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

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.

Lofar, Vla, and Chandra Observations of the Toothbrush Galaxy Cluster

“…Applying this to the Toothbrush cluster, the distance ratio between shock and cold front location ( 2 » ) is consistent with our obtained Mach number (Equation 11, Farris & Russell 1994). This confirms the association between the southern subclusterʼs cold front and the shock ahead of it.…”

Evolution of Coronal Mass Ejection Morphology With Increasing Heliocentric Distance. Ii. In Situ Observations

“…While adopting the low Mach number approximation of Farris & Russell (1994) from Equation (4), we obtain Δ R c = 0.204 + 0.815…”

“…This work also produced the relationship of D T /D OB = 1.35, where D T is defined as the terminator distance. Later, Farris & Russell (1994) assumed that the value of this ratio defines the radius of curvature, R c , of the obstacle-i.e., the curvature of the magnetopause boundary, or in our case, the ICME leading edge. The radius of curvature was then assumed to equal half the vertical size of the obstacle-i.e., half the vertical size of the ICME.…”

Evolution of CIR storm on 22 July 2009

“…The data is shifted in time to the bow shock nose. Field and plasma parameters determined at an appropriate time and the bow shock model of Farris and Russell [1994] with the magnetopause model of Shue et al [1997] are used to determine the position of the bow shock.…”