The STARfall pathway: forging intermediate-mass black holes through stellar collisions in dense star clusters

Abstract

Intermediate-mass black holes (IMBHs, $10^2 < m_{\rm BH}/\mathrm{M}_{\odot} < 10^5$) are elusive objects bridging the gap between stellar-mass and supermassive black holes, whose origin remains uncertain. They may form from the collapse of very massive stars (VMSs, $m_*\geq150\,\mathrm{M}_{\odot}$) assembled through repeated stellar collisions in compact and fast evolving star clusters. We investigate the formation of VMSs and IMBH seeds via repeated mergers and collisions as a function of cluster initial conditions, assessing the implications for globular clusters and dense high-redshift system. We develop STARfall, a semi-analytic tool that follows the evolution of a massive stellar binary via binary-single interactions, mergers, collisions, and stellar evolution, while consistently accounting for the host cluster evolution. Our results show that clusters with central densities above $10^6\,\mathrm{M}_{\odot}\,\mathrm{pc}^{-3}$ can undergo a catastrophic sequence of stellar collisions, or "starastrophe", within $3$ Myr. Through this process, VMSs rapidly grow in mass and collapse into IMBHs with masses of up to $10^3-10^4\,\mathrm{M}_{\odot}$, despite the effects of intense stellar winds. Applying our models to observed systems, we find that compact clusters in the Cosmic Gems Arc and Milky Way globular clusters could have hosted VMSs that collapsed into IMBHs in this mass range. Despite their longer core-collapse timescales, the inferred central densities of Little Red Dots may also support IMBH formation in the same mass interval. Our models show that VMS assembly requires two essential ingredients: short core-collapse times and large central densities. Compared to observed systems, our models suggest that clusters in the Cosmic Gems Arcs and several Galactic globular clusters could have nurtured VMSs that directly collapsed to IMBHs with masses $10^3-10^4\,\text{M}_{\odot}$.