3
spectra generated by other model grids (BT-Settl (Allard 2014, 2016) and Lacy & Burrows (2023)),
for reference. Appendix C provides transformations between ground-based near-infrared, Spitzer
(Werner et al. 2004), and Wide-field Infrared Survey Explorer (WISE, Wright et al. 2010) colors and
JWST colors.
2. PRESSURE-TEMPERATURE PROFILES AND THE ATMO2020++ MODELS
One-dimensional models, such as the ATMO and Sonora models, represent the atmosphere as a
pressure (P) - temperature (T) profile that maps the cooling from the core out to the surface, and
by a chemical abundance profile that maps the chemical changes that occur through the atmosphere
as P and T change. The P - T profile can be thought of as a slice through the atmosphere, where
both temperature and pressure decrease with increasing altitude. Energy transport in a cool dwarf
atmosphere is predominantly convective, with radiative cooling becoming important high in the
atmosphere where the pressure is too low for convection to be efficient. Convection is treated as an
adiabatic process where P(1−γ)Tγ = constant. For an ideal gas, γ is the ratio of specific heats at
constant pressure and volume and, for a gas composed entirely of molecular hydrogen, γ = 1.4 (see
Marley & Robinson 2015; Zhang 2020, for reviews of atmospheric processes).
However isolated brown dwarfs rotate rapidly, with periods of a few hours, as demonstrated by
rotational line broadening (e.g. Hsu et al. 2021) and inferred from observed variability (e.g. Metchev
et al. 2015; Miles-Pa´ez et al. 2017; Tannock et al. 2021), and rotation strongly modulates the heat
transport from the interior of the brown dwarf. Three-dimensional simulations of turbulent, convec-
tive, rotating atmospheres produce vertical velocities consistent with observed chemical mixing, and
surface features consistent with observed variability (Showman & Kaspi 2013). Simulations also show
that rotation dramatically changes the P - T profile. For example, Tan & Showman (2021) explore
the profile of a brown dwarf atmosphere with and without rotation, and find that the rotating cloud-
free atmosphere is significantly cooler in the lower atmosphere, and has an almost isothermal upper
atmosphere (their Figure 4). The three-dimensional models also show that the surface of rotating
brown dwarfs varies with latitude (Showman et al. 2019), suggesting that the observed properties of
brown dwarfs are dependent on both rotational speed and axis inclination (Lipatov et al. 2022).
The turbulent convective atmospheres of brown dwarfs are also likely to be subject to diabatic
processes, as described by Tremblin et al. (2019) (see also Tan & Showman 2017). These could
include compositional changes of carbon and nitrogen bearing molecules (CO/CH , N /NH ), and
4 2 3
condensation of the alkalis, chlorides and sulfides (e.g. Morley et al. 2012, 2014).
In Leggett et al. (2021) we used the ATMO2020 disequilibrium models (Phillips et al. 2020) as a
starting point, and treated the adiabatic parameter γ as a variable, along with T , surface gravity
eff
g, metallicity [m/H], and the diffusion coefficient K which characterizes the transport of gas and
zz
resulting disequilibrium chemistry. The adiabat parameter γ was set to the standard value (i.e.
≈ 1.4) at a depth in the atmosphere defined by pressure P(γ,max) bar, and deeper, and reduced to a
constant, smaller, value higher in the atmosphere. This approach was tested against the SEDs of one
late-T dwarf and six Y dwarfs. By tuning T , g, [m/H], K , γ, and P(γ,max) for each brown dwarf,
eff zz
good fits across the entire SED were obtained. A limited grid of models with K = 107 cm2 s−1,
zz
γ = 1.25, and P(γ,max) = 15 bar was generated, which demonstrated significant and comprehensive
improvements in the agreement between modeled and observed colors for a large sample of late-T
and Y dwarfs.