Asymptotic Opening Angles for Colliding-Wind Bow Shocks: the Characteristic-Angle Approximation

TL;DR

This paper derives simple analytic formulas for the asymptotic opening angles of wind-collision shock cones in colliding stellar winds, considering both radiative and adiabatic regimes, and discusses limitations of existing approximations.

Contribution

It introduces a characteristic-angle approximation to analytically describe the shock cone shape in colliding winds, including new expressions linking wind momentum ratios and shock angles.

Findings

Analytic expressions for shock opening angles in different regimes.

Comparison of radiative and adiabatic limits.

Insights into the Dyson approximation's limitations.

Abstract

By considering the advection and interaction of the vector momentum flux in highly supersonic spherically diverging winds, we derive a simple analytic description of the asymptotic opening angle of a wind-collision shock cone, in the approximation that the shocked gas is contained in a cone streaming out along a single characteristic opening angle. Both highly radiative and highly adiabatic limits are treated, and their comparison is the novel result. Analytic closed-form expressions are obtained for the inferred wind momentum ratios as a function of the observed shock opening angle, allowing the conspicuous shape of the asymptotic bow shock to be used as a preliminary constraint on more detailed modeling of the colliding winds. In the process, we explore from a general perspective the limitations in applying to the global shock geometry the so-called Dyson approximation, which asserts a local balance in the perpendicular ram pressure across the shock.