On the proper Mach number and ratio of specific heats for modeling the Venus bow shock

Abstract

When considering local solutions for the jump in plasma conditions across planetary bow shocks, a magnetohydrodynamic (MHD) formalism of the Rankine‐Hugoniot relations is used. However, when planetary shocks are modeled on a global scale, gas dynamic (GD) treatments are frequently employed which neglect the magnetic field effect on the shock structure and the flowing plasma. These treatments require the specification of a free‐stream Mach number and a ratio of specific heats. Herein observations of the Venus bow shock are used to illustrate how closely one can approximate the observed magnetic field jump with MHD and GD treatments if one chooses a particular Mach number and ratio of specific heats. As expected theoretically, it is found that the observed magnetosonic Mach number (and not the sonic Mach number) when used in the GD calculations gives the best approximate solutions to the MHD problem using reasonable value for the ratio of specific heats. At Venus we find that the best value for the ratio of specific heats (γ) is 1.85 (rather than 5/3 or 2), although this ratio depends on the Alfvenic Mach number MA and the angle between the shock normal and the upstream field, θBN. We cannot determine how well the GD solution reproduces the shock shape at Venus, because of the possible influence of both MHD and mass‐loading effects. In fact, the Venus bow shock is much farther away from the planet at the terminator than the GD model would predict for either γ = 5/3 or 2. Thus we must depend on terrestrial studies to determine how best to approximate shock shape with GD modes.