The collapse of unstable isothermal spheres

Similarity solutions provide simple analytical descriptions of modes of collapse of gravitationally unstable isothermal spheres, both before and after a collapsed core has formed. A new class of similarity solutions has been found, to add to the solutions obtained earlier by Larson, Penston, and Shu. Numerical integrations of collapses were performed to study their resemblance to the similarity solutions. None of the collapses studied showed any strong tendency to a similarity solution. Computed behaviors were generally intermediate between those described by similarity solutions, with the Larson-Penston solution giving the best description of the flow in the immediate neighborhood of the point of core formation. It was also found that perturbed gravitationally unstable spheres do not necessarily collapse; they may instead perform periodic oscillations of large amplitude.