The dynamics of a rapidly escaping atmosphere - Applications to the evolution of earth and Venus

A simple model for the rapid escape of a hydrogen thermosphere is presented in order to establish the energy-limited flux of escaping particles. The model assumes that the atmosphere is tightly bound by gravity at the lower boundary, that all the EUV is absorbed in a narrow region where the optical depth is unity, and that the main source of heating is solar EUV. The flux is limited by the amount of EUV energy absorbed, which is in turn controlled by the radial extent of the thermosphere. It is found that, regardless of the amount of hydrogen in the thermosphere, the low temperatures which accompany rapid escape limit its extent and thus constrain the flux. The results are applied to the earth and Venus, showing that the escape of hydrogen from these planets would have been energy-limiting if their primordial atmospheres contained total hydrogen mixing ratios exceeding only a few percent. This conclusion places a constraint on the theory of the origin and evolution of the planets.