Dynamics of Self-Gravitating Gaseous Spheres--III: Analytical Results in the Free-fall of Isothermal Cases

Abstract

For a cold gas, the analytical solutions for collapse in various symmetries give density and velocity profiles at the instant when a singularity develops in the initially densest part. These profiles follow generally from assuming that the density variation is smooth initially. For spherical and planar symmetries we have extended these solutions to a short time before this singularity occurs.