论文标题
银河核中的黑洞盘和球 - 探索矢量谐振弛豫平衡的景观
Black Hole Discs and Spheres in Galactic Nuclei -- Exploring the Landscape of Vector Resonant Relaxation Equilibria
论文作者
论文摘要
媒介谐振弛豫（VRR）是已知是最快的引力过程，它塑造了核星簇中恒星轨道的几何形状。这导致了几百万年的相应VRR时间尺度上的轨道平面$ t _ {\ rm vrr} $在相应的VRR时间尺度上重新调整，而怪异$ e $和semimajor axis $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $保留。轨道倾斜的分布达到了一个内部平衡，其特征是两个保守量，恒星轨道之间的总势能，$ e _ {\ rm tot} $和总角动量，$ l _ {\ rm rm tot} $。在时间尺度长于$ t_ \ mathrm {vrr} $上，偏心率和半轴轴变化缓慢，轨道倾斜的分布有望通过一系列VRR平衡来发展。使用Monte Carlo Markov链方法，我们确定了固定的$ e _ {\ rm tot} $和$ l _ {\ rm _ {\ rm tot} $的轨道倾斜合奏的平衡分布，用于隔离核星形群体，具有$ a $，$ e $，$ m $，$ m $，$ m $，$ m $的势力分布。我们以$ 9 $代表性$ e _ {\ rm tot} $ - $ l _ {\ rm tot} $对探索可能的平衡，以覆盖可能的参数空间。在所有情况下，平衡均显示各向异性质量隔离，其中更大的物体的分布比较轻的物体更平坦。鉴于恒星黑洞比普通的主序列恒星更大，因此这些发现表明，黑洞位于核星团内的圆盘状结构中，可在广泛的初始条件下。
Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters. This leads to the realignment of the orbital planes on the corresponding VRR time scale $t_{\rm VRR}$ of a few million years, while the eccentricity $e$ and semimajor axis $a$ of the individual orbits are approximately conserved. The distribution of orbital inclinations reaches an internal equilibrium characterised by two conserved quantities, the total potential energy among stellar orbits, $E_{\rm tot}$, and the total angular momentum, $L_{\rm tot}$. On timescales longer than $t_\mathrm{VRR}$, the eccentricities and semimajor axes change slowly and the distribution of orbital inclinations are expected to evolve through a series of VRR equilibria. Using a Monte Carlo Markov Chain method, we determine the equilibrium distribution of orbital inclinations in the microcanonical ensemble with fixed $E_{\rm tot}$ and $L_{\rm tot}$ for isolated nuclear star clusters with a power-law distribution of $a$, $e$, and $m$, where $m$ is the stellar mass. We explore the possible equilibria for $9$ representative $E_{\rm tot}$--$L_{\rm tot}$ pairs that cover the possible parameter space. For all cases, the equilibria show anisotropic mass segregation where the distribution of more massive objects is more flattened than that for lighter objects. Given that stellar black holes are more massive than the average main sequence stars, these findings suggest that black holes reside in disc-like structures within nuclear star clusters for a wide range of initial conditions.
