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Nonaxisymmetric instabilities driven by self-gravity and rapid rotation may play a critical role during the collapse and accretion phases of star formation. To date, except for studies of tori, most work on global dynamic instabilities of rotating, self-gravitating equilibrium states has focused on only moderately compressible equations of state and on two extreme cases of the specific angular momentum distribution. In the most commonly considered case, uniform initial cloud conditions yield an angular momentum distribution equivalent to that of the Maclaurin spheroids. Rapidly rotating starlike objects with this angular momentum distribution are subject to barlike instabilities. Hydrodynamic simulations have demonstrated that these instabilities generally result in spiral arm ejection of mass and angular momentum, producing a ring of material about a central, tumbling bar (Williams and Tohline 1988 Astrophys. J.\/ 315\/, 594). Strongly centrally condensed initial cloud conditions yield the other extreme. A star/disk protostellar system forms which is subject to multiple spiral instabilities. Previous work (Yang, Durisen, Cohl, Imamura, and Toman 1991 BAAS\/ 22\/, 1257) has suggested that these systems display complex behavior, with many tightly wrapped spiral modes present and growing simultaneously.
We have recently begun a survey of dynamic instabilities for a wider range of equations of state and of specific angular momentum distributions. The evolution of our equilibrium objects is followed using a second-order 3D hydrodynamics code. We present results for simulations of isentropic, n=3/2 and 5/2 polytropic stars with angular momentum distributions intermediate between the two extremes. In general, only modest shifts away from the Maclaurin spheroid angular momentum distribution lead to behavior resembling that of star/disk systems. This work is supported by NASA Grant NAGW-3399.
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