THERMAL ESCAPE IN THE HYDRODYNAMIC REGIME: RECONSIDERATION OF PARKER's ISENTROPIC THEORY BASED ON RESULTS OF KINETIC SIMULATIONS

Abstract

The one-dimensional steady-state problem of thermal escape from a single-component atmosphere of mon- and diatomic gases is studied in the hydrodynamic (blow-off) regime using the direct simulation Monte Carlo method for an evaporative-type condition at the lower boundary. The simulations are performed for various depths into an atmosphere, indicated by a Knudsen number, Kn 0, equal to the ratio of the mean free path of molecules to the radial position of the source surface, ranging from 10 to 10–5, and for the range of the source Jeans parameter, λ0, equal to the ratio of gravitational and thermal energies, specific to blow-off. The results of kinetic simulations are compared with the isentropic model (IM) and the Navier-Stokes model. It is shown that the IM can be simplified if formulated in terms of the local Mach number and Jeans parameter. The simulations predict that at Kn 0 < ~ 10–3 the flow includes a near-surface non-equilibrium Knudsen layer, a zone where the flow can be well approximated by the IM, and a rarefied far field. The corresponding IM solutions, however, only approach Parker's critical solution as λ0 approaches the upper limit for blow-off. The IM alone is not capable for predicting the flow and requires boundary conditions at the top of the Knudsen layer. For small Kn 0, the scaled escape rate and energy loss rate are found to be independent of λ0. The simulation results can be scaled to any single-component atmosphere exhibiting blow-off if the external heating above the lower boundary is negligible, in particular, to sublimation-driven atmospheres of Kuiper belt objects.