Criteria for Fragmentation of Rotating Isothermal Clouds. I. Semianalytic Approach

Abstract

The isothermal collapse of an initially uniform-density, uniform-rotating, molecular cloud core with pressure and self-gravity is investigated using a spheroid model to determine the conditions under which a cloud is unstable to fragmentation. A semianalytic model for the collapse of rotating spheroids is developed with the method of characteristics for inwardly propagating rarefaction waves. It is shown that the criterion for fragmentation is modified from that in the literature if the property of nonhomologous collapse is taken into account. The fate of the collapsing clouds can be divided into three classes: (1) runaway collapsing clouds that approach self-similar solutions with moderate ellipsoid axial ratio (2-5) and are expected to form single adiabatic cores in the center, (2) clouds that collapse and rotationally bounce without fragmentation and are expected to develop bars and filaments, and (3) clouds that collapse into pancakes and fragment during the isothermal stage. We derive the criterion for fragmentation considering the evolution of the flatness of the central core after relaxation in the z-direction. In the small rotation limit, the evolution is determined by only one parameter, ?0 (initial ratio of the thermal energy to the gravitational energy), that has the critical value, ?0 = 5/?2.