Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation

TL;DR

This study provides an ab initio equation of state for hydrogen-helium mixtures, improving the understanding of giant planet interiors and revising the mass-radius relation, especially for hot, Jupiter-mass exoplanets.

Contribution

It introduces a comprehensive ab initio EOS table for hydrogen-helium mixtures and revises the giant planet mass-radius relationship based on these results.

Findings

Revised mass-radius relation increases hot exoplanet radii by ~0.2 Jupiter radii.

Ab initio EOS shows deviations from semi-analytical models, especially for Jupiter-mass planets.

Implications for understanding inflated giant exoplanets.

Abstract

Using density functional molecular dynamics simulations, we determine the equation of state for hydrogen-helium mixtures spanning density-temperature conditions typical of giant planet interiors, ~0.2-9 g/cc and 1000-80000 K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy using an ab initio thermodynamic integration technique. A comprehensive equation of state (EOS) table with 391 density-temperature points is constructed and the results are presented in form of two-dimensional free energy fit for interpolation. Deviations between our ab initio EOS and the semi-analytical EOS model by Saumon and Chabrier are analyzed in detail, and we use the results for initial revision of the inferred thermal state of giant planets with known values for mass and radius. Changes are most pronounced for planets in the Jupiter mass range and below. We present a revision to the mass-radius relationship which makes the hottest exoplanets increase in radius by ~0.2 Jupiter radii at fixed entropy and for masses greater than ~0.5 Jupiter mass. This change is large enough to have possible implications for some discrepant "inflated giant exoplanets".