Energy-limited escape revised

TL;DR

This study revises the energy-limited escape model for planetary atmospheres, showing its validity depends on planetary gravity, and provides new scaling laws for better mass-loss rate estimates across different planet types.

Contribution

The paper introduces revised scaling laws for energy-limited escape, accounting for planetary gravity and irradiation, improving mass-loss rate estimates for diverse exoplanets.

Findings

Energy-limited escape is valid only for planets with low gravitational potential.

Massive planets re-emit absorbed energy through hydrogen Lyα and free-free emission.

Scaling laws depend on gravitational potential and irradiation, refining mass-loss estimates.

Abstract

Gas planets in close proximity to their host stars experience photoevaporative mass loss. The energy-limited escape concept is generally used to derive estimates for the planetary mass-loss rates. Our photoionization hydrodynamics simulations of the thermospheres of hot gas planets show that the energy-limited escape concept is valid only for planets with a gravitational potential lower than $\log_\mathrm{10}\left( -\Phi_{\mathrm{G}}\right) < 13.11~$erg$\,$g$^{-1}$ because in these planets the radiative energy input is efficiently used to drive the planetary wind. Massive and compact planets with $\log_\mathrm{10}\left( -\Phi_{\mathrm{G}}\right) \gtrsim 13.6~$erg$\,$g$^{-1}$ exhibit more tightly bound atmospheres in which the complete radiative energy input is re-emitted through hydrogen Ly$\alpha$ and free-free emission. These planets therefore host hydrodynamically stable thermospheres. Between these two extremes the strength of the planetary winds rapidly declines as a result of a decreasing heating efficiency. Small planets undergo enhanced evaporation because they host expanded atmospheres that expose a larger surface to the stellar irradiation. We present scaling laws for the heating efficiency and the expansion radius that depend on the gravitational potential and irradiation level of the planet. The resulting revised energy-limited escape concept can be used to derive estimates for the mass-loss rates of super-Earth-sized planets as well as massive hot Jupiters with hydrogen-dominated atmospheres.