MHD simulations of Earth's bow shock at low Mach numbers: Standoff distances

Global, three‐dimensional, ideal MHD simulations of Earth's bow shock are reported for low Alfven Mach numbers M A and quasi‐perpendicular magnetic field orientations. The simulations use a hard, infinitely conducting magnetopause obstacle, with axisymmetric three‐dimensional location given by a scaled standard model, to directly address previous gasdynamic (GD) and field‐aligned MHD (FA‐MHD) work. Tests of the simulated shocks’ density jumps X for 1.4 ≲ M A ≲ 10 and the high M A shock location, and reproduction of the GD relation between magnetosheath thickness and X for quasi‐gasdynamic MHD runs with M A ≫ M S , confirm that the MHD code is working correctly. The MHD simulations show the standoff distance a s increasing monotonically with decreasing M A . Significantly larger a s are found at low M A than predicted by GD and phenomenological MHD models and FA‐MHD simulations, as required qualitatively by observations. The GD and FA‐MHD predictions err qualitatively, predicting either constant or decreasing a s with decreasing M A . This qualitative difference between quasi‐perpendicular MHD and FA‐MHD simulations is direct evidence for a s depending on the magnetic field orientation θ. The enhancement factor over the phenomenological MHD predictions at M A ∼ 2.4 agrees quantitatively with one observational estimate. A linear relationship is found between the magnetosheath thickness and X , modified both quantitatively and intrinsically by MHD effects from the GD result. The MHD and GD results agree in the high M A limit. An MHD theory is developed for a s , restricted to sufficiently perpendicular θ and high sonic Mach numbers M S . It explains the simulation results with excellent accuracy. Observational and further simulation testing of this MHD theory, and of its predicted M A , θ, and M S effects, is desirable.