{ "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. (), ", "() (), ' (/− ) −−− " ] }