Intermediate-mass black hole seeding in galactic nuclei from star cluster migration

Abstract

Nuclear star clusters are one of the most favorable sites to host hierarchical black hole (BH) mergers, potentially bridging the gap from stellar-mass to massive BHs. However, their assembly and the evolution of their BH populations remain poorly constrained. We investigate the process of intermediate-mass BH (IMBH) seeding in galactic nuclei from star cluster migration. We introduce inSpyral, a new semi-analytic model that draws star cluster populations from a galaxy formation model (L-Galaxies 2020),and integrates their evolution across a wide range of spatial scales, from BH core dynamics to the orbital motion in the host galaxy. We find that dynamical friction drives the inspiral of the most massive clusters in galaxies with $M_{\mathrm{\star, gal}} \lesssim 5 \times 10^{10} \,\mathrm{M_\odot}$, seeding their nuclei with IMBHs as early as $z \sim 6$. The BH mass distribution from BH mergers in migrating clusters extends to $\sim 300 \, \mathrm{M_\odot}$, a factor of five above the upper limit from in-situ formation. If clusters form with sub-parsec scale radii ($\lesssim 0.5 \, \mathrm{pc}$), hierarchical mergers significantly enhance BH mass growth before migration, and seed galactic nuclei with IMBHs above $10^4 \, \mathrm{M_\odot}$. The most massive and highly spinning gravitational-wave events are well reproduced by BH mergers involving second-generation remnants that experienced relatively small relativistic kicks ($\lesssim 100 \, \mathrm{km \, s^{-1}}$). GW231123 is consistent with BH mergers between a third-generation primary and a second-generation secondary, which occur in star clusters with mass $> 2 \times 10^{6} \, \mathrm{M_\odot}$.