Next-Generation Improvements in Giant Exoplanet Evolutionary and Structural Models

TL;DR

This work assesses how modern physics alters giant exoplanet evolution compared with legacy models. Using the APPLE code, it isolates and quantifies the impact of updated hydrogen–helium and heavy‑element equations of state, helium rain, fuzzy and non‑adiabatic envelopes, and ammonia cloud–inclusive atmospheric boundary conditions, validating against past models before constructing representative next‑generation evolutions for $0.3$–$4\,M_{\rm J}$. It finds that adopting modern EOSs and metal distributions shifts radii by roughly $5$–$10\%$, while helium rain and convection treatment can modify cooling histories and atmospheric compositions by $\sim5$–$20\%$, with heavier effects at lower masses. The results underscore the necessity of incorporating these processes into future exoplanet models for physically consistent interpretation of observations, while also identifying current limitations (e.g., semiconvection treatment, ternary EOS) and outlining directions for a comprehensive model suite.

Abstract

We present a comprehensive comparison between legacy and modern evolutionary models for giant exoplanets, using our planetary evolution code, APPLE, to emulate and extend previous studies. Our analysis isolates and quantifies the impact of recent physical advances motivated by detailed modeling of Jupiter and Saturn, including updated hydrogen-helium and heavy-element equations of state, helium rain, "fuzzy" cores, and non-adiabatic, inhomogeneous envelopes, alongside improved atmospheric boundary conditions that incorporate ammonia cloud physics. We first examine the influence of each new physical ingredient individually, then construct combined baseline models for masses between 0.3 to 4 Jupiter masses to assess their collective effect on planetary structure and observable properties. We find that the adoption of modern equations of state and realistic heavy-element distributions leads to systematic, but sometimes subtle, differences (~5 to 10%) in radius evolution, while helium rain and the treatment of convection can significantly alter thermal histories and atmospheric compositions (by ~5 to 20%). These updated physical processes must be incorporated into the next-generation exoplanet evolutionary models to achieve physically consistent interpretations of planetary observations.

Figures (11)

• Figure 1: Reproduction of various heritage exoplanet evolutionary models (dashed black curves) using the model setups and inputs in those papers, as computed with APPLESur2024a (solid colored lines) for a range of planetary masses. Masses are indicated next to each line (in units of solar masses) and luminosities are in solar units. Unless explicitly stated otherwise, all models are adiabatic, have no solid core, neglect rotation, and neglect helium rain. Top left: Evolutionary sequences from Burrows1997. The envelope helium mass fraction is $Y = 0.25$, and the interior is modeled with the SCvH95 equation of state Saumon1995. Atmospheric boundary conditions are taken from the isolated, non-gray model atmosphere grids of Burrows1997. Top right: Evolutionary sequences computed using the irradiated atmospheric boundary tables of Fortney2011 for Jupiter- and Saturn-mass planets, assuming 3.16 $Z_{\odot}$ metallicity and the SCvH95 EOS for hydrogen-helium mixture. The Jupiter model includes a $10 \,M_{\oplus}$ core composed of iron and post-perovskite, with an envelope heavy-element mass fraction $Z = 0.059$ and using the AQUA EOS Haldemann2020. The Saturn model assumes a $21 M_{\oplus}$ core with an envelope $Z = 0.03$. Bottom left: Models from Phillips2020, which extend the earlier Baraffe2003 evolutionary calculations. In APPLE, we implement the ATMO atmospheric grids from Phillips2020 together with the CMS19 H–He EOS Chabrier2019, adopting as they did an effective helium fraction $Y^{\prime} = Y + Z = 0.2919$ to approximate a mixture of helium and heavy elements. No dedicated heavy-element EOS is employed in these models. Bottom right: Models from the Sonora-Bobcat suite Marley2021 with [M/H]$=-0.5$ (corresponding to $Z=0.00484$), which also treat the interior with the SCvH95 H–He EOS, using an effective $Y^{\prime} = Y + Z = 0.27834$ (with $Y=0.2735$) to approximate the contribution of heavy elements (as did they) and their published atmosphere boundary conditions.
• Figure 2: Comparison of adiabatic evolution models of giant planets with different treatments of heavy elements: solid lines correspond to models where heavy elements in the envelope are treated with the AQUA EOS Haldemann2020, while dashed lines represent models in which the effect of heavy elements is not modeled with a dedicated $Z$ EOS, but is instead approximated by an effective helium fraction $Y^{\prime} = Y + Z = 0.27834$ (as has traditionally been done). The top panel shows the evolution of the effective temperatures and radii, while the bottom panel shows the temperature profiles at 1 and 5 Gyr, respectively. All calculations use the Sonora Bobcat atmospheric boundary conditions Marley2021 with [M/H] $= +0.5$, and cover planetary masses ranging from $0.3$ to $4\,M_{\rm Jup}$. The helium mass fraction in the envelope is fixed at $Y = 0.3219$, treated with the SCvH95 EOS. All models assume coreless, non-rotating planets. For the various masses, the median relative errors range from $\sim 0.6\%$ to $0.75\%$ for $T_{\rm eff}$, $\sim 0.3\%$ to $0.5\%$ for the radii, and $\sim 4.5$ to $7\%$ for the temperature profiles.
• Figure 3: Evolution of giant planets comparing models where (i) metals are uniformly mixed throughout the envelope without a compact core and (ii) all metals are concentrated entirely in the core. The bulk metallicity for all the models is 3.16 $Z_\odot$ ($Z = 0.0484$). This corresponds to 4.61, 15.38, 30.76, 76.9 M$_\oplus$ for the 0.3, 1, 2, and 5 M$_{\rm Jup}$ models, respectively. All calculations adopt the Sonora Bobcat atmospheric boundary conditions Marley2021. The helium mass fraction in the envelope is fixed at $Y = 0.2735$ and treated with the SCvH95 EOS, while heavy elements are represented by the AQUA EOS in both the core and the envelope. Assuming that the same heavy elements reside in the core versus in the envelope results in a difference of $\sim 0.9$ to 1.3% in the radius for all times. This suggests that, contrary to the common simplifying assumption of radius being independent of the heavy-element distribution at fixed mass fraction, modest but systematic differences can arise even in adiabatic models. The median relative errors for $T_{\rm eff}$ range from $0.12\%$ for 0.3 M$_{\rm Jup}$ to $5\%$ for 5% M$_{\rm Jup}$ over 5 Gyr.
• Figure 4: Adiabatic evolution of giant planets, comparing two hydrogen–helium equations of state: the old SCvH95 Saumon1995 and the latest CD21 Chabrier2021 using atmospheric boundary conditions from the Sonora Bobcat grids. The left panel shows the evolution of effective temperature, while the right panel shows the evolution of planetary radius, for masses ranging from $0.3$ to $4\,M_{\rm Jup}$. All models are isolated, nonrotating, and coreless, with an envelope metallicity of $[{\rm M/H}] = -0.5$ ($Z=0.00484$) and a helium mass fraction fixed at $Y = 0.2735$. The contribution of heavy elements is not modeled with a dedicated EOS, but is instead approximated by adopting an effective helium fraction $Y^{\prime} = Y + Z = 0.27834$, following the approach of Marley2021. The median relative errors over 10 Gyr between the two EOSs for $T_{\rm eff}$ range from $1.9\%$ for 0.3 M$_{\rm Jup}$ to $0.6\%$ for 4 M$_{\rm Jup}$. The effect of the modern EOS on radius is more pronounced, increasing from $\sim 0.6\%$ at higher masses to $\sim 6.7\%$ at lower masses.
• Figure 5: Adiabatic evolution of giant planets comparing three atmospheric boundary conditions: Chen2023, Marley2021, and Burrows1997. Models are shown for planetary masses ranging from $0.3$ to $4\,M_{\rm Jup}$. All calculations assume coreless planets with homogeneous and adiabatic hydrogen–helium envelopes mixed with heavy-element ices, treated using the AQUA EOS. The helium mass fraction in the envelope is fixed at $Y = 0.2735$, modeled using the CD21 EOS, and an atmospheric metallicity of $3.16$$Z_{\odot}$ is adopted and taken as homogeneous throughout the structure for all models. At late times, the effective temperature differences among the various atmospheric boundary conditions range from about $7\%$ for lower-mass planets to $\sim 3\%$ for higher-mass cases. The corresponding radii differ by approximately $3$ to $6\%$ at late times, while at early times the discrepancies can be significantly larger. Note that at early times, the issue of the proper initial thermal profiles inherited from the formation is of primary relevance.