Analytical model of the planetary bow shock for various magnetic field directions based on MHD calculations

Study of physical processes in plasma near planets often requires knowledge of the position and shape of the planetary bow shock. Empirical models are usually used since theoretical MHD and kinetic models consume too much computer time and cannot be used to track fast processes. M.I. Verigin proposed a semi-empirical approach based on the use of exact theoretical expressions with a small number of parameters, which have a clear physical meaning. These parameters are estimated by fitting experimental data or detailed MHD calculations. A model of the bow shock near an arbitrary-shaped obstacle has previously been developed for a gas-dynamic flow. This model can be applied to any sonic Mach numbers and large values of the Alfven Mach number. In addition, the asymptotic Mach cone - the angle of inclination of the shock wave at an infinite distance from the planet - has been calculated analytically in the MHD approximation. In this paper, we propose a model of the bow shock for any direction of the magnetic field with respect to the upcoming flow and for any Mach numbers. Parameters of the model are the distance of the nose point from the obstacle, radius of curvature and bluntness of the bow shock at the nose point, a parameter related to the transition to the asymptotic downstream slope of the shock, and a skewing angle appearing when the interplanetary magnetic field is directed at an angle to the solar wind velocity.