Mass fractionation during transonic escape and implications for loss of water from Mars and Venus

Hydrodynamic escape of hydrogen from a planetary atmosphere can remove heavier gases as well as hydrogen, provided that the escape rate is sufficiently large. Here, analytic approximations for the degree of mass fractionation of a trace species during hydrodynamic escape are compared with accurate numerical solutions for the case of transonic outflow. Even the simplest analytic approximation is found to be surprisingly good, despite numerous assumptions made in the course of its derivation. The analytic approximations are most accurate when the ratio of molecular weights of the heavier and lighter constituents is large so that nonlinear terms in the momentum equation for the heavy constituent become small. The simplest analytic formula is readily generalized to the case where a heavy constituent is also a major species. Application of the generalized formula to hypothetical episodes of hydrodynamic escape from Venus and Mars suggests that both hydrogen and oxygen could have escaped; thus, substantial quantities of water may have been lost without the need to oxidize large amounts of the crust. Mars could have lost large amounts of rare gases in this manner, but if so it may also have lost significant quantities of carbon dioxide and nitrogen. Venusian argon and neon isotope ratios indicate that Venus lost little or no argon and 50% or less of its original complement of neon. Terrestrial noble gas patterns resemble those that would have resulted had an initially Venus-like Earth undergone a short-lived but locally very energetic escape event.