Exact Analytic Solutions for a Ballistic Orbiting Wind

TL;DR

This paper derives an exact analytical solution for the structure of a ballistic stellar wind in a binary system, revealing spiral shock geometries and streamlines in a steady-state corotating frame.

Contribution

It introduces a novel exact solution for the wind's density and shock structure in a binary system, emphasizing curved streamlines and spiral shock surfaces.

Findings

Exact density distribution at all pre-shock locations

Analytic geometry of spiral shock surfaces

Identification of streamline crossings and shock overlaps

Abstract

Much theoretical and observational work has been done on stellar winds within binary systems. We present a new solution for a ballistic wind launched from a source in a circular orbit. Our method emphasizes the curved streamlines in the corotating frame, where the flow is steady-state, allowing us to obtain an exact solution for the mass density at all pre-shock locations. Assuming an initially isotropic wind, fluid elements launched from the interior hemisphere of the wind will be the first to cross other streamlines, resulting in a spiral structure bounded by two shock surfaces. Streamlines from the outer wind hemisphere later intersect these shocks as well. An analytic solution is obtained for the geometry of the two shock surfaces. Although the inner and outer shock surfaces asymptotically trace Archimedean spirals, our tail solution suggests many crossings where the shocks overlap, beyond which the analytic solution cannot be continued. Our solution can be readily extended to an initially anisotropic wind.