Giant Planet Evolution with MESA

TL;DR

This work addresses the need for public, flexible giant-planet evolution tools by modifying the open-source MESA code to model planetary interiors and atmospheres. It introduces a planetary EoS built from hydrogen–helium mixtures and heavy elements using a linear mixing approach, implemented via the Python tinyeos module and 66 composition tables, with support for bases $(\log \rho, \log T)$ and $(\log p, \log T)$: $\rho^{-1}(p,T,\vec{X}) = \sum_i X_i \rho_i^{-1}(p,T)$. Opacity is extended to include grain, cloud, and opacity-window effects, while convective mixing is refined with gentle_mixing and convective_premixing enhancements, and helium rain/sedimentation is treated with multiple modes and phase-diagram guidance. The authors provide open-source code on GitHub to enable robust, extensible simulations of giant-planet evolution, with the aim of enabling deeper insights into planetary formation and interiors.

Abstract

The evolution of gaseous planets is a complex process influenced by various physical parameters and processes. In this study, we present critical modifications to the Modules for Experiments in Stellar Astrophysics (MESA) code to enhance its applicability to giant planet modelling. We introduce an equation of state specifically tailored for materials at planetary conditions. The equation of state considers the thermodynamic properties of hydrogen-helium mixtures and heavy elements, improving the accuracy of internal structure calculations. We also present modifications to the radiative opacity to allow the modelling of grains, clouds and opacity windows. Furthermore, we refine the treatment of convective mixing processes in MESA to better replicate convective mixing with the presence of composition gradients. Finally, we add a treatment for helium rain and settling. These modifications aim to enhance the predictive capabilities of MESA for giant planet evolution and are publicly available. We hope that these improvements will lead to a deeper understanding of giant planet evolution in the solar system and beyond.

Figures (9)

• Figure 1: Time evolution of two homogeneous planets in the $(\log \rho, \log T)$ space with $Z = 0.012$ (dash-dotted purple lines) and $Z = 0.20$ (solid red lines) for times between 1 Myr and 4.5 Gyr. More transparent lines correspond to earlier times. The contours show the entropy, and the dashed black lines show the boundaries of the EoS.
• Figure 2: Time evolution of two homogeneous planets in the $(\log p, \log T)$ space with $Z = 0.012$ (dash-dotted purple lines) and $Z = 0.20$ (solid red lines) for times between 1 Myr and 4.5 Gyr. More transparent lines correspond to earlier times. The contours show the difference in density for the two compositions, and the dashed black lines show the boundaries of the EoS.
• Figure 3: Opacity profile of a $M = 1{\rm{M_J}}$ planet with $T_\textrm{eq} = 200$ K at about 4.5 Gyr. The pressure-temperature conditions were from the baseline model using the Freedman et al. opacity (blue line). The orange line includes grains with a scaling factor $f_\textrm{grains} = 0.1$. The effect of a single optically thick cloud deck at 10 bar with $\delta_c = 10$ and $\kappa_{\rm{clouds}, 0} = 1$ cm$^2$/g is shown in the green line. The dashed purple line illustrates how an opacity window could be created due to a lack of alkali metals.
• Figure 4: Sketch of the gentle_mixing algorithm. Rather than transitioning directly from the initial to the final heavy-element profile, the algorithm inserts several intermediate steps. The inset in the top right corner shows how the damping of mixing efficiency is accompanied by a reduction in time step.
• Figure 5: Evolution of the composition profile for a 1 planet and an entropy of 8, starting from an extended composition profile (top) and a core-like structure (bottom).