Selfsimilar collapse of isothermal spheres and star formation.
Abstract
Similarity solutions are obtained which describe the gravitational collapse of isothermal spheres that originated as gas clouds not far removed from the condition of marginal stability. It is argued that the similarity solution of Larson and Penston (1969) for the stages before core formation is physically artificial, but the gasdynamic flow subsequent to core formation exhibits selfsimilar properties. Similarity solutions are determined for the collapse of singular isothermal spheres, minus solutions without critical points are obtained by imposing the condition that the fluid velocities are negligible at the 'initial instant', and an expansionwave collapse solution is evaluated. The results are illustrated with a numerical example roughly corresponding to conditions appropriate for Bok globules or the central regions of a nonmagnetic molecular cloud. Two possible applications of the solutions are discussed: analyzing the stability to gravitational fragmentation of collapsing pressurefree gas spheres and determining the amount of energy radiated away during protostar formation.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1977
 DOI:
 10.1086/155274
 Bibcode:
 1977ApJ...214..488S
 Keywords:

 Density Distribution;
 Gravitational Collapse;
 Isothermal Flow;
 Protostars;
 Star Formation;
 Stellar Structure;
 Critical Point;
 RungeKutta Method;
 Similarity Theorem;
 Steady State;
 Stellar Envelopes;
 Astrophysics