The fragmentation of isothermal rings and star formation

Numerical studies of the collapse of a rotating interstellar cloud predict the formation of a ring of matter embedded in the infalling gas cloud. The assumption of axisymmetry in those calculations most likely limits their range of validity to the early stages of collapse before nonaxisymmetric perturbations become important. This paper presents the results of calculations on the stability of an isothermal ring to nonaxisymmetric perturbations by numerical integration of the equations of hydrodynamics in three space dimensions. It is found that the ring fragments primarily into two or three bodies in less than one-half of a rotation period of the ring. The implication for the observational fact that most stars occur in multiple systems is clear. The mass and specific angular momentum for each of the resulting bodies are found to be roughly 10% of those quantities of the initial gas cloud. A 'cascading' process in star formation is discussed where each of the resulting bodies would form rings in its collapse, which would fragment, etc.