The collapse to equilibrium of rotating, adiabatic spheroids. I - Protostars

The role that rotation plays during the dynamic collapse of a protostellar gas cloud is examined here under the assumptions that the cloud conserves angular momentum and evolves along a fixed adiabat. An analytic model is presented that predicts what the final radius, density, temperature, and rate of rotation of the protostellar cloud will be for any chosen adiabatic exponent of the gas from the knowledge only of what the cloud's initial ratio of thermal to gravitational energy (..cap alpha../sub 0/) and the initial ratio of rotational to gravitational energy (..beta../sub 0/) are. Assuming that all gas clouds are susceptible to fragmentation if they collapse to configurations having ..beta..> or =0.274, the model also predicts, from initial conditions alone, when a protostellar object will fragment into a multiple stellar system. All isothermal evolutions lead to fragmentation; evolutions in which the adiabatic exponent is greater than 3/4 are susceptible to fragmentation only if ..cap alpha../sub 0/ is very small.