Gravitational instability of spheroidal expansions: A cosmogonic fragmentation mechanism

Abstract

Expanding flows of self-gravitating gas are common in astronomy and their stability therefore of some concern. Recently, gravitational instability in anisotropic expansions was proposed as an effective mechanism for the fragmentation called for in various cosmogonic hypotheses. (The anisotropy permits strong linear instabilities, while expansion avoids some nonlinear problems.) Here we analyze in detail the gravitational stability of spheroidal expansions of rotating gas masses. This extends Jeans' static results, and includes the well-known special cases of nonrotating spherical expansion and nonexpanding rotation. We obtain generalized Jeans criteria for instability, and in particular, a criterion for the instability to grow exponentially is derived. For an important class of asymptotic flows, we explicitly evaluate the instability strength and show that it is enough to initiate a fragmentation process. From the instability criteria we estimate a lower bound to the possible fragment masses. The Appendix discusses another asymptotic flow, modeling a ‘high energy jet’ which is highly unstable.