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Abstract:

Galactic nuclei harbouring a central supermassive black hole (SMBH), possibly surrounded by a dense nuclear cluster (NC), represent extreme environments that house a complex interplay of many physical processes that uniquely affect stellar formation, evolution, and dynamics. The discovery of gravitational waves (GWs) emitted by merging black holes (BHs) and neutron stars (NSs), funnelled a huge amount of work focused on understanding how compact object binaries (COBs) can pair up and merge together. Here, we review from a theoretical standpoint how different mechanisms concur with the formation, evolution, and merger of COBs around quiescent SMBHs and active galactic nuclei (AGNs), summarising the main predictions for current and future (GW) detections and outlining the possible features that can clearly mark a galactic nuclei origin.

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 tVRR 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 characterized by two conserved quantities, the total potential energy among stellar orbits, Etot, and the total angular momentum, Ltot. On time-scales longer than tVRR, 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 Etot and Ltot 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 nine representative Etot–Ltot 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.