Ring formation in rotating protostellar clouds

The formation of a ring during the dynamic collapse of a rotating gas cloud is shown to be an understandable physical phenomenon. By analytically integrating the equation of motion for particles in the equatorial plane of a rotating cloud which collapses in a gravitational potential well defined by a (1-r2) mass density distribution we demonstrate the mechanism which initiates the growth of the toroidal structure. An analysis of the ring formation process indicates that the ring should develop in rotating, self-gravitating gas clouds which collapse from a wide range of axisymmetric initial conditions; the degree of central condensation and the initial distribution of angular momentum in a cloud should affect only the position and size of the developing ring. Ring formation, being a dynamic process in collapsing gas clouds, cannot be explained in terms of the classical ring instability that arises in rapidly rotating, equilibrium spheroids. Conditions in a cloud which should inhibit ring formation are also discussed