Black Hole Discs and Spheres in Galactic Nuclei -- Exploring the Landscape of Vector Resonant Relaxation Equilibria

TL;DR

This paper investigates the equilibrium configurations of stellar orbits in galactic nuclei under vector resonant relaxation, revealing that more massive objects tend to form flattened, disc-like structures due to anisotropic mass segregation.

Contribution

It introduces a Monte Carlo Markov Chain approach to determine VRR equilibria in nuclear star clusters, highlighting the tendency of massive objects to form flattened structures.

Findings

Massive objects are more flattened than lighter ones in equilibrium.

Black holes are likely to reside in disc-like structures within nuclear star clusters.

Equilibria show anisotropic mass segregation across various initial conditions.

Abstract

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.