jsons_folder/2013MNRAS.428.1225S.json

{
  "(<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 ) "
  ]
}