Modeling Nonaxisymmetric Bow Shocks: Solution Method and Exact Analytic Solutions

A new solution method is presented for steady-state, momentum-conserving,non-axisymmetric bow shocks and colliding winds in the thin-shell limit. Thisis a generalization of previous formulations to include a density gradient inthe pre-shock ambient medium, as well as anisotropy in the pre-shock wind. Forcases where the wind is unaccelerated, the formalism yields exact, analyticsolutions. Solutions are presented for two bow shock cases: (1) that due to a starmoving supersonically with respect to an ambient medium with a density gradientperpendicular to the stellar velocity, and (2) that due to a star with amisaligned, axisymmetric wind moving in a uniform medium. It is also shownunder quite general circumstances that the total rate of energy thermalizationin the bow shock is independent of the details of the wind asymmetry, includingthe orientation of the non-axisymmetric driving wind, provided the wind isnon-accelerating and point-symmetric. A typical feature of the solutions isthat the region near the standoff point is tilted, so that the star does notlie along the bisector of a parabolic fit to the standoff region. The principaluse of this work is to infer the origin of bow shock asymmetries, whether dueto the wind or ambient medium, or both.Comment: 26 pages and 6 figures accepted to ap