Fragmentation of Rapidly Rotating Gas Clouds. II. Polytropes---Clues to the Outcome of Adiabatic Collapse

The Hachisu (1986) self-consistent field code is used to construct axisymmetric equilibrium models of rotating polytropic gas clouds; by carefully evaluating the equilibrium sequences generated for various angular momentum distributions, several important general properties of rotating gas clouds are deduced. It is established that, for clouds having an angular momentum distribution comparable to that of the Maclaurin spheroids, a toroidal equilibrium sequence bifurcates from the spheroidal surface at a value of T/abs value W of 0.44-0.45, for all polytropic indices between 0 and 3, where T is the rotational kinetic energy and W is the gravitational potential energy of the cloud.