Evaporation of Low-mass Planet Atmospheres: Multidimensional Hydrodynamics with Consistent Thermochemistry

Abstract

Direct and statistical observational evidence suggests that photoevaporation is important in eroding the atmosphere of sub-Neptune planets. We construct full hydrodynamic simulations, coupled with consistent thermochemistry and ray-tracing radiative transfer, to understand the physics of atmospheric photoevaporation caused by high-energy photons from the host star. We identify a region on the parameter space where a hydrostatic atmosphere cannot be balanced by any plausible interplanetary pressure, so that the atmosphere is particularly susceptible to loss by Parker wind. This region may lead to an absence of rich atmosphere (substantially H/He) for planets with low mass ( M  ≲ 3 M ⊕ ). Full numerical simulations of photoevaporative outflows show a typical outflow speed ∼ 30 km s − 1 and M ˙ ∼ 4 × 10 − 10 M ⊕ yr − 1 for a 5 M ⊕ fiducial model rocky-core planet with 10 −2 of its mass in the atmosphere. The outflows modulated by strong stellar wind (ram pressure up to 5 times the total wind pressure) are collimated toward the nightside of the planet, while the mass-loss rate is only ∼25% lower than the fiducial model. By exploring the parameter space, we find that EUV photoionization is most important in launching photoevaporative wind; other energetic radiations have secondary importance. Based on simulation results we propose a semiempirical formula of photoevaporation rate (error ≲ 20%), which is a function of high-energy irradiation, planet mass, and envelope mass fraction (error ≲20%). We then reproduce the observed bimodal radius distribution of sub-Neptune Kepler planets semiquantitatively.