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

Abstract

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 ∼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.

Simulating the tidal disruption of stars by stellar-mass black holes using moving-mesh hydrodynamics

“…Intermediate-mass black holes (IMBHs; see Greene et al 2020 for a review), with masses greater than those of stellar-mass black holes ( 10 2 M ) and less than those of supermassive black holes ( 10 6 M ), are expected to exist in the centers of dwarf galaxies (e.g., Kunth et al 1987;Filippenko & Sargent 1989;Reines 2022;Gültekin et al 2022) and globular clusters (e.g., Davis et al 2011;Farrell et al 2014;Pechetti et al 2022). Among several IMBH formation mechanisms (see Volonteri et al 2021 for review), one possible avenue is runaway mass growth through tidal capture and disruption, which has been examined analytically (e.g., Stone et al 2017) and numerically (e.g., Rizzuto et al 2023;Arca Sedda et al 2023). One of the most critical factors in this mechanism for BH growth is the amount of debris mass that ultimately accretes onto the BH.…”

“…One of the most critical factors in this mechanism for BH growth is the amount of debris mass that ultimately accretes onto the BH. For example, Rizzuto et al (2023) assumed that a star approaching a BH within the nominal tidal radius r t is fully destroyed and 50% of the stellar mass is accreted onto the BH.…”

“…Although µTDEs have lower observable rates (Perets et al 2016), they can shed light on the processes occurring in the centers of globular and nuclear star clusters where they are most likely to occur. In particular, they are an important avenue in the mass growth of SBHs to form intermediate-mass black holes (IMBHs, e.g., Stone et al 2017;Rizzuto et al 2023). However, these studies make simplistic assumptions about the mass accreted onto a black hole after a TDE, which highlights the need for detailed simulations to model this interaction more accurately for the next generation of globular cluster simulations.…”