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

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.