ATMO Evolutionary Models

• ATMO evolutionary models are coupled atmosphere–interior calculations that provide non-grey boundary conditions for cooling tracks of cool brown dwarfs and self-luminous giant exoplanets.
• They integrate a 1D radiative-convective ATMO code with the Lyon evolution solver, yielding predictions for luminosity, radius, and synthetic spectra across a detailed parameter grid.
• The framework features updated molecular opacities, multiple chemical branches, and a refined H–He equation of state to enhance accuracy and match benchmark objects.

Searching arXiv for recent and foundational papers on ATMO evolutionary models and closely related atmosphere–interior coupling work. {"query":"ATMO 2020 evolutionary models brown dwarfs giant exoplanets ATMO atmosphere evolutionary boundary conditions", "max_results": 10} ATMO evolutionary models are coupled atmosphere–interior calculations for substellar objects in which the 1D ATMO radiative-convective atmosphere code supplies non-grey surface boundary conditions to an interior evolution solver, yielding cooling tracks, radii, luminosities, gravities, and synthetic spectra for brown dwarfs and self-luminous giant exoplanets. In the literature, however, “ATMO” also denotes a broader atmospheric code family used in non-evolutionary forward spectroscopy, including hot-Jupiter transmission grids; that usage should be distinguished explicitly from thermal-evolution calculations (Phillips et al., 2020, Goyal et al., 2017).

1. Terminology and scope

The term “ATMO evolutionary models” properly refers to the coupled framework presented for cool T–Y brown dwarfs and self-luminous giant exoplanets, not to every application of the ATMO atmosphere code. In its broader atmospheric role, ATMO is a 1D radiative-convective equilibrium code that can solve hydrostatic structure, radiative transfer, equilibrium or non-equilibrium chemistry, and transmission spectra. That broader capability underlies a hot-Jupiter transmission library for 117 exoplanets, but that 2017 grid is explicitly a forward atmospheric spectroscopy product rather than a planetary evolution calculation (Goyal et al., 2017).

That distinction is technically important because the 2017 hot-Jupiter library uses isothermal $P$–$T$ profiles with equilibrium chemistry including condensation with rainout, whereas evolutionary ATMO models use self-consistent radiative-convective atmospheres as non-grey outer boundary conditions for interior cooling tracks. In other words, the former computes wavelength-dependent transit observables for fixed observed planets; the latter computes the secular evolution of luminosity, radius, and temperature for substellar objects as a function of mass and age (Goyal et al., 2017, Phillips et al., 2020).

2. Coupled atmosphere–interior architecture

The canonical ATMO evolutionary grid is ATMO 2020, which couples a grid of 1D atmosphere models from the ATMO radiative-convective equilibrium code to the Lyon interior/evolution code (Phillips et al., 2020). The atmosphere grid spans $T_{\mathrm{eff}}=200$–$3000\,\mathrm{K}$ and $\log(g)=2.5$–$5.5$ in cgs, with $100\,\mathrm{K}$ spacing for $T_{\mathrm{eff}}>600\,\mathrm{K}$, $50\,\mathrm{K}$ spacing for $T_{\mathrm{eff}}<600\,\mathrm{K}$, and $T$0 dex spacing in $T$1. The resulting evolutionary calculations cover masses from $T$2 to $T$3 and ages from $T$4 to $T$5 (Phillips et al., 2020).

In this framework, the atmosphere models provide the outer boundary condition to the interior structure equations, and the atmosphere and interior are matched at optical depth

$T$6

The atmospheric radial extension at that depth is taken to be negligible compared with the total radius, so the usual relation

$T$7

remains valid for the evolutionary tracks (Phillips et al., 2020). The atmosphere code itself is solved on a logarithmic optical-depth grid defined in the $T$8–$T$9 spectral region with 100 model levels, outer boundary pressure fixed at $T_{\mathrm{eff}}=200$0, and a Newton–Raphson iteration requiring flux balance and hydrostatic equilibrium to $T_{\mathrm{eff}}=200$1 in each level (Phillips et al., 2020).

A defining feature of ATMO 2020 is that it supplies three self-consistent atmospheric chemistry branches over the same thermal and gravity domain: one in thermodynamic chemical equilibrium and two with non-equilibrium chemistry due to vertical mixing. The atmosphere grid is then used both for evolutionary boundary conditions and for synthetic spectra and absolute magnitudes, so the coupling is not limited to a tabulated $T_{\mathrm{eff}}=200$2–$T_{\mathrm{eff}}=200$3 closure but extends to observational predictions (Phillips et al., 2020).

3. Physical ingredients and internal assumptions

ATMO 2020 introduced several updates relative to legacy AMES-Cond-like grids. The interior calculation replaces the older semi-analytic SCVH equation of state with the H–He EOS of Chabrier et al. (2019), which includes ab initio quantum molecular dynamics calculations in the pressure dissociation/ionization regime. In the published comparisons, this new EOS yields interiors up to $T_{\mathrm{eff}}=200$4 cooler and $T_{\mathrm{eff}}=200$5 denser in the core for a $T_{\mathrm{eff}}=200$6, 10 Gyr object, and raises the stellar-substellar boundary by $T_{\mathrm{eff}}=200$7-$T_{\mathrm{eff}}=200$8 in mass (Phillips et al., 2020).

The atmosphere physics was also substantially revised. ATMO 2020 uses updated molecular opacities, especially more complete line lists for $T_{\mathrm{eff}}=200$9, $3000\,\mathrm{K}$0, and $3000\,\mathrm{K}$1, improved $3000\,\mathrm{K}$2 and $3000\,\mathrm{K}$3 CIA, and an updated treatment of the collisionally broadened potassium resonance doublet based on Allard et al. (2016). These changes lead to warmer atmospheric temperature structures below $3000\,\mathrm{K}$4, modify cooling curves, and materially affect $3000\,\mathrm{K}$5-, $3000\,\mathrm{K}$6-, and $3000\,\mathrm{K}$7-band spectra (Phillips et al., 2020).

Chemically, the equilibrium branch uses Gibbs free-energy minimization with 76 gas-phase species, 92 condensates, and 23 elements, together with a rainout prescription. The two non-equilibrium branches use the chemical relaxation scheme of Tsai et al. (2018), solving explicit departures from equilibrium for $3000\,\mathrm{K}$8, CO, $3000\,\mathrm{K}$9, $\log(g)=2.5$0, $\log(g)=2.5$1, and $\log(g)=2.5$2. Vertical mixing is parameterized by a constant eddy diffusion coefficient $\log(g)=2.5$3 within each model atmosphere, scaled so that $\log(g)=2.5$4 changes by one order of magnitude for each 0.5 dex step in $\log(g)=2.5$5; the weak-mixing branch adopts $\log(g)=2.5$6 at $\log(g)=2.5$7, and the strong-mixing branch adopts $\log(g)=2.5$8 at $\log(g)=2.5$9 (Phillips et al., 2020).

The published grid is solar metallicity only. The adopted elemental composition follows Asplund et al. (2009) with C, N, O, P, S, K, and Fe revised using Caffau et al. (2011). The interior helium mass fraction is $5.5$0, and metals are represented in the EOS through the legacy approximation

$5.5$1

with $5.5$2 and $5.5$3 in order to remain consistent with earlier Lyon calculations (Phillips et al., 2020). This approximation later became a focus of criticism in next-generation boundary-condition work, because it conflates helium and heavy-element effects in the EOS (Chen et al., 12 Jun 2026).

4. Empirical tests and observational use

ATMO evolutionary models have been tested both directly and indirectly against benchmark brown dwarfs. In the eclipsing brown dwarf LHS 6343 C, ATMO-2020 atmospheric models with strong non-equilibrium chemistry yield the best fit to the observed HST/WFC3, Kepler, and Spitzer eclipse data across all modelled bandpasses, while the ATMO-2020 evolutionary grid gives an age of $5.5$4 from the measured mass and bolometric luminosity (Frost et al., 2024). In the same system, the semi-empirical luminosity and radius imply $5.5$5, while the ATMO-2020 evolutionary grid predicts $5.5$6, with radius and $5.5$7 likewise consistent with the independently measured values (Frost et al., 2024). This supports the internal consistency of the coupled ATMO atmosphere–evolution framework in the T-transition regime.

A related benchmark is WD 0806-66 B, where ATMO 2020++ is used as a forward atmospheric grid and then checked against separate Marley et al. evolutionary tracks. The preferred ATMO atmospheric solution has $5.5$8, $5.5$9, $100\,\mathrm{K}$0, and $100\,\mathrm{K}$1, while the independent luminosity-plus-age evolutionary inference gives $100\,\mathrm{K}$2, $100\,\mathrm{K}$3, $100\,\mathrm{K}$4, and $100\,\mathrm{K}$5 (Leggett et al., 2 Jun 2026). This is not an ATMO evolutionary track in the strict code-lineage sense, but it is an important validation of ATMO atmospheric inferences against benchmark substellar evolution.

Large-sample atmosphere–evolution comparisons have also clarified where ATMO should and should not be used as an evolutionary reference. In the Hawaii Infrared Parallax Program study of 1054 ultracool dwarfs, ATMO 2020 is used only as an atmospheric fitting grid, while evolutionary parameters are inferred from BHAC15 and SM08 rather than ATMO evolution. In that comparison, ATMO 2020 tends to overestimate temperatures by about 100–200 K for T dwarfs, whereas the greatest atmosphere-versus-evolution discrepancies overall occur at the M/L transition and are driven mainly by BT-Settl (Sanghi et al., 2023). This reinforces the point that ATMO 2020 is most mature in the cool cloud-free T/Y regime for which it was designed (Sanghi et al., 2023, Phillips et al., 2020).

5. Boundary-condition generalizations and next-generation extensions

A broader literature has recast the ATMO evolutionary problem as one of atmosphere-informed outer boundary conditions, often with different atmospheric solvers but conceptually similar coupling. For Jupiter and Jupiter-like planets, updated atmospheric tables from CoolTLusty provide the specific entropy at the base of the atmosphere’s radiative zone, together with $100\,\mathrm{K}$6 and $100\,\mathrm{K}$7, for use in post-formation cooling calculations. In that framework, the evolution code interpolates atmospheric results to close the planetary structure problem, and the fiducial Jupiter calibration with $100\,\mathrm{K}$8, $100\,\mathrm{K}$9, $T_{\mathrm{eff}}>600\,\mathrm{K}$0, and $T_{\mathrm{eff}}>600\,\mathrm{K}$1 reproduces present-day Jupiter within about 2% in brightness temperature/radius (Chen et al., 2023). Although this is not the ATMO code, it addresses the same atmosphere–interior boundary-condition problem.

The next major extension is compositional. A 2026 giant-planet atmosphere grid built with CoolTLusty introduces a four-dimensional boundary-condition relation

$T_{\mathrm{eff}}>600\,\mathrm{K}$2

with 972 cloudless, isolated, equilibrium-chemistry atmosphere models over $T_{\mathrm{eff}}>600\,\mathrm{K}$3, $T_{\mathrm{eff}}>600\,\mathrm{K}$4, $T_{\mathrm{eff}}>600\,\mathrm{K}$5, and $T_{\mathrm{eff}}>600\,\mathrm{K}$6 (Chen et al., 12 Jun 2026). The central conceptual change is that $T_{\mathrm{eff}}>600\,\mathrm{K}$7 and $T_{\mathrm{eff}}>600\,\mathrm{K}$8 are varied independently in the EOS rather than being combined through the legacy approximation $T_{\mathrm{eff}}>600\,\mathrm{K}$9. In the published non-adiabatic 1-$50\,\mathrm{K}$0 example with fuzzy-core mixing and helium rain, on-the-fly interpolation in $50\,\mathrm{K}$1 and $50\,\mathrm{K}$2 causes helium rain to begin earlier by $50\,\mathrm{K}$3 Gyr and produces stronger atmospheric helium depletion than fixed-composition boundary conditions (Chen et al., 12 Jun 2026). This suggests that future ATMO-style evolutionary models need composition-aware atmospheric interpolation if the envelope composition evolves.

The APPLE comparison study extends the same point to giant-exoplanet structure more generally. It explicitly emulates Phillips et al. (2020) ATMO-grid-based models and then shows that atmospheric boundary conditions alone can shift late-time $50\,\mathrm{K}$4 by about $50\,\mathrm{K}$5–$50\,\mathrm{K}$6 and radius by about $50\,\mathrm{K}$7–$50\,\mathrm{K}$8, while updated H/He EOS, explicit heavy-element EOS, helium rain, fuzzy cores, and non-adiabatic composition gradients can introduce additional changes of comparable or greater magnitude (Sur et al., 9 Oct 2025). In that sense, ATMO evolutionary models remain central, but atmosphere-grid sophistication is only one part of a broader modernization of giant-planet cooling calculations (Sur et al., 9 Oct 2025).

6. Limitations, misconceptions, and present status

Several recurring misconceptions surround ATMO evolutionary models. The first is terminological: the public ATMO hot-Jupiter transmission library is not an evolutionary model. It computes forward transmission spectra for fixed observed planets using isothermal $50\,\mathrm{K}$9–$T_{\mathrm{eff}}<600\,\mathrm{K}$0 profiles and equilibrium chemistry with rainout, and its relevance to “evolution” is only indirect through atmospheric composition and formation-history inference (Goyal et al., 2017).

The second is domain of validity. ATMO 2020 is explicitly targeted at very cool brown dwarfs and self-luminous giant exoplanets, and its stated range of validity is only up to about $T_{\mathrm{eff}}<600\,\mathrm{K}$1, even though the atmosphere grid extends to $T_{\mathrm{eff}}<600\,\mathrm{K}$2 for evolutionary continuity (Phillips et al., 2020). It is solar metallicity only, cloud-free in radiative transfer, and its non-equilibrium chemistry is limited to a small set of C–N–O species under a simple constant-$T_{\mathrm{eff}}<600\,\mathrm{K}$3 prescription (Phillips et al., 2020). It is therefore not a general-purpose solution for cloudy L dwarfs, irradiated gas giants, or non-solar metallicity populations.

The third limitation concerns composition and EOS consistency. The approximation $T_{\mathrm{eff}}<600\,\mathrm{K}$4 used in ATMO 2020 and related legacy grids is now regarded as thermodynamically inconsistent when helium rain or envelope metallicity evolution is modelled explicitly. Closely related next-generation work argues that helium and heavy elements should affect the atmospheric entropy boundary separately, because helium depletion and metal enrichment are not interchangeable processes in coupled evolution (Chen et al., 12 Jun 2026). A plausible implication is that future ATMO evolutionary grids will need explicit $T_{\mathrm{eff}}<600\,\mathrm{K}$5–$T_{\mathrm{eff}}<600\,\mathrm{K}$6 dimensionality rather than a single effective-helium proxy.

The present status of ATMO evolutionary modelling is therefore twofold. As a mature published framework, ATMO 2020 remains a modern replacement for AMES-Cond-like cloud-free cooling tracks in the cool T–Y and self-luminous giant-planet regime (Phillips et al., 2020). As an evolving methodology, however, it now sits within a larger atmosphere–interior coupling program that emphasizes composition-aware boundary conditions, improved heavy-element thermodynamics, helium rain, and non-adiabatic inhomogeneous interiors (Sur et al., 9 Oct 2025, Chen et al., 12 Jun 2026). This suggests that the long-term significance of ATMO evolutionary models lies not only in the published 2020 grid, but also in the boundary-condition philosophy that links detailed atmospheres to substellar thermal evolution.