THE DYNAMIC STABILITY OF ROTATING PROTOSTARS AND PROTOSTELLAR DISKS .1. THE EFFECTS OF THE ANGULAR-MOMENTUM DISTRIBUTION

Modern studies of collapse and fragmentation of protostellar clouds su ggest a wide variety of outcomes, depending on the assumed initial con ditions. Individual equilibrium objects that result from collapse are likely to be in rapid rotation and can have a wide range of structures . We have undertaken a survey of parameter space in order to examine t he role of dynamic instabilities in the subsequent evolution of these objects. Such instabilities can produce significant mass and angular m omentum transport or, if violent enough, can lead to the breakup of th e original object. For the purposes of conducting a systematic study, we have so far considered only the n = 3/2 polytropic equilibrium stat es that might form from the collapse of uniformly rotating spherical c louds. We do not follow the collapses themselves, but use a simple pro cedure to connect presumed initial conditions to postcollapse equilibr ium states. By varying the central concentration of the assumed initia l cloud, we obtain equilibrium states distinguished primarily by their different specific angular momentum distributions. These equilibrium states range between starlike objects with angular momentum distributi ons analogous to the Maclaurin spheroids and objects that have moderat ely extended Keplerian-disk-like regions. Using a new self-consistent field code to generate the n = 3/2 axisymmetric equilibrium states and an improved three-dimensional hydrodynamics code, we have investigate d the onset and nature of global dynamic instabilities in these object s. The starlike objects are unstable to barlike instabilities at T/\W\ greater than or similar to 0.27, where T/\W\ is the ratio of total ro tational kinetic energy to gravitational potential energy. These insta bilities are vigorous and lead to violent ejection of mass and angular momentum. As the angular momentum distribution shifts to the other ex treme, one- and two-armed spiral instabilities begin to dominate at co nsiderably lower T/\W\. These instabilities seem to be driven by mecha nisms related to swing and SLING but operating under conditions that a re very different from those that are usually considered. In flattened objects, one-armed spirals dominate all other disturbances. Although these spirals tend to saturate at nonlinear amplitude, they do transpo rt significant amounts of mass and angular momentum. It is unclear at present whether or not they ultimately lead to breakup of the equilibr ium object. We conclude that the nature of the global instabilities en countered during the process of star formation can be quite sensitive to the angular momentum distribution of the protostar.