Irradiation-driven escape of primordial planetary atmospheres. II. Evaporation efficiency of sub-Neptunes through hot Jupiters

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 (Ï p ¡ GMp/Rp) and stellar X-ray and extreme ultraviolet (XUV) irradiation (FXUV) 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 Ï p log Ïpthr [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 Ï p, by up to 4 orders of magnitude below the energy-limited value. Whether or not planets with Ï p Ï pthr exhibit energy-limited outflows is primarily regulated by the stellar irradiation level. Specifically, for low-gravity planets, above FXUVthr 104-5 erg cm2 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 Ï p. Further, we show that whereas η increases as FXUV increases for planets above Ï pthr, 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.