Asymptotic Steady State Solution to a Bow Shock with an Infinite Mach Number

TL;DR

This paper derives an asymptotic steady-state solution for a bow shock with infinite Mach number, analyzing its structure, calculating drag and spectra, and discussing astrophysical implications.

Contribution

It provides a novel analytical solution for a bow shock at infinite Mach number, verified by simulations, and explores astrophysical applications.

Findings

Shock front forms a parabolic solid of revolution at large distances

Hydrodynamic equations solved in parabolic coordinates

Drag force and spectra calculated for optically thin and thick media

Abstract

The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force and expected spectra are calculated for such shock, both in case of an optically thin and thick media. Finally, relations to astrophysical bow shocks and other analytic works on oblique shocks are discussed.