标题： 快速旋转恒星的长期条纹模式不稳定性再探讨 显示英文标题

标题： The Secular Bar-Mode Instability in Rapidly Rotating Stars Revisited

摘要： 均匀旋转的、同质的、不可压缩的麦克拉伦扁球体在粘性存在的情况下，当自转足够快时，会表现出对非轴对称棒模扰动的长期不稳定性。直观的解释是，粘性引起的能量耗散可以驱动一个不稳定的扁球体到达一个能量更低且更稳定的三轴配置——即雅可比椭球体。但是，对于快速旋转的可压缩恒星又如何呢？与没有内部能量且因此能立即释放所有粘性耗散能量的不可压缩恒星不同，可压缩恒星具有内部能量，并且能够将耗散的能量保留为内部热量。已知那些旋转得足够快并且能够迅速释放这些耗散能量的可压缩恒星，像它们的不可压缩对应物一样，会对棒模扰动表现出不稳定性。但对于那些旋转得非常快且冷却时间尺度很长以至于所有的粘性耗散能量都被保留在热量中的可压缩恒星，情况又是怎样的呢？在这种情况下，恒星的总能量在一个长期（粘性）演化的时间尺度上是否仍然保持不变？这类恒星是否会由于棒模非线性增长而变得不稳定，还是粘性加热足以使它们膨胀，降低旋转动能与引力势能之比 T/|W| ~ 1/R （其中 R 是赤道半径），从而在不稳定性开始之前将其关闭？如果这种不稳定性仍然存在于这类恒星中，那么它们会在什么自转率下变得不稳定，并向何种最终状态演化？我们在旋转恒星的可压缩椭球体模型背景下提供了这些问题的答案。这些结果应能为三维+时间维度上的旋转恒星数值模拟提供有用的指导。 显示英文摘要

摘要： Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy dissipation by viscosity can drive an unstable spheroid to a stable, triaxial configuration of lower energy - a Jacobi ellipsoid. But what about rapidly rotating compressible stars? Unlike incompressible stars, which contain no internal energy and therefore immediately liberate all the energy dissipated by viscosity, compressible stars have internal energy and can retain the dissipated energy as internal heat. Now compressible stars that rotate sufficiently rapidly and also manage to liberate this dissipated energy very quickly are known to be unstable to bar-mode perturbations, like their incompressible counterparts. But what is the situation for rapidly rotating compressible stars that have very long cooling timescales, so that all the energy dissipated by viscosity is retained as heat, whereby the total energy of the star remains constant on a secular (viscous) evolution timescale? Are such stars also unstable to the nonlinear growth of bar modes, or is the viscous heating sufficient to cause them to expand, drive down the ratio of rotational kinetic to gravitational potential energy T/|W| ~ 1/R, where R is the equatorial radius, and turn off the instability before it gets underway? If the instability still arises in such stars, at what rotation rate do they become unstable, and to what final state do they evolve? We provide answers to these questions in the context of the compressible ellipsoid model for rotating stars. The results should serve as useful guides for numerical simulations in 3+1 dimensions for rotating stars containing viscosity.