Gravitational torques among objects orbiting a supermassive black hole drive the rapid reorientation of orbital planes in nuclear star clusters (NSCs), a process known as vector resonant relaxation. In this Letter, we determine the statistical equilibrium of systems with a distribution of masses, semimajor axes, and eccentricities. We average the interaction over the apsidal precession time and construct a Monte Carlo Markov chain method to sample the microcanonical ensemble of the NSC. We examine the case of NSCs formed by 16 episodes of star formation or globular cluster infall. We find that the massive stars and stellar mass black holes form a warped disk, while low mass stars resemble a spherical distribution with a possible net rotation. This explains the origin of the clockwise disk in the Galactic center and predicts a population of black holes (BHs) embedded within this structure. The rate of mergers among massive stars, tidal disruption events of massive stars by BHs, and BH-BH mergers are highly increased in such disks. The first two may explain the origin of the observed G1 and G2 clouds, the latter may be important for gravitational wave detections with LIGO and VIRGO. More generally, black holes are expected to settle in disks in all dense spherical stellar systems assembled by mergers of smaller systems including globular clusters.

中文翻译：

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银河核中的黑洞盘

绕超大质量黑洞运动的物体之间的引力力矩驱动着核星团（NSC）中轨道平面的快速重新定向，这一过程称为矢量共振弛豫。在这封信中，我们确定质量，半长轴和偏心距分布的系统的统计平衡。我们平均在两点进动时间之间的相互作用，并构建了蒙特卡洛马尔可夫链方法来对NSC的微经典集合进行采样。我们研究了由16次星际形成或球状星团倒塌形成的NSC的情况。我们发现，大质量恒星和恒星质量黑洞形成了扭曲的圆盘，而低质量恒星类似于具有可能的净旋转的球形分布。这解释了银河系中心顺时针磁盘的起源，并预测了嵌入该结构的黑洞（BH）的数量。在这样的磁盘中，大质量恒星之间的合并率，BH对大质量恒星的潮汐破坏事件以及BH-BH合并都大大增加了。前两个可以解释观测到的G1和G2云的起源，后者对于用LIGO和VIRGO探测重力波可能很重要。更普遍的是，黑洞有望在由包括球状星团在内的较小系统合并而成的所有致密球形恒星系统的磁盘中沉降。前两个可以解释观测到的G1和G2云的起源，后者对于用LIGO和VIRGO探测重力波可能很重要。更一般地说，黑洞有望在由包括球状星团在内的较小系统合并而成的所有致密球形恒星系统的磁盘中沉降。前两个可以解释观测到的G1和G2云的起源，后者对于用LIGO和VIRGO探测重力波可能很重要。更普遍的是，黑洞有望在由包括球状星团在内的较小系统合并而成的所有致密球形恒星系统的磁盘中沉降。