Irradiation-driven escape of primordial planetary atmospheres
Andrea Caldiroli, Francesco Haardt, Elena Gallo, Riccardo Spinelli, Isaac Malsky, Emily Rauscher
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 , Ly α 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.