Kinetic simulations of thermal escape from a single component atmosphere

Abstract

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 λ0 (ratio of the gravitational energy to thermal energy of the molecules) and Knudsen number Kn0 (ratio of the mean free path to the source radius) ranging from 0 to 15 and from 0.0001 to ∞, respectively. In the collisionless regime, flows are analyzed for λ0=0-100 and analytical equations are obtained for asymptotic values of gas parameters that are found to be non-monotonic functions of λ0. 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 λ0 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, λ0≤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 λ0 in the limit of small Knudsen numbers. Supercritical, λ0≥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 Kn0 spanning the range from ∼0.01 to ∼2. At λ0≥6, the ratio of the actual escape rate to the Jeans escape rate at the exobase is found to be ∼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 λ0>∼10. At λ0<6, the actual escape rate can be well approximated by a modified Jeans escape rate, which accounts for non-zero gas velocity.

Thermal escape from extrasolar giant planets

“…These observations indicate that close-in EGPs such as HD209458b are surrounded by a hot thermosphere composed of atomic hydrogen that extends to several planetary radii and provide the required line of [20,21] and their application to close-in EGPs [8,9]. We then proceed to generalize the results to a sample of known EGPs to make specific predictions about the nature of their upper atmospheres.…”

Simulating Pluto's Atmosphere with Hybrid Fluid/Kinetic Models

“…), ! is the mass of a N 2 molecule, Volkov et al, 2011).The lower boundary of our fluid domain is set at 1450 km, consistent with the occultation results and the assumptions of . To determine an escape rate and enforce the upper boundary condition, the exobase needs to be within the simulation domain.…”

“…J m -1 K -1 and ! = 1 to compare with and because this is consistent with the variable hard sphere model for collisions between N 2 molecules used in the DSMC model of the exosphere (Tucker et al, 2012;Volkov et al, 2011).…”

“…Using the DMSC method Volkov et al (2011) demonstrated earlier that for a monatomic or diatomic gas in the absence of heating above some lower boundary for ! ≳ 3 the escape is Jeans-like at the exobase (i.e.…”

“…To be consistent with the fluid equations, I also consider expressions with a drifting Maxwell-Boltzmann to include the bulk velocity ! in the velocity distribution Volkov et al, 2011). Typically these equations are applied at a level called the exobase where !…”