentrifugalforceboostedbyagaininangularmomentum.Thepericentre-likefeatureisalsoseeninthebottom-rightpanelofFig.,whichshowsadecreasingfsofthestarparticle(line)thatbringsthestarparticleclosertothespiralarminazimuthangle(squaresymbols)att ˘ 1.96 Gyr.",
+    "Att ˘ 1.99 Gyr,thestarparticlepassesthespiralarmandbeginstoloseangularmomentum(rightpanelsinFig.(<>)9).Uptot ˘ 1.99 Gyr,thisnon-migratorexhibitedsimilarevolutiontoType1gpositivemigrators,butitdifferedafterthistimebycrossingthespiralarminsteadofremainingbehindit.Thisisentirelybecausethisnon-migratoristooclose",
+    "Table 1. Summary of orbital characteristics for each orbital type. Columns show 1) orbital type name 2) the time at which the particle first feels the tangential force, tcapture(measured by eye to provide an indication) 3) initial particle position with respect to the spiral arm at tcapture4) the epicycle phase of the particle at tcapture5) the e˙ect on their epicycle amplitude 6) whether or not they remain on the same side of the spiral throughout the spiral lifetime. ",
+    "Figure 10. Close up of the density map in the R − fsplane at t = 1.976 Gyr, with contours of the tangential force over-plotted in white. Solid lines indicate positive tangential force (acting in the direction ˆ) and dashed lines indicate negative tangential force (acting in the direction −ˆ). The position of the Type 1l negative migrator and Type 2n non-migrator are represented by a blue star and black square respectively, and their orbit histories shown by the solid lines of the same colour. ",
+    "tothespiralarm,suchthatevenavθthatisslightlyfasterthanthespiralarmrotationvelocitywilltaketheparticlepastthespiralarm.Againthishighlightstheimportanceofazimuthangleofthestarparticlewithrespecttothespiralarm.Thistypeofnon-migratorexhibitsshortenedepicycleamplitudewhileitremainsonthesamesideofthespiralarm.ThisisdifferentfromType2n,whichshowsextendedepicycleamplitude,anditisalsodifferentfromType1n,whichshowsshortenedepicycleamplitudeasitcirclesthespiralarm.ThisType3nnon-migratorisfoundbothinfrontofandbehindthespiralarm,unlikeType2n."
+  ],
+  "5.4 The tangential force ": [
+    "Wehaveshownabovethattimeperiodsofsustainedtangentialforce,whichcausestrongradialmigration,depend",
+    "onthestarparticlepositionwithrespecttothespiralarm.Forexample,thenegativemigratorsthatfeelstrongpositivetangentialforcesloseangularmomentumwhiletheyfeelthatforce,whichispossiblebecausetheparticlealwaysremainsinfrontofthespiralarm.However,thereexistsomenon-migratorsthatspendtimeinsimilarregionsaroundthespiralasmigrators,butuponwhichalmostnotangentialforceacts.",
+    "Toexplorethis,wecomputeamapofthetangentialforce.Fig.(<>)10showsthedensitymapofthespiralarmwithcontoursoftangentialforceover-plottedinwhiteatt = 1.976 Gyr(solidforpositivevaluesanddashedfornegativevalues).Asexpected,thetangentialforceiszeroatthedensitypeakofthespiralarm.Thetangentialforcebecomesstrongerwithincreasingazimuthaldistancefromthespiralarm,untilitreachesamaximum,˘ 10-20 degreeawayfromthedensitypeakoneitherside.Atfartherdistancesfromthepeakofthespiralarm,thetangentialforcedecreasesandeventuallychangesthesign,owingtotheforcecontributionsfromneighbouringspiralarms.Itisinterestingtoseethedifferencebetweenthefront-andback-sidesofthespiralarm.Onthefront-sideofthearmthepointofthemaximumtangentialforceisclosertothedensitypeakofthespiralarmthanthatontheback-sideofthespiralarm.Thisisbecausetheneighbouringspiralarmonthefront-sideiscloserthantheoneontheback-side.Ontheback-side,thesmalldensityenhancementmergestothemainspiralarmaroundR = 8.5 kpc,whichpushesthepointofthemaximumtangentialforcefartherfromthedensitypeakofthemainspiralarm.",
+    "WeshowtheorbithistoryoftheType1lnegativemi-grator(bluestarandsolidbluelineinFig.(<>)10)showninSection.5.2.1andtheType2nnon-migrator(blacksquareandsolidblacklineinFig.(<>)10)showninSection5.3.2.Thefig-ureshowsthatthenegativemigratoriscapturedinaregionofstrongtangentialforceinfrontofthespiralarm,whichcontinuesoverthespiralarmlifetime(see2nd-rightpanelofFig.(<>)8).However,thenon-migrator,despitebeinglocatedinfrontofthespiralarmandhavingaverysimilarorbittothenegativemigrator,feelsalmostnotangentialforceoverthistimeperiod(see2nd-rightpanelofFig.(<>)9)becausethestarparticleistooclosetothepeakofthespiralarm.Thisimpliesthatitisnotenoughthatthestarparticleislocated",
+    "Figure 11. The change in angular momentum, Lz, between t = 1.0 and 2.0 Gyr of the disc particles as a function of their angular momentum at t = 1.0 Gyr. Red colours indicate regions of high number density. ",
+    "Figure 12. The cumulative profiles of total disc mass fraction (upper curve) and angular momentum (lower curve). The solid red and dashed black curves show the profiles at t = 1.0 and t = 2.0 Gyr, respectively. ",
+    "ononesideofthespiralarminordertobecomeamigra-tor:themigratormustbefarenoughawayfromthespiralarmpeakline-yetnottoofar!-inordertobecapturedbyregionsofstrongtangentialforcesuchasthoseshowninFig.(<>)10.Wethereforerefinetheconditionforastrongpositive(negative)migratortobeastarparticleabletoremainatasuitable distancebehind(infrontof)thespiralarm.Thisre-emphasizestheimportanceoftheR parameterindistinguishingstrongmigratorsfromnon-migrators."
+  ],
+  "6 BROADER IMPLICATIONS OF RADIAL MIGRATION ": [
+    "Themainresultsofthispaperfocusonthecomplicatedinteractionsbetweenthespiralarmandavarietyoforbitaltypes,ontimescalesroughlyequaltothespiralarmlifetime.Eachtypeofmigratorparticleexperiencesachangeinangularmomentumonthesetimescales(Fig.(<>)3).Onlongertimescales,i.e.1Gyr,astarparticlemayinteractwithaspiralseveraltimes.Thecumulativeeffectofconsecutivespiralarm-starparticlesinteractionsisreflectedintheevolutionofglobalpropertiesofthedisc,suchasthemassandmetaldistribution.Inthissection,webrieflydiscusstheeffectsofradialmigrationinthissimulationonlongertimescales.",
+    "Co-rotatingspiralarmshavebeenshowntocauseradialmigrationatmanyradii,andthisworkconfirmsthatmigrationwillcontinueaslongasthestarparticleremainsonthesamesideofthespiralarminaregionofstrongtangentialforce.Thismeansthatradialmigrationinthissimulationisefficientattransportingstarparticlestodifferentguidingradii.ThisisshowninFig.(<>)11,whichshowsthechangeinangularmomentumofdiscparticlesbetweenthetimesof1.0 and2.0 Gyrasafunctionoftheirangularmomenumatt = 1.0 Gyr.ThisshowsmuchmoreradialmigrationthanfortheshortertimescaleshowninFig.(<>)3(˘ 5 timesasmuch).Althoughthisradialmigrationredistributestheindividualangularmomentaofstarparticles(seealsoFigs.(<>)7,(<>)8and(<>)9),",
+    "theoverallangularmomentumdistributionofthediscandthecumulativemassprofileremainalmostunchanged(seeFig.(<>)12).",
+    "Themovementofstarparticlesfromoneguidingradiustoanotheraffectsthedistributionofmetalsinthedisc.Toindicatetheeffectonthemetaldistributionoftheradialmigrationinthissimulation,weartificiallyassignmetallic-ityvaluestoeachstarparticleinthesimulationatatimeoft = 1.0 Gyr.Werandomlyassigneachstarparticleametalvaluebydrawingfromthegaussianmetallicitydistributionfunctionateachradiuswithadispersionof0.05 dex.Themeanonwhichagaussianiscentredatagivenradiusisdefinedbyametallicitygradientof−0.05 dex/kpc,and[Fe/H](R = 0)=0.25dex.ThetoprowofFig.(<>)13showsthesmootheddistributionofstarsinmetallicityasafunctionofradiusatt = 1.0 Gyr(leftpanel)andt = 2.0 Gyr(rightpanel).Themetallicitygradientdoesnotchangemuchatallbetween1.0and2.0Gyr.Thisisbecausetheradialmigrationisnotstrongenoughtomixstarsatsucharateastoaffecttheslope.However,themetallicitydistributionatanygivenradiusbroadenswithtime.ThebottomrowofFig.(<>)13showsthesameasthetoprowbutforaninitialradialmetallicitygradientof−0.1 dex/kpc.Att = 2.0 Gyr,althoughtheradialmetallicitygradientremainsunchanged,themetallicitydistributionshowsamuchlargerbroadeningowingtothethesteepergradient,asexpected.Despiteourcrudemetallicityanalysis,asimilareffectisseeninFig.16of(<>)Casagrandeetal.((<>)2011),whoshowthatinthesolarneigh-bourhood,themetallicitydistributionofstarsagedbetween1 − 5 Gyriscomparativelybroadincomparisonwiththatofstarsyoungerthan1 Gyr,andbothpopulationshavethesamepeakmetallicityvalue(seealso(<>)Haywood(<>)2008).Westressthattheseresultsarefromthissimulationonly,andshouldnotbetakenasthegeneralcaseforsimulatedspiralgalaxies.Forexample,parameterssuchasspiralarmstrengthandpitchanglelikelyplayaroleintheamountofradialmigrationandthereforethedegreeofmixingthatoc-",
+    "cursinaspiraldisc.Moreover,thisresultisderivedfromaN-bodysimulationinwhichmetallicitieshavebeenassignedartificiallyatanarbitrarytime.Forarobustanalysisontheeffectofspiralmorphologyonmetaldistributions,manysimulationsthatincludethegascomponentandrecipesforstarformationandchemicalevolutionneedtobeanalysedandcomparedwitheachotherandobservation.Thistopicdeservesathoroughnumericalstudy,andwereservefurtherdiscussionuntilthen.",
+    "Alloftheanalysispresentedinthispaperhasbeenwithregardtoonesimulation,whichhasaflocculentspiralstructurewithnobulgeorbaratthecentre.However,wehaveseensomeevidencethatthegroupcharacteristicsofthepositive,negativeandnon-migratorsarepresentalsoinsimulatedgalaxiesofdifferentspiralstructure,andshowsimilarseparationsinthephasespaceplanesshowninFig.(<>)4.Thesesimulationsincludea3-4armedgalaxywithastaticbulgeinthecentre(simulationFin(<>)Grandetal.(<>)2013),andthebarred-spiralgalaxyoftwoarmspresentedin(<>)Grandetal.((<>)2012b)."
+  ],
+  "7 CONCLUSIONS ": [
+    "WehaveperformedhighresolutionN-bodysimulationsofaspiraldiscembeddedinastaticdarkmatterhalopotential.Wefocusonasampleofstarparticlestakenfromaroundthespiralarmanddividethissampleintothreegroupsaccordingtotheamountofchangeinangularmomentum,i.e.radialmigration,ofthestarparticlesoveragiventimeperiodwhenthespiralarmisstrong.Thesegroupsare:starparticlesthatgainthemostangularmomentum(positivemigrators),starparticlesthatlosethemostangularmomentum(negativemigrators)andstarparticlesthatshowalmostnochangeinangularmomentum(non-migrators).",
+    "Wefollowtheevolutionofthesegroupsinvθ− vR,vθ− R andvθ− R planes,andcometothefollowingconclusions:",
+    "Theslopeinthevθ− R spaceofthedistributionofnon-migratorsindicatesthatnon-migratorslocatedbehindthearmhavehigherazimuthalvelocitiesthefartherbehindthearmtheyare.Similarly,thenon-migratorsinfrontofthespiralarmhavelowerazimuthalvelocitiesthefartherinfrontofthespiralarmtheyarewhenthespiralisforming.",
+    "Wethenexaminedtheorbitalevolutionofindividualstarparticlesineachparticlegroupindetail.Wecategorisedandcontrastedseveralorbitaltypesofeachgroup,eachof",
+    "whichisanewtypeoforbitshownforthefirsttimeinthispaper.",
+    "Therearethreetypesofpositivemigrators,eachchar-acterisedbythetimetheyfeelthetangentialforce,theirphaseofepicyclemotionwhenthisforceisintroducedandtheirazimuthaldistancefromthespiralarm:",
+    "Type3goriginatesfartherfromthearmthanTypes1gand2g,andbeginstomigrateatlatertimesthanTypes1gand2g,aroundthepericentrephase,andasaresultexhibitsrapidchangesinradius.",
+    "Thisvarietyoforbitsshowsthatpositivemigratorscanbeinanyepicyclephaseatthetimethetangentialforceisintroduced.However,migratorsthatoriginatefarfromthespiralarmmustbeinthepericentrephaseoforbitinordertocatchthespiralarmandundergolargeangularmomentumchanges.Migratorsthatarelocatedclosertothespiralarmbegintomigratearoundapocentrebecauseiftheyareinpericentre,theywillpassthespiralarmandanyincreaseinangularmomentumwillbearrested,asweshowinSection.5.3.Hence,thekeyforstrongpositivemigratorsistostaybehindthespiralarm,whichisverifiedinthebottom-rightpanelofFig.(<>)7foreachpositivemigratorexample.Inthisway,irrespectiveofthephaseofepicyclemotion,thestarparticlescontinuetogainangularmomentumfromthespiralarm.Wefindsimilartypesoforbitsforthenegativemigrators.However,wedidnotfindanyType2negativemigratoranaloguetoType2gpositivemigrator.Wethinkthatthisisbecausethespiralarmonwhichwefocushasdifferentpropertiesandformationprocessesonthefront-andback-sideofthespiralarm.",
+    "Wefoundthreetypesofnon-migrators:",
+    "Figure 13. Metallicity distribution of all disc stars as a function of radius at t = 1.0 Gyr (left panel) and t = 2.0 Gyr (right panel). Top: The initial assigned metallicity gradient is −0.05 dex/kpc, and the dispersion of the gaussian metallicity distribution function is 0.05 dex. Bottom: The initial assigned metallicity gradient is −0.1 dex/kpc, and the dispersion of the gaussian metallicity distribution function is 0.05 dex. In all panels the initial metallicity gradient is shown by the dashed black line. Contours and red colours indicate regions of high number density. ",
+    "Eachtypeofnon-migratorshowsthatpositionrelativetothespiralarmisveryimportant,andhasconsequencesforthestarparticleevolution.ItisagainimportanttonotethatalthoughtheseparticleswereselectedasshowingLz˘ 0 withintheselectedmigrationtimewindow,theymaygoontomigratearoundotherspiralarmsatlatertimes,andmayhaveundergonemigrationaroundpastspiralarmsatearliertimes.",
+    "Theimportanceoftheproximityofthestarparticletothespiralarmandtheepicyclephaseofmotionoftheparticlefoundintheorbitalanaylsisisconsistentwiththe",
+    "trendseeninthesampledistributionintheR − vθplaneshowninthemiddlerowofFig.(<>)4.Itshowsthatstrongmi-gratorsarealwayslocatedonthesamesideofthespiralarmthroughoutthelifetimeofthespiralarm,whilenon-migratorstendtopass/bepassedbythespiralarmowingtothefaster/slowerrotationvelocitiesofthenon-migratorsrelativetothatofthespiralarm,givencloseenoughproximity.Thisunderscoresthecriterionforstarparticlestobecomestrongpositive(negative)migratorsastheabilityofastarparticletoremainbehind(infrontof)andstayclosetothespiralarmaslongasitispresent.",
+    "Wehavefoundthattherearecertaindistancesfromthespiralarmatwhichexistregionsofstrongtangentialforce.Migratorstendtobecapturedbytheseregions,whereasnon-migratorsmaymissthestrongforceregionsbymovingtooclosetothespiralarm.Inthatcase,thestarparticledoesnotfeelmuchtangentialforceanddoesnotchangeangularmomentum.Thisemphasizestheimportanceofazimuthaldistancefromthespiralarm.Indeedwefindthatstrongmigratorsremainatasuitabledistancefromthespiralarm.",
+    "Thedetailedinformationofparticleorbithistoriesoflargestarsamplesmayprovidecluestohowthespiralarmisformedanddestroyed.Thisinformationislikelytobefoundinnotjuststrongmigratorsandnon-migrators,butfrommuchlargerstarparticlesamplesthatexhibitmanydifferentdegreesofradialmigration.Fromthesekindofdata,itmaybepossibletoseehowthespiralarmisconstructedastheinfluxofstarparticlesfromregionsaroundthediscintotheformingspiralarmincreasesthedensityandeventuallyleadstothefullyformedspiralfeatures.Inthesamespirit,thefuturetrajectoriesofmanystarparticlesthatmakeupthespiralfeaturesmaygiveusaninsightintohowthesefeaturesaredisrupted.Thenon-linearnatureoftheparticlemotionthatwehaveglimpsedmakesthismethodofanalysisapromisingdirectiontopursue,andweleavethiscomplicatedinvestigationtofuturestudies.",
+    "Theapplicabilityoftheseresultstotransientspiralsislimitedtotheco-rotatingspiral,giventhattheresultsholdformanyradii.Therefore,thisprecludestheclassicdensitywavetheory,whichisbasedonasingleco-rotationradius.Furthermore,therapidgrowthofspiralarmsfromsmallseedsandthepersistenceofspiralstructureintheabsenceoflargeperturbingmasses(seealsoD’Onghiaetal.2013)indicatestheimportanceofhighlynon-linearprocessesinthediscthatareatleastnotfullycapturedinlinearapproximationssuchasclassicswingamplificationtheory.Itmaybethatthespiralstructurearisesfromswingamplifi-cationatmanyradiithatoriginatesatoneormoreradii,andamplifiesandspreadstootherregionsofthediscwhenthepreviousamplificationspillsoverintoneighbouringradiiandpropagatesthegrowthmechanism(seealso(<>)Grandetal.(<>)2012a).Westressthatthisisourspeculation,andnotethatadetailedstudyisrequiredtoexploreotherpossiblemechanismsofspiralarmformation.",
+    "Finally,weremarkupontheapplicabilityoftheseresultstorealspiralgalaxies.Weexpectthattheorbitalbe-haviourfoundinthispaperappliestoanyco-rotatingspiralarm,andassuch,allisolatedgalaxiesincludingthosewithabar(Grandetal.2012ab).However,itispossiblethatgalaxieswithcompanionsatellitesareexperiencingdifferentevolution((<>)Dobbsetal.(<>)2010;(<>)Purcelletal.(<>)2011).Therefore,forthemomentwerestrictourfindingstobeimportantforisolatedgalaxies."
+  ],
+  "ACKNOWLEDGEMENTS ": [
+    "Theauthorsthanktherefereeforthoughtfulandconstructivecommentsthatledtotheimprovementofthemanuscript.ThecalculationsforthispaperwereperformedontheUCLLegion,theCrayXT4atCenterforComputationalastrophysics(CfCA)ofNationalAstronomicalObservatoryofJapanandtheDiRACFacilities(through",
+    "theCOSMOSconsortium)jointlyfundedbySTFCandtheLargeFacilitiesCapitalFundofBIS.WealsoacknowledgePRACEforawardingusaccesstoresourceCartesiusbasedintheNetherlandsatSURFsara.Thisworkwascarriedout,inpart,throughtheGaia ResearchforEuropeanAstronomyTraining(GREAT-ITN)network.TheresearchleadingtotheseresultshasreceivedfundingfromtheEuropeanUnionSeventhFrameworkProgramme([FP7/2007-2013]undergrantagreementnumber264895."
+  ]
+}

jsons_folder/2014MNRAS.440.1712C.json

@@ -0,0 +1,229 @@
+{
+  "ABSTRACT ": [
+    "One of the most striking properties of galaxies is the bimodality in their star-formation rates. A major puzzle is why any given galaxy is star-forming or quiescent, and a wide range of physical mechanisms have been proposed as solutions. We consider how observations, such as might be available in upcoming large galaxy surveys, might distinguish di erent galaxy quenching scenarios. To do this, we combine an N-body simulation and multiple prescriptions from the literature to create several quiescent galaxy mock catalogues. Each prescription uses a di erent set of galaxy properties (such as history, environment, centrality) to assign individual simulation galaxies as quiescent. We find how and how much the resulting quiescent galaxy distributions di er from each other, both intrinsically and observationally. In addition to tracing observational consequences of di erent quenching mechanisms, our results indicate which sorts of quenching models might be most readily disentangled by upcoming observations and which combinations of observational quantities might provide the most discriminatory power. ",
+    "Our observational measures are auto, cross, and marked correlation functions, projected density distributions, and group multiplicity functions, which rely upon galaxy positions, stellar masses and of course quiescence. Although degeneracies between models are present for individual observations, using multiple observations in concert allows us to distinguish between all ten models we consider. In addition to identifying intrinsic and observational consequences of quiescence prescriptions and testing these quiescence models against each other and observations, these methods can also be used to validate colors (or other history and environment dependent properties) in simulated mock catalogues. "
+  ],
+  "1 INTRODUCTION ": [
+    "As time marches forward, collapsed objects in the universe grow hierarchically via merging and accretion. Gas accreting onto halos serves as the fuel for star formation in the galaxies residing in dark matter halos. Not all galaxies are forming stars at a significant rate today however, so a central puzzle in galaxy formation is: why are some galaxies star-forming while others are quiescent? Several possible mechanisms to quench star-forming in galaxies have been identified. For instance, the gas may already be used up in stars, or might be stripped from the galaxies, or prevented from accreting onto them, or heated, and so on (see, e.g., the galaxy formation textbook by (<>)Mo, van den Bosch & White (<>)2010). Determining which of these processes are most significant for quenching is a major challenge. Due to the vast range of physical processes and scales which can contribute to the quenching of star-formation (e.g. formation of stars, stellar feedback, and accretion onto and outflows from black-holes) empirical constraints can play a vital role. ",
+    "Here we consider ways in which large statistical galaxy ",
+    "surveys can be used to distinguish between di erent models for galaxy quenching, motivated by the tremendous impact of the Sloan Digital Sky Survey ((<>)York et al. (<>)2000) on studies of local galaxies, and other large surveys either beginning or being planned. We take such surveys to provide a set of galaxy positions and stellar masses and whether or not the star-formation in the galaxy is quenched. We shall not consider here detailed measurements of individual galaxies on smaller scales, such as galaxy structural properties, properties such as winds, or AGN signatures. While these are indeed valuable, our focus is on properties associated with large-scale structure as is available in large surveys. ",
+    "We expect that using even relatively little information per galaxy can be highly informative when combined with large statistical samples, because many proposed galaxy quenching mechanisms di er in their dependence upon galaxy formation histories and environments. These di er-ences lead to di erent overall statistical properties. For example, heating of a galaxy by an AGN may be more likely to occur when the galaxy is in the core of a massive halo, ",
+    "while stripping of gas could be more likely when a galaxy is moving through a very dense environment (e.g. as a satellite in a massive halo). The two resulting populations have di erent demographics. ",
+    "In this work we create mock, quenched galaxy samples in N-body simulations, based upon 10 di erent models and prescriptions drawn from or motivated by models in the literature. Each model assigns quiescence to individual mock galaxies based upon history and/or environmental criteria, which we expect to be correlated with the underlying physical (and baryonic) processes a ecting star-formation. We identify similarities and di erences between these models, both intrinsic and observable. Our mock observations of these data help elucidate which future observations might best disentangle such models, and how precise those observations need to be. How the observations interlock and constrain the models is also valuable information for refining mock catalogs – created via any method – which are used in the design and analysis of large surveys. ",
+    "We shall only consider a single redshift here (z≃0.5); while connecting galaxies across time is a powerful technique, it also involves further assumptions. At low redshifts (z≃0.1) the wealth of data and in depth analysis of rich data sets such as SDSS (www.sdss.org) has provided many powerful constraints on environments and other properties of quenched galaxies. Some of our models incorporate these insights. By going back to z≃0.5, we explore the implications of these mechanisms for a significantly earlier cosmic time, and one for which we expect large statistical samples in the near future 1 (<>). Note that z≃0.5 is approximately 5 Gyr ago, which is longer than the main-sequence lifetime of >1.4 M⊙stars. Any galaxy less massive than 2×1010 M⊙on the star forming main sequence would at least double its stellar mass in this period2 (<>). It is also around z≃0.5 that we see a rapid rise in the number density of intermediate-mass quiescent galaxies, making this a particularly interesting time to study. ",
+    "We also focus exclusively on a single galaxy property, quiescence. Comparing measurements for one observed galaxy property, while fixing the others, makes this work similar to the approach of e.g. (<>)Hearin & Watson ((<>)2013); (<>)Masaki, Lin & Yoshida ((<>)2013) at z≃0.1. This forms a complement to more complex models, such as semi-analytic models, which provide more information on each galaxy across cosmic time but also more dependencies between inputs, assumptions and observations (see e.g. (<>)Lu et al. (<>)2010; (<>)Neistein & Weinmann (<>)2010; (<>)Lu et al. (<>)2013, for recent examples of fitting a suite of parameters in such models to a suite of observations). ",
+    "The outline of the paper is as follows. In Section (<>)2 we describe the N-body simulation and our observation-based assignments of galaxy stellar mass and total quiescent fraction. In Section (<>)3 we describe our 10 di erent prescriptions for selecting quiescent galaxies based on histories and environments, and in Section (<>)4 and Section (<>)5 we compare intrinsic and observational properties of the resulting catalogues ",
+    "respectively. Section (<>)7 summarizes and concludes. Throughout we use lg to denote log10, express stellar masses in M⊙(with no factors of h), and halo masses in units of h−1 M⊙. All distances and volumes are comoving and expressed in h−1 Mpc or h−3 Mpc3 . "
+  ],
+  "2 SIMULATIONS AND STELLAR MASS ASSIGNMENTS ": [
+    "In order to compare di erent models and mechanisms for quiescence, we would like to have a sample of mock galaxies with environments, formation histories and stellar masses which are close to what is seen in observations. To this end we associate mock galaxies with dark matter subha-los (defined in more detail below) in an N-body simulation. Such associations are currently the standard tool for analyzing galaxy surveys, as dark matter simulations of the cosmic web are well converged (e.g. (<>)Heitmann et al. (<>)2008) and di erences between dark matter subhalo definitions and merger trees are becoming similarly well characterized ((<>)Onions et al. (<>)2012). The N-body simulation provides sub-halo properties such as positions, velocity, (dark matter) mass, environment and history. As dark matter is the dominant contribution to the mass density in the Universe, these quantities are expected to be close approximations 3 (<>)to their values when baryons and all interactions are included (a comprehensive simulation of the latter is currently infeasible). We use the terms galaxy and subhalo interchangeably henceforth. ",
+    "We employ an N-body simulation performed in a periodic box of side 250 h−1 Mpc. This box has a similar volume to the main galaxy survey of the SDSS, though without boundaries or gaps. At z≃0.5 it would subtend around 10◦on a side in the plane of the sky. The cosmology is of the CDM family with ( m,,h,n,σ8) = (0.274,0.726,0.7,0.95,0.8). The simulation evolved 2048 3 equal mass particles from initial conditions generated at z= 150 with second order Lagrangian perturbation theory, using the code described in (<>)White ((<>)2002). Phase space data for all of the particles were dumped starting at z= 10 and for 45 times equally spaced in lg(1 + z) down to z= 0. We use the z≃0.5 (a= 0.676) output as our observation time. Further details about this simulation can be found in (<>)White, Cohn & Smit ((<>)2010). ",
+    "For each output, halos are identified using the Friends of Friends (FoF) algorithm ((<>)Davis et al. (<>)1985), with a linking length of 0.168 times the mean inter-particle spacing. Halo masses quoted below are FoF halo masses unless otherwise specified. When halos merge, part of the smaller halo can survive as a self-bound substructure within the larger host halo. In such a situation we call the core of the larger halo the “central subhalo” (or central) of the final system and the core of the smaller halo which “fell in” a “satellite subhalo” (or satellite). We reserve the term “halo” to ",
+    "refer to the parent FoF structure which will host a central subhalo and possibly several satellite subhalos. The subhalos are tracked as overdensities in phase space using the FoF6D algorithm ((<>)Diemand, Kuhlen & Madau (<>)2006) as implemented in (<>)White, Cohn & Smit ((<>)2010). Merger trees and histories are calculated using the methods described in (<>)Wetzel, Cohn & White ((<>)2009); (<>)Wetzel & White ((<>)2010). ",
+    "As in (<>)Wetzel & White ((<>)2010) we only consider halos (and their descendant subhalos) with masses above 1011.3h−1 M⊙to avoid resolution issues (note that sub-halos tracked using Subfind ((<>)Springel, Yoshida & White (<>)2001) require a higher minimum mass cut, as discussed in (<>)Guo & White (<>)2012). This cut results in 310,687 galaxies in our z≃0.5 box or n¯ = 7 ×10−3 Mpc−3 (comoving). There are in addition 1, 18 and 110 (roughly cluster sized) halos with mass above 1015h−1 M⊙, 2 ×1014h−1 M⊙and 10 hM⊙. 14 −1 "
+  ],
+  "2.1 Stellar mass assignments ": [
+    "Observationally, star formation is correlated with stellar mass, and many of the models we investigate use as an input the stellar mass of the galaxy. We thus need a way to assign stellar masses to our mock galaxies which results in the right demographics and environmental properties. We assign stellar mass to each galaxy using subhalo abundance matching (e.g. (<>)Vale & Ostriker (<>)2006; (<>)Conroy, Wechsler & Kravtsov (<>)2006) to the z≃0.5 stellar mass function of (<>)Drory et al. ((<>)2009). We use this stellar mass function 4 (<>)in part because several of our prescriptions start with the quiescent fractions of central and satellite galaxies proposed by (<>)Wetzel et al. ((<>)2013a, hereafter (<>)WTCB) based upon these data. ",
+    "We choose to abundance match stellar mass to the maximum mass in a subhalo’s history. For a satellite subhalo, this maximum mass is often the mass right before it becomes a satellite, sometimes known as the infall mass. (Using the maximum mass is along the lines recommended by (<>)Reddick et al. ((<>)2013), who compared several possible abundance matching proxies for stellar masses and luminosities at z≃0.05, although the peak velocity was an even better proxy in their case.) We include a 0.16 dex scatter in stellar mass at fixed maximum mass (again motivated by the choices of (<>)WTCB) but we clip the scatter at ±2σto avoid outliers in the more massive halos which are rare in ",
+    "Figure 1. Top: The stellar mass function of (<>)Drory et al. ((<>)2009, smooth curve) and the histogram (dotted line) of stellar masses in our box. This is used as input to all 10 of our methods. Bottom: Satellite fraction at z ≃0.5 (solid black line), prescriptions for redshift independent (dotted red line) and dependent (dashed blue line) quiescent satellite fractions, and their corresponding quiescent central fractions. These come from (<>)WTCB and are used to construct the “fix sat” and “fix c/s” models described in Section (<>)3. ",
+    "our simulation box. After assigning M⋆, we keep only galaxies with M⋆ ≥109.5 M⊙. Of the 310,687 mock galaxies in the box making the halo resolution mass cut, 254,950 then remain (of which 185,532 are central). This galaxy sample is starting point for each of our catalogues below. The stellar mass functions for (<>)Drory et al. ((<>)2009) and for the simulation box are shown in Fig. (<>)1 where we see good agreement, as expected. "
+  ],
+  "2.2 Quiescent fraction as a function of stellar mass ": [
+    "Each prescription we consider below assigns a subset of the galaxies in our simulation box to be quiescent. Matching observations of this fraction is clearly a key property, and is built into the specification of several of our models. For example, many of our models are taken from prescriptions of (<>)WTCB, which are in turn based upon the (<>)Drory et al. ((<>)2009) quiescent fraction as a function of stellar mass, fQ,all(M⋆) (see Fig. (<>)2). Others require a quiescent fraction as function of stellar mass as input, again we choose that of (<>)Drory et al. ((<>)2009). Specifically, we take fQ,all(M⋆) as the number of quiescent galaxies divided by the sum of quiescent and active galaxies in the double Schechter function fits of Eq. (1) and Table 3 of (<>)Drory et al. ((<>)2009). ",
+    "There is a large diversity in observed quiescent fractions as a function of stellar mass. The origins of some of these di erences are understood, in particular, the (<>)Drory et al. ((<>)2009) quiescent fractions are defined through SED fit-",
+    "Figure 2. The quiescent fraction in our mock catalogues, all of which are tuned to the (<>)Drory et al. ((<>)2009) observational fits (smooth blue lines). The central smooth blue line is the ratio of the best-fit quiescent stellar mass function to the quiescent plus active stellar mass functions (from the double Schechter fits in (<>)Drory et al. ((<>)2009) Eq. (1) and table 3). The two flanking blue curves are the ±1 ˙ variation of the 4 normalizations (° b and ° f for both quiescent and active galaxies) to give an indication of the range of observational uncertainty. The prescriptions based upon “fix sat”, “fix c/s”, “maxmass,” and zstarve all match the (<>)Drory et al. ((<>)2009) curve by construction, and so are all essentially degenerate. The red lines are for “fix sat” and the blue are for “fix c/s”. The solid line is for random quiescent assignment, dot-dashed is our version of galactic conformity (“conf”) while dotted is satellite history (“h”). The solid cyan line is the “max-mass” model, while dashed cyan denotes M˙ h; magenta solid is M⋆ 5 and magenta dotted is zstarve. ",
+    "ting, and thus di er from those employing other definitions (e.g. specific star formation rate, color cuts, morphology or some combination). (<>)Pozzetti et al. ((<>)2010) compare samples of quiescent galaxies selected by several di erent definitions for a data set at z≃0.5. The galaxy samples di er physically and in number density, with color cut based samples tending to include more galaxies because of dust. Two of our models are based upon non-SED based criteria for quiescence. To take this additional (in part definitional) complexity out of our comparisons, we modify our prescriptions, if needed, to improve agreement with the SED based (<>)Drory et al. ((<>)2009) fQ,all(M⋆). Unfortunately there is not always a unique modification to match to the SED quiescent fraction, or matching it exactly is diÿcult. We shall discuss these cases in detail below. Our quiescent fraction choice produces approximately 55,000-65,000 quiescent galaxies for each catalogue, depending upon model. "
+  ],
+  "3 PRESCRIPTIONS FOR ASSIGNING QUIESCENT GALAXIES ": [
+    "We now describe the di erent quiescent galaxy prescriptions we apply and the 10 resulting catalogues. ",
+    "Our starting point is the z≃0.5 box of mock galaxies with stellar masses assigned as described above. (By fixing this underlying galaxy distribution for all 10 catalogues, any di erences in quiescent galaxy catalogues are due solely to the di erences in assigning quiescence.) ",
+    "The first and simplest model is motivated by a method by (<>)Skibba & Sheth ((<>)2009) used at z≃0.1 to assign colors to mock galaxies. The method assumes we have a luminosity and central/satellite assignment for each object, and that the color depends only on these properties. Such a method gives good agreement with a number of observations at z≃0.1. In our case, we use each galaxy’s stellar mass, M⋆, and whether it is a satellite or central galaxy to determine the probability that it is quiescent. Individual galaxies are then marked, at random, using these probabilities. With our assumptions, there is only one free function that we must specify to determine the model, and we can take it to be the probability that a satellite galaxy of stellar mass M⋆ is quiescent: fQ,sat(M⋆). The central quiescent fraction then is given by the requirement that we match the overall quiescent fraction fQ,all(M⋆) of (<>)Drory et al. ((<>)2009). In more detail, and because conventions can di er, we define fQ,sat(M⋆) as the fraction of satellites which are quiescent, i.e. the total number of satellite galaxies of a given M⋆ which are quiescent is fQ,sat(M⋆) fsat(M⋆) Ngal(M⋆), where fsat is the fraction of M⋆ galaxies which are satellites and Ngal(M⋆) is the total number of galaxies with stellar mass M⋆. The definition of fQ,cen(M⋆) is analogous. ",
+    "These functions have all been well constrained at z≃0.1, but we expect them to change with redshift. Unfortunately, a precise measurement of these functions at higher redshift is diÿcult as it requires a good group catalog and quiescence classification over a cosmologically representative volume 5 (<>). To overcome this, (<>)WTCB suggest extrapolating from z≃0.1 to higher zin two ways and using the di erence as a measure of uncertainty in the model. As more observations become available we can use the measured fQ,sat(M⋆) rather than these extrapolations. In the meantime, including both models helps us to understand the observational signatures we see later. "
+  ],
+  "3.1 Fixed fQ,sat ": [
+    "The first extrapolation to redshift z= 0.5, which we refer to as “fix sat”, assumes ((<>)Wetzel et al. (<>)2013a) ",
+    "(1) ",
+    "It is shown for our redshift in Fig. (<>)1 as the dotted (red) line. For the stellar masses of interest to us, the overall quiescent fraction of galaxies is observed to drop rapidly to increasing redshift, while the satellite fraction evolves more modestly ",
+    "(see e.g. table 1 of (<>)Wetzel et al. (<>)2013a, for a recent compilation). If we hold fQ,sat fixed, the decrease in fQ,all must be obtained by decreasing fQ,cen. Thus, in order to match the observed evolution of the total quiescent fraction, the fraction of central galaxies which are quiescent in this prescription drops rapidly with increasing redshift. ",
+    "To implement Eq. ((<>)1) and the related models described below, we assign the specified quiescent fractions in 100 bins covering 9.5 ≤lg M⋆/M⊙<12.06. If either fQ,sat(M⋆) or fQ,cen(M⋆) go outside the region [0,1], we clip its value and choose the other fraction to reach the desired fQ,all(M⋆). For our first prescription, we thus randomly assign galaxies to be quiescent only requiring that Eq. ((<>)1) above and the corresponding fQ,cen(M⋆) are satisfied in each stellar mass bin. ",
+    "1",
+    "We extended this prescription in 2 ways, to get 2 more catalogues. The first extension is a version of “galactic conformity” 6 (<>). The quiescent centrals are taken to be the same as those in the “fix sat” case above. Satellites of quiescent centrals are initially all taken to be quiescent as well. If the resulting number of quiescent satellites is too small to satisfy Eq. () in a given M⋆ bin, more satellites are randomly assigned to be quiescent. If the number of quiescent satellites is instead too large, quiescent satellites are randomly changed to active to get agreement. Both cases occur, for higher and lower M⋆ respectively. (As we shall see later, in a similar model with more quiescent centrals, many more halos have star-forming satellites but quiescent centrals, while there are no cases of quiescent satellites with star-forming centrals. We shall explore the observational consequences of this below.) On average, ∼70% of the satellites in high mass halos are quiescent in this variant, compared to about 60% for the (random) “fix sat” model. We call this prescription “fix sat-conf”. ",
+    "We explored a stronger form of galactic conformity as well, which we did not include in our family of catalogues. With our fixed choice of quiescent centrals, inherited from the “fix sat” prescription, we assigned a rank to each halo. Halos with quiescent centrals were ranked first, in order of descending (total) richness. Halos with star-forming centrals followed the centrally quiescent halos but were ranked in ascending order of richness. Each satellite galaxy then inherited the ranking of its parent halo. Within a bin of stellar mass the first ranked fQ,sat(M⋆)Nsat(M⋆) of the satellites were marked as quiescent, with the rest being star-forming. This prescription resulted in no star forming galaxies in the richest halos which have quiescent centrals (down to halo masses below 1014h−1M⊙). As this is in clear conflict with observations, we work with the less extreme “fix sat-conf” prescription described above. ",
+    "The second extension based upon Eq. ((<>)1), “fix sat-h”, introduces a quenching ordering (and thus an implied time scale). Central galaxies from the “fix sat” model are again left unchanged. Each satellite is then ranked by its infall time. To deal with the discreteness in the output times from ",
+    "Figure 3. Quenching times found for “fix sat-h” (filled red triangles), “fix c/s-h” (filled blue squares) and “maxmass” (open cyan squares) models as described in the text. The solid black line shows the z = 0 quenching times suggested for a model by (<>)WTCB which is similar to the “maxmass” model. The (lower) dashed, black line gives a suggested extrapolation to z = 0.5 of the z = 0 solid line, from (<>)Tinker & Wetzel ((<>)2010). At the highest stellar masses there are very few satellites, leading to the larger scatter in quenching time. ",
+    "the simulation we take the infall time to be random, uniformly distributed between the time step when the galaxy was last a central and when it became a satellite. 7 (<>)We take some satellites as quiescent upon infall with a probability based on the extrapolations in (<>)WTCB for fQ,cen(M⋆,z) in this model as a function of redshift. (They give estimates for 4 stellar mass bins and we extend the redshift scaling of their highest mass bin to apply to the most massive satellites.) We then take the remaining satellites in each stellar mass bin to be quiescent in order of infall time (earliest first) to reach fQ,sat(M⋆) in each stellar mass bin. The quenched satellite which fell in most recently of the latter set determines a quenching time, shown as solid (red) triangles in Fig. (<>)3. (At the highest stellar masses there are very few satellites, leading to the larger scatter in quenching time.) ",
+    "These first three models di er in how they include environment or history, but the quiescent central galaxies are identical, as is the quiescent satellite fraction as a function of M⋆. In particular these models all have a relatively low central quiescent fraction, as a direct consequence of Eq. ((<>)1). We now consider the second extrapolation of fQ,cen(M∗) from low redshift of (<>)WTCB, to illustrate the impact of this assumption. "
+  ],
+  "3.2 Fixed fQ,cen/fQ,sat ": [
+    "An alternate way to evolve the quiescent satellite fraction, also suggested by (<>)WTCB, is to fix not fQ,sat(M⋆) but the ratio of the central and satellite quiescent fractions. To match the observed drop in fQ,all towards higher z, both fQ,sat and fQ,cen decrease. However, since the drop is shared between the two sources this prescription leads to a larger quiescent central fraction than the assumption of Eq. ((<>)1). Specifically we take ",
+    "(2) ",
+    "Note, for lg M⋆/M⊙<9.56 the ratio is negative because the quiescent central fraction at z= 0 goes negative. For these values of M⋆ we take all central galaxies to be active (fQ,cen(M⋆) ≡0) and set the quiescent satellite fraction to obtain fQ,all(M⋆) of (<>)Drory et al. ((<>)2009). ",
+    "We can construct the same three variant models, random, conformity, and satellite infall, using Eq. ((<>)2) above as a base instead of Eq. ((<>)1) as was done earlier. Some di erences are immediately notable. As just described, in comparison to the “fix sat” model, the “fix c/s” model has more (or the same number of) quiescent centrals in all M⋆ bins at z≃0.5. Due to the increase in number of quiescent centrals relative to the “fix sat” models, the “fix c/s-conf” variation has many more (roughly four times as many) satellites which are active in halos with quiescent centrals, relative to the “fix sat-conf” variation. Furthermore, unlike the “fix sat-conf” case, there are no quiescent satellites in halos with active centrals. We shall see the implications of this below. For the “-h” variation, we again find a the quenching time by assigning galaxies with the earliest infall time as quiescent, but now up to the fraction required by Eq. ((<>)2). This quenching time is much longer than that found for the “fix sat” models, hovering above 4 Gyr for almost all stellar masses, as can be seen in Fig. (<>)3. Satellites take longer to quench because many more are quiescent upon infall, and because many fewer are needed as quiescent overall, given Eq. ((<>)2). ",
+    "Further and more detailed comparisons between these prescriptions and our other prescriptions are considered in Sections (<>)4 and (<>)5. "
+  ],
+  "3.3 Other models ": [
+    "Our four other prescriptions for when a galaxy becomes quiescent did not use satellite and central quiescent fractions as a constraint. All are based on models presented in the literature, although we have modified or applied them to obtain the (<>)Drory et al. ((<>)2009) quiescent fraction fQ,all(M⋆) as a function of stellar mass. "
+  ],
+  "3.3.1 Maximum mass ": [
+    "In the “maxmass” prescription, satellites are quenched in order of the earliest time since their maximum mass, up to the number needed to reach the required fQ,all(M⋆) in each M⋆ bin. Similarly to our infall times for satellites, we ",
+    "smooth out the discreteness of the output times in the N-body simulation by assigning the time of maximum mass for each galaxy randomly and uniformly between the relevant bracketing time steps (again this will erase some correlations between galaxies sharing the same halo upon in-fall). For satellites this maximum mass is also taken to be at or before infall time – we thus exclude mass gains through satellite merging, which can be significant (e.g. (<>)Angulo et al. (<>)2009; (<>)Simha et al (<>)2009; (<>)Wetzel, Cohn & White (<>)2009). This implicitly assumes that mass gains due to merging after in-fall do not induce further star formation, which seems reasonable. Matching fQ,all(M⋆) in each M⋆ bin then determines a quenching time, which is comparable to that of the “fix sat-h” model (open cyan circles and red filled triangles respectively in Fig. (<>)3). ",
+    "As the time of maximum mass is correlated with the time of first infall into any larger halo ((<>)Wetzel et al. (<>)2013b), this model is similar to the (<>)WTCB model for quenching. For comparison with their model, we also show their quenching times in Fig. (<>)3, both for z= 0 (which they use, solid line) and one estimate ((<>)Tinker & Wetzel (<>)2010) for the z≃0.5 extension (dashed line). "
+  ],
+  "3.3.2 Halo growth ": [
+    "The second of these prescriptions, which we label M˙ h, is based on a property of average star formation histories highlighted by (<>)Behroozi, Wechsler & Conroy ((<>)2013a,(<>)b). They calculated the average star formation rate as a function of stellar mass from 0 <z<8, and compared with simulations to find an approximate relation ",
+    "(3) ",
+    "i.e. star formation rate proportional to baryon accretion rate, where the baryon accretion rate is fb dMh/dtand fb = 0.17 in their cosmology. For α(Mh) independent of redshift, Eq. ((<>)3) would imply a redshift-independent M⋆(Mh) relation. While the M⋆(Mh) relation does not evolve strongly, it is not completely redshift independent (e.g. (<>)Yang et al. (<>)2012; (<>)Wetzel et al. (<>)2013a; (<>)Moster, Naab & White (<>)2013; (<>)Behroozi, Wechsler & Conroy (<>)2013b; (<>)Watson & Conroy (<>)2013), and thus this model can only be an approximation 8 (<>). We make further approximations by using Eq. ((<>)3) to estimate the sSFR for individual galaxies and then apply a cut on sSFR to classify a galaxy as quiescent or star-forming, which is similar but not identical to an SED-based classification (as mentioned above, and expanded upon below). ",
+    "The halo mass change in Eq. ((<>)3), dMh/dt, is the change in Mvir halo mass. We approximate the Mvir mass gain by the FoF mass gain as the two mass definitions are close at this redshift. In addition, the change in observed stellar mass (the observed star formation rate, of interest to us) has a factor of 1.11 relative to the change in the true stellar mass given above (from Eq. (7) in (<>)Behroozi, Wechsler & Conroy ((<>)2013a)). ",
+    "Two additional assumptions are needed to identify which galaxies are quiescent. First of all, this approach does not indicate what to do with satellite galaxies. In addition, many central halos have their last significant mass gain earlier than z≃0.5. Setting all galaxies in these categories to have zero star formation well exceeds the (<>)Drory et al. ((<>)2009) quiescent fraction constraint. We instead make an ansatz, again based upon the models in (<>)WTCB: we take galaxies to have a star formation rate from their most recent halo mass gain (using dMh for that step and dtfor that step), but if that time is before the present time step, we add a damping factor assuming that the star formation is decaying from an earlier time. (Again, mass gains for satellites after infall, due to merging, are not included.) Following (<>)WTCB, we assume star formation actually started at z= 3 and that its value at the time of most recent mass gain (given by Eq. (<>)3) has decayed by the time of observation. Taking the star formation history for central galaxies ∝texp [−t/τcen], with t= t−tform and tform = t(z= 3), (<>)WTCB find τcen within 1.9 −3.8 Gyr. We take τcen = 3 Gyr. The star-formation rate at z≃0.5 is then evolved from the value given by Eq. ((<>)3) at the time of most recent mass gain using SFR ∝texp [−t/τcen]. With only this prescription, however, the model does not have enough quenched galaxies. So in addition to increasing the star formation by using earlier time steps, some quenching is needed to decrease the star formation by the current time. We thus augment the model by setting sSFR = 10−13 yr−1 for any central or satellite galaxy which had its more recent mass gain more than a quenching time ago, assuming this quenching time depends upon stellar mass, similar to our earlier models. We have three examples of quenching times from our above constructions: that of the “fix sat-h”, “fix c/s-h” and “maxmass” models, in Fig. (<>)3. We chose to use the “fix sat-h” quenching times as they gave the closest agreement to the desired quiescent fraction fQ,all(M∗) when combined with the sSFR cut below. (This allows some interesting model comparisons below, as for“fix sat-h” model the times were only defined by and used for the satellites, with centrals were assigned randomly; and here the times are used for all galaxies.) The quenching time is responsible for the quiescence of about 1/5 of the quiescent centrals and about 4/5 of the quiescent satellites (these latter overlap with the “fix sat-h” satellites as a result of using that prescription’s time scale). ",
+    "The last piece needed to get some estimate of quiescence is a comparison of this sSFR estimate to a quiescence classification based on SEDs. The sSFR assignments in (<>)WTCB suggest a cut 9 (<>)between active and quiescent galaxies at sSFR= 10−11yr−1 . A comparison of SED and sSFR cuts for galaxies at similar redshifts is found in fig. 1 of (<>)Pozzetti et al. ((<>)2010). Taking those numbers at face value, a sSFR cut of 10−11yr−1 does not include any active galaxies by the SED definition, but also neglects some quiescent ones. We change the maximum specific star formation rate for quiescent galaxies to 3 ×10−11yr−1 , which in (<>)Pozzetti et al. ",
+    "((<>)2010) would allow some admixture of active SED galaxies but also includes more quiescent SED galaxies. The resulting galaxy sample gives better agreement numerically with the SED determined quiescent fraction as a function of M⋆ in (<>)Drory et al. ((<>)2009). ",
+    "Finally, we note that we do not include any scatter in the sSFR, taking it directly from Eq. ((<>)3), and we do not self-consistently integrate dM⋆/dtover time, instead applying it instantaneously at z≃0.5. A forward integration of Eq. ((<>)3) may couple M⋆ and dM⋆/dtmore closely, while inclusion of scatter would obviously weaken such a correlation. "
+  ],
+  "3.3.3 Stellar mass and density ": [
+    "Our third additional prescription, which we label “M⋆ 5”, is based on (<>)Peng et al. ((<>)2010, see also (<>)Kovac et al. (<>)2013). These authors found that the red and blue fractions of the zCOSMOS sample could be described by the product of two factors, depending upon projected density 5 and stellar mass, ",
+    "(4) ",
+    "with (p1,p2,p3,p4) functions of redshift. Here 5 is the projected density, defined by fifth nearest neighbor in a redshift cylinder of ±1000 km s−1 , including galaxies down to MB,AB ≤−19.8 (for z≃0.5, (<>)Kovac et al. (<>)2010; (<>)Peng et al. (<>)2010). ",
+    "This model is particularly interesting for our purposes because it does not specifically refer to halo mass or to central/satellite designation. However we need to modify it slightly. Although we have M⋆ for each galaxy, the projected density assignment as used by (<>)Peng et al. ((<>)2010) relies upon a sample selected with MB , and MB depends upon color, which is related to quiescence, which we are trying to find. In addition, the parameters pi in Eq. ((<>)4) are tuned to separate galaxies into red and blue (i.e. using observations based upon a color cut), rather than quiescent and active. We make two modifications as a result. ",
+    "Instead of using an MB -limited sample to define projected density, we use an M⋆-limited sample. We choose the minimum M⋆ to give the same galaxy number density as the number of galaxies passing the MB cut of (<>)Peng et al. ((<>)2010). At z≃0.5, the MB limit is MB,AB ≤−19.8. This corresponds to a density of 10−2 h3 Mpc−3 using the COMBO-17, DEEP2 and VVDS B-band luminosity functions quoted in (<>)Faber et al. ((<>)2007). Matching this number density fixes our threshold M⋆ ≃8 ×10 9 M⊙. The projected density 5 is then the inverse square of the distance to the 5th nearest neighbor within the cylinder divided by its average value for a sample of random positions within the box. ",
+    "Using 5 and M⋆ in Eq. (<>)4 gives each galaxy in our box a probability of being red, defined by the color cut chosen in (<>)Peng et al. ((<>)2010). The resulting fQ,all(M⋆) well exceeds that of (<>)Drory et al. ((<>)2009). This is not surprising. As mentioned earlier, color cuts tend to classify more galaxies as quiescent (red) than an SED (our comparison (<>)Drory et al. ",
+    "((<>)2009) sample) or sSFR based cut. 10 (<>)Our 5 assignment based upon M⋆ rather than MB might be also a factor, however, this red fraction in our box is a good match to that in (<>)Knobel et al. ((<>)2013), including central and satellite red fractions as a function of M⋆. (For this test we also use the (<>)Knobel et al. ((<>)2013) stellar mass function for consistency.) ",
+    "Our prescription is thus to keep the form of the (<>)Peng et al. ((<>)2010) model, but to modify the parameters to match the fQ,all(M⋆) of (<>)Drory et al. ((<>)2009). As (<>)Peng et al. ((<>)2010) tuned their parameters using the measured distributions of quiescence as a function of both 5 and M⋆, while we only have fQ,all(M⋆), our modifications cannot be unique. (Some degeneracy is expected as there is some correlation of high M⋆ with high 5.) We found (p1,p2,p3,p4) = (202,1.71,1.56 ×1011 ,0.69) fit our fiducial fQ,all(M⋆,z= 0.5) quite well, which corresponds to multiplying the (<>)Peng et al. ((<>)2010) default values (from their table 2, averaged for two redshift bins) by (3.2,2.5,2.5,1.1). "
+  ],
+  "3.3.4 Starvation ": [
+    "Our last prescription is based upon a proposal by (<>)Hearin & Watson ((<>)2013), see also (<>)Zentner, Hearin & van den Bosch ((<>)2011), of “age matching”. These authors assign r-band luminosities to a simulation similar to ours using subhalo abundance matching, and then order galaxies in luminosity bins according to a redshift zstarve (roughly a quenching time). Galaxies with the earliest zstarve are taken to be quiescent, up to the total number required (for us set by (<>)Drory et al. (<>)2009). (<>)Hearin & Watson ((<>)2013) define zstarve as the maximum (earliest) of three possible redshifts: ",
+    "-when the host halo equals or exceeds 1012 h−1M⊙. -when the galaxy becomes a satellite. ",
+    "Each of these redshifts is taken to be zero if it never occurs. (<>)Hearin & Watson ((<>)2013) use Mvir in the first condition, while we shall instead use MFoF. The two definitions are close at the redshifts of interest. The halo growth rate is taken from (<>)Wechsler et al. ((<>)2002). While (<>)Hearin & Watson ((<>)2013) use a relation between concentration and halo growth rate, we instead use the definition of (<>)Wechsler et al. ((<>)2002): dlog Mhalo/dlog a≡ log MFoF/ log a<2. We search through the time steps in the simulation to find the earliest time that the halo growth rate dropped below, and subsequently stayed below, the threshold growth rate. ",
+    "As in our previous models, we bin on M⋆ (rather than r-band luminosity). We assign quiescent galaxies based upon the galaxies with the highest zstarve in each of 100 stellar mass bins. The last condition (slow down in growth) accounts for slightly more than 60 per cent of the zstarve, with the remainder of the assignments split approximately equally between the other two conditions. ",
+    "A fifth additional model which we implemented, but which we do not include below, is that of (<>)Lu et al. ((<>)2013). These authors assign star formation rate based upon halo mass, infall time for satellites, and stellar mass. Using their ",
+    "preferred model we found quiescent fractions too large to be consistent with (<>)Drory et al. ((<>)2009). In particular their model had a very short satellite quenching time, making essentially all satellites quenched. While there are combinations of parameters in their prescription which give longer quenching times, without repeating their full likelihood analysis we could not identify combinations which matched the our required quiescent fraction and the other constraints they imposed.11 (<>)"
+  ],
+  "3.4 Summary of the models ": [
+    "The quiescence criteria above result in 10 galaxy catalogues, di ering only by which galaxies are marked as quiescent. The next step is to compare measurements on all these cat-alogues, however it is first useful to summarize how the prescriptions di er. A comparison of the criteria used in determining quiescence (central or satellite in halo, infall time, halo mass change, etc.) is given in Table (<>)1. In words, the criteria for quiescence can be briefly described as: ",
+    "M⋆ 5 quiescent probability from the stellar and (projected) local density using Eq. ((<>)4). "
+  ],
+  "4 COMPARISONS: INTRINSIC ": [
+    "With these catalogs in hand we wish to see in what ways the di erent prescriptions lead to di erent populations of quiescent galaxies. We begin with a discussion of the intrinsic properties, before turning to the observational consequences in Section (<>)5. ",
+    "Two intrinsic properties are imposed on the catalogues by construction. The first is the stellar mass function, shown in Fig. (<>)1 and implemented identically in all the catalogues. The second, the quiescent fraction of all galaxies as a function of stellar mass, fQ,all(M⋆), was used implicitly or explicitly in the catalogue construction as well (and used to exclude the model of (<>)Lu et al. (<>)2013 which did not provide a good match to this function). In Fig. (<>)2, the observations ",
+    "Table 1. Summary of which physical properties were used to assign quiescence for each of the galaxy catalogues. Some catalogues assign quiescence only using whether a galaxy is a central or satellite, in contrast, the M⋆ 5 catalog does not refer to host halos at all. Only one model (zstarve) depends upon host halo mass explicitly. Several models depend upon infall time for satellites, the “maxmass” model only does because mass gain by definition does not happen after infall. ",
+    "of (<>)Drory et al. ((<>)2009) are shown along with the measurements from the models. While the models generally reproduce fQ,all(M⋆) quite well, the match is not perfect for all of them. In particular, the M⋆ 5 and M˙ h prescriptions have slight excesses at low M⋆, and the M˙ h model is also high at high M⋆, although in-between it matches the others fairly well. ",
+    "We now consider measurement other than these two intentionally degenerate properties to highlight di erences between the catalogues. "
+  ],
+  "4.1 Central and Satellite Quiescent Fractions ": [
+    "The quiescent fraction of all galaxies as a function of stellar mass, fQ,all(M∗) above, can be decomposed into central and satellite contributions. These are challenging to obtain observationally, which is in part the reason why (<>)WTCB propose two di erent z≃0.5 quiescent satellite and central decompositions (the starting points for our “fix sat” and “fix c/s” models). However, understanding the way in which these functions di er between the models will help us to understand the observational trends in the next section, and which observations bear most directly upon this separation. ",
+    "The breakdowns into quiescent central (fQ,cen fcen) and quiescent satellite (fQ,sat fsat) galaxies for our catalogues are shown in Fig. (<>)4. For context we also reproduce the total quiescent galaxy fraction of (<>)Drory et al. ((<>)2009) from Fig. (<>)2. The solid and dot-dashed lines for the “fix sat” (red) and “fix c/s” (blue) models show the “fix c/s” model almost always has the same number or more quiescent central galaxies than the “fix sat” model, as we have remarked before. This is a direct consequence of the assumed redshift dependence of fQ,sat. If the decrease in quenched fraction with increasing redshift is borne entirely by the central galaxies, rather than being shared equally by the central and satellite galaxies, then fQ,cen is very small. ",
+    "Note that the models separate into two groups, with the zstarve prescription lying in-between. The trends in the central, quiescent galaxies are mirrored for the quiescent satellites as the sum is fixed. The models with conformity and the “-h” models have the same fractions as their parent models, because those models simply “shue” the quiescent or satellite galaxies into di erent halos. ",
+    "Three of the four models which do not specify the satellite and central quiescent fractions directly have strong sim-",
+    "ilarities to the “fix sat” or “fix c/s” models. In part this is because the quenching prescriptions lead to overlap of the quenched populations. The M˙ h model uses the quenching time after satellite infall of the “fix sat-h” model, ∼90 per cent of the M˙ h model quenched satellites coincide with 80 per cent of the “fix sat-h” quenched satellites. The “max-mass” model also has ∼90 per cent of its satellites in common with the “fix sat-h” model (and a similar percentage in common with the M˙ h satellites). These models have much less overlap in their quiescent centrals: quiescent centrals are randomly chosen for “fix sat-h”, while those for M˙ h are quiescent because recent mass gain was too small or too long ago, and for “maxmass” because largest mass was too long ago. About 2/3 of the “maxmass” quiescent centrals are also M˙ h centrals, but only about 1/3 of M˙ h and “maxmass” centrals overlap with “fix sat-h” quiescent centrals. As about three times as many central galaxies as satellite galaxies di er between the “maxmass” and M˙ h models relative to the “fix sat” models, central galaxy population di erences might be the source of observational di erences between the “maxmass” and M˙ h models and the “fix sat” model. ",
+    "At lower M⋆ the satellite fraction is relatively large, and satellites can saturate the required red fraction. Since the halos of central galaxies tend to gain mass more rapidly than those of satellites (whose last mass gain was prior to their infall) the M˙ h and “maxmass” models predict a very small fraction of quiescent, low M⋆ centrals. ",
+    "By contrast, the M⋆ 5 model lies close to the initial “fix c/s” fractions. This model has more low-M⋆, quiescent centrals than most of the others. In practice, the model makes little distinction between centrals and satellites, as the parameters (p1,p2,p3,p4) which we found to fit the fQ,all(M⋆) constraint imply fQ,sat(M⋆) ≈fQ,cen(M⋆). These fractions are also fairly close for the “fix c/s” models in Fig. (<>)1. If the satellite and central quiescent fractions are close, more central galaxies will be quiescent because they outnumber satellites at any given M⋆. (This satellite/central blindness is not necessarily part of the M⋆ 5 form for assigning quiescence. At fixed stellar mass, there is a 5 di erence on average between satellites and centrals, and parameters such as those in (<>)Peng et al. ((<>)2010) can lead to a large di erence between fQ,sat(M⋆) and fQ,cen(M⋆).) But by sampling a wide range of parameters, it seems that getting fQ,all(M⋆) low enough at low M⋆ requires raising p1 at low M⋆, thus taking fQ,sat(M⋆) towards fQ,cen(M⋆) as we found.) ",
+    "Figure 4. Contributions to the total quiescent fraction from central (left) and satellite (right) quiescent galaxies, as a function of stellar mass. Line types for each of the catalogues are as in Fig. (<>)2, as are the smooth blue lines representing an observational range for the total quiescent fraction. The prescriptions roughly separate into two groups for both central and satellite galaxies, with the zstarve prescription lying in-between. The “fix c/s” prescription lies in the group with more quiescent central galaxies as a function of M⋆, while the “fix sat” prescription is in the group with fewer quiescent central galaxies. (The trend is reversed for the satellite quiescent galaxies, as the sum is fixed). ",
+    "We now turn from quiescent satellite and central stellar mass functions to the question of which halos these satellites and central galaxies occupy. "
+  ],
+  "4.2 Quiescent Galaxy Halo Occupation ": [
+    "The manner in which the low-and high-mass quiescent central and satellite galaxies are distributed among halos di ers significantly between the models. In this section we ask: “in which types of halos are quiescent galaxies found?” ",
+    "Fig. (<>)5 shows the average number of quiescent galaxies per halo (the “halo occupation number” or HON; (<>)Peacock & Smith (<>)2000; (<>)Seljak (<>)2000; (<>)Cooray & Sheth (<>)2002), as a function of halo mass. At left we plot all quiescent galaxies, at right only central quiescent galaxies. The average number of all galaxies per halo is also shown for reference as the black line (and is the same for all models). The quiescent fraction as a function of halo mass is just the ratio of each model line to this black line, it is largest at high mass for the “fix sat-conf”, “maxmass” and M˙ h models. (The active galaxy HON – the di erence of the black solid line and any of the other curves – follows a rising power law for all of the models as well 12 (<>)). ",
+    "As was the case for the quiescent fractions, the quiescent galaxy HON’s split roughly into two groupings, which cross around Mh ≃2 ×1012 h−1M⊙. ",
+    "The “fix c/s” model has more quiescent, central galaxies at low M⋆ than the “fix sat” model. This in turn implies more quiescent galaxies in low mass halos and a shallower HON. Within the “fix sat” and “fix c/s” classes, the “-conf” ",
+    "models have more quiescent satellites in more massive halos, as these are the halos most likely to host quiescent centrals. Similarly, the “-h” models have more quiescent galaxies in massive halos than their random counterparts because such halos typically host more satellites (of a given stellar mass) that fell in long ago – arising from a combination of reduced dynamical friction and earlier halo formation time. A similar e ect operates for the “maxmass” prescription, because satellites which have reached their highest mass long ago tend to have fallen in long ago, and thus are again more prevalent in high mass halos. ",
+    "The M⋆ 5 model HON again seems very similar to the random “fix c/s” model. In both, the satellite and central quiescent fractions are much closer to each other than the other models. This large central quiescent fraction at low M⋆ can be seen in Fig. (<>)4 for both models. Since low M⋆ centrals live in low mass halos, this in turn explains the low Mh behavior of the HON. Again, this behavior seems to be built into the M⋆ 5 model by requiring the form of Eq. ((<>)4) to have low enough quiescent fraction at low M⋆ (to match our (<>)Drory et al. ((<>)2009) constraint). 13 (<>)",
+    "It is notable that the quiescent galaxy richness of clusters can vary by over a factor of two, i.e. the quiescent galaxy HON is very model dependent. This implies that the HON, or the cluster luminosity function for clusters of a wide range of masses, can provide a strong discriminant between models (this has been considered in e.g. (<>)Tinker et al. (<>)2012). The di erences in the number of quiescent galaxies as a function ",
+    "Figure 5. Left: quiescent galaxy HON for our models (line types as in Fig. (<>)2). The top mass bin is wider than the lower ones in order to have at least ten halos in it: the halo to halo scatter can be large, especially in the “-conf” model where changing a central galaxy between quiescent and active in principle changes all the satellites as well. This leads to the features in the dot-dashed, blue “fix c/s-conf” model. Note that the quiescent galaxy richness can vary by a factor of two between models for the highest mass halos, i.e. galaxy clusters. Right: quiescent central galaxy HON. In both panels, the black solid line is the HON of all galaxies. ",
+    "of host halo mass has implications for the physical role halo environments and membership play in turning galaxies from active to quiescent. "
+  ],
+  "4.3 Quiescent Galaxy Distribution in Clusters ": [
+    "In addition to measuring the number of galaxies in a halo of a given mass, we can ask how these galaxies are distributed within the halos (i.e. the profile). Aside from the M⋆ 5 prescription, and to some extent the “-conf” models, spatial properties are not used to define which galaxies are quiescent – so any dependence arises due to correlations with other properties which are used in the models. ",
+    "For the 18 most massive clusters in the simulation (Mh ≥2 ×10 14 h−1M⊙) we stacked the counts of quiescent galaxies in bins of radial distance from the most bound particle within the halo (which is very close to the minimum of the halo potential and the density peak). We used logarithmically spaced bins in r/rvir, where rvir is the virial radius 14 (<>). The total number of quiescent galaxies in clusters changes from model to model, as already shown in Fig. (<>)5. To highlight the additional information given by the profile, we normalize the stacked counts for each model at r= rvir. The resulting profiles are shown in Fig. (<>)6. ",
+    "In all of the models the quiescent galaxy radial profiles tend to be more centrally concentrated than those of all ",
+    "galaxies (the solid black line), reminiscent of the well-known morphology-and color-density relations (e.g. (<>)Dressler et al (<>)1997; (<>)Treu et al (<>)2003; (<>)Balogh et al (<>)2004; (<>)Kau mann et al (<>)2004; (<>)Postman et al (<>)2005; (<>)Christlein & Zabludo (<>)2005; (<>)Loh et al (<>)2008; (<>)Skibba et al (<>)2009; (<>)Cibinel et al (<>)2013; (<>)Lackner & Gunn (<>)2013; (<>)Muzzin et al. (<>)2012). Amongst the models, the “fix c/s-h” and zstarve models are the most centrally concentrated (this increase in concentration is due to a quicker drop o in quiescent galaxy density at high radius compared to many of the other models). The weak but non-zero correlation between infall time and radius ((<>)Oman, Hudson & Behroozi (<>)2013)15 (<>)imprints a radial dependence for the zstarve model. The large number of quiescent galaxies in the M⋆ 5 model near the cluster centers is a direct consequence of the increase of the quiescent fraction with projected density (Eq. (<>)4). "
+  ],
+  "5 COMPARISONS: OBSERVATIONAL ": [
+    "In summary, the models produce di erent numbers of quiescent centrals and satellites, place them in di erent halos (HON) and in di erent places in halos (profile). These results are very useful for understanding the di erences between the models but are challenging to access observationally. They do however drive di erences in quantities which can be probed observationally, for example the change in the HON leads to changes in the galaxy correlation function or in the richness distribution of groups. We now turn to such statistics and describe how the di erences we have seen above translate into di erences in the observables. ",
+    "Figure 6. Quiescent galaxy radial profile, for the 18 z ≃0.5 clusters with M ≥2 ×1014 h−1M⊙, rescaled at r = rvir to agree with the total galaxy distribution (black line). Line types are as in Fig. (<>)2. "
+  ],
+  "5.1 Quiescent galaxy correlation function ": [
+    "One of the most basic measurements that can be made on any population of objects is its two-point correlation function. In recent years it has become standard to use measurements of the correlation function to infer the halo occupation distribution (shown in Fig. (<>)5). We thus expect the correlation function to be a useful diagnostic of these models. "
+  ],
+  "5.1.1 Auto-correlations ": [
+    "We use the (<>)Landy & Szalay ((<>)1993) estimator to measure the (auto-)correlation functions for our catalogs. The results for the real-space correlation function are shown at the top of Fig. (<>)7, with the ratios of each model to the full galaxy real-space correlation function below (to highlight the di erences between models). Errors are shown for only 4 cases to avoid clutter in this and subsequent figures. The box is split into octants to compute the errors, which represent the error in the mean of the octants. They thus indicate how well a survey of comparable volume to our box could determine ξ(r). 16 (<>)Clearly, several of our prescriptions cleanly separate with a volume comparable to our simulation. The di erence between the curves in comparison to the errors can be used to indicate the observational requirements to distinguish them. ",
+    "The correlation function trends are as expected from ",
+    "the halo occupations in Fig. (<>)5: models with more galaxies in higher mass halos cluster more strongly on both large and small scales. The large-scale clustering is set by the bias, which is determined by the mean, galaxy-weighted, halo mass. The small-scale clustering is set by the number of central-satellite and satellite-satellite pairs within a single halo. Satellites with the longest time since infall (taken as quiescent for “fix sat-h”) or since maximum mass (taken as quiescent for “maxmass”) reside in the most massive clusters, so the corresponding quiescent samples cluster more strongly than the randomly chosen quiescent galaxy sample does. In addition, the “-conf” models tend to put more quiescent satellites in high mass halos, as most of the high mass halo central galaxies are quiescent. (This model also has the largest variance as changing one central galaxy to or from quiescent in a rare halo can significantly change the number of quiescent satellites for that halo mass and thus the number of quiescent galaxies with many nearby neighbors. This suggests that surveys aimed at ruling out this model need to sample a large volume with a representative sample of high-mass halos.) ",
+    "The impact of the radial profile within massive halos on ξ(r) is not very strong. While the models separate in Fig. (<>)6 we see two degeneracies seen in the HON in ξ(r) as well: the M⋆ 5 and random“fix c/s” models, and M˙ h and “fix sat-h” models are also close (the latter two have significant overlap in their populations as mentioned earlier). ",
+    "In practice the three dimensional real-space correlation function is found by “deprojecting” either the projected correlation function (to minimize the influence of redshift-space distortions) or the angular correlation function (if only coarse distance estimates are available). If accurate redshifts are available for the galaxies, the redshift space correlation function can in principle carry additional information, at least in part because the small-scale clustering is a ected by fingers-of-god and thus is sensitive to the satellite fraction in massive halos. To bring the comparison closer to the observational plane, the projected correlation function ",
+    "(5) ",
+    "is shown in Fig. (<>)8, where we see it exhibits similar behavior to ξ(r). In Eq. ((<>)5), rp is the separation in the plane of the sky, zis the separation along the line-of-sight in redshift space and zcut is a cuto in the line-of-sight direction. Ideally zcut is very large so that the the cuto doesn’t matter, however, our 125 h−1Mpc on-a-side octants are relatively small which argues against using very large zcut. One can still define and measure wp(rp) with a small zcut, but the zcut should be matched when comparing theory and observation. Throughout we use zcut = 25 h−1Mpc, thus considering cylinders 50 h−1Mpc deep in the redshift (velocity plus position) direction within each of the eight 125 h−1Mpc octants in the box. ",
+    "We also computed the angle-averaged, or monopole, redshift correlation function, ξ(s). The trends and di er-ences between the models in ξ(s) closely followed those seen in ξ(r), indicating that both statistics are comparable in their discriminating power and the additional sensitivity to e.g. the fingers-of-god is small. (The most noticeable di er-ence in ξ(s) is that the “fix c/s-conf” model increases its ",
+    "Figure 7. Top: three dimensional real-space correlation function, ˘(r). The solid black line is the correlation function of all galaxies, ˘all(r); other line types are as in Fig. (<>)2. For clarity, representative error bars are shown only for four examples. Just as in the HON, the M⋆5 model and random “fix c/s” models are roughly degenerate, as are the Mh ˙ and “hist sat” models (which have ∼80% overlap in their populations). The strongest clustered prescription at short distances (red dot-dashed line) is “fix sat conf”, i.e. the galactic conformity model with the larger number of quiescent satellites, as expected again from the HON. The zstarve quiescent galaxy correlation lies between the other two sets of trends, again as expected from the HON in Fig. (<>)5. Bottom: ˘(r)/˘all(r) for each quiescence prescription, which highlights di erences between the models. Note the linear vertical scale. ",
+    "Figure 8. Projected correlation function, wp, for same 10 models as in Fig. (<>)2, integrating over ±25 h−1Mpc in the redshift direction. The model separations are similar to those seen in the isotropic three dimensional correlation function (Fig. (<>)7, top). ",
+    "relative clustering at low separation, making it easier to differentiate it from the “fix c/s-h” model.) "
+  ],
+  "5.1.2 Cross-correlations ": [
+    "While it is not as commonly employed, it is also possible to measure the cross-correlation 17 (<>)between quiescent and star-forming galaxies (or between either population and the full sample). As an example we show the cross-correlation function, ξ×(r), between quiescent and star-forming galaxies at top in Fig. (<>)9. The di erences between models are not large, and appear mostly at small scales. This cross-correlation is most useful in testing the models which invoke conformity (especially the “fix sat-conf” model from the rest). Models which exhibit galactic conformity have fewer pairs of quiescent and star-forming galaxies within a single halo (preferring to have all of one type, the same as the central) so the cross-correlation is suppressed on small scales. The trend is less pronounced in the “fix c/s-conf” model, which has more halos where central and satellite galaxy quiescence are mismatched. The cross correlation divided by a reference power law model, shown in the lower half of Fig. (<>)9, more clearly separates the models. ",
+    "We also show the projected cross correlation function in Fig. (<>)10. It is defined analagously to Eq. (<>)5 and again limited to small zcut = 25 h−1Mpc in the redshift direction because of our box size. ",
+    "Figure 9. Top: Three dimensional cross-correlation function between quiescent and active galaxies for each catalogue. Line types are as in Fig. (<>)2. The “fix sat-conf” model most clearly separates out from the others at small separations. Bottom: Dividing by a reference power law model, ˘ref (r) = 20(r[Mpc/h])−1.7 . Just as in the auto-correlation function, this highlights di erences between the models, although due to the larger error bars many di erences here are not significant. ",
+    "Figure 10. Projected (±25 h−1Mpc in redshift space) cross-correlation function between quiescent and active galaxies for each catalogue, showing similar trends to its isotropic counterpart at top in Fig. (<>)9. Line types are as in Fig. (<>)2. ",
+    "Figure 11. Group multiplicity function (the number density of groups with N or more quiescent galaxies) for the mocks with line types as in Fig. (<>)2. Groups are defined using a redshift space Friends-of-Friends algorithm as discussed in the text. "
+  ],
+  "5.2 Group multiplicity function ": [
+    "One way to constrain the manner in which galaxies occupy halos is to model the galaxy correlation function, assuming a particular profile and parameterized halo occupation distribution. An alternative method is to measure the number of groups of objects of a given richness, i.e. the group multiplicity function. Di erences between models or between models and observations are of course easier to interpret the more closely the richness measure (or other observable) tracks halo mass, but even relatively coarse measures can be interpreted with the aid of mock catalogs. ",
+    "There are numerous methods for constructing group catalogs, which rely on a wide array of di ering assumptions. It is not our intention here to perform an exhaustive comparison, but rather to illustrate the potential of this measurement as a diagnostic. For our example we assume we have redshifts for each of our quiescent galaxies and find groups using a Friends-of-Friends algorithm in redshift space (e.g. (<>)Huchra & Geller (<>)1982). We follow (<>)Berlind et al. ((<>)2006, see also (<>)Hearin et al. (<>)2013a, who used it to study abundance matching) and set the linking lengths in the line-of-sight and perpendicular directions as b⊥= 0.14 and b= 0.75, both measured in units of the mean inter-galaxy separation and including only quiescent galaxies in the input catalog. We define richness to be the number of (quiescent) galaxies associated with each group. Fig. (<>)11 shows the cumulative number density of groups as a function of richness, for the di erent catalogs. ",
+    "The basic trends in Fig. (<>)11 can be understood by reference to the HON in Fig. (<>)5. The “fix c/s” and M⋆ 5 models have the fewest rich groups, because they have the fewest quiescent galaxies per massive halo (Fig. (<>)5). By contrast ",
+    "the “maxmass” and “fix sat-conf” models, which have many quiescent galaxies in massive halos, have a relatively large number density of rich groups. In general we see that the imperfections involved in constructing the group finder (i.e. the impurity and incompleteness) do not qualitatively change the trends present in the underlying models. This suggests that a suÿciently accurate group catalog would provide a strong discriminant between the models. Because it opens up a large parameter space, we leave an examination of other group finding methods, and methods which can work with photometric redshifts, for future work. "
+  ],
+  "5.3 Two dimensional profile in clusters ": [
+    "One can also consider the observational counterpart of the three dimensional cluster profile (Fig. (<>)6), the two dimensional cluster profile. Here galaxies are counted within a redshift cylinder of the cluster center. However, accurately estimating the observational scatter is more challenging with our mock catalogues, as it relies upon the accuracy of the cluster mass (determining rvir) and cluster centering, both of which include significant assumptions besides those used in the construction of the catalogue. To bound the information one could obtain from this measurement we consider the case where the group center and rvir are known perfectly. In this limit the most notable distinction this measurement provides is between the M⋆ 5 and “fix c/s” models. However as we will see below, this can be obtained with other more direct observations. "
+  ],
+  "5.4 Distribution of projected density: 5 ": [
+    "2012",
+    "Muldrew et al. ",
+    "2012",
+    "The M⋆ 5 model of (<>)Peng et al. ((<>)2010) used a projected density, 5, in determining which galaxies are classified as quiescent. This is a property that can be used to help discriminate amongst models, even when the models make no explicit reference to it. There are many types of density one could define (for a comparison, see, e.g., (<>)Haas, Schaye & Jeeson-Daniel (); ()), we shall consider 5 because it has been studied in this context by (<>)Peng et al. ((<>)2010) and is used as input to one of our models. ",
+    "The distribution of 5 across the whole galaxy sample is approximately lognormal, as expected. However the distributions of 5 for the quiescent galaxies, in raw counts and as a fraction of all galaxies (Fig. (<>)12), discriminate quite strongly among the models. Models split into two groups, mostly determined by the quiescent satellite fraction as a function of stellar mass. Models with a large number of quiescent central galaxies tend to have overall more galaxies at lower 5 (Fig. (<>)12, top). (Central galaxies are a minority population for high densities, only reaching at least half 10.) A slightly dif->10 ), com- ∼most pronounced at the high density tail (5 2 <of the galaxies for projected densities ∼ferent division between the models is seen in the quiescent galaxy fraction (Fig. (<>)12, bottom). Di erences become the posed almost entirely of satellites in rich groups or clusters. The general shape of the quiescent fraction (Fig. (<>)12, bottom) is expected: the rise of the quiescent fraction to high M⋆ implies that higher M⋆ satellites are generally quiescent and such satellites lie predominantly in massive halos. ",
+    "The “fix c/s” model has the lowest quiescent fraction at ",
+    "high 5 – Eq. ((<>)2) requires many low-M⋆, central galaxies to be quiescent. This means the satellite galaxies in the same M⋆ bin must be star-forming, removing the high-5 population in Fig. (<>)12. The “fix c/s-conf” model favors galaxies in high mass halos with a star-forming central to be star-forming, removing quiescent galaxies from these high density halos. This is somewhat counteracted for the “fix c/s-h” models as the longest lived satellites tend to be in the higher mass halos. The M⋆ 5 model has the highest quiescent fraction for highest 5, partly by construction. Next highest are the “fix sat-h”, M˙ h and “maxmass” models. These models turn galaxies quiescent based upon infall time and galaxies that fell in earlier tend to be in higher mass halos and thus denser environments. ",
+    "In is encouraging that two models which were quite close in their HON, M⋆ 5 and “fix c/s”, separate cleanly by looking at the high projected density tail of the quenched fraction. "
+  ],
+  "5.5 Marked Correlation Functions ": [
+    "In addition to looking at the distribution of 5, we can use the projected density as a weight when computing the two point function, creating a “marked” correlation function ((<>)Sheth, Connolly & Skibba (<>)2005; (<>)Harker et al. (<>)2006; (<>)Skibba et al (<>)2013). Such a function is straightforward to compute if ξ(r) can be computed and can be used to break degeneracies in modeling the occupation distribution ((<>)White & Padmanabhan (<>)2009). ",
+    "The marked correlation function, M(r), is defined as ",
+    "(6) ",
+    "where the sum is over all galaxy pairs, iand j, which are separated by rand mi and mj are the marks, n(r) is the number of pairs in the bin and m¯ is the average mark in the sample. M(r) = 1 on scales where the clustering of objects depends upon the mark. One of the advantages of a marked correlation function, from an observational perspective, is that it is simple to modify a code which computes ξ(r) to also compute M(r). No further information is needed (beyond the marks and galaxy positions). In fact, one does not even need a random catalogue due to the cancellation between the numerator and denominator. It is also relatively easy to estimate the errors ((<>)Sheth, Connolly & Skibba (<>)2005). We will focus here on the three dimensional marked correlation function but there is no reason one cannot use the projected or angular version instead. ",
+    "If we take our mark, mi, to be the projected density 5 of the ith galaxy, the resulting M(r) is shown in Fig. (<>)13. For comparison, we also show the marked correlation function for all (not just quiescent) galaxies as the solid black line. As expected, the M⋆ 5 quiescent galaxies cluster di erently, as the mark 5 was used in their selection. There is a feature between 1 and 2 h−1Mpc, roughly at the virial radius of massive halos. Some similarities between the model ordering at small radius and the stacked and rescaled cluster profiles (Fig. (<>)6) is apparent. ",
+    "If the dynamic range in the mark is very large, then there is some concern that M(r) can become sensitive to rare outliers. A simple way around this is to modify the ",
+    "Figure 12. Total number (top) and fraction (bottom) of quiescent galaxies at a given projected density, 5, which are quiescent. Line types as in Fig. (<>)2. ",
+    "mark from 5 to ",
+    "(7) ",
+    "14",
+    "with e ≃5 for 5 ≪max and e ≤max. Fig. (<>)12 suggests that max = 300 is a reasonable choice, and we take that as our fiducial value. The resulting Mf(r) is shown in Fig. . Similar behavior is seen as we vary max from 30 to 300 suggesting the features we see in Fig. (<>)13 are stable and robustly present in the catalogs. As M(r) and Mf(r) combine projected density and galaxy number, an enhancement at small scales could be due to many galaxies with a small mark, or few galaxies with a large mark. To di erentiate, we removed the 3-7 per cent of galaxies with 5 ≥102 from the catalog. This only decreases the radius below which these models dominate (to ∼800 h−1kpc/h), but does not erase the separation. Thus we infer the small-scale enhancement ",
+    "Figure 13. Marked correlation function, M(r), for quiescent galaxies. Line types are as in Fig. (<>)2 and the solid black line is M(r) for all galaxies. The mark is the 5th nearest neighbor projected density, 5, of (<>)Peng et al. ((<>)2010). Error bars indicate the error on the mean M(r) from 8 disjoint octants of the box. The M⋆ 5 models separates out cleanly from the others. ",
+    "is driven by a large number of galaxies, not simply the dense tail of the distribution. ",
+    "In this section we considered several observational measurements and how they separated out the di erent quiescent galaxy catalogues. Now we turn to general results and implications of the intrinsic and observational measurements the the ensemble of catalogues. "
+  ],
+  "6 DISCUSSION ": [
+    "We generated a set of mock galaxies by assigning stellar masses to subhalos in an N-body simulation via abundance matching. These mock galaxies match, by construction, the stellar mass function of (<>)Drory et al. ((<>)2009), as shown in Fig. (<>)1. We then marked a fraction of these galaxies as quiescent, using 10 prescriptions adapted from the literature. All of the prescriptions are tuned give a good fit to the total quiescent fraction as a function of M⋆, as shown in Fig. (<>)2, but di er in their assumptions about which properties are important in determining quiescence and in how they incorporate centrality, environment and history. ",
+    "The number of implied quenching mechanisms di ers as well. Two are used in the “fix sat”, “fix sat-h”,“fix c/s”, “fix c/s-h” models (for satellite and for central galaxies), and for the M⋆ 5 model (stellar mass and projected density), while “fix sat-conf”, “fix c/s-conf” might allow one mechanism across a shared halo. The “maxmass”, M˙ h models have one mechanism, combined with no mass gains for satellites, while the zstarve model has three mechanisms. ",
+    "We investigated the consequences of these di erent ",
+    "Figure 14. Marked correlation function, Mf(r), for quiescent galaxies using Eq. ((<>)7) as the mark with max = 300. Line types are as in Fig. (<>)13 and the solid black line is Mf(r) for all galaxies. ",
+    "quiescence assumptions for intrinsic galaxy properties and observational measurements, at one fixed redshift. Models di ered in intrinsic properties such as halo occupation and galaxy profiles within massive halos, although the cen-tral/satellite split as a function of stellar mass was degenerate for several of them. Observationally, we considered measurements derived from galaxy positions and stellar masses. Promisingly, we found that almost all of the models could be separated from each other by some combination of observations, if measurement errors could be made small enough. While many of the models could be distinguished based on very traditional measurements such as the auto-and cross-correlation functions, we also saw that less often considered statistics such as the group multiplicity function and the (projected) density-marked correlation function allowed us to further break degeneracies between models. We advocate that these statistics be reported in future. ",
+    "We now turn to intrinsic and observational properties and how they relate to each other and to mecha-nisms/models for quenching star formation. We saw that the fraction of lgM⋆/M⊙≃10 quenched galaxies which were central or satellite roughly divided the models into two groups. The strongest division was between di erent choices for the evolution of the quenched satellite fraction with redshift, as expected, but this division also strongly separated the M⋆ 5 model from the ones in which SFR ∝M˙ h or where quiescence was based upon the time at which the subhalo achieved its maximum mass, for example. This division further implied a change in the way quiescent galaxies occupied halos, i.e. the HON (Fig. (<>)5) which showed up clearly in the relative clustering (Fig. (<>)7). This argues that measures of quiescent galaxy clustering can be used to constrain the redshift evolution of the quiescent fraction of satellite and central ",
+    "galaxies and thus the timescale over which star-formation quenching acts (see also (<>)Wetzel et al. (<>)2013a; (<>)Tinker et al. (<>)2013, for similar conclusions). ",
+    "Models which are degenerate in their satellite or central quenched galaxy fractions as a function of stellar mass can still di er significantly in other measures, depending upon environment and history. Those which invoke conformity tend to have the largest number of quiescent satellites in massive halos within their class. Observationally this leads to enhanced auto-correlation, since massive halos have a large bias. These models also have a depressed cross-correlation between active and quiescent galaxies at small separations, as galaxies in a halo tend to all be either active or quiescent. Conformity might point to quenching properties acting on larger scales than those of a halo, as for fixed stellar mass it can give similar quenching likelihoods to satellites at the outskirts and satellites near the center. ",
+    "The models based upon conformity have central galaxy assignments identical to those of their associated models based on satellite infall or random selection. It was therefore encouraging that there were significant, observable differences associated with the variations in satellite quiescence mechanisms. (This is in part why conformity was introduced at lower redshifts in the SDSS ((<>)Ross & Brunner (<>)2009), but here it also separated out the models where satellite infall was related to quiescence.) ",
+    "The associated “-h” models are best further considered along with the other three models using infall time (where satellite infall stops mass gain or generally increases quiescence probability – our “maxmass”, M˙ h and zstarve models). If halo growth is considered a proxy for baryonic accretion (and satellite infall a proxy for strangulation, or cessation of baryonic accretion), these can be thought of as “feeding limited” models. Observationally, these five models most prominently group together in the projected density marked correlation functions M(r) and Mf(r). They are large at short distances, only being surpassed by the M⋆ 5 model (which uses 5 in its construction). This observation thus seems to separate out models which are feeding limited or in which group pre-processing played an important role. ",
+    "The di erences between the three “feeding limited” models which have similar satellite populations (“fix sat-h”, “maxmass”, M˙ h) are interesting as well. All quench satellites after infall (with similar although not identical decay times). The first assigns the central galaxies randomly, while the other two depend upon halo mass gain or time of maximum mass. Di erences between these models might thus indicate which intrinsic properties and observations are impacted by the history of central mass gains. (Although the central and satellite quiescent fractions are not identical, in raw numbers there are more di erences in the quiescent central populations.) They are quite close in the full HON at high mass, but di er very slightly at low stellar mass (also seen in the central galaxy HON). The three models separate out most clearly (but not by much) from each other in the auto-correlation function. The “maxmass” is slightly larger at high richness in the group multiplicity function, and the M˙h model also has a relatively depressed quiescent-active galaxy cross-correlation at short distances. Otherwise, the history of central mass gains seems to not have much of an e ect on the observations we considered. ",
+    "All of the models make an explicit distinction between ",
+    "central and satellite galaxies except for the M⋆ 5 model. Due to the way it is constructed, this model shows a very different distribution of 5 for quiescent galaxies than the other models, which results in a strong enhancement of the projected density-marked correlation function at small scales, and the quiescent fraction as a function of projected density. In the other observations it is close to degenerate with the model sharing its HON and profile, which assigns quiescent galaxies depending only upon centrality (“fix c/s”). ",
+    "Several observations were quite good proxies for the intrinsic di erences we saw between the models. For example, the group multiplicity function we used orders models in almost the same way as the HON at high richness or halo mass (only two models reverse). The two dimensional stacked cluster profile has information similar to the three dimensional stacked cluster profile and the projected density distribution (for 5 ∼10 −100) showed a similar ranking of models to the quiescent satellite fraction at intermediate M⋆. If one can reliably infer which galaxies belong to which dark matter halo from a group catalog, and has a reliable method of determining the central galaxy, then the central and satellite quiescent fractions become directly observable. As we saw, these functions were extremely helpful in partitioning the models. Conversely the di erences in quiescent fraction at high projected density and di erences in the radial profile may impact the calculations of purity and completeness for color-selected cluster finders which are trained on mock catalogs (which make either implicit or explicit assumptions about these properties). ",
+    "We used ten catalogues with quiescence based upon dark matter subhalo histories, environment and centrality. However, these tests could be expected to shed light on many other proposed models, including those based upon fewer simulation properties (e.g. without subhalos, such as (<>)Peacock & Smith (<>)2000; (<>)Seljak (<>)2000; (<>)Cooray & Sheth (<>)2002), more simulation properties (e.g. including histories, for instance, (<>)Wetzel et al. (<>)2013a; (<>)Moster, Naab & White (<>)2013; (<>)Mutch, Croton & Poole (<>)2013; (<>)Cattaneo et al. (<>)2013; (<>)Baugh (<>)2006; (<>)Benson (<>)2012, or baryons, e.g., (<>)Schaye et al. (<>)2010; (<>)Almgren et al (<>)2013; (<>)Vogelsberger et al. (<>)2013), or other simulation properties (e.g., density as in (<>)Scoville et al. (<>)2013). Other tests may also add more information (e.g. lensing was used by (<>)Masaki, Lin & Yoshida ((<>)2013) for similar tests at lower redshifts, we did not consider it here as galaxy shapes are required as well). Some tests to constrain quiescence were recently reported by (<>)Tinker et al. ((<>)2013) at similar redshifts (clustering, weak lensing, group catalogue) as this work was being prepared for publication. "
+  ],
+  "7 CONCLUSIONS ": [
+    "One of the most striking features of the galaxy population is that it exhibits bimodality in color, morphology and star-formation rate. In particular, the existence of two broad types of galaxies (those which are actively star-forming and those which are quiescent) cries out for a theoretical explanation. Unfortunately the range of physics and of physical scales involved in setting the star-formation rate in a galaxy is enormous, making empirical models of the phenomenon of great importance. Many such models have been proposed to explain the color or star-formation rate bimodality at ",
+    "z≃0. Motivated by the wealth of data on the higher zUniverse which we expect to have soon from large surveys, and using high-resolution cosmological N-body simulations, we have investigated the predictions for a range of models for star-formation quenching to see in what way they di er and what observations (of what accuracy) can be used to discriminate amongst them. The advantage of using large surveys is that statistical errors can be controlled and are more accessible and one can disentangle the many correlations between galaxy properties which limit inferences from small samples. The disadvantage is that information is more circumstantial and so requires a di erent sort of detective work. ",
+    "We have focused our attention at z≃0.5, which is at high enough zthat we expect significant galaxy evolution but low enough zthat we expect to have large statistical samples of galaxies in the near future. Note that z≃0.5 is approximately 5 Gyr ago, which is longer than the main-sequence lifetime of >1.4 M⊙stars. Any galaxy less massive than 2×1010 M⊙on the star forming main sequence would at least double its stellar mass in this period. It is also around z≃0.5 that we see a rapid rise in the number density of intermediate-mass, quiescent galaxies, making this a particularly interesting time to study. ",
+    "We considered several di erent galaxy properties which are expected to correlate with star-formation quenching and investigated how statistical measurements might be used to distinguish them. We created di erent mock catalogues, all sharing the same stellar mass for each galaxy and close to the same overall quenched fraction as a function of stellar mass, but with di erent criteria for classifying a galaxy as quiescent. Many of these models had degeneracies in basic intrinsic properties (satellite/central fraction, for instance), or halo occupation (HON), but the suite of observations we used could nonetheless separate them out, given small enough measurement errors. Fixing the quenched central galaxies and varying the satellite quenching gave models which were distinguishable, similarly, models where the majority of di erences were in the central galaxies also could be di erentiated. ",
+    "More specifically, in addition to the quiescent galaxy auto and cross-correlation functions and quiescent fraction as a function of stellar mass, we found that projected density counts, the projected density marked correlation function, and the group multiplicity function could further serve to separate models, and also seemed to correlate with centrality in host halo, feeding limited quenching and halo occupation respectively. These observational measurements increase the galaxy formation information available from surveys possessing galaxy stellar masses and positions. ",
+    "We have mostly considered how these observational measurements can be used to distinguish models from each other, using observations. Alternatively this provides a particularly discriminating set of tests for validating mock cata-logues, constructed by any means. They can also be used to decode associations of other galaxy properties with galaxy histories, environments and centrality, for instance AGN activity or morphology. ",
+    "While we were completing this work we became aware of (<>)Tinker et al. ((<>)2013) which compared several di erent measurements of a survey at similar redshifts to constrain quiescent fraction evolution and of (<>)Hearin et al. ((<>)2013b) which ",
+    "considered measurements at low redshift to constrain color and developed a formalism for comparing dark matter simulation properties which are correlated with color. ",
+    "We thank E. Bell, F. van den Bosch, K. Bundy, N. Dalal, C. Knobel, M. George, A. Hearin, C. Heymans, C. Lackner, Z. Lu, P. Behroozi, D. Watson, A. Wetzel for conversations, and D. Watson, A. Hearin, R. Skibba, A. Wetzel and the referee for helpful suggestions on the draft. JDC also thanks the Royal Observatory, Edinburgh, and Kavli IPMU for their hospitality and invitations to speak on this work as it was being completed. JDC was supported in part by DOE. MW was supported in part by NASA. "
+  ]
+}

jsons_folder/2014MNRAS.441..243I.json

@@ -0,0 +1,116 @@
+{
+  "ABSTRACT ": [
+    "We examine a possible formation scenario of galactic thick discs with numerical simulations. Thick discs have previously been argued to form in clumpy disc phase in the high-redshift Universe, which host giant clumps of <109 M⊙ in their highly gas˘ rich discs. We performed N-body/smoothed particle hydrodynamics simulations using isolated galaxy models for the purpose of verifying whether dynamical and chemical properties of the thick discs formed in such clumpy galaxies are compatible with observations. The results of our simulations seem nearly consistent with observations in dynamical properties such as radial and vertical density profiles, significant rotation velocity lag with height and distributions of orbital eccentricities. In addition, the thick discs in our simulations indicate nearly exponential dependence of σ and σz with radius, nearly isothermal kinematics in vertical direction and negligible metallic-ity gradients in radial and vertical directions. However, our simulations cannot reproduce altitudinal dependence of eccentricities, metallicity relations with eccentricities or rotation velocities, which shows striking discrepancy from recent observations of the Galactic thick disc. From this result, we infer that the clumpy disc scenario for thick-disc formation would not be suitable at least for the Milky Way. Our study, however, cannot reject this scenario for external galaxies if not all galaxies form their thick discs by the same process. In addition, we found that a significant fraction of thick-disc stars forms in giant clumps. ",
+    "Key words: methods: numerical – galaxies: formation – Galaxy: disc – Galaxy: formation. "
+  ],
+  "1 INTRODUCTION ": [
+    "Duplex structures of thin and thick discs seem to be ubiquitous among disc galaxies (e.g. (<>)Burstein (<>)1979; (<>)Dalcanton & Bernstein (<>)2002; (<>)Yoachim & Dalcanton (<>)2006), including the Milky Way (MW) (e.g. (<>)Yoshii (<>)1982; (<>)Gilmore & Reid (<>)1983). Because thick-disc stars are generally old and α-enhanced population which implies their early and rapid formation (e.g. (<>)Allende Prieto et al. (<>)2006; (<>)Haywood et al. (<>)2013), structures of the thick discs are expected to reflect galactic formation history. The origin of the thick discs is, however, still an open question, and a number of possible formation scenarios have been proposed so far. Ones frequently discussed in recent studies are as follows: stellar accretion from disrupted satellites (e.g. (<>)Abadi et al. (<>)2003), thickening of a thin disc by minor mergers (e.g. (<>)Quinn et al. (<>)1993; (<>)Kazantzidis et al. (<>)2008), multiple gas-rich minor mergers ((<>)Brook et al. (<>)2004, (<>)2005, (<>)2012), and radial migration by spiral arms and barred structures in a disc (e.g. ",
+    "(<>)Sch¨onrich & Binney (<>)2009a,(<>)b). (<>)Sales et al. ((<>)2009) have discussed that distribution of orbital eccentricities of thick-disc stars reflects their formation processes and can be used as a probe of these scenarios. Afterwards, some observations were performed for the thick disc of the MW and elucidated that the thick-disc stars have a mono-modal distribution with the peak at the eccentricity of ≃0.2 ((<>)Dierickx et al. (<>)2010; (<>)Lee et al. (<>)2011; (<>)Casetti-Dinescu et al. (<>)2011; (<>)Ruchti et al. (<>)2011; (<>)Kordopatis et al. (<>)2011, (<>)2013). They argued that the multiple gas-rich minor mergers would be a favourable scenario for the Galactic thick-disc formation, and the radial migration scenario could also reproduce the eccentricity distribution in acceptable matching. On the other hand, the stellar accretion scenario results in relatively higher eccentricities than the observations, and the thin-disc thickening by dwarf galaxies seems to bring about a bi-modal distribution. In addition, observations of (<>)Lee et al. ((<>)2011) found that correlations between metallicities and some kinematic properties are obviously di erent between the Galactic thin and thick discs. ",
+    "In the high-redshift Universe, some galaxies have been ",
+    "observed to be clumpy 1 (<>), and they have giant clumps the masses of which are <∼109 M⊙in their highly gas-rich discs (e.g. (<>)van den Bergh et al. (<>)1996; (<>)Elmegreen et al. (<>)2004; (<>)F¨orster Schreiber et al. (<>)2006; (<>)Genzel et al. (<>)2006; (<>)Guo et al. (<>)2012; (<>)Buitrago et al. (<>)2013; (<>)Tadaki et al. (<>)2014). Numerical simulations demonstrated the evolution from clump clusters to disk galaxies (e.g. (<>)Noguchi (<>)1998, (<>)1999; (<>)Immeli et al. (<>)2004; (<>)Bournaud et al. (<>)2007; (<>)Agertz et al. (<>)2009; (<>)Dekel et al. (<>)2009; (<>)Ceverino et al. (<>)2010; (<>)Mandelker et al. (<>)2013). In the evolutionary process, giant clumps fall into the galactic centre by dynamical friction and can eventually form a galactic bulge ((<>)Noguchi (<>)1998, (<>)1999; (<>)Elmegreen et al. (<>)2008a; (<>)Inoue & Saitoh (<>)2012; (<>)Dekel & Krumholz (<>)2013; (<>)Bournaud et al. (<>)2014; (<>)Perez et al. (<>)2013). In addition, the clumps are so massive that they can change dark matter (DM) density profiles ((<>)Elmegreen et al. (<>)2008b; (<>)Inoue & Saitoh (<>)2011; see also (<>)Del Popolo & Hiotelis (<>)2014) and induce significant net rotation of halo stars and globular clusters around galactic discs ((<>)Inoue (<>)2013). ",
+    "(<>)Noguchi ((<>)1996) has pointed out the possibility of thick-disc formation in such a clumpy phase of galaxy evolution: Orbital motions of giant clumps kinematically can heat up a galactic disc, and disrupted clumps supply stars to the thick disc to some extent. Afterwards, (<>)Bournaud et al. ((<>)2009) demonstrated it by numerical simulations. Their numerical simulations showed that the clumpy disc scenario can reproduce observed thick discs with exponential density profiles (see also (<>)Bournaud et al. (<>)2007; (<>)Elmegreen & Struck (<>)2013) and scale heights independent from radius. Thick discs of external galaxies were indeed observed to have a constant thickness ((<>)van der Kruit & Searle (<>)1981; (<>)Jensen & Thuan (<>)1982; (<>)Shaw & Gilmore (<>)1990; (<>)Matthews (<>)2000; (<>)Dalcanton & Bernstein (<>)2002). They suggested that the reproducibility of the constant thickness is a characteristic point of this formation scenario; the thin-disc thickening by minor mergers lead to flaring of thick discs in outer disc regions (e.g. (<>)Kazantzidis et al. (<>)2008). Observations also seemed to show that the disc-like structures in the clumpy galaxies are consistent with thick discs in nearby galaxies in their thickness and age ((<>)Elmegreen & Elmegreen (<>)2005, (<>)2006), and spatial distributions of clumps are nearly exponential although surface brightness profiles of the discs are clearly not ((<>)Elmegreen et al. (<>)2005). Thus, it could be said that the thick-disc formation in clumpy galaxies is also a possible scenario and should be examined in detail. However, the properties of the thick discs formed in this scenario have not been compared with observations in the way of (<>)Sales et al. ((<>)2009). ",
+    "In this study, we performed several runs of high-resolution N-body/smoothed particle hydrodynamics (SPH) simulation using isolated models and study dynamical and chemical properties of thick discs formed in the clumpy disc scenario. Our aim in this paper is to scrutinize the credibility of this thick-disc formation scenario and discuss whether we can verify or discard the scenario. We describe our simulation settings in §(<>)2 and analyses of the thick-disc properties in §(<>)3. We present discussion and conclusions in §(<>)4 and §(<>)5. "
+  ],
+  "2 SIMULATION ": [
+    "The detailed description of our computing schemes has been presented in (<>)Inoue & Saitoh ((<>)2011, (<>)2012), therefore we describe it briefly here. We employed an N-body/SPH code, ASURA ((<>)Saitoh et al. (<>)2008, (<>)2009) using the standard scheme of (<>)Monaghan ((<>)1992) and (<>)Springel ((<>)2010).2 (<>)The code adopts the time-step limiter of (<>)Saitoh & Makino ((<>)2009) so that we can handle strong shocks with an individual time-step method ((<>)McMillan (<>)1986; (<>)Makino (<>)1991). It also employs the FAST method ((<>)Saitoh & Makino (<>)2010) which accelerates the simulations by using di erent time-steps for the gravitational and hydrodynamical parts. Gravity is solved by a parallel tree with GRAPE (GRAvity PipE) method ((<>)Makino (<>)2004; (<>)Tanikawa et al. (<>)2013). ",
+    "A metallicity-dependent cooling function of gas assumes optically thin radiative cooling and covers a temperature range of 10 −108 K ((<>)Wada et al. (<>)2009). Feedback from a uniform far-ultraviolet radiation was taken into account. A gas particle spawns a stellar particle the mass of which is one-third of the initial gas particle under the criteria: 1) ρgas >100 atm cm−3 , 2) temperature T<100 K, 3) ∇·v<0 and 4) there are no SNe around the particle. The local star formation rate follows the Schmidt law ((<>)Schmidt (<>)1959). We assumed the Salpeter initial mass function ((<>)Salpeter (<>)1955) ranging from 0.1 M⊙to 100 M⊙on a stellar particle and that stars heavier than 8 M⊙cause type-II SNe, return their masses to ambient gas and inject thermal energy into it at the rate of 1051 erg per SN. The initially primordial gas is contaminated with heavy elements released from the SNe. Our simulation code tracks only the total metal abundance, Z, and does not follow the evolution of each element. We did not take type-Ia (or other) SNe or stellar wind from intermediate mass stars into account in our simulation. ",
+    "Our initial condition followed the spherical models of (<>)Kaufmann et al. ((<>)2006, (<>)2007) and (<>)Teyssier et al. ((<>)2013) that have been used to study the formation of disc galaxies in isolated environments. We assumed equilibrium systems with the Navarro-Frenk-White profile ((<>)Navarro et al. (<>)1997, hereafter NFW) with a virial mass of Mvir = 5.0 ×1011 M⊙, a virial radius of rvir = 1.67 ×10 2 kpc and a concentration parameter of c= 6.0. Baryon mass fractions of the systems are set to 0.06. The baryonic components are initially primordial (zero-metal) gas with virial temperature and follows the same density profile as the DM. We executed four runs of simulations with di erent initial conditions for the gas spheres: two spin parameters of λ= 0.04 and 0.1, two types of angular momentum distributions (see below). The choice of λ= 0.04 is motivated by the averaged spin parameter of DM haloes in pure N-body cosmological simulations (e.g. (<>)Bullock et al. (<>)2001; (<>)Ishiyama et al. (<>)2013). However, observational measurements of spin parameters of high-redshift galaxies are still challenging and debated; for instance, (<>)Dutton et al. ((<>)2011) advocated consistency with the results of the pure DM simulations, whereas (<>)Bouch´e et al. ((<>)2007) proposed λ≃0.1 on average for star-",
+    "Table 1. Summery of initial conditions of our simulations. From left to right, the columns are simulation names, spin parameters and radial distributions of specific angular momentum. The other parameters are the same in all runs. ",
+    "forming galaxies in the high-redshift Universe (see also (<>)Kimm et al. (<>)2011). Hence, we adopt this value as another choice of the initial spin parameters. As for the angular momentum distributions, the pure N-body simulations indicated specific angular momenta of haloes follow the profile of j∝rin all radial ranges ((<>)Bullock et al. (<>)2001). On the other hand, (<>)Kimm et al. ((<>)2011) performed cosmological simulations including baryonic physics and showed that specific angular momentum distributions of gas fallow those of DM inside 0.1rvir and are constant outside 0.1rvir; moreover, they found that this distribution is almost independent of redshift. Therefore, we take these two cases as initial conditions of angular momentum distributions. Table (<>)1 sum-marises our initial settings of the gas spheres.3 (<>)Although some of them might be unrealistic, we show that properties of the resultant galaxies are qualitatively consistent in all runs (see §3). The DM and the gas are represented by 107 and 5.0 ×106 particles, i.e. the masses of the DM and gas particles are 4.7 ×104 M⊙and 6.0 ×103 M⊙. Softening lengths are 10 pc for all particles.4 (<>)"
+  ],
+  "3 RESULTS ": [
+    "Fig. (<>)1 displays snapshots of stellar and gas distributions and star-forming regions in the run of B01-λ004, where the clumpy phase of the disc can be seen in t<∼2 Gyr. Fig. (<>)2 shows stellar density maps of the other runs. In K11λ004 and K11-λ010, the formation of clumps may be involved with ‘ring’ instability caused by the initial setting of the angular momentum distributions ((<>)Gingold & Monaghan (<>)1983; (<>)Cha & Whitworth (<>)2003). We run our simulations until t= 6 Gyr except the run of K11-λ010. Because this run took ∼8 Gyr to settle into a stable state, we continued the run until t= 10 Gyr; in this sense, K11-λ010 may not be a realistic initial condition since the clumpy phase is too long in comparison to other numerical simulations ((<>)Bournaud et al. (<>)2007, (<>)2014; (<>)Bournaud & Elmegreen (<>)2009; (<>)Dekel et al. (<>)2009; (<>)Ceverino et al. (<>)2010, (<>)2012; (<>)Dekel & Krumholz (<>)2013; (<>)Perez et al. (<>)2013). In the following subsections, we analyse the final state of the galaxies in our simulations. ",
+    "Figure 3. Stellar surface density profiles seen face-on in the final state of our simulations (red lines). Minimum ˜2 fittings are also plotted: S´ersic profiles for bulges (blue short-dashed lines), the exponential profiles for discs (pink dotted lines) and disc+bulge (green long-dashed lines). The insert diagrams illustrate the same profiles with the logarithmic abscissa. The centres of the systems are defined to be the positions at which the stellar densities become the highest. "
+  ],
+  "3.1 Density profiles ": [],
+  "3.1.1 Radial profiles ": [
+    "To begin with, we decompose a stellar surface density profile of the simulated galaxy into an exponential disc and a S´ersic bulge, ",
+    "(1) ",
+    "where d,b and Rd,b are central surface densities and scale radii of the disc and bulge, and nb is a S´ersic index of the bulge. The profiles are shown in Fig. (<>)3, and the best-fit parameters and the integrated disc and bulge masses are tabulated in Table (<>)2. The discs of B01-λ010 and K11-λ010 have large scale lengths of >∼7 kpc; in this sense, B01-λ010 and K11-λ010, i.e. the large spin parameter of λ= 0.1, may be unsuitable for reproducing MW-like galaxies. Although the disc scale lengths of B01-λ004 and K11-λ004 may still be a little larger than that of the MW in recent observations (e.g. (<>)Juri´c et al. (<>)2008; (<>)Bovy et al. (<>)2012c; (<>)Bovy & Rix (<>)2013) or within a range of uncertainty (e.g. (<>)Cheng et al. (<>)2012a), these are compatible with typical values of disc galaxies (e.g. (<>)Kent (<>)1985; (<>)Binney & Merrifield (<>)1998; (<>)Fathi et al. (<>)2010; (<>)Fathi (<>)2010). ",
+    "In all runs, both the discs and the bulges can be fitted well with exponential profiles: the S´ersic indices of the bulges are ≃1. Such small S´ersic indices mean that the bulges should be classified into pseudo-bulges (e.g. (<>)Kormendy & Kennicutt (<>)2004; (<>)Drory & Fisher (<>)2007; (<>)Fisher & Drory (<>)2008). However, other studies using numerical simulations with isolated models have supported the formation of classical bulges with high S´ersic indices as remnants of the clump coalescence ((<>)Elmegreen et al. (<>)2008a; (<>)Perez et al. (<>)2013). In addition, cosmological simulations also seem to indicate nb = 3–5 (D. Ceverino et al. in prep.). The diversity of the S´ersic indices between these studies and ours may be related to gas fraction of the clumps. If the progen-",
+    "Figure 1. Stellar and gas density maps in the central 40 ×40 kpc region in the run of B01-004. The first and second rows indicate the surface density of all stars from the edge-on and face-on views, respectively. The third row plots the density of stars younger than 40 Myr as star forming region. The fourth row shows the volume density of gas on the disc plane. Time in units of Gyr is indicated on right bottom corner of each panel. ",
+    "Table 2. The best-fit parameters for the radial profiles. Surface density profiles of discs and bulges are fitted with equation ((<>)1), and Md and Mb are disc and bulge masses computed by integrating the fitting profiles. fgas is a mass fraction of gas particles to the total baryon in the region of R < 5Rd and |z|< 5hT in the final state (see equation ((<>)2) and Table (<>)3 for hT). ",
+    "Stellar density [Me pc-2] ",
+    "101 ",
+    ",02 ",
+    "Figure 2. Stellar density maps seen edge-on and face-on in the runs of B01-.X0lO, Kll-.X004 and Kll-.X0lO from top to bottom. The depicted regions are the central 40 x 40 kpc region for Kll-.X004 (the third and forth rows) and 60 x 60 kpc regions for B01-.X0lO (the first and second rows) and Kll-.X0lO (the fifth and sixth rows). Time in units of Cyr is indicated on right bottom corner of each panel. ",
+    "Figure 4. Vertical density profiles of stars in projected edge-on view at the final state of the simulations. The profiles are normalized by the surface density at z = 0 and shifted right at intervals of 1 kpc for visibility. ",
+    "itor clumps and the remnant bulges are gas-rich, the dissipative gas can contract to the centre and may form highly concentrated density profiles, which leads to a high S´ersic index. On the other hand, an opposite expectation may also be possible. High S´ersic indices can be considered as results of violent relaxation of dissipationless mergers like elliptical galaxies. In this case, coalescence of gas-poor clumps may lead to a high S´ersic index, rather than gas-rich clumps. Thus, the dynamical properties of ‘clump-origin bulges’ are to be investigated further in future studies. 5 (<>)"
+  ],
+  "3.1.2 Vertical profiles ": [
+    "Fig. (<>)4 shows vertical density profiles of the projected stellar discs at di erent galactocentric radii. The profiles can be fitted with superposition of two exponential profiles with breaks at z≃1 kpc: thin and thick discs. In agreement with the results of (<>)Bournaud et al. ((<>)2009), vertical scale heights of the thick discs are almost independent from radius in all of our simulations; we found that the variation of the scale heights were smaller that 20 per cent in the range of 1 6 R/Rd 6 3. In addition, scale radii and central densities of the thin and thick discs can be measured by the fitting of the vertical profiles with double-exponential models, ",
+    "(2) ",
+    "where the subscript itakes thin and thick discs, and Riand hiare scale radii and scale heights of the discs. The fitting is performed in the range of 1 6 R/Rd 6 3 to avoid the bulge contribution. We found that the scale radii are hardly di erent between the thin and thick discs. The best-fit parameters and masses of the thin and thick discs are tabulated in Table (<>)3. ",
+    "In all runs, however, the thick discs are more massive than the thin discs; we found mass ratios of the thick to ",
+    "Figure 5. Radial profiles of circular and mean rotation velocities of stars. The circular velocity is computed as vc= p GM(< R)/R, where G is the gravitational constant and M(< R) is the mass of the system spherically enclosed in radius of R. The mean rotation velocity vθis measured at each height above the plane. ",
+    "the thin discs to be greater than 2 in all runs. Thick discs have been observed to account for 5–40 per cent of the total stellar masses in real galaxies ((<>)Yoachim & Dalcanton (<>)2006). Although (<>)Fuhrmann ((<>)2008) and (<>)Comer´on et al. ((<>)2011) suggested that typically thick and thin discs have similar masses, the thin discs in our simulations would be still too less massive. This is because our initial conditions assumed single collapse models, do not include late accretion to feed gas to the thin discs after the clumpy disc formation ((<>)Bournaud et al. (<>)2009). We warn the reader that this point is a limitation of our simulations. It should be noted that the thick-disc scale heights would be somewhat shortened by the thin-disc formation that is lacked in our simulations ((<>)Bournaud et al. (<>)2009). Moreover, the scale radii of the thin discs may become shorter or longer than those of their thick discs after the completion of the thin-disc formation. "
+  ],
+  "3.2 Kinematics ": [],
+  "3.2.1 Rotation velocities ": [
+    "Fig. (<>)5 shows radial profiles of circular and mean rotation velocities of stars. The galaxies have nearly flat rotation curves in the runs of B01-λ004 and K11-λ004 in their disc regions, whereas the circular velocities gently increase in B01-λ010 and K11-λ010 (see also Fig. (<>)8). It should be noted, however, that the massive bulges cause the mass concentrations of the galaxies to be high as seen in Fig. (<>)3, and contribution of the bulges to the circular velocity curves would be substantially present in all simulated runs. ",
+    "The mean rotation velocities in the figure show significant asymmetric drift in the cases of B01-λ004 and K11λ004: velocity lags of dvθ/dz∼−10 km s−1 kpc−1 . In B01λ010 and K11-λ010, however, the velocity lags are weak. In the MW, rotation velocity has been observed to decrease significantly with distance from the plane although determinations do not seem be consistent quantitatively: from −36 to −9 km s−1 kpc−1 ((<>)Chiba & Beers (<>)2000; (<>)Carollo et al. (<>)2010; (<>)Spagna et al. (<>)2010; (<>)Lee et al. (<>)2011; (<>)Casetti-Dinescu et al. ",
+    "Table 3. The best-fit parameters for vertical density profiles with equation ((<>)2). Subscriptions of ‘T’ and ‘t’ mean values for thick and thin discs. ",
+    "Figure 6. Dispersions of radial, rotation and vertical velocities as functions of distance from the plane at the galactocentric radius of R = 2Rd. ",
+    "(<>)2011; (<>)Moni Bidin et al. (<>)2012); in this sense, B01-λ004 and K11-λ004 seem to be more similar to the MW. Meanwhile, in external galaxies, (<>)Yoachim & Dalcanton ((<>)2008) have observed that massive galaxies in their sample indicate little di erences of rotation velocities between thin and thick discs. "
+  ],
+  "3.2.2 Velocity dispersions ": [
+    "Fig. (<>)6 shows vertical profiles of velocity dispersions. As seen from the figure, the velocity dispersions are almost constant, and the discs can be considered to be isothermal along the vertical direction. Hereafter, we follow the analytical discussion of (<>)Lewis & Freeman ((<>)1989). If the surface mass density is dominated by the stellar disc and the vertical density profile can be assumed to be a single exponential function, from the Jeans equation with the isothermality, ",
+    "(3) ",
+    "Furthermore, if we assume uniform velocity anisotropy throughout the discs: σθ/σz≃const, σθ2(R) ∝exp (−R/Rd). Finally, if σR2 is exponential with a scale length of RR, ",
+    "where the second equality is derived from the epicyclic approximation (e.g. (<>)Binney & Tremaine (<>)2008). In the case of ",
+    "Figure 7. Radial, rotation and vertical velocity dispersions as functions of galactocentric distance. Stars in 1 kpc < |z|< 4 kpc are taken into account for the measurements. For the sake of comparison, normalized profiles of the square roots of stellar surface densities are also plotted with the black thin dotted lines. ",
+    "a flat rotation curve, since the right-hand side (RHS) is constant, the two scale lengths must be RR= Rd; moreover, σθ2/σR2 = 1/2. To summarise, if all of these assumptions hold, it can be expected that ",
+    "(5) ",
+    "To compare our simulations with the above analyses, Fig. (<>)7 shows radial profiles of velocity dispersions of thick-disc stars in our simulations. We confirmed that the profiles hardly depend on height above the plane because of the isothermality shown √in Fig. (<>)6. As discussed above, the profiles of σθ, σzand s seem to indicate exponential be-haviour with nearly similar scale lengths although σθhave shallower slopes in 1 <R/Rd <2 in B01-λ010 and K11λ010. The decrease of σRwith radius, however, are much slower than the other profiles and not exponential. This means that the assumption of uniform velocity anisotropy between σRand the other dispersions is not valid in the simulated discs. Fig. (<>)8 shows the left-and RHS of equation ((<>)4). The ratios of σθ2/σR2 are not constant and decrease with radius in outer regions although the RHS is ≃1/2, indicating that the circular velocity curves can be considered to be almost flat. It is particularly worth noting that σθ2/σR2 largely decrease and deviate from the RHS in R>∼2.5Rd except the region of |z|<1 kpc in K11-λ010. This implies that the epicyclic approximation would not be valid in the ",
+    "Figure 8. The left-and right-hand sides of equation ((<>)4) as func-for stars in the regions of |z|< 1 kpc and 1 kpc < |z|< 4 kpc, respectively. tions of radius. The thin and thick lines indicate 2/˙ RThe horizontal dotted-lines indicate 1/2. ",
+    "outer disc regions in our simulations. Another notable point in Fig. (<>)7 is that the behaviour of the velocity dispersions are almost the same among the simulation runs. "
+  ],
+  "3.2.3 Distributions of orbital eccentricities ": [
+    "As we mentioned in §(<>)1, (<>)Sales et al. ((<>)2009) have found that distribution of orbital eccentricities of thick-disc stars reflects their formation process. Therefore, it is worthwhile to inquire into eccentricity distributions in our simulations. Following the manner of (<>)Sales et al. ((<>)2009), we fitted the circular velocity curves of Fig. (<>)5 with combined models of an NFW halo, a Hernquist bulge ((<>)Hernquist (<>)1990) and a Miyamoto-Nagai disc ((<>)Miyamoto & Nagai (<>)1975). Orbit calculations are executed in the modeled potentials, and peri-and apo-centre distances rpe,ap are computed, in which the final states of our simulations are used as the initial positions and velocities of the orbit calculations. The orbital eccentricity is defined as ǫ≡(rap −rpe) /(rap + rpe). ",
+    "The top panel of Fig. (<>)9 shows the eccentricity distributions in thick-disc regions of 1 kpc <|z|<4 kpc. These distributions are almost consistent with the observations of the Galactic thick disc. The distributions do not indicate significant dependence on the initial conditions although the peak values are high in B01-λ010 and K11-λ010 and the position of the peak tends to be a little high eccentricity in K11-λ004. The bottom panel of Fig. (<>)9 shows dependence of the distributions on distance from the planes. Although the lowest regions of |z|<1 kpc may have slightly low eccentricities (see below), the thick-disc stars in our simulations do not indicate altitudinal gradients of orbital eccentricities. It is noteworthy that this would be discrepant from observations: (<>)Dierickx et al. ((<>)2010) observed that mean eccentricities decrease with height in the Galactic thick disc, and their observed distributions become broader in higher regions. We discuss the dependence of this result on the galaxy models in Appendix (<>)A and find that the eccentricity distributions are qualitatively independent from the details of the galaxy models. ",
+    "From integration of the fitting profiles of vertical density ",
+    "Figure 9. Top: Eccentricity distributions of stars in the region of 2 < R/Rd < 3 and 1 kpc < |z|< 4 kpc in the final states. Observational results by (<>)Lee et al. ((<>)2011, in 0.8 kpc < |z|< 2.4 kpc) and (<>)Casetti-Dinescu et al. ((<>)2011, in 1 kpc < |z|< 3 kpc) are overplotted for comparison. Bottom: Eccentricity distributions at di erent heights in our simulations. ",
+    "distributions, thin disc stars occupy stellar mass fractions of 0.17, 0.52, 0.19 and 0.36 in B01-λ004, B01-λ010, K11-λ004 and K11-λ010 in the lowest regions of |z|<1 kpc. The slightly lower eccentricities in this regions may be due to the contamination of the thin-disc stars if thin-disc stars have more regular kinematics than thick-disc stars. "
+  ],
+  "3.3 Metallicity relations ": [
+    "Metallicity distribution can also be a key to investigate the formation history of the thick-disc stars. Fig. (<>)10 shows radial and vertical distributions of averaged metallicity in our simulations. 6 (<>)In all runs, stars in the thick-disc regions have metallicities similar to the solar value and are more metal-rich than the observed thick-disc stars (e.g. (<>)van der Kruit & Freeman (<>)2011, and reference therein). This can be attributed to metal-enrichment caused inside the giant clumps since a significant fraction of thick-disc stars are born in massive clumps in our simulations (see §(<>)3.4). Thus, ",
+    "Figure 10. Radial and vertical distributions of mean metallicities of stars. The radial (the right panel) and vertical profiles (the left panel) are measured in 1 kpc < |z|< 4 kpc and 2 < R/Rd < 3, respectively. We set the solar metallicity to Z⊙= 0.02. ",
+    "the existence of giant clumps during the disc-formation epoch can lead to significantly high metallicity of thick-disc stars; however, it should be noted that the metal-enrichment would depend on the intensity of feedback in the simulations since gas outflow from the clumps could refresh the gas inside them (see §(<>)4.1). Besides, the metallicity gradients in our simulations are weak in both radial and vertical directions. This would be because perturbations of massive clumps vehemently stir the disc stars and wash out their metallicity gradients which could have appeared in quiet disc formation. Although the runs of B01-λ010 and K11λ010 show metallicity gradients in R<∼2Rd, the radial variations in metallicities are as small as ∼0.3 dex. Thus, we expect that the clumpy disc formation would lead to the chemical uniformity of a thick disc if our single collapse models well represent the formation of clumpy galaxies in the high-redshift Universe. The MW thick disc has been observed to have only weak radial and vertical gradients: e.g. ∂Z/∂R≃−0.003 ±0.005 dex kpc−1 ((<>)Hayden et al. (<>)2013), and ∂Z/∂z≃−0.1±0.05 dex kpc−1 ((<>)Kordopatis et al. (<>)2011, (<>)2013) and −0.26±0.02 dex kpc−1 ((<>)Hayden et al. (<>)2013). Radial and vertical gradients of [Fe/H] are observed to be between 0.0028 and 0.041 dex kpc−1 ((<>)Nordstr¨om et al. (<>)2004; (<>)Ruchti et al. (<>)2011; (<>)Co¸skunoˇgLu et al. (<>)2012; (<>)Cheng et al. (<>)2012b; (<>)Carrell et al. (<>)2012) and between −0.14 and −0.068 dex kpc−1 ((<>)Chen et al. (<>)2011; (<>)Kordopatis et al. (<>)2011; (<>)Katz et al. (<>)2011; (<>)Ruchti et al. (<>)2011; (<>)Carrell et al. (<>)2012), respectively. ",
+    "(<>)Lee et al. ((<>)2011) and (<>)Kordopatis et al. ((<>)2011, (<>)2013) have recently revealed that orbital eccentricity and rotation velocity seem to correlate with metallicity: ǫdecreases and vθincreases with metallicity for Galactic thick-disc stars. They found that these chemo-dynamical relations of the thick disc are distinct from those of the thin disc and can be used as proof of thick-disc formation scenarios. Fig. (<>)11 shows these chemo-dynamical relations of thick-disc stars in our simulations. As clearly seen from the figure, neither ǫnor vθindicate correlation with metallicities. In connection to the above discussion, this result can be taken as a natural consequence of the weak gradients of metallicity and eccentricity shown in Fig. (<>)10 and the bottom panel of Fig. (<>)9. Accordingly, we can see that the clumpy disc scenario for thick-disc formation could not reproduce the correlations of ǫand vθwith metallicity observed in the Galactic thick disc ",
+    "Figure 11. Orbital eccentricities and rotation velocities as functions of metallicities of stars in the region of 2 < R/Rd < 3 and 1 kpc < |z|< 4 kpc. ",
+    "since the violent mixing by massive clumps can erase the metallicity relations. "
+  ],
+  "3.4 Where do thick-disc stars form? ": [
+    "It would be of great worth to discuss how and where the thick-disc stars formed in our simulations. In Fig. (<>)1, intense star formation can be seen in the clumps, and the inter-clump regions scarcely form stars. Notwithstanding, the galactic disc accounts for the greater fraction of the stellar mass in the final state. This implies that the giant clumps supply significant amount of stars to the disc. Giant clumps are totally or partly disrupted by tidal force while migrating toward the galactic centre. Besides, in merging with one another, the clumps scatter the inter-clump regions with stars. (<>)Elmegreen et al. ((<>)2009) have inferred that some fraction of the clump mass disperses into the inter-clump medium from their observations, and (<>)Bournaud et al. ((<>)2007, hereafter BEE07) estimated that ∼20 per cent of disc mass is supplied from massive clumps in their simulations. ",
+    "Taking advantage of the high mass-resolutions of our simulations, here we compute the mass fractions of stars released from clumps to discs. First, we identify stellar clumps in snapshots every 4 Myr using the friends-of-friends (FOF) method, in which the linking lengths are set to (ms/ρt)1/3 , where ms is the mean mass of stellar particles and ρt is the stellar density at the radius where surface densities of a bulge and a disc become equal in the fittings of Fig. (<>)3. We found that the results do not depend very much on the linking length within a factor of approximately two. The minimum group (clump) mass mmin have to be given in the FOF algorithm, and we treat it as a parameter of the analyses. Here, we define FOF-grouped stars in the final snapshot to be bulge stars and the others to be disc stars. Next, we search for new stars born in the FOF clumps in each snapshot. If the new stars in the clumps are identified to be disc stars in the final snapshot, we consider these stars as the mass supply ",
+    "Figure 12. Mass fractions between stars released from clumps to the disc and the final stellar disc. The horizontal axis means minimum clump mass defined in the FOF method. The thick lines are for all disc stars, and the thin lines are for stars in the region of 2 < R/Rd < 3 and 1 kpc < |z|< 4 kpc in the final snapshot. The ×-marks designate the results of BEE07; however, be aware of their di erent analysing technique (see the text). ",
+    "from the clumps to the disc. 7 (<>)Finally, we sum up the mass supply in all snapshots, estimate the mass ratio between the stars released from the clumps and the final disc at a given mmin. The lowest-mass clump of mmin = 2×105M⊙consists of more than one hundred particles. ",
+    "Fig. (<>)12 shows the results of the analysis as function of mmin. We notify readers that this figure indicates mass-contribution cumulated from large to small clumps: steepness of the slopes at a certain mmin corresponds to contribution from the clumps having the mass. In the runs of B01λ004 and K11-λ004, massive clumps of >��108 M⊙largely contribute to disc formation, and the thick discs have almost the same composition as the entire discs. In B01-λ010 and K11-λ010, the contribution from smaller clumps is relatively larger than in the other runs, and all mass ranges contribute nearly equally, i.e. relatively straight profiles in the figure. We consider that this variance between the runs could be attributed to the di erence of mass functions of clumps (see §(<>)4.1). In any runs, it can be said that significant fractions of the thick-discs stars are born in the clumps, and disrupted clumps seem to be a major supplier of stars to galactic discs in our simulations. For comparison, we also show the results of simulations of BEE07 in the figure. Here we have to note that BEE07 have used di erent clump detection and analysis methods for the sake of fair comparison with observations: They deteriorated resolutions of their face-on density maps down to 200 pc and searched for pixels with high contrast. BEE07 defined regions less extended than 3 kpc and more massive than 2 ×108 M⊙as their clumps. Therefore, it should be kept in mind that fairness is not ensured in the comparison between our and BEE07 simulations in Fig. (<>)12. Our results of B01-λ010 and K11-λ010 are nearly consistent ",
+    "with BEE07, but the runs of B01-λ004 and K11-λ004 indicate much larger mass contributions from massive clumps of >2 ×108M⊙. ",
+    "Fractional mass contribution from clumps of 10 7 – 109 M⊙thus seems to depend on the initial conditions of our simulations, therefore we could not assert that our simulations represent well the clumpy galaxies in the high-redshift Universe. In addition, feedback processes such as SNe and radiation pressure may be influential on the picture of disc formation and mass function of clumps ((<>)Genel et al. (<>)2012; (<>)Perez et al. (<>)2013). It is noteworthy, however, that the dynamical and chemical properties shown in the previous subsections were well consistent between the runs although Fig. (<>)12 showed the somewhat diverse results. "
+  ],
+  "4 DISCUSSION ": [],
+  "4.1 The validity and robustness of our simulations ": [
+    "First, we have to mention that numerical simulations for star-forming galaxies are still to be developed. Especially, implementation of feedback processes at the sub-grid level have long been debated (e.g. (<>)Stinson et al. (<>)2006, (<>)2012; (<>)Dalla Vecchia & Schaye (<>)2012; (<>)Agertz et al. (<>)2013). Such feedback processes may be crucial for fate of giant clumps. (<>)Noguchi ((<>)1996) has firstly pointed out the possibility that giant clumps may be transient objects if they are largely losing their mass by outflow. Recently, (<>)Genzel et al. ((<>)2011) and (<>)Newman et al. ((<>)2012) observed that some clumps indeed seem to be subjected to such strong outflow. Afterwards, (<>)Genel et al. ((<>)2012) performed numerical simulations using a parametrised method for representing the superwinds and seemed to show that the clumps could not grow massive and would be disrupted in timescales shorter than their orbital periods. Some other observations also determined young ages of clumps in agreement with the ephemerality of clumps under the strong feedback (e.g. (<>)Wuyts et al. (<>)2012; (<>)Swinbank et al. (<>)2012). On the other hand, recent analytical studies and numerical simulations have taken the stellar feedback into account, and they seemed to show that giant clumps can accrete ambient gas to keep their masses even under the strong outflow ((<>)Krumholz & Dekel (<>)2010; (<>)Forbes et al. (<>)2013; (<>)Dekel & Krumholz (<>)2013; (<>)Bournaud et al. (<>)2014; although see (<>)Hopkins et al. (<>)2012). In this case, the clumps are expected to be long-lived and migrate toward the galactic centres. In addition, radial gradients of ages, specific star-formation rates and gas fractions of clumps were observed and could be taken as indicative of the longevity and the migration of clumps ((<>)F¨orster Schreiber et al. (<>)2011; (<>)Guo et al. (<>)2012; (<>)Tadaki et al. (<>)2014); additionally, (<>)Mandelker et al. ((<>)2013) confirmed the presence of these radial gradients in their simulations where their clumps are long-lived and form central bulges. ",
+    "Because the stellar feedback processes have not been implemented in our simulation code yet, star formation rate would possibly be overestimated in the clumpy phase (e.g. (<>)Saitoh & Makino (<>)2010; (<>)Dalla Vecchia & Schaye (<>)2012; (<>)Agertz et al. (<>)2013). The reader should be aware that our results may be sensitive to this issue. (<>)Perez et al. ((<>)2013) have performed N-body/SPH simulations using isolated disc ",
+    "models and shown how a mass function of clumps varies with strength of SN feedback between 0 and 1.0 ×1051 erg per SN. They found that a typical clump mass becomes more massive in a run with stronger SN, and the most frequent clump mass in the run with the strongest SN is ∼0.5 dex larger than in the case excluding the feedback. Thus, less massive clumps are disrupted due to the feedback, whereas massive ones can survive if they grow rapidly. (<>)Bournaud et al. ((<>)2014) also performed simulations with isolated galaxy models in which they took into account various feedback processes such as HII region photo-ionization, radiation pressure from young stars and non-thermal feedback from SNe. They demonstrated that clumps more massive than ≃108 M⊙can survive and keep their masses nearly constant even under the feedback stronger than in our study and (<>)Perez et al. ((<>)2013); moreover, this result was confirmed in cosmological simulations (N. Mandelker et al. in prep.) In our study, Fig. (<>)12 indicates that more than 50 per cent of the thick-disc stars form in clumps more massive than 108 M⊙in the runs of B01-λ004 and K11-λ004 although the fractions are ≃20 per cent in B01-λ010 and K11-λ010. Therefore, it could be expected that the thick-disc properties in B01λ004 and K11-λ004 would be robust with respect to the feedback eÿciency in simulations. On the other hand, the thick discs in B01-λ010 and K11-λ010 may not be formed from dissolved clumps if the other feedback processes are implemented. Moreover, bulge masses could also be a ected by the feedback. If the feedback dissolves the majority of clumps, the bulges could not grow massive. In this sense, contribution by the bulges to potentials of entire galaxies may depend on the strength of the feedback, thereby the feedback eÿciency may be influential on dynamical properties of disc stars via the bulge potentials. ",
+    "Significance of the metallicity gradients would be affected by the strength of feedback. Cosmological simulations of (<>)Gibson et al. ((<>)2013) have demonstrated that strong stellar feedback can wash out metallicity gradients in their discs although the gradients can be seen in the case of weak feedback. Our simulations would correspond to the case of weak feedback, therefore we could expect that the weak metallic-ity relations in this study would be due to the violent perturbation by the massive clumps. However, metallicity of the disc stars would become lower than in our simulations if the other feedback processes are implemented since star formation would be considerably suppressed and metal-enriched gas in clumps would be discharged by the feedback. ",
+    "Our simulations are, in addition, not cosmological; our models are lacking continuous gas accretion which is expected to feed thin discs. The thin-disc formation could shorten the scale heights of the thick discs and might influence the velocity dispersions. In the cosmological context, smooth and cold gas streams are thought to penetrate a halo and keep a galaxy gas-rich until the streams are turned o in the high-redshift Universe (e.g. (<>)Dekel & Birnboim (<>)2006; (<>)Dekel et al. (<>)2009). As noted in §(<>)3.1.1, gas fraction in the clumps may a ect some properties of the clump-origin bulges such as density profile and mass. In isolated models like our simulations, properties of giant clumps would be more or less controlled by the initial settings. For example, spin parameter is responsible for mass function of clumps: Small and large spin parameters of the initial conditions lead to high and low surface gas density of the ",
+    "discs. The wavelength at which dynamical instability first appears becomes longer in a disc with a higher surface density, which allows to form more massive clumps preferentially ((<>)Toomre (<>)1964; (<>)Binney & Tremaine (<>)2008). This inferand K11-λ004. As we showed in §(<>)3, however, the kinematic and chemical properties of the thick discs in our simulations are qualitatively consistent between the runs and do not seem to depend very much on the initial conditions. "
+  ],
+  "4.2 The thick disc formation in clumpy galaxies ": [
+    "Here we inspect how realistic the scenario of thick-disc formation in clumpy galaxies is. As (<>)Bournaud et al. ((<>)2009) showed, the thick-disc formation in clumpy galaxies has the advantages that constant thickness and old age of thick discs can be well reproduced in agreement with observations. These were confirmed in our simulations. In the scenarios of thin disc heating and radial migration, thick discs seem to form with scale heights increasing with galac-tocentric radius, i.e. flaring thick discs ((<>)Kazantzidis et al. (<>)2008; (<>)Minchev et al. (<>)2012), although radial migration seems able to explain the relation between vθand metallicity ((<>)Curir et al. (<>)2012). In our simulations, although the scale radii of the discs were contingent to the initial rotation of gas, the scale heights of hT ≃1 kpc seem to be consistent with observed thick discs and almost independent of the initial conditions. Significant asymmetric drift, dvθ/dz, was also confirmed in the runs of B01-λ004 and K11-λ004. Radial profiles of velocity dispersions except σRwere also nearly exponential. The pioneering work of (<>)Lewis & Freeman ((<>)1989) has observed exponential decrease of σRand σθfor old disc stars with scale lengths similar to that of surface density, whereas (<>)Casetti-Dinescu et al. ((<>)2011) observed the only significant radial gradient of σzin the MW thick-disc stars. Moreover, we found that vertical profiles of velocity dispersions are almost isothermal in our simulations. In observations of the MW thick disc, (<>)Moni Bidin et al. ((<>)2012) have observed velocity dispersion profiles weakly increasing with height above the plane (although see (<>)Sanders (<>)2012); however, some observations indicated steep vertical gradients of σR((<>)Casetti-Dinescu et al. (<>)2011) and σz((<>)Kordopatis et al. (<>)2011). Distributions of orbital eccentricities in the entire thick discs in our simulations showed excellent agreement with observations of the MW thick disc. However, vertical dependence of the eccentricities cannot be reproduced. Thus, we can see that the comparisons of dynamical properties between our simulations and the observations do not indicate evident discrepancies, except the vertical variation of orbital eccentricities observed in the MW ((<>)Dierickx et al. (<>)2010). ",
+    "We found that metallicity gradients are quite weak in our simulations. In observations of the MW, thick-disc stars do not seem to have steep metallicity gradients in radial or vertical directions (e.g. (<>)Allende Prieto et al. (<>)2006; (<>)Bensby et al. (<>)2011; (<>)Ruchti et al. (<>)2011; (<>)Kordopatis et al. (<>)2011; (<>)Carrell et al. (<>)2012). However, our simulations did not show metallicity relations with orbital eccentricities and rotation velocities, which have recently been observed in the MW thick disc ((<>)Lee et al. (<>)2011; (<>)Kordopatis et al. (<>)2011, (<>)2013). We consider that this lack of chemo-dynamical re-",
+    "lations is the most striking discrepancy between our simulations and the observations. We infer that disc stars are stirred by violent perturbation of giant clumps and such chemo-dynamical relations would be washed out in the clumpy phase. In the observations of (<>)Lee et al. ((<>)2011), their samples of thin-and thick-disc stars showed distinct chemo-dynamical relations, this is thought to reflect distinct formation processes of these discs. Thus, the chemical relations are expected to be susceptible to formation scenarios of discs, and the inconsistency between our simulations and the observations of the MW implies that the thick-disc formation scenario in clumpy galaxies may not be suitable for the MW. ",
+    "(<>)Tadaki et al. ((<>)2014) have observed that 41 per cent of Hαemitters of stellar masses from 109 to 1011.5 M⊙have clumpy morphologies at redshifts of 2.2 and 2.5, and the fraction of clumpy galaxies becomes the largest at the mass of 1010.5 M⊙(see also (<>)Murata et al. (<>)2014). However, (<>)van Dokkum et al. ((<>)2013) observationally argued that MW progenitors would have stellar masses of 109.5 –1010 M⊙in this redshift range (see their fig. 1). From these observations, typical clumpy galaxies may be too massive to evolve into the MW-size galaxies. If it is the case, the thick-disc formation in a clumpy disc would not be suitable for the MW and smaller galaxies. ",
+    "It should be noted, however, that thick discs in external galaxies show a wide variety of kinematic properties, which is discussed to correlate with Hubble types and/or galaxy masses (e.g. (<>)Yoachim & Dalcanton (<>)2006, (<>)2008; (<>)Comer´on et al. (<>)2011). Presumably, this may mean that the formation process of thick discs is not a single scenario and the diverse kinematics of the thick discs could be the consequence of the variety of formation history. Observational studies of chemo-dynamical properties of thick-disc stars in external galaxies are, unfortunately, far from sufficient. First, orbital eccentricity of each thick-disc star is not observable in these galaxies since three-dimensional position and velocity of a star are not accessible even if we could resolve its stellar image. However, it may be possible to observe the relation between metallicity and rotation velocity. (<>)Yoachim & Dalcanton ((<>)2008) have observed some edge-on galaxies and obtained rotation curves at different height above disc planes. They found that relatively massive galaxies in their sample do not indicate significant vertical gradient of rotation velocities. On the other hand, their less massive galaxies show a wide range of behaviour such as counter-rotation between thin and thick discs, but they tend to indicate asymmetric drift more clearly than the massive galaxies. If altitudinal dependence of metallic-ity is observed in these galaxies, one can discuss whether they have a chemo-dynamical relation like the MW thick disc and whether it is a universal relation or not. ",
+    "The authenticity of the clear distinction between the thin and thick discs is still under discussion, and the Galactic thick disc may be a superposition of relatively old components which are continuously connected to the thin disc (e.g. (<>)Dove & Thronson (<>)1993; (<>)Bovy et al. (<>)2012a,(<>)b,(<>)c; (<>)Stinson et al. (<>)2013). (<>)Bovy et al. ((<>)2012c) discussed that each component consisting of the Galactic disc is a simple structure with a single exponential density profile and isothermal kinematics. Recent observations by (<>)Haywood et al. ((<>)2013), however, indicated that the Galactic thick- and thin-disc stars have obviously distinguishable age-[α/Fe] and -[Fe/H] relations ",
+    "although the durations of their star formation somewhat overlap. Their result would prefer distinct formation processes between the thin and thick discs. They discussed the formation epoch of the thick disc to be the first 4–5 Gyr of the Galaxy formation with starburst; this period corresponds to redshift of z= 2–3. Thus, further investigation is needed to obtain more detailed and accurate information for the Galactic thick disc. In addition, observations for external galaxies are also essential to compare with the MW and inspect the universality and individuality of thick discs. "
+  ],
+  "5 CONCLUSIONS ": [
+    "In this study, we found that properties of thick discs are almost consistent among our runs with di erent initial conditions. Our simulations indicated that kinematic properties such as density and velocity profiles and distributions of orbital eccentricities are in acceptable agreement with Galactic and external galactic observations. However, altitudinal dependence of the eccentricities and metallicity relations with rotation velocities and eccentricities are not confirmed in our simulations, which are discrepant from recent observations of the Galactic thick disc. Therefore, we infer that the thick-disc formation scenario by clumpy discs would not be suitable at least for the MW. "
+  ],
+  "ACKNOWLEDGMENTS ": [
+    "We would like to thank the referee for a careful reading of the manuscript and useful comments. We are grateful to Daisuke Kawata, Junichi Baba, Kohei Hattori, Shunsuke Hozumi, Ken-ichi Tadaki, Daniel Ceverino and Avishai Dekel for their helpful discussion. The numerical simulations reported here were carried out on Cray XT4 kindly made available by CfCA (Center for Computational Astrophysics) at the National Astronomical Observatory of Japan. SI acknowledges support from the Lady Davis Fellowship. "
+  ]
+}