Towards an MHD theory for the standoff distance of Earth's bow shock

Abstract

An MHD theory is developed for the standoff distance a s of the bow shock and the thickness Δ ms of the magnetosheath, using the empirical Spreiter et al. relation Δ ms = kX and the MHD density ratio X across the shock. The theory includes as special cases the well‐known gasdynamic theory and associated phenomenological MHD‐like models for Δ ms and a s . In general, however, MHD effects produce major differences from previous models, especially at low Alfven ( M A ) and sonic ( M S ) Mach numbers. The magnetic field orientation, M A , M S , and the ratio of specific heats γ are all important variables of the theory. In contrast, the fast mode Mach number need play no direct role. Three principal conclusions are reached. First, the gas‐dynamic and phenomenological models miss important dependances on field orientation and M S and generally provide poor approximations to the MHD results. Second, changes in field orientation and M S are predicted to cause factor of ∼ 4 changes in Δ ms at low M A . These effects should be important when predicting the shock's location or calculating γ from observations. Third, using Spreiter et al.'s value for k in the MHD theory leads to maximum a s values at low M A and nominal M S that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter‐like relation and larger k found in recent MHD simulations and/or a breakdown in the Spreiter‐like relation at very low M A .