  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.
