Determining the standoff distance of the bow shock: Mach number dependence and use of models

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Abstract
We explore the factors that determine the bow shock standoff distance. These factors include the parameters of the solar wind, such as the magnetosonic Mach number, plasma beta, and magnetic field orientation, as well as the size and shape of the obstacle. In this report we develop a semiempirical Mach number relation for the bow shock standoff distance in order to take into account the shock's behavior at low Mach numbers. This is done by determining which properties of the shock are most important in controlling the standoff distance and using this knowledge to modify the current Mach number relation. While the present relation has proven useful at higher Mach numbers, it has lacked effectiveness at the low Mach number limit. We also analyze the bow shock dependence upon the size and shape of the obstacle, noting that it is most appropriate to compare the standoff distance of the bow shock to the radius of curvature of the obstacle, as opposed to the distance from the focus of the object to the nose. Last, we focus our attention on the use of bow shock models in determining the standoff distance. We note that the physical behavior of the shock must correctly be taken into account, specifically the behavior as a function of solar wind dynamic pressure; otherwise, erroneous results can be obtained for the bow shock standoff distance.