On the fragmentation of rotating interstellar clouds

Simple physical arguments are used to estimate the time scale for fragmentation of a collapsing, rotating, isothermal, interstellar cloud. This time scale is compared with a similarly estimated time scale for the collapse upon itself of a transitory ring structure. It is shown to be plausible for a cloud with a given ratio of rotational to gravitational energy (beta) that as the ratio of thermal to gravitational energy (alpha) is varied, there is an intermediate range of alpha where a ring forms and collapses on itself, prior to fragmentation. For higher or lower alpha, however, the cloud fragments prior to ring self-collapse. The analysis is compared with the results of numerical multidimensional, gravitational, hydrodynamical collapse and shown to be in good agreement with them.