Three-dimensional modeling of Earth's bow shock: Shock shape as a function of Alfvén Mach number

Earth's bow shock changes its three‐dimensional (3‐D) location in response to changes in the solar wind ram pressure Pram, Alfvén Mach number MA, magnetic field orientation, fast mode Mach number Mms, and sonic Mach number MS. Using shock locations from global 3‐D ideal MHD simulations [Cairns and Lyon, 1995], empirical models are derived for the 3‐D shape and location of Earth's bow shock in the near‐Earth regime as a function of solar wind conditions. Multiple simulations with different MA and Pram but two orientations of the interplanetary magnetic field BIMF are analyzed: θIMF = 45° and 90° with respect to the solar wind direction vsw. Models for the (paraboloid) flaring parameter bs as a function of MA, azimuthal angle ϕ, and θIMF = 45° or 90°, show bs decreasing with MA, corresponding to the shock becoming blunter and less swept back (with a larger cross section), as expected. Together with models for the shock's standoff distance (which increases with decreasing MA) the models for bs(MA, ϕ) predict the shock's 3‐D location. Variations of bs with ϕ represent eccentricities in the shock's cross section (i.e., a departure from circularity), with the shock extending further perpendicular to vms (the fast mode speed) than parallel, as MA → 1. An additional effect is observed in which the shock shape is “skewed” for θIMF = 45° (but not for θIMF = 90°) in the plane containing BIMF and vsw. These latter two effects are consistent with the fast mode velocity varying with propagation direction relative to BIMF.