Overcoming the limitations of the energy-limited approximation for planet atmospheric escape

TL;DR

This paper develops an improved analytical model for planetary atmospheric mass-loss rates, based on a large grid of hydrodynamic simulations, surpassing the accuracy of the traditional energy-limited approximation.

Contribution

It introduces a new analytical formula derived from extensive hydrodynamic models, enhancing the accuracy of atmospheric escape estimates for diverse exoplanets.

Findings

The new formula significantly outperforms the energy-limited approximation.

It covers a wide parameter space including planetary and stellar properties.

Enables more precise planetary evolution modeling without extra computational cost.

Abstract

Studies of planetary atmospheric composition, variability, and evolution require appropriate theoretical and numerical tools to estimate key atmospheric parameters, among which the mass-loss rate is often the most important. In evolutionary studies, it is common to use the energy-limited formula, which is attractive for its simplicity but ignores important physical effects and can be inaccurate in many cases. To overcome this problem, we consider a recently developed grid of about 7000 one-dimensional upper-atmosphere hydrodynamic models computed for a wide range of planets with hydrogen-dominated atmospheres from which we extract the mass-loss rates. The grid boundaries are [1:39] MEARTH in planetary mass, [1:10] REARTH in planetary radius, [300:2000] K in equilibrium temperature, [0.4:1.3] MSUN in host star's mass, [0.002:1.3] au in orbital separation, and about [10^{26}:5*10^{30}] erg/s in stellar X-ray and extreme ultraviolet luminosity. We then derive an analytical expression for the atmospheric mass-loss rates based on a fit to the values obtained from the grid. The expression provides the mass-loss rates as a function of planetary mass, planetary radius, orbital separation, and incident stellar high-energy flux. We show that this expression is a significant improvement to the energy-limited approximation for a wide range of planets. The analytical expression presented here enables significantly more accurate planetary evolution computations without increasing computing time.