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

We recently developed a Monte Carlo method (GNC) that can simulate the dynamical evolution of a nuclear star 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 similar to 17t(rh) by GNC, where t(rh) is the time of half-mass relaxation. We use GNC to study the cosmological evolution of the properties of NSCs and the mass of MBHs 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 we compare the simulation results with the observations of NSCs in the Milky Way or nearby galaxies. It is possible for such a scenario to produce MBHs with mass 10(5)-10(7)M(circle dot) for NSCs with stellar mass of 10(6)-10(9)M(circle dot). In the Milky Way's NSC, to grow an MBH up to 4 x 10(6)M(circle dot), its size needs to be similar to 1.7 times more compact in early Universe than the current value. MBHs with current masses >6 x 10(7)M(circle dot) seem difficult to explain by loss-cone accretion alone, and thus they may require other additional accretion channels, such as gas accretion.