Irradiation-driven escape of primordial planetary atmospheres

II. Evaporation efficiency of sub-Neptunes through hot Jupiters

¹ Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
e-mail: andrea.caldiroli@univie.ac.at
² Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy
³ INFN, Sezione Milano-Bicocca, P.za della Scienza 3, 20126 Milano, Italy
⁴ INAF, Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, Italy
⁵ Department of Astronomy, University of Michigan, 1085 S University, Ann Arbor, MI 48109, USA

Received: 26 November 2021
Accepted: 22 March 2022

Abstract

Making use of the publicly available 1D photoionization hydrodynamics code ATES we set out to investigate the combined effects of specific planetary gravitational potential energy (ϕ_p ≡ GM_p/R_p) and stellar X-ray and extreme ultraviolet (XUV) irradiation (F_XUV) on the evaporation efficiency (η) 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 thermal escape (i.e., η ≃ 1) is unattainable can be inferred analytically, by means of a balance between the ion binding energy and the volume-averaged mean excess energy. For log ϕ_p ≳ log ϕ_p^thr ≈ [12.9 − 13.2] (in cgs units), most of the energy absorption occurs within a region 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 ϕ_p, by up to 4 orders of magnitude below the energy-limited value. Whether or not planets with ϕ_p ≲ ϕ_p^thr exhibit energy-limited outflows is primarily regulated by the stellar irradiation level. Specifically, for low-gravity planets, above F_XUV^thr ≃ 10^4–5 erg cm⁻² s⁻¹, Lyα 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 ϕ_p. Further, we show that whereas η increases as F_XUV increases for planets above ϕ_p^thr, the opposite is true for low-gravity planets (i.e., for sub-Neptunes). 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 η is given in the appendix.