旋转黑洞星团的热力学
The Thermodynamics of Rotating Black-Hole Star Clusters
摘要：
利用引力相互作用轨道椭圆的Touma-Tremaine热力学研究了超大质量黑洞附近的旋转星团。本文描述了一种计算任意质量和半长轴分布恒星热力学平衡态的简单数值方法。严格证明了非旋转团簇在正低温下的自发对称性破缺和热力学崩溃。通过第二类温度参数引入旋转。发现轴对称和不平衡的旋转平衡;不平衡的平衡进动的角速度是由两个温度的比率。仙女座星系核中的偏心星盘可能是旋转黑洞星团不平衡热力学平衡的一个例子。恒星质量的黑洞在对称性破缺的星团中占据高偏心轨道，在旋转的星团中形成扁平的盘状结构。它们被吸引到在参照系中以星团的角速度旋转的静止轨道上。在球状星团中，如果温度为负，恒星质量的黑洞的轨道比较轻的恒星的轨道更偏心，如果温度为正，则更圆。最后，我们注意到，行星，彗星，暗物质粒子和其他轻体倾向于形成一个球对称的非旋转子集群的最大熵偏心率分布$\mathscr{P}(e)=2e$，即使他们的主集群是旋转和不平衡的。
英文摘要：
Rotating star clusters near supermassive black holes are studied using Touma-Tremaine thermodynamics of gravitationally interacting orbital ellipses. A simple numerical procedure for calculating thermodynamic equilibrium states for an arbitrary distribution of stars over masses and semimajor axes is described. Spontaneous symmetry breaking and breakdown of thermodynamics at low positive temperatures are rigorously proven for non-rotating clusters. Rotation is introduced through a second temperature-like parameter. Both axially symmetric and lopsided rotational equilibria are found; the lopsided equilibria precess with the angular velocity that is given by the ratio of the two temperatures. Eccentric stellar disc in the nucleus of Andromeda galaxy may be an example of a lopsided thermodynamic equilibrium of a rotating black hole star cluster. Stellar-mass black holes occupy highly eccentric orbits in broken-symmetry star clusters, and form flattened disc-like configurations in rotating star clusters. They are attracted to orbits that are stationary in the frame of reference rotating with the angular velocity of the cluster. In spherical clusters, stellar-mass black holes' orbits are significantly more eccentric than those of the lighter stars if the temperature is negative, and more circular if the temperature is positive. Finally we note that planets, comets, dark matter particles and other light bodies tend to form a spherically symmetric non-rotating sub-cluster with maximum-entropy eccentricity distribution $\mathscr{P}(e)=2e$, even if their host cluster is rotating and lopsided.
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