Physics-Based Analytical Model of the Planetary Bow Shock Position and Shape

摘要

In studies of physical processes near planetary bow shocks, empirical models of the latter are usually used. While computational magneto-hydrodynamics (MHD) or kinetic models of bow shocks are often more accurate, their computationally extensive nature limits their applicability to routine analysis of large volumes of data. We suggest an analytical model of the bow shock position based on MHD calculations and accurate analytical solutions. The analytical expressions for the bow shock position and shape include the following parameters: The distance of the bow shock nose point from the planet, radii of curvature and bluntnesses of the shock surface at this point and a parameter describing the transition to the asymptotic downstream slope of the shock. It is shown that for an analytical description of the surface of the shock, it is sufficient to approximate its radius of curvature and bluntness in two perpendicular planes. Another parameter used in this model is the bow shock skewing angle, appearing when the interplanetary magnetic field directed at an angle with respect to the solar wind velocity. This parameter naturally vanishes when the magnetic field of the solar wind is directed either parallel or perpendicular to the velocity vector. The exact analytical solution for the asymptotic downstream slope of the MHD Mach cone is modified to take into account the skewing angle of the bow shock.