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.
