Approximate Analytical Expressions of the Wind-driven Bow Shock

Abstract

Previous analytical works on the wind-driven thin-shell bow shock neglected the centrifugal force exerted on the shell material. We reanalyze the dynamic equations including the centrifugal force, and we present approximate formulae in a Cartesian coordinate system for the general quantities describing the thin-shell bow shock. The shocked interstellar medium and the shocked stellar wind are treated as mixed and separated, respectively. These formulae are more accurate than previous analytical results.