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.”

“We also examined predictions from the Saumon & Marley (2008) evolutionary models which include cloud opacity effects in brown dwarf thermal evolution, and found identical values for mass (M = 14+2 −2 MJ) and surface gravity (log g = 4.12+0.05 −0.10), whether or not cloud opacity is included.”

“The SLC calibration relies on model atmospheres described in Saumon & Marley (2008), and references therein.”

“The next step will be to investigate selection effects with, for example, Simulation-Based Inference (SBI) methods, which offer more flexibility and ease of implementation in modelling selection processes.”

“…the largest for transiting BDs at Rb=1.580 0.070 0.074 - + RJ. Substellar evolutionary models predict that BDs form highly inflated and then contract, rapidly at first, then slowing over the course of ∼10 Gyr (Burrows et al. 2001; Baraffe et al. 2003; Saumon & Marley 2008; Phillips et al. 2020).”

“A sharp peak in the observed LF at the L dwarf/T dwarf transition reported in Kirkpatrick et al. (2019) may be a consequence of delayed evolution due to thick condensate clouds (Saumon & Marley 2008) or blended-light binaries (Burgasser 2007; see below).”

“We used a Monte Carlo approach to build distributions for four different models (Burrows et al. 2001; Saumon & Marley 2008; Baraffe et al. 2003).”

“T transition, there is a good chance that they have non-uniform cloud cover (Saumon & Marley 2008).”

“…using grids of forward models that rely on speci fi c input physics ( e.g., Burrows & Liebert 1993; Allard et al. 1996; Marley et al. 1996; Tsuji et al. 1996; Saumon et al. 2000; Geballe et al. 2001; Hubeny & Burrows 2007; Saumon & Marley 2008; Yamamura et al. 2010; Patience & King 2012 ) .”

“P profiles in radiative–convective equilibrium (McKay et al. 1989; Marley et al. 1996; Burrows et al. 1997; Marley & McKay 1999; Marley et al. 2002; Saumon & Marley 2008; Fortney et al. 2008).”

“These objects’ masses predicted by Saumon & Marley (2008) hybrid evolution models given their ages and Lbol are all consistent with their dynamical masses, although these L dwarfs have older ages (≈ 2 Gyr) than HD 130948BC and Gl 417BC (≈ 800 Myr).”

“…†NASA Postdoctoral Program Fellow. and luminosity are degenerate parameters for these objects, and the presence (and evolution) of dust clouds in the photosphere further complicates the interpretation of their spectra (Burrows, Sudarsky & Hubeny 2006; Saumon & Marley 2008).”

“…and a sudden sedimentation of condensed species below the photosphere when the local temperature is .1,500 K, and by the appearance of methane absorption in the 1.0–2.5µm region (Allard et al. 1997, 2001; Chabrier et al. 2000; Ackerman & Marley 2001; Burrows et al. 2006; Saumon & Marley 2008).”

“These cloud changes are so signifi- 1 INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, I-35122, Italy cant that they may even affect the luminosity evolution of the brown dwarf itself (Saumon & Marley 2008; Dupuy et al. 2015).”

“…p(µ), I have em- ployed one-dimensional, non-grey, hydrostatic and radiative-convective atmospheric models for a range of effective temperature Teff and surface gravities g appropriate for T and L dwarfs (Ackerman & Marley 2001; Marley et al. 2002; Freedman et al. 2008; Saumon & Marley 2008).”

“Theoretical evolutionary models predict that an object with luminosity logL/L = −4.5 with lithium must be ∼ 1.5 billion years old or younger (Burrows et al. 1997; Baraffe et al. 2003; Saumon & Marley 2008).”

“A gravity this large is unlikely, given that at Teff ≈ 600 K an increase in age from 1 to 10 Gyr corresponds to an increase in gravity of 0.6 dex (Saumon & Marley 2008; their Figure 4).”

“Although stars and brown dwarfs (objects with a mass too low for stable hydrogen fusion e.g. Burrows & Liebert (1993); Saumon & Marley (2008); Phillips et al. (2020)) are not blackbodies, an increasing amount of energy is emitted at longer wavelengths as their effective temperature ( T eff )…”

“0 object: near the L/T transition probing the dissipation of clouds at high altitude in substel-lar atmospheres (e.g. Saumon & Marley 2008).”

“To estimate masses, we use two sets of models; the hybrid models from Saumon & Marley (2008) and those from Phillips et al. (2020).”

“The first brown dwarf binary systems, defined here as systems where both components are below the hydrogenburning minimum mass (∼0.07 Me; Saumon & Marley 2008), required the use of high-resolution imaging (e.g., Martín et al. 1998; Martin et al. 1999) or high-resolution spectroscopic monitoring…”

“…work, the one-dimensional model has seen extended applications to exoplanets (e.g., Fortney et al. 2005, 2008; Morley et al. 2017) and brown dwarfs (e.g., Marley et al. 1996; Saumon & Marley 2008a; Morley et al. 2012; Morley et al. 2014; Robinson & Marley 2014; Marley et al. 2021 submitted).”

“…affected by uncertainties in the treatment of convection, since they are almost entirely convective and the convective transport is nearly adiabatic (Saumon & Marley, 2008). iii) The MSK has a lower global error budget – Recent empirical evidence indicates that the MSK provides absolute cluster…”

“A typical example of best-fit values is an age of 240+330−130 Myr, masses of M1 = 0.044 +0.019 −0.013 and M2 = 0.030 +0.015 −0.010, and a mass ratio of q = 0.68+0.03−0.03 (obtained using Saumon & Marley 2008 and bolometric luminosities).”

“The nuclear burning calculation follows that of Saumon & Marley (2008) and takes into account the H, 2 H (deuterium), and “effective” He mass fractions ( X , X D , and Y ′ , respectively) in computing the nuclear energy generation rate per unit mass ϵ nuc .”

“Saumon & Marley (2008) predict a pileup at 1300K due to atmospheric cloud clearing changing the cooling rate – a prediction that is confirmed by Kirkpatrick et al. (2021) using very wide bins in effective temperature but complicated by Best et al. (2021), who instead emphasize a narrow gap at 1300K…”

“As done in Filippazzo et al. (2015), to obtain a radius estimate and Teff, we used Saumon & Marley (2008) hybrid cloud evolutionary models as well as the Chabrier et al. (2000) and Saumon & Marley (2008) fsed= 2 evolutionary models to determine the radius ranges for all comparative sources.”

“…the detection of a much fainter feature in the CMD (fainter by ∼7 mag), but (i) it is much more populated because the stellar luminosity function increases toward lower masses and (ii) it should be less affected by model uncertainties, such as the treatment of convection (Saumon & Marley 2008).”

“The Tremblin et al. (2015) models provide flux at 10 pc (assuming a radius of 0.1 R⊙), which we have re-scaled for the appropriate radius taken from Saumon & Marley (2008).”

“…predicted limiting mass, as can be seen in Chabrier et al. (2000) who suggested a limiting mass of 0.065M for models that include dust formation, Saumon & Marley (2008) who suggested a limiting mass of 0.075M for cloudless models, and 0.070M for cloudy models; all for solar metallicity and an…”

“–?? are calculated using template stellar spectra convolved with the DES filter responses - for the L & T dwarfs (Saumon & Marley 2008; Marley et al. 2002; Ackerman & Marley 2001) and M dwarfs (Bochanski et al. 2007).”

“…on the initial conditions: hot-start models considering an initial spherical contracting state (Chabrier et al. 2000; Baraffe et al. 2003; Saumon & Marley 2008) and core accretion models coupling planetary thermal evolution to the predicted core mass and thermal structure of a…”

“All heritage exoplanet models, such as Burrows et al. (1997); Chabrier & Baraffe (1997); Baraffe et al. (1998, 2003); Fortney & Hubbard (2004); Saumon & Marley (2008); Marley et al. (2021), used the SCvH95 (Saumon et al. 1995) EOS tables for modeling hydrogen and helium.”

“The hybrid cloud grid from Saumon & Marley (2008) was used to calculate the mass limits accessible with the given contrast in Figure 6, as this model incorporates deuterium burning.”

“The Brewster forward model uses the two-stream radiative transfer technique of Toon et al. (1989), including scattering, as first introduced by McKay et al. (1989) and subsequently used by Marley et al. (1996); Saumon & Marley (2008); Morley et al. (2012).”

“Overall, there is minimal variation between the predictions of these models, with the single exception of the Saumon and Marley (2008) hybrid model which predicts significantly older ages for both components ( ∼ 650 Myr for Luhman 16 B and ∼ 900 Myr for Luhman 16 A).”

“The shift from L to T spectral types may be accompanied by a change from small to large particles, leading to the fragmentation of clouds and a transition to cloud-free atmospheres (Burningham et al., 2017; Saumon and Marley, 2008).”

“…clouds has been proposed to explain both the reddening of L-dwarf spectra as BDs cool across their lifetimes and the transition starting at ∼1300 K to relatively cloud-free and blue mid-to-late T-dwarf spectra (Tsuji et al. 1996b; Ackerman & Marley 2001; Allard et al. 2001; Saumon & Marley 2008).”

“Using the temperature range from the MCMC (1686–1908 K) and assuming an age range of 5–45Myr, we infer a mass range between 7 and 21MJup, estimated using the minimum and maximum ranges of the evolutionary models of Burrows et al. (2001), Baraffe et al. (2003, 2015), and Saumon & Marley (2008).”

“The isochrones of Saumon & Marley (2008) combined with synthetic photometry from Saumon et al. (2012) predict IRAC photometry as a function of temperature and system age.”

“The coldest brown dwarfs modeled by Saumon & Marley (2008) and Saumon et al. (2012) (∼ 200 K) have M4.”

“…MARCS: Gustafsson et al. 2008; PHOENIX: Hauschildt, Baron & Allard 1997, Allard et al. 2001, Dehn 2007, Helling et al. 2008, Witte et al. 2009, Rice et al. 2010; Tsuji 2005; Ackerman & Marley 2001, Saumon & Marley 2008; Burrows et al. 2001) are used to inferTeff , log g and element abundances.”

“Atmospheric modeling with BT-Settl (Allard et al. 2013) predict SIMP 0136 to be 0.82 R Jup , while evolutionary model SM08 (Saumon & Marley 2008) given the age estimation provides 1.22 R Jup (Gagn´e et al. 2017).”

“K diagram with respect to the field by about 0.5–1 mag (K), as expected for its youth: although at a slower pace than at much younger ages, Pleiades brown dwarfs and planetary-mass objects are still collapsing under their own gravity (Burrows et al. 1993; Baraffe et al. 2002; Saumon & Marley 2008).”

“In the cloudy case (right panel), the behavior of the mass tracks matches the expectation as seen in the comparison between cloud-free and cloudy models in Saumon & Marley (2008).”

“We estimated a radius using the best age approximation and the solar metallicity, hybrid cloud evolutionary model isochrones from Saumon & Marley (2008).”

“5) is already low for a high-gravity planet like HAT-P-2 (Saumon & Marley 2008; Gao et al. 2018).”

“These free-floating planets have lower observed surface gravity than field brown dwarfs and (based on their ages and temperatures) are predicted to have masses below the deuterium-burning limit by theoretical models Saumon & Marley (2008).”

“Several ideas have been suggested to ex- plain this observed property, namely the effect of a single second parameter like gravity [Burrows et al (2006)] or a mixture of effects, namely metallicity, cloud parameters, ages and unresolved binaries [Saumon and Marley (2008)].”

“If its color (F200W − F444W) and absolute magnitude in F444W follow the trend characteristic of observed giant planets (Saumon & Marley 2008; Phillips et al. 2020), the candidate qualifies for further inspection.”

“The Sonora Diamondback model grid (DBack; Morley et al. 2024) is based on the radiative-convective equilibrium framework described in McKay et al. (1989) and Saumon & Marley (2008), and assumes radiative–convective and chemical equilibrium throughout the atmosphere.”

“One-dimensional, static models of brown dwarfs and directly imaged planets have been remarkably successful (e.g Saumon & Marley 2008; Phillips et al. 2020; Marley et al. 2021) and enable major advances in our understanding of the fundamental physical and chemical processes that shape these…”

“Schneider et al. (2022) used the evolutionary models of Saumon & Marley (2008) and Phillips et al. (2020) to estimate the masses of newly discovered objects.”

“Saumon & Marley (2008) is our only model that incorporates the effects of dust during the L-T transition, seen as atmospheric cloud cover at the spectral type transition (Burrows et al. 2006).”

“Metallicity, one of the fundamental parameters that contribute to the physical properties of stars, is expected to also affect the photometry of ultracool dwarfs ( Burrows et al. 2001; Fortney et al. 2008; Saumon & Marley 2008; Marley et al. 2021 ) .”

“Using radiative-transfer models, we can provide an interpretation of the heterogeneous cloud layers that are introducing the variability measured, at each pressure level (Saumon & Marley 2008).”

“We have examined other cooling models (Burrows et al. 2001; Baraffe et al. 2003; Saumon & Marley 2008; Marley & Saumon 2020; Phillips et al. 2020, but see Appendix C for more details), and find results similar to those presented below, but over a narrower range of observed parameters.”

“…grid of pressure-temperature (P-T) profiles (e.g., Marley et al. 2021; JensenClem et al. 2020; Marley & Sengupta 2011; Sengupta & Marley 2010, 2009; Saumon & Marley 2008; Marley et al. 2002; Ackerman & Marley 2001) calculated for the atmospheres of the substellar mass objects by using…”

“Ultracool objects cool over time, becoming fainter as they age (e.g., Saumon & Marley 2008).”

“The third model we apply is the 2008 hybrid model from Saumon & Marley (2008) (hereafter SM08).”

“…suffer from large uncertainties in the assumptions for the atmosphere of the companions ( clouds, molecular opacities; e.g., Baraffe et al. 2003; Saumon & Marley 2008 ) and for the accretion process ( post-formation luminosity, which sets up the initial condition for the subsequent thermal…”

“A model from Saumon & Marley (2008) and Marley et al. (2010) proposes the sinking of parts of the cloud deck, creating thinner, patchy clouds as an explanation for the change in variability patterns around the L/T transition.”

“2 Age and mass constraints for the tight spectral binary 2MASS J0320-0446AB, based on component spectral types (curved solid and dotted lines), RV orbit (dashed line) and evolutionary models from Saumon & Marley (2008).”

“…a high initial entropy (“hot-start”) configuration and compute cooling tracks using both (i) a standard adiabatic interior model (Fortney et al. 2007; Saumon & Marley 2008; Marley et al. 2021) (for com-Atmosphere parison with existing literature) and (ii) a composition-dependent model (e.g.…”