A critical assessment of the applicability of the energy-limited approximation for estimating exoplanetary mass-loss rates

TL;DR

This study critically evaluates the energy-limited approximation for estimating exoplanetary atmospheric mass-loss rates, revealing its limitations across different planetary conditions and advocating for hydrodynamic model-based methods.

Contribution

It revises the energy-limited formalism and compares its estimates with hydrodynamic simulations across a broad planetary parameter space.

Findings

EL approximation is accurate within an order of magnitude for about 76% of planets.

Significant deviations up to three orders of magnitude occur in some cases.

EL approximation fails for planets with extreme gravitational potentials or irradiation conditions.

Abstract

Context: The energy-limited (EL) atmospheric escape approach is used to estimate mass-loss rates for a broad range of planets that host hydrogen-dominated atmospheres as well as for performing atmospheric evolution calculations. Aims: We aim to study the applicability range of the EL approximation. Methods: We revise the EL formalism and its assumptions. We also compare its results with those of hydrodynamic simulations, employing a grid covering planets with masses, radii, and equilibrium temperatures ranging between 1 $M_{\oplus}$ and 39 $M_{\oplus}$, 1 $R_{\oplus}$ and 10 $R_{\oplus}$, and 300 and 2000 K, respectively. Results: Within the grid boundaries, we find that the EL approximation gives a correct order of magnitude estimate for mass-loss rates for about 76% of the planets, but there can be departures from hydrodynamic simulations by up to three orders of magnitude in individual cases. Furthermore, we find that planets for which the mass-loss rates are correctly estimated by the EL approximation to within one order of magnitude have intermediate gravitational potentials as well as low-to-intermediate equilibrium temperatures and irradiation fluxes of extreme ultraviolet and X-ray radiation. However, for planets with low or high gravitational potentials, or high equilibrium temperatures and irradiation fluxes, the approximation fails in most cases. Conclusions: The EL approximation should not be used for planetary evolution calculations that require computing mass-loss rates for planets that cover a broad parameter space. In this case, it is very likely that the EL approximation would at times return mass-loss rates of up to several orders of magnitude above or below those predicted by hydrodynamic simulations. For planetary atmospheric evolution calculations, interpolation routines or approximations based on grids of hydrodynamic models should be used instead.