Resizing the giants: How modelling adiabatic interiors impacts predicted planetary radii

TL;DR

This study examines how different numerical methods for calculating adiabatic temperature gradients affect the inferred structure and radii of giant planets, revealing significant deviations that impact current measurement precision.

Contribution

It systematically compares numerical approaches for adiabatic gradient calculation, recommending best practices to improve planetary interior modeling accuracy.

Findings

Choice of numerical method significantly affects inferred planetary radius.

Using the logarithmic temperature equation can cause deviations exceeding 3%.

Spline derivatives with the non-logarithmic equation minimize errors below 1%.

Abstract

The interiors of giant planets are commonly assumed to be convective and adiabatic, making the adiabatic temperature gradient a key ingredient in interior and evolution models. Multiple numerically distinct methods exist for computing this gradient, yet their impact on inferred planetary structure and radius has not been systematically assessed. We investigate how the numerical treatment of adiabatic temperature profiles affects inferred planetary radii and internal structure, comparing different methods for evaluating the adiabatic gradient against a ground-truth isentropic baseline, for both the logarithmic and non-logarithmic forms of the temperature differential equation. Static interior models of a one Jupiter mass planet were computed using a state-of-the-art hydrogen-helium equation of state. The choice of numerical method significantly impacts the inferred interior structure and radius. Using the logarithmic temperature equation, central temperatures deviate by several thousand Kelvin and surface radii differ by up to 3.4%, exceeding the one-percent precision of current giant exoplanet radius measurements threefold. The non-logarithmic form reduces deviations to below about 1% for most methods. We recommend spline derivatives to evaluate the adiabatic gradient, combined with the non-logarithmic temperature equation. Finite differencing and direct use of tabulated gradients or derivatives should be avoided.