Stability analysis of bow shocks

We present a linear stability analysis of bow shocks created by the interaction of a spherical wind moving with respect to its surrounding medium. The bounding shocks are assumed isothermal and with Mach number M = infinity. Following Soker, we study the evolution of short-wavelength perturbations. We find that the motion is unstable in this limit. Moreover, the ratio of the wind velocity upsilon(w) to the star velocity upsilon* characterizes the stability properties. Bow shocks with fast winds for which upsilon*/upsilon(w) much less than 1 are more stable than bow shocks with slow winds, i.e., upsilon*/upsilon(w) much greater than 1.