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

利用Hachisu的自洽场程序，我们建立了大量轴对称的、平衡的旋转多变气云模型，考虑了许多不同的角动量分布。通过对生成的平衡序列的仔细研究，我们得到了旋转气体云的几个重要的一般性质：对于像Maclaurin球体这样具有角动量分布的云团，对于N=0到N=3的所有多变指数，在T/|W|的某个地方，球体序列在0.44到0.45之间分叉出一个环形平衡序列。这里，T是旋转动能，W是云的引力势能。这表明在线性微扰下，对于较大范围的多变指数，动力学环模不稳定性几乎与T/|W|相同。此外，我们还证明了在非线性区域，中心凝聚平衡组态T/|W|&gt；0.41对环的形成是不稳定的。由于这些高T/|W|系统对非轴对称Jeans不稳定性几乎肯定是不稳定的，我们假设环模和扇形模不稳定性的耦合将导致所有T/|W|&gt；0.41的云经历动力学碎裂。利用我们的非线性环形成分析，我们可以准确地预测在什么初始条件下轴对称塌缩云经历碎裂。对于大多数其他选择的角动量分布，发生非线性环形成和非轴对称Jeans不稳定性的T/|W|的精确值略有变化，但定性行为保持不变。

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.