The Dynamics of a Rapidly Escaping Atmosphere: Applications to the Evolution of Earth and Venus

A simple, idealized model for the rapid escape of a hydrogen thermosphere provides some quantitative estimates for the energy-limited flux of escaping particles. The model assumes that the atmosphere is "tightly bound" by the gravitational field at lower altitudes, that diffusion through the lower atmosphere does not limit the flux, and that the main source of heating is solar euv. Rather low thermospheric temperatures are typical of such escape and a characteristic minimum develops in the temperature profile as the escape flux approaches its maximum possible value. The flux is limited by the amount of euv energy absorbed, which is in turn controlled by the radial extent of the thermosphere. Regardless of the amount of hydrogen in the thermosphere, the low temperatures accompanying rapid escape limit its extent, and thus constrain the flux. Applied to the Earth and Venus, the results suggest that the escape of hydrogen from these planets would have been energy-limited if their primordial atmospheres contained total hydrogen mixing ratios exceeding a few percent. Hydrogen and deuterium may have been lost in bulk, but heavier elements would have remained in the atmosphere. These results place constraints on hypotheses for the origin of the planets and their subsequent evolution.