The Effect of Adiabatic Index on Radius Evolution and the Mass Loss

Abstract

Models that track the size evolution of exoplanets often assume a prescribed initial thermal state or a single adiabatic index to describe the planetary interior structure, the latter of which is taken to be $γ\sim1.4$ which is likely appropriate for evolved planets ($\gtrsim$1 Gyr). Extrapolating this high $γ$ to earlier ages (down to $\sim$million years old) is problematic since, according to thermodynamics, the adiabatic index of young planets is $\sim$1.2, which is low enough to drastically change how interior mass is distributed. We quantify the effect of varying the adiabatic index from 1.2 to 1.4 on the expected radius of the exoplanet over time. We find that envelopes of larger adiabatic indices start puffier with all else equal and undergo faster radius contraction with accelerated mass loss. Assumption of high $γ$ can therefore overestimate the effect of mass loss in shaping the exoplanetary population, especially when young planets are considered. We highlight the need for a more careful consideration of the initial thermal condition of planets in evolutionary models to properly interpret the radii measurements of exoplanets.