The Evolution of L and T Dwarfs in Color‐Magnitude Diagrams

“We use the elemental abundances of Lodders (2003).”

“Figures 2 and 3 compare our cloudless sequence with the COND03models of Baraffe et al. (2003) and our cloudy fsed ¼ 2 sequence with the DUSTY00 models of Chabrier et al. (2000b) and Baraffe et al. (2002), respectively.”

“3Heþ : ð5Þ We use the nuclear reaction cross sections from the NACRE database (Angulo et al. 1999) and apply the screening corrections developed by Chabrier, which include both ionic and electronic screening (Saumon et al. 1996; Chabrier & Baraffe 1997; G. Chabrier 1999, private communication).”

“…of isolated brown dwarfs—a relatively simple case of stellar evolution—has been studied extensively for the past 20 years and is well understood (D’Antona & Mazzitelli 1985; Nelson et al. 1986; Burrows et al. 1989, 1997; Burrows & Liebert 1993; Chabrier et al. 2000a, 2000b; Baraffe et al. 2002).”

“For these evolution sequences with solar metallicity atmospheres, the minimum hydrogen-burning mass, defined by objects that reach stable H burning at an age of 10 Gyr, is 0.075M , where TeA ¼ 1910 K for the cloudless sequence.”

“Our chemical equilibrium grid of molecular, atomic, and ionic abundances as a function of temperature, pressure, and metallicity is based on the work of Fegley & Lodders (1994,1996), Lodders (1999, 2002), and Lodders & Fegley (2002, 2006).”

“For a 10 Gyr old brown dwarf of 0.06 M , we find a luminosity that is 0.104 dex lower than that of Baraffe et al. (2003), which is in perfect agreement with the value given in Chabrier et al. (2000b) for the change in luminosity brought by introducing conduction in the evolution.”

“Our thermal radiative transfer follows the source function technique of Toon et al. (1989) allowing inclusion of arbitrary Mie scattering particles in the opacity of each layer.”

“From stellar modeling, estimates of the minimum mass for hydrogen burning range from 0.07Me to 0.09Me (Burrows et al. 1993, 1997; Baraffe et al. 1998, 2003; Chabrier et al. 2000; Saumon & Marley 2008).”

“Although the CMDs most directly probe the color evolution of brown dwarfs (i.e., cloud dispersal), in the theoretical perspective of Saumon & Marley (2008) this pileup and gap are inextricably tied to luminosity evolution as well.”

“We first fit the observed J and H band spectra using standard cloud-free equilibrium-chemistry models, constrained to have radii for a given mass as given by evolutionary tracks, similar to those in ( 35 ).”

“However, this mass depends on metallicity, helium fraction, the presence or absence of clouds, etc. (Saumon & Marley 2008; Spiegel et al. 2011).”

“The most widely used hot-start models for imaged planets are the Cond and Dusty grids from Baraffe et al. (2003) and Chabrier (2001), Burrows et al. (1997), and Saumon & Marley (2008).”

“The introduction of “dusty” models was a leap forward in the study of brown dwarfs (see e.g. Allard et al. 2001; Kirkpatrick 2005; Saumon & Marley 2008), and our results suggests that a similar effort may be useful for hot planets like HD 189733b. c© 2012 RAS, MNRAS 000, 1–31”

“Cloud Sedimentation Efficiency For the L dwarfs, we are generally able to match photometric colors by including silicate, iron, and corundum clouds with a sedimentation efficiency parameter offsed=2±1 (Stephens et al. 2009; Saumon & Marley 2008).”

“Stellar templates with an effective temperature Teff 4000 K are rejected in the case that the physical parameters do not satisfy the constraints from Saumon & Marley (2008).”

“…et al. (2008) (hereafter, F08) we presented a detailed discussion of atomic and molecular line opacities used by our group in modeling the atmospheres of brown dwarfs and giant planets (e.g. Marley et al. 2002; Fortney et al. 2005; Saumon & Marley 2008; Fortney et al. 2008; Marley et al. 2010).”

“We have used the models of Saumon & Marley (2008) to generate and fit synthetic spectra to the red through mid-infrared spectra of 21 L and T dwarfs.”

“We used the cloudless structure models of Saumon & Marley (2008) because they used atmospheric models that are nearly identical to the ones we used in our analysis for boundary conditions.”

“Evidence for a gravity dependence for the L-to-T transition has already been reported (Metchev & Hillenbrand 2006; Saumon & Marley 2008) and, recently, Stephens et al. (2009) found that low-gravity brown dwarfs in their sample remain cloudy at lower effective temperatures, with the L-to-T…”

“The TRAPPIST-1 spectrum is calculated for this paper using the radiative-convective atmosphere models described in McKay et al. (1989), Marley et al. (1996), Saumon & Marley (2008), Fortney et al. (2008), and Morley et al. (2015), assuming a dust-free model atmosphere.”

“The mass range for ages from 2 to 8 Gyr in the Saumon & Marley (2008) cloudless models is 12 to 29 MJ , while the cloudy models give 10 to 25 MJ .”

“We used the inferred age and calculated Lbol for each object to find the range of predicted radii from the solar metallicity, hybrid cloud (SMHC08) evolutionary model isochrones of Saumon & Marley (2008) (Figure 4).”

“Saumon & Marley (2008) provide a model atmosphere grid over a wide range of Teff , log(g), and cloud properties based on the cloud treatment of Ackerman & Marley (2001), which is parameterized by the sedimentation 14Dupuy et al. (2016a) have recently determined the individual component dynamical…”

“The evolution of very low mass stars and brown dwarfs is reviewed by Burrows et al. (2001), while Saumon & Marley (2008) present more recent calculations.”

“Saumon & Marley (2008) have contributed to this endeavor.”

“With a measured Lbol and an age estimate, we use the Saumon & Marley (2008) evolutionary models with fsed = 2 to compute the remaining physical properties.”

“We note that the pile up of objects in the transition region reported in Saumon & Marley (2008) still occurs in this new calculation but it is more spread out in Teff , as would be expected from the broader span of the transition in Teff (Figure 11).”

“The fsed = 1,2 parameters best fit the L dwarf sequence and fsed = 4 (corresponding to a very thin cloud layer) best fit the late-type T dwarf sequence using the Saumon & Marley (2008) models.”

“This scenario is possible only for low primary masses (M1 10 MJup) and low mass ratios (q 0.05 − 0.1), such that a semi-detached binary with a 15.44 hr period would have to be a young ( 20 Myr), double planetary-mass system.”

“…based on theoretical work over the last two decades (e.g., Saumon et al. 1994; Baraffe et al. 1995; Burrows et al. 1997; Chabrier & Baraffe 1997; Lodders 1999; Chabrier et al. 2000; Burrows et al. 2001; Baraffe et al. 2003; Saumon & Marley 2008; MacDonald & Mullan 2009; Baraffe et al. 2015).”

““Hot-start” models (e.g., Burrows et al. 1997; Saumon & Marley 2008) slowly radiate their initial gravitational potential energy over time and therefore best represent formation via disk instability (e.g., Boss 1997; Mayer 2002).”

“Leggett et al. (2007) also note this source as being unusually red in mid-infrared colors, and comparison to model colors suggest the presence of strong vertical mixing and thick condensate clouds in its atmosphere (Ackerman & Marley 2001; Saumon & Marley 2008).”

“T) profiles for the atmosphere of Titan (McKay et al. 1989), Uranus (Marley & McKay 1999), brown dwarfs (Marley et al. 1996; Burrows et al. 1997; Saumon & Marley 2008), and irradiated exoplanets (Fortney et al. 2005, 2008; Cahoy et al. 2010; Morley et al. 2013).”

“…values of ∼102–106 cm2 s−1 typically produce the best fits to near- and mid-infrared photometry and spectroscopy of field L and T dwarfs (Leggett et al. 2007b; Saumon et al. 2007; Stephens et al. 2009; Geballe et al. 2009) using the Saumon & Marley atmospheric models (e.g., Saumon & Marley 2008).”

“In contrast to the results of Kirkpatrick et al. (2019), we now find that the evolutionary code of Saumon & Marley (2008) is highly favored over that of Baraffe et al. (2003), and the reason for this is the inclusion in this paper of space density measurements over the cloudyto-clear transition…”

“The same conclusion was reached by Artigau et al. (2009) for SIMP0136 based on comparison of models by Allard et al. (2003) and Tsuji (2005) to their ground-based ∆J/∆K observations and by Radigan et al. (2012) for 2M2139 through comparison to models by Saumon & Marley (2008).”

“Studies of L dwarfs find thatfsed∼1– 3 for the majority of field L dwarfs (Stephens et al. 2009; Saumon & Marley 2008).”

“We compute absolute magnitudes and colors with the ultracool dwarf evolution models of Saumon & Marley (2008).”

“We began with a library of high-resolution synthetic template spectra computed as described in Marley et al. (2002) and Saumon & Marley (2008).”

“…cool through the L-to-T transition and clouds are theorized to sink below the visible atmosphere (Kirkpatrick et al. 1999; Allard et al. 2001; Saumon & Marley 2008) • The variability seen in brown dwarfs (Artigau et al. 2009; Metchev et al. 2015), which is most prominent near the L-to-T…”

“…find incorporating such an absorber into the 1D radiative-convective atmosphere model of Marley and collaborators (e.g. Marley & McKay 1999; Marley et al. 2002; Fortney et al. 2008; Saumon & Marley 2008; Marley et al. 2012) would likely heat the atmosphere of WASP-121b by ∼ 500 K at mbar pressures.”

“The observations are not explained by canonical model spectra of L and T brown dwarfs (Burrows et al. 2006; Saumon & Marley 2008) at the same Teff , indicating that the present objects might form a new class with geometrically thicker clouds than those inferred for L and T dwarfs, as also suggested…”

“For field brown-dwarfs, the L→T spectral type transition, occurs at ∼1200-1400 K, where dust clouds settle/condense below the photosphere (Saumon & Marley 2008), and CO is converted to CH4 (Burrows et al. 2003; Geballe et al. 2002).”

“…introduced by a brightness selection, as field brown dwarfs with similar temperatures but different gravities have very similar luminosity, because the radius does not change significantly after the first ∼100 Myr (e.g., Burrows et al. 1997, their Figure 10; Saumon & Marley 2008, their Figure 4.)”

“5 corresponds to 3 MJup using the models from Burrows et al. (2003) for 1 Gyr while the bright limit implies 10 MJup according to the models from Saumon & Marley (2008) for 10 Gyr.”

“For a given fsed, our model produces clouds optically thicker than the model by Saumon & Marley (2008) and Marley et al. (2010).”

“These models are more extensively described in McKay et al. (1989); Marley et al. (1996); Burrows et al. (1997); Marley et al. (1999, 2002); Fortney et al. (2005); Saumon & Marley (2008); Fortney et al. (2008).”

“As the object cools the entropy decreases, and forTeff = 200K the entropy is close to the entropy of cloudy atmospheres used in Saumon & Marley (2008).”

“Additionally, the adiabat calculated by the atmospheric models provides the upper boundary conditions of the interior evolutionary models of substellar objects like giant planets and brown dwarfs (Hubbard 1977; Burrows et al. 1997; Chabrier et al. 2000; Saumon & Marley 2008).”

“Despite the scale was generated using another family of atmospheric models (e.g. Saumon & Marley 2008), this spectral type range is consistent with that infered from the location of β Pictoris with respect to field dwarfs in J-H vs H − Ks and color-magnitudes diagrams.”

“…exoplanets (e.g., Barman et al. 2011; Madhusudhan et al. 2011; Marley et al. 2012; Lee et al. 2013) and has long been an obstacle plaguing advances in the understanding of brown dwarfs (e.g., Saumon & Marley 2008; Artigau et al. 2009; Burrows et al. 2011; Helling et al. 2011; Buenzli et al. 2012).”

“5 We use the corrected version of the equations in SCvH; see theapp ndix of Saumon & Marley (2008). that region.”

“Evolutionary models from Saumon & Marley (2008) predict that an object with the luminosity and mass of HR7672B is still cooling, but that it will eventually stabilize on the main sequence once it reaches an age of several Gyr.”

“We have used the thermal profile from a Teff = 1700K, log g = 5.0 self-consistent grid model from Saumon & Marley (2008), but have included only a simple set of 8 gases with arbitrarily selected mixing ratios, given in Table 2.”

“It has also been used for modeling the spectra of brown dwarfs with effective temperatures between 500 and 2400 K, with excellent agreement with the observations (e.g., Cushing et al. 2008; Saumon & Marley 2008).”

“This was noted in Figure 13 of Saumon & Marley (2008) and is a consequence of the hybrid models in which the cooling timescale increases from 1400K to 1200K, at the transition between L and T dwarfs.”

“The gravity, effective temperatures, and ages of this sample are also in line with expectations from population synthesis evolutionary models (Figure 9 in Saumon & Marley 2008) for late T-dwarfs and observations of mass-calibrated binary systems (Dupuy & Liu 2017).”

“Extrasolar giant planets (EGPs) have modest surface gravities (g of order 103 cm/s2) and extended scale heights (e.g., Burrows et al. 1997; Saumon & Marley 2008)1.”

“Leggett et al. (2010a) found that colours of the late-T dwarfs that were identified in UKIDSS suggest they are a predominantly young and low-mass population from comparisons to the model atmospheres of Saumon & Marley (2008).”

“In addition to the photometry of 51 Eri b and the field and young brown dwarfs we also over-plot two low mass, 5 and 14 MJup, evolutionary model tracks (assuming hot-start conditions) from Saumon & Marley (2008); Marley et al. (2012).”

“Burgasser et al. (2002) and Saumon & Marley (2008) found that their socalled Cloudy models could not produce the M-L-T spectral transition with a single value of fsed.”

“…models have frequently been provided by theorists for only a restricted set of parameters (e.g., at solar metallicity) and for a single ad hoc prescription for clouds (or with no clouds) (Burrows et al. 1993,1997,2001,2006; Chabrier & Baraffe 1997; Baraffe et al. 1998,2003; Saumon & Marley 2008).”

“Atmospheric models have been much improved over the last decade (Allard et al. 2001; Tsuji 2005; Burrows et al. 2006; Saumon & Marley 2008; Helling et al. 2008).”

“The distinction is thought to be gravity dependent8 (Burrows et al. 2006; Saumon & Marley 2008; Metchev & Hillenbrand 2006; Bowler et al. 2010; Liu et al. 2013).”

“K colors (Burrows et al. 2006; Saumon and Marley 2008; Allard et al. 2001), several problems remain unsolved: • The driving mechanism of the cloud dynamics remains poorly understood.”

“We compare in Figure 13 the luminosity of the companion at the adopted range of ages with the Saumon & Marley (2008) and BT-Settl models (Allard & Barman 2004) and with presently known young substellar objects, compiled by Bowler et al. (2013) updated with recently reported young T-dwarf companion…”

“At this transition, it is expected that the iron/silicate clouds, important source of opacity for L dwarfs (Saumon & Marley 2008; Stephens et al. 2009), gradually become less important, either because they sink or become patchy, which allows the emergent flux to come from a deeper layer of the…”

“These authors compared atmosphere models of Saumon & Marley (2008) computed using the Ackerman & Marley (2001) cloud model to a variety of L- and T-type brown dwarf spectra from 0.8 to 15 μm.”

“This model is similar in spirit to a long history 1D brown dwarf atmosphere models (e.g Burrows et al. 1997, 2006, Marley et al. 2002, 2010, Saumon & Marley 2008), except that most of these models assume steady state and solve for the radiative-convective-equilibrium, 24 In a hydrostatically…”

“Nevertheless, using models from Saumon & Marley (2008), Cushing et al. (2008) are able to fit the spectra of L4 and L5 dwarfs with their Teff=1700 K, log(g)=4.5 models and L6 dwarfs with their Teff=1400 K, log(g)=4.5 atmospheric models, achieving good-fits past spectral type L8.”

“These same atmosphere models have been honed over the past 10 years on excellent spectra of hundreds of brown dwarfs with Teff down to ∼550 K (Allard et al. 2001; Marley et al. 2002; Burrows et al. 2006; Saumon et al. 2006; Saumon & Marley 2008).”

“Again the result from the literature (e.g. Burrows & Liebert 1993; Burrows et al. 2001; Baraffe et al. 2002; Saumon & Marley 2008; Dupuy et al. 2015) is reproduced, as in the former section, that the choice of the atmospheric model has only a limited impact on the evolution of the bolometric…”

“Still, the details of this transition remain poorly understood (e.g. Saumon & Marley 2008).”

“There is also evidence for a cloud-gravity dependence near the L-T transition (e.g., Burrows et al. 2006; Metchev & Hillenbrand 2006; Saumon & Marley 2008).”

“…the L/T transition itself remains poorly understood; it occurs over a surprisingly small range of effective temperature and accompanies a J-band brightening that are not easily captured by standard 1D models (Chabrier et al. 2000; Allard et al. 2001; Burrows et al. 2006b; Saumon & Marley 2008).”

“Clouds tend to trap the outgoing radiation in the atmosphere in shorter wavelengths, causing an overall “reddening” of observable spectra (e.g., Mar-ley et al. 2002; Saumon & Marley 2008; Morley et al. 2012, 2014b).”

“10e of Saumon & Marley (2008)) 3.”

“…of clouds sinking below the visible photosphere (Ackerman & Marley 2001; Cooper et al. 2003; Tsuji 2005) or breaking apart (Burgasser et al. 2002a; Marley et al. submitted), although the details of this transition remain poorly understood (Burrows et al. 2006; Burgasser 2007; Saumon & Marley 2008).”

“In a change from previous models (e.g., Saumon & Marley 2008), but in accord with prior chemistry modeling (Visscher et al. 2010), we assume that both forsterite and enstatite can condense.”

“We used the bolometric luminosity versus spectral-type relations of Faherty et al. (2016) combined with the Saumon & Marley (2008) evolutionary tracks to obtain a rough estimate of the spectral types that correspond to the substellar regime at the age of each young association considered here.”

“The L/T transition poses the largest challenge to models (e.g. Saumon & Marley 2008), and the physical mechanism behind cloud dispersal in T dwarfs is not yet well understood.”

“The “COND” and “DUSTY” models suggest a mass range of 5-21 MJup, while the Saumon & Marley (2008) models suggest a mass range of 4-15 MJup (Figures 11 and 12).”

“The mechanism for cloud dispersion is not well understood, and different models have been proposed that invoke cloud thinning and rain-out (e.g., Knapp et al. 2004; Tsuji 2005; Burrows et al. 2006; Saumon & Marley 2008) or patchy clouds (Marley et al. 2010).”

“Given that this is a dusty, young red object, we expect the Saumon & Marley (2008) models, which take clouds into account, to provide the most reliable estimates of the properties of these objects among the model choices available.”