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

Abstract

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.Plain Language SummaryThe solar wind is a stream of charged particles emitted by the Sun. The interplanetary magnetic field embedded in the solar wind is the solar magnetic field dragged out from the solar corona. Bulk velocity of the solar wind is higher than sonic velocity and higher than the velocity of Alfven waves. Planets with their magnetospheres and ionospheres create obstacles to the solar wind flow, and in front of planetary magnetosphere, bow shock forms, similar to the shock wave formation ahead of a supersonic aircraft. To study many physical processes in the vicinity of planets, it is necessary to have a useful physical model of the position and shape of the bow shock. Magneto‐hydrodynamics (MHD) and kinetic simulations provide accurate models but they are too computationally extensive. To analyze experimental data empirical models are mainly used, but they are not equally accurate in all space. We suggest an analytical model of the bow shock position and shape based on MHD calculations and accurate analytical solutions. This model is easy to use and describes the bow shock well near the planet and far downstream.Key PointsFor an arbitrary direction of the interplanetary magnetic field, the bow shock nose is skewed from the direction of the solar wind flowAsymptotic bow shock slope downstream from the planet in magneto‐hydrodynamics approximation is calculated analytically in the skewed reference frameAnalytical expressions are obtained for the bow shock parameters as functions of the solar wind parameters