Hydrodynamics of the Solar Wind Expansion

A pedagogical introduction to the classical hydrodynamic steady state solutions for flows in a spherically symmetric atmosphere is presented along with a detailed analysis of the stability of such flows and a discussion of the Parker/Bondi phase diagram of solutions in the Mach number – stellar radius plane. This leads naturally to the scenario presented by Velli (1994) for wind-accretion transitions, which helps to explain results from numerical simulations in many contexts and gives a more comprehensive answer to the question of why the solar wind and other steady state flows in spherical symetry must quite generally become supersonic.