## Kinetic simulations of thermal escape from a single component atmosphere

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The one-dimensional steady-state expansion of a monatomic gas from a spherical source in a gravity field is studied by the direct simulation Monte Carlo method. Collisions between molecules are described by the hard sphere model, the distribution of gas molecules leaving the source surface is assumed to be Maxwellian, and no heat is directly deposited in the simulation region. The flow structure and the escape rate (number flux of molecules escaping the atmosphere) are analyzed for the source Jeans parameter lambda(0) (ratio of the gravitational energy to thermal energy of the molecules) and Knudsen number Kn(0) (ratio of the mean free path to the source radius) ranging from 0 to 15 and from 0.0001 to infinity, respectively. In the collisionless regime, flows are analyzed for lambda(0)=0-100 and analytical equations are obtained for asymptotic values of gas parameters that are found to be non-monotonic functions of lambda(0). For collisional flows, simulations predict the transition in the nature of atmospheric loss from escape on a molecule-by-molecules basis, often referred to as Jeans escape, to an organized outflow, often referred to as hydrodynamic escape. It is found that the structure of the flow and the escape rate exhibit drastic changes when lambda(0) varies over a narrow transition range 2-3. The lower limit of this range approximately corresponds to a critical Jeans parameter equal to 2.06, which is the upper limit for isentropic, supersonic outflow of a monatomic gas from a body in a gravity field. Subcritical, lambda(0)<= 2, flows are qualitatively similar to free outgassing in the absence of gravity, resulting in hypersonic terminal Mach numbers and escape rates that are independent of lambda(0) in the limit of small Knudsen numbers. Supercritical, lambda(0)>= 3, flows are controlled by thermal conduction and demonstrate qualitatively different trends. The ratio of the actual escape rate to the Jeans escape rate at the source surface is found to be a non-monotonic function of Kn(0) spanning the range from similar to 0.01 to similar to 2. At lambda(0)>= 6, the ratio of the actual escape rate to the Jeans escape rate at the exobase is found to be similar to 1.4-1.7. This is unlike the predictions of the slow hydrodynamic escape model, which is based on Parker's model for the solar wind and intended for the description of the atmospheric loss at lambda(0)>similar to 10. At lambda(0) < 6, the actual escape rate can be well approximated by a modified Jeans escape rate, which accounts for non-zero gas velocity. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3592253]