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APPENDIX
A. ATMO2020++ MODELS: ADDITIONAL INFORMATION
The ATMO2020++ models include rainout of condensates which depletes refractory species, but
they do not include clouds. The chemistry includes 277 species, and out-of-equilibrium chemistry
was performed using the model of Tsai et al. (2017).
In the Leggett et al. (2021) study of the SEDs of seven brown dwarfs, values of 1.2 ≤ γ ≤ 1.33
were found for the upper-atmosphere adiabat. Values of 7 ≤ P(γ,max) bar ≤ 15 were found for
the pressure of the layer below which the adiabat increases to the standard value (around 1.4 for a
diatomic gas). Exceptions were the late-T dwarf where P(γ,max) was undefined, and the extremely
cold 260 K dwarf, where P(γ,max) = 50 bar. Interestingly, for the Y dwarfs the values of T at
P(γ,max) are all ∼ 800 K, a temperature where the nitrogen chemistry is changing and chlorides
and sulfides are condensing, processes which may disrupt convection.
The larger grid of Meisner et al. (2023) generalized the atmospheric parameters in the following
ways:
• The levels with a modified adiabat are between 0.15 and 15 bars at log g = 4.5 and are scaled
by ×10log(g)−4.5 at other surface gravities. For these layers a value of γ = 1.25 is adopted.
Higher and lower layers use the standard adiabat for that layer, typically a value around 1.4
(the ratio of specific heats for the gas at that layer).
• Out-of-equilibrium chemistry is used with K = 105 cm2 s−1 at log g = 5.0 which is scaled by
zz
×102(5−log(g)) at other surface gravities.
• The mixing length is assumed to be 2 scale heights at 1.5 bars, and higher pressures, at log
g = 4.5, and is scaled down by the ratio between the local pressure and the pressure at 1.5 bars
for lower pressures. The 1.5 bars limit is scaled by ×10log(g)−4.5 at other surface gravities.
The ATMO2020++ synthetic Y dwarf SEDs are similar to those calculated by the earlier Leggett
et al. (2021) models, except at YJH (1.0 ≤ λ µm ≤ 1.5) where the ATMO2020++ flux is smaller by
∼ 0.5 magnitudes. We trace this to the parametrization of the mixing length, which leads to stronger
convective fluxes that reduce the temperatures in the deep atmosphere, where the near-infrared flux
originates. The agreement with observations of T and Y dwarfs remains good, as can be seen in
Figures 2 and 3 of Meisner et al. (2023), and Section 3 of this work.
B. COMPARISON TO BT-SETTL AND LACY & BURROWS SYNTHETIC SPECTRA
Figure 4 compares the observed spectrum for WISE 0359 to synthetic spectra generated by BT-
Settl (Allard 2014, 2016) and Lacy & Burrows (2023) model atmospheres. These models produce an
inferior fit compared to the Sonora suite and ATMO2020++ (Figure 1), at these temperatures.
C. COLOR TRANSFORMATIONS
Figures 5 and 6 show relationships between JWST colors and those of ground based, Spitzer and
WISE. These have been calculated using the ATMO2020++ models. Table 3 gives polynomial
relationships between the colors.