2021MNRAS.505.2753S

Intermediate-mass black holes (IMBHs) could form via runaway merging of massive stars in a young massive star cluster (YMC). We combine a suite of numerical simulations of YMC formation with a semi-analytic model for dynamical friction and merging of massive stars and evolution of a central quasi-star, to predict how final quasi-star and relic IMBH masses scale with cluster properties (and compare with observations). The simulations argue that inner YMC density profiles at formation are steep (approaching isothermal), producing some efficient merging even in clusters with relatively low effective densities, unlike models that assume flat central profiles resembling those of globular clusters after central relaxation. Our results can be approximated by simple analytic scalings, with M_ IMBH_ ∝v_ cl_^3/2 where v_ cl_² = G M_ cl_/r h_ is the circular velocity in terms of initial cluster mass M_cl and half-mass radius r_h. While this suggests IMBH formation is possible even in typical clusters, we show that predicted IMBH masses for these systems are small, ∼100-1000 M_☉ or ∼0.0003 M_ cl_, below even the most conservative observational upper limits in all known cases. The IMBH mass could reach ≳10⁴ M_☉ in the centres nuclear star clusters, ultra-compact dwarfs, or compact ellipticals, but in all these cases the prediction remains far below the present observed supermassive BH masses in these systems.