Examining the exobase approximation: DSMC models of Titan's upper atmosphere

Chamberlain ([1963] Planet. Space Sci., 11, 901-960) described the use of the exobase layer to determine escape from planetary atmospheres, below which it is assumed that molecular collisions maintain thermal equilibrium and above which collisions are deemed negligible. De La Haye et al. ([2007] Icarus., 191, 236-250) used this approximation to extract the energy deposition and non-thermal escape rates for Titan's atmosphere by fitting the Cassini Ion Neutral Mass Spectrometer (INMS) density data. De La Haye et al. assumed the gas distributions were composed of an enhanced population of super-thermal molecules (E >> kT) that could be described by a kappa energy distribution function (EDF), and they fit the data using the Liouville theorem. Here we fitted the data again, but we used the conventional form of the kappa EDF. The extracted kappa EDFs were then used with the Direct Simulation Monte Carlo (DSMC) technique (Bird [1994] Molecular Gas Dynamics and the Direct Simulation of Gas Flows) to evaluate the effect of collisions on the exospheric profiles. The INMS density data can be fit reasonably well with thermal and various non-thermal EDFs. However, the extracted energy deposition and escape rates are shown to depend significantly on the assumed exobase altitude, and the usefulness of such fits without directly modeling the collisions is unclear. Our DSMC results indicate that the kappa EDFs used in the Chamberlain approximation can lead to errors in determining the atmospheric temperature profiles and escape rates. Gas kinetic simulations are needed to accurately model measured exospheric density profiles, and to determine the altitude ranges where the Liouville method might be applicable.