Escape from Titan's Atmosphere: Kenetic Monte Carlo Simulations

Loss of atmosphere by molecular escape to space is an important aspect of the evolution of a planetary body. Saturn’s moon Titan is a prime candidate for studying atmospheric loss because it possesses an atmosphere thicker than the Earth’s but has a much smaller mass. Studies have shown that other satellites similar in size to Titan, like Jupiter’s moon Ganymede, lost a Titan-like atmosphere over the age of the solar system. Therefore, a principal goal of the Cassini mission to Saturn has been to investigate atmospheric escape from Titan in order to understand the nature of its present atmosphere. Before Cassini started collecting data on Titan’s atmosphere, the escape estimates were consistent with Titan retaining a large atmosphere over its lifetime in the solar system. As indicated by the ratio of its gravitation binding energy to the thermal energy of molecules, known as the Jeans parameter, the two principal species, N2 and CH4, are strongly bound to Titan whereas the trace species, H2, is not. Although H2 escape was assumed to be evaporative, the escape of N2 and CH4 was assumed to be driven by non-thermal processes. Surprisingly, a series of recent fluid and diffusion models of Titan’s upper atmosphere, constrained to Cassini density data, suggested that the N2 and CH4 thermal escape rates were orders of magnitude larger than the pre-Cassini estimates.

A fluid approach, referred to as the slow hydrodynamic escape model, was used to propose that thermal conduction in the most dilute regions of the atmosphere can power a supersonic expansion leading to the significant escape rates. If these rates were correct Titan would have lost a significant portion of its current atmosphere over its lifetime. Because applying fluid models to the rarefied regions is problematic, I used molecular kinetic Monte Carlo simulations to test the fluid results and to compare with Cassini density data for Titan’s atmosphere.
For temperatures characteristic of Titan’s upper atmosphere my molecular simulations reproduced the N2 and CH4 Cassini density measurements without requiring escape rates orders of magnitude larger than the evaporative rates. This was also the case when the upper atmospheric temperature was significantly increased. Therefore, our computational space science group at the University of Virginia performed a series of simulations to characterize the dependence of the escape rate on the Jeans parameter and the Knudsen number, which is an indicator of the rarefaction of a gas flow. Surprisingly, these simulations confirmed that for very small Knudsen number at the lower boundary of the simulation region the escape rate was evaporative in nature even for Jeans parameters typically considered in the slow hydrodynamic escape models.

Because Pluto’s upper atmosphere has a composition similar to that at Titan but with much smaller Jeans parameters, I worked with fellow student Justin Erwin on a combined fluid/ molecular Monte Carlo simulation to model Pluto’s upper atmosphere structure and atmospheric escape rate. This method was used to test hydrodynamic models in anticipation of the New Horizon spacecraft encounter with Pluto in 2015. This study also determined that thermal escape from Pluto’s atmosphere was evaporative in nature, and the upper atmospheric structure differed significantly from the predictions of the hydrodynamic models.

Finally, Cassini data for varying levels of incident plasma bombarding Titan’s upper atmosphere appear to have an effect on the N2 density vs. altitude, but not on the H2 density vs. altitude. Therefore, I performed molecular simulations of the diffusion and escape of H2 in a background atmosphere of N2 and CH4 at temperatures that corresponded to various levels of plasma heating. Over the range of characteristic temperatures of Titan’s upper atmosphere used in the molecular model, the H2 escape rates were similar, but the H2 densities diffusively separated from the N2 densities at lower altitudes with decreasing temperatures. This result appears to be contrary to the Cassini density data as I discuss.

Therefore, it appears that to correctly describe escape it is often necessary to couple continuum models for a planet’s upper atmosphere with a kinetic model, because neglecting the non-equilibrium nature of the rarefied region can result in inconsistent escape rates and density and temperature structures.