A New Criterion for Bar{forming Instability in Rapidly Rotating Gaseous and Stellar Systems. Ii. Nonaxisymmetric Form

We have previously introduced the parameter as an indicator of stability to m = 2 nonaxisymmetric modes in rotating, self{gravitating, axisymmetric, gaseous ( < 0:34) and stellar ( < 0:25) systems. This parameter can be written as = (ft=2), where t T=jW j, T is the total rotational kinetic energy, W is the total gravitational potential energy, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. In this paper, we extend the stability criterion to nonaxisymmetric equilibrium systems by determining empirically the appropriate form of the function f for ellipsoids and elliptical disks and cylinders. For oblate{like ellipsoidal systems, we nd that