The Diffusion Limit of Photoevaporation in Primordial Planetary Atmospheres

Photoevaporation is thought to play an important role in the early planetary evolution. In this study, we investigate the diffusion limit of X-ray and ultraviolet induced photoevaporation in primordial atmospheres. We find that compositional fractionation resulting from mass loss is more significant than currently recognized because it is controlled by the conditions at the top of the atmosphere, where particle collisions are less frequent. Such fractionation at the top of the atmosphere develops a compositional gradient that extends downward. Mass outflow eventually reaches a steady state in which hydrogen loss is diffusion limited. We derive new analytic expressions for the diffusion-limited mass loss rate and the crossover mass.