We investigate in this work two different types of instabilities that set limits on the rotation rates of neutron (compact) stars. The first one is that caused by rotation at the Kepler frequency, at which mass shedding at the star's equator sets in. The second limit is set by instabilities driven by the growth of gravitational radiation-reaction (GRR) driven -modes of order , which are moderated by shear and bulk viscosity. The calculations are performed for two relativistic models for the nuclear equation of state, DD2 and ACB4. The latter accounts for a phase transition that gives rise to the existence of so-called mass-twin compact stars. Our results confirm that the stable rotation periods of cold neutron stars are determined by the modes and that these modes are excited at rotation periods between 1 and 1.4 ms (20–30% above the Kepler periods of these stars). The situation is reversed in hot neutron stars where bulk viscosity damps the GRR modes, pushing the excitation period of the -mode instability to values below the Kepler period. For cold mass-twin compact stars, we find that the instability sets in at rotation periods between 0.8 and 1 ms (25–30% below the Kepler period). This feature may allow one to distinguish conventional neutron stars from their possibly existing mass-twin counterparts observationally, provided the -mode instability, which is expected to compete with the -mode instability, sets the limit on stable rotation of compact stars.

中文翻译：

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旋转中子星中引力辐射反应驱动的不稳定性

我们在这项工作中研究了两种不同类型的不稳定性，它们对中子（致密）星的旋转速率设置了限制。第一个是由以开普勒频率旋转引起的，在该频率下，恒星赤道处的质量脱落开始。第二个限制是由引力辐射反应 (GRR) 驱动的有序模式的增长驱动的不稳定性设置的 ，其中受剪切和体积粘度调节。计算是针对核状态方程 DD2 和 ACB4 的两个相对论模型进行的。后者解释了导致所谓的质量孪生致密星存在的相变。我们的结果证实冷中子星的稳定自转周期是由模式并且这些模式在 1 到 1.4 ms 之间的旋转周期（比这些恒星的开普勒周期高 20-30%）时被激发。在热中子星中，情况相反，其中体积粘度抑制 GRR 模式，将α 模式不稳定性的激发周期推到开普勒周期以下的值。对于冷质量孪生致密星，我们发现不稳定性在 0.8 到 1 毫秒（比开普勒周期低 25-30%）的自转周期开始。这一特征可以让人们在观测上将常规中子星与其可能存在的质量孪生对应物区分开来，前提是α 模式不稳定性与α 模式不稳定性相竞争，设定了致密星稳定旋转的限制。