Irradiation-driven escape of primordial planetary atmospheres II. Evaporation efficiency of sub-Neptunes through hot Jupiters

TL;DR

This study uses hydrodynamic simulations to analyze how planetary gravity and stellar XUV irradiation influence atmospheric evaporation efficiency in gaseous exoplanets, identifying a threshold potential energy that limits energy-limited escape.

Contribution

It introduces an analytical framework to predict evaporation efficiency based on planetary potential and stellar irradiation, extending understanding of atmospheric escape mechanisms.

Findings

Existence of a potential energy threshold for energy-limited escape.

Evaporation efficiency drops sharply above this threshold.

For low-gravity planets, efficiency decreases with increasing stellar irradiation.

Abstract

Making use of the publicly available 1D photoionization hydrodynamics code ATES we set out to investigate the combined effects of planetary gravitational potential energy ($\phi_p\equiv GM_p/R_p$) and stellar X-ray and Extreme Ultraviolet (XUV) irradiation ($F_{\rm XUV}$) on the evaporation efficiency ($\eta$) of moderately-to-highly irradiated gaseous planets, from sub-Neptunes through hot Jupiters. We show that the (known) existence of a threshold potential above which energy-limited escape (i.e., $\eta\simeq 1$) is unattainable can be inferred analytically. For $\log \phi_p\gtrsim \log \phi_p^{\rm thr}\approx [12.9-13.2]$ (in cgs units), most of the energy absorption occurs where the average kinetic energy acquired by the ions through photo-electron collisions is insufficient for escape. This causes the evaporation efficiency to plummet with increasing $\phi_p$,. Whether or not planets with $\phi_p\lesssim \phi_p^{\rm thr}$ exhibit energy-limited outflows is regulated primarily by the stellar irradiation level. Specifically, for low-gravity planets, above $F_{\rm XUV}\simeq 10^{4-5}$ erg cm$^{-2}$s$^{-1}$ Ly$\alpha$ losses overtake adiabatic and advective cooling and the evaporation efficiency of low-gravity planets drops below the energy-limited approximation, albeit remaining largely independent of $\phi_p$Further, we show that whereas $\eta$ increases as $F_{\rm XUV}$ increases for planets above $\phi^{\rm thr}_p$, the opposite is true for low-gravity planets. This behavior can be understood by examining the relative fractional contributions of advective and radiative losses as a function of atmospheric temperature. This novel framework enables a reliable, physically motivated prediction of the expected evaporation efficiency for a given planetary system; an analytical approximation of the best-fitting $\eta$ is given in the appendix.