Gas evaporation from collision-determined planetary exospheres

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Abstract
From the general concept of the Boltzmann equation a new method for the calculation of collision-dominated exospheric velocity distribution functions is derived. At each exospheric point the velocity distribution function is composed of two parts which separately describe those particles that have or have not already undergone collisions in the exosphere. The two parts of the velocity distribution function are given for ballistic, hyperbolic, and elliptic particles as well. Here for the first time an explicit method is developed to determine the satellite particle population of elliptic particle orbits in the exosphere. The effect of exospheric collisions on the rate of escape of atmospheric hydrogen from the Earth's exosphere is studied in detail. Here a reduced hydrogen temperature is consistently determined taking into account the requirement of energy continuity for exobasic regions. It is shown that, depending on the temperature of the main gas constituent at exobasic levels, the escape rate is reduced by 30 to 50 per cent compared to that calculated with the Jeans formula. The ratio R of the effective rate of escape compared with the Jeans escape rate thus varies strongly with the temperature of the atmospheric background gas. Comparison with other authors shows that present results for the ratio R lie between the so-called lid-approximation by Gross as a lower limit and the various Monte Carlo results not accounting for energy continuity as an upper limit. The present results for the escape rates allow for a satisfactory fit of the exobasic hydrogen densities inferred from geocoronal Lyman-α observations without bringing up the necessity for the existence of a non-thermal escape mechanism.

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