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Modern studies of collapse and fragmentation of protostellar clouds suggest a wide variety of outcomes, depending on the assumed initial conditions. Individual equilibrium objects which 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 the role of dynamic instabilities in the subsequent evolution of these objects.
For the purposes of conducting a systematic study, we so far have considered only the $n = 3/2$ polytropic equilibrium states that might form from the collapse of uniformly rotating spherical clouds. By varying the central concentration of the assumed initial cloud, we obtain equilibrium states distinguished primarily by their different specific angular momentum distributions. These equilibrium states span the range between starlike objects with angular momentum distributions analogous to the Maclaurin spheroids and objects more accurately described as massive Keplerian disks around stars. Using a new SCF code to generate the $n = 3/2$ axisymmetric equilibrium states and an improved 3D hydrodynamics code, we have investigated the the onset and nature of global dynamic instabilities in these objects.
The starlike objects are unstable to barlike instabilities at $T/|W|$ $\gtorder$ 0.27, where $T/|W|$ is the ratio of total rotational kinetic energy to gravitational potential energy. These instabilities are vigorous and lead to violent ejection of mass and angular momentum. As the angular momentum distribution shifts to the other extreme, one- and two-armed spiral instabilities begin to dominate at considerably lower $T/|W|$. These instabilities appear to be driven by the SLING and swing mechanisms. In extremely flattened disks, one-armed spirals dominate all other disturbances but eventually saturate at nonlinear amplitude without producing fragmentation. We conclude that the nature of the global instabilities encountered during the process of star formation can be quite sensitive to the angular momentum distribution of the protostar. This research is supported by NASA grant NAGW 3399.
