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

¹ University of Technology Graz, Rechbauerstraße 12, 8010 Graz, Austria
e-mail: a_krenn@gmx.at
² Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, 8042 Graz, Austria
³ School of Physics, Trinity College Dublin, the University of Dublin, College Green, Dublin-2, Ireland

Received: 28 January 2021
Accepted: 20 April 2021

Abstract

Context. The energy-limited atmospheric escape approach is widely 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 energy-limited atmospheric escape approximation.

Methods. We revise the energy-limited atmospheric escape formalism and the involved assumptions. We also compare the results of the energy-limited formalism with those of hydrodynamic simulations, employing a grid covering planets with masses, radii, and equilibrium temperatures ranging between 1 M_⊕ and 39 M_⊕, 1 R_⊕ and 10 R_⊕, and 300 and 2000 K, respectively.

Results. Within the grid boundaries, we find that the energy-limited 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 two to three orders of magnitude in individual cases. Furthermore, we find that planets for which the mass-loss rates are correctly estimated by the energy-limited approximation to within one order of magnitude have intermediate gravitational potentials (≈2.5–5.5 ×10⁸ J kg⁻¹) 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 energy-limited 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 energy-limited 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.