2023MNRAS.521.2930R

We present N-body simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 M_⊙. The models are evolved with the N-body code BIFROST to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star-BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About ∼20-30 per cent of the stars within the spheres of influence of the black holes form Bahcall-Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500-1300 TDEs, depending on the initial cluster structure. Most (>95 per cent) of the TDEs originate from stars in the Bahcall-Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density, and velocity dispersion of the clusters ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}}\rho \sigma ^{-3}$). We find that TDEs can lead a 300 M_⊙ BH to reach $\sim 7000 \, \mathrm{{M}_{\odot }}$ within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters.