Self-consistent Solutions of Evolving Nuclear Star Clusters with Two-Dimensional Monte-Carlo Dynamical Simulations

Abstract

We recently developed a Monte-Carlo method (GNC) that can simulate the dynamical evolution of a nuclear stellar cluster (NSC) with a massive black hole (MBH), where the two-body relaxations can be solved by the Fokker-Planck equations in energy and angular momentum space. Here we make a major update of GNC~ by integrating stellar potential and adiabatic invariant theory, so that we can study the self-consistent dynamics of NSCs with increasing mass of the MBH. We perform tests of the self-adaptation of cluster density due to MBH mass growth and Plummer core collapse, both finding consistent results with previous studies, the latter having a core collapse time of $\sim 17t_{\mathrm{rh}}$ by GNC, where $t_{\mathrm{rh}}$ is the time of half-mass relaxation. We use GNC~ to study the cosmological evolution of the properties of NSC and the mass of MBH assuming that the mass growth of the MBH is due to loss-cone accretion of stars (e.g., tidal disruption of stars) and stellar black holes, and compare the simulation results with the observations of NSCs in Milky-Way or near-by galaxies. Such scenario is possible to produce MBHs with mass $10^5\sim 10^7{M}_{\odot }$ for NSCs with stellar mass of $10^6\sim 10^9{M}_{\odot }$. In Milky-Way's NSC, to grow MBH up to $4\times 10^6{M}_{\odot }$, its size needs to be $\sim 1.7$ times more compact in early universe than the current value. MBHs with current masses $>6\times 10^7{M}_{\odot }$ seem difficult to explain by loss-cone accretion alone, and thus may require other additional accretion channels, such as gas accretion.

27 pages, 11 figures, ApJ, 2025, 980, 210, typos corrected

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