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 (ϕp ≡ 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 ϕp ≳ log ϕpthr ≈ [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 ϕp, by up to 4 orders of magnitude below the energy-limited value. Whether or not planets with ϕp ≲ ϕpthr exhibit energy-limited outflows is primarily regulated by the stellar irradiation level. Specifically, for low-gravity planets, above FXUVthr ≃ 104–5 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 ϕp. Further, we show that whereas η increases as FXUV increases for planets above ϕpthr, 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.

Intense X-ray and ultraviolet stellar irradiation can heat and inflate the atmospheres of closely orbiting exoplanets, driving mass outflows that may be significant enough to evaporate a sizable fraction of the planet atmosphere over the system lifetime. The recent surge in the number of known exoplanets, together with the imminent deployment of new ground and space-based facilities for exoplanet discovery and characterization, requires a prompt and efficient assessment of the most promising targets for intensive spectroscopic follow-ups. For this purpose, we developed ATmospheric EScape (ATES), a new hydrodynamics code that is specifically designed to compute the temperature, density, velocity, and ionization fraction profiles of highly irradiated planetary atmospheres, along with the current, steady-state mass loss rate. ATES solves the one-dimensional Euler, mass, and energy conservation equations in radial coordinates through a finite-volume scheme. The hydrodynamics module is paired with a photoionization equilibrium solver that includes cooling via bremsstrahlung, recombination, and collisional excitation and ionization for the case of a primordial atmosphere entirely composed of atomic hydrogen and helium, whilst also accounting for advection of the different ion species. Compared against the results of 14 moderately to highly irradiated planets simulated with The PLUTO-CLOUDY Interface (TPCI), which couples two sophisticated and computationally expensive hydrodynamics and radiation codes of much broader astrophysical applicability, ATES yields remarkably good agreement at a significantly smaller fraction of the time. A convergence study shows that ATES recovers stable, steady-state hydrodynamic solutions for systems with log(−Φp)≲12.9 + 0.17 log FXUV, where Φp and FXUV are the planet gravitational potential and stellar flux (in cgs units). Incidentally, atmospheres of systems above this threshold are generally thought to be undergoing Jeans escape. The code, which also features a user-friendly graphic interface, is available publicly as an online repository.