The growth of intermediate mass black holes through tidal captures and tidal disruption events

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 (N∙_TDE ∝ M_BHρσ⁻³). We find that TDEs can lead a 300 M_⊙ BH to reach ∼ 7000 M_⊙ 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.