On the hydrodynamic model of thermal escape from planetary atmospheres and its comparison with kinetic simulations

Parkers' model of thermal escape implies the search of solutions of one-dimensional hydrodynamic equations for an inviscid but thermally conducting gas with a critical point and vanishing temperature far from the source. The properties of solutions of this model are studied for neutral mon- and diatomic gases with the viscosity index varying from 1/2 to 1. The domains of existence and uniqueness of solutions in terms of the source Jeans escape parameter and Knudsen number are established. The solutions are found to exist only in a narrow range of the critical point Jeans parameter. The lower and upper limits of this range correspond to solutions that are dominated by either heat conduction or adiabatic expansion. Thermal escape described by Parker's model occurs in two asymptotic regimes: the low-density (LD) regime, when escape is dominated by heat conduction, and the high-density (HD) regime, when escape is dominated by adiabatic expansion. Expressions for the mass and energy escape rates in these regimes are found theoretically. The comparison of results of hydrodynamic and kinetic simulations performed in identical conditions shows that Parker's model is capable of describing thermal escape only in the HD regime, providing decent agreement with the kinetic model in terms of the atmospheric structure below the exobase and the mass and energy escape rates. In the LD regime, Parker's model predicts a much faster drop in atmospheric temperature and less extended atmospheres, and can both over- and underestimate the escape rates in orders of magnitude.