Existence of Transonic Solutions in the Stellar Wind Problem with Viscosity and Heat Conduction

The one-fluid stellar wind problem for steady, radial outflow is considered, including effects of heat conduction and viscosity. The associated nondimensionalized equations of conservation of mass, momentum, and energy are singularly perturbed in the large Reynolds number limit, and stellar wind profiles are constructed rigorously in this regime using geometric singular perturbation techniques. Transonic solutions, which accelerate from subsonic to supersonic speeds, are identified as folded saddle canard trajectories lying in the intersection of a subsonic saddle slow manifold and a supersonic repelling slow manifold, returning to subsonic speeds through a viscous layer shock, the location of which is determined by the associated far-field boundary conditions.

Automated summary

This study focuses on the one-fluid stellar wind problem for steady, radial outflow, taking into account the effects of heat conduction and viscosity. Using geometric singular perturbation techniques, stellar wind profiles are rigorously constructed in the large Reynolds number limit, identifying transonic solutions that accelerate from subsonic to supersonic speeds. These solutions are identified as folded saddle canard trajectories lying in the intersection of a subsonic saddle slow manifold and a supersonic repelling slow manifold.