Supersonic Solutions of the Solar-Wind Equations

Abstract

We reexamine the inviscid solar-wind equations with heat conduction from below and establish a fundamentally new approach for finding supersonic solutions. Although the problem is fourth order, only two independent integration constants can be arbitrarily assigned, since two boundary conditions that are required to specify well-behaved supersonic solutions determine the values of the other two constants. Valid numerical solutions can be integrated only by recognizing that the asymptotic values of temperature and kinetic energy are determined by the integration constants previously admitted. The Noble and Scarf (1963, Astrophys. J. 138, 1169-1191) solar-wind models are essentially accurate for practical purposes, but in a fundamental sense they are not self-consistent. The ratio of thermal energy to gravitational potential at the supersonic point, ( kTr/GMm) s, must lie between 0.4375 and about 0.405 to permit stable supersonic solutions for ionized hydrogen.