The mass budget for intermediate-mass black holes in dense star clusters

ABSTRACT Intermediate-mass black holes (IMBHs) could form via runaway merging of massive stars in a young star cluster (YMC). We combine suite numerical simulations YMC formation with semi-analytic model for dynamical friction and evolution central quasi-star, to predict how final quasi-star relic IMBH masses scale properties (and compare observations). The argue that inner density profiles at are steep (approaching isothermal), producing some efficient even clusters relatively low effective densities, unlike models assume flat resembling those globular after relaxation. Our results can be approximated by simple analytic scalings, $M_{\rm IMBH} \propto v_{\rm cl}^{3/2}$ where $v_{\rm cl}^{2} = G\, M_{\rm cl}/r_{\rm h}$ is the circular velocity terms initial mass Mcl half-mass radius rh. While this suggests possible typical clusters, we show predicted these systems small, $\sim \! 100-1000\, {\rm M}_{\odot }$ or 0.0003\, cl}$, below most conservative observational upper limits all known cases. reach $\gtrsim 10^{4}\, centres nuclear ultra-compact dwarfs, compact ellipticals, but cases prediction remains far present observed supermassive BH systems.