Three-dimensional equilibrium structures of rotating and self-gravitating gas clouds and its application to astrophysics

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Using Hachisu's self-consistent field code, we have constructed a large number of axisymmetric, equilibrium models of rotating polytropic gas clouds, allowing for a number of different angular momentum distributions. By carefully studying the generated equilibrium sequences, we have deduced several important general properties of rotating gas clouds.For clouds having an angular momentum distribution like that of Maclaurin spheroids, a toroidal equilibrium sequence bifurcates from the spheroidal sequence at a value of T/|W| somewhere between 0.44 and 0.45 for all polytropic indices between N = 0 and N = 3. Here, T is the rotational kinetic energy and W is the gravitational potential energy of the cloud. This suggests that a dynamical ring mode instability sets in at almost the same value of T/|W| for a wide range of polytropic indices in the linear perturbation regime.In addition, we show that centrally condensed equilibrium configurations with T/|W| > 0.41 are unstable to ring-formation in the nonlinear regime. Since these high T/|W| systems are almost certainly unstable to a nonaxisymmetric Jeans-type instability, we hypothesize that the coupling of the ring mode and the sector mode instability will cause all clouds with T/|W| > 0.41 to undergo dynamical fragmentation. Utilizing our nonlinear ring formation analysis, we can precisely predict under what initial conditions initially axisymmetric collapsing clouds experience fragmentation. For most other chosen angular momentum distributions, the exact value of T/|W| at which nonlinear ring formation occurs and at which the nonaxisymmetric Jeans-type instability sets in changes somewhat, but the qualitative behavior remains the same.