Rapid intermediate-mass black hole formation via runaway mergers of black holes

Abstract

Observations indicate that supermassive black holes (SMBHs) in high-redshift galaxies formed on timescales far shorter than classical growth models allow. One hypothesis suggests intermediate-mass black hole (IMBH) seeds as an efficient growth channel. Using N-body simulations, we demonstrate that in dense stellar-mass black hole (BH) clusters ($\ge 5\times10^9 M_{\odot}/{\rm pc}^3$), runaway gravitational-wave binary BH (BBH) mergers can produce a $\sim 10^3 M_\odot$ IMBH within 10 Myr from the formation of the BH subsystem. This scenario is simple and avoids large uncertainties regarding stellar mergers and evolution in the IMBH formation via very massive stars channel. We find that the runaway GW-merger mechanism relies on hard BBH formation through a chain of exchanged soft BBHs with accumulated hardening, which is far more efficient than three-body scattering. We analyze how IMBH formation depends on cluster density, total mass, initial mass function, and stellar halo potential. We find that due to cluster expansion, the systems forming IMBHs have densities consistent with present-day nuclear star clusters, such as those in the Milky Way and M33. Furthermore, we show that IMBH spin remains low due to repeated mergers, and we estimate the rate of GW190521 and GW231123-like events within the first 100 Myr to be $2.27-247.52$ and $3.23-63.63 $ per Gyr per cluster.