Steady hydromagnetic flows in open magnetic fields. I - A class of analytic solutions

This paper introduces a class of axisymmetric steady hydromagnetic flows along open stellar magnetic fields. The full set of hydromagnetic equations that describes these flows in spherical coordinates is reduced to a set of ordinary differential equations in the radial distance from the origin. A judicious choice of free functions admits solutions for a spherically symmetric density in an otherwise nonspherically symmetric flow. In general, the flow requires a formal, steady energy addition whose amount and spatial distribution are calculated self-consistently to conserve energy everywhere. These solutions provide a rare opportunity to study the basic physics of hydromagnetic stellar winds in terms of exact relationships. The rich variety of solutions presented include flows along dipolar magnetic fields that are purely radial and those that, in addition, have θ-components.