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 planetary gravitational potential energy ($\phi_p\equiv GM_p/R_p$) and stellar X-ray and Extreme Ultraviolet (XUV) irradiation ($F_{\rm XUV}$) on the evaporation efficiency ($\eta$) 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 escape (i.e., $\eta\simeq 1$) is unattainable can be inferred analytically. For $\log \phi_p\gtrsim \log \phi_p^{\rm thr}\approx [12.9-13.2]$ (in cgs units), most of the energy absorption occurs 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 $\phi_p$,. Whether or not planets with $\phi_p\lesssim \phi_p^{\rm thr}$ exhibit energy-limited outflows is regulated primarily by the stellar irradiation level. Specifically, for low-gravity planets, above $F_{\rm XUV}\simeq 10^{4-5}$ erg cm$^{-2}$s$^{-1}$ Ly$\alpha$ 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 $\phi_p$Further, we show that whereas $\eta$ increases as $F_{\rm XUV}$ increases for planets above $\phi^{\rm thr}_p$, the opposite is true for low-gravity planets. 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 $\eta$ is given in the appendix.