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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 which assume flat central profiles resembling those of globular clusters (GCs) {em after} central relaxation. Our results can be approximated by simple analytic scalings, with $M_{rm IMBH} propto v_{rm cl}^{3/2}$ where $v_{rm cl}^{2} = G,M_{rm cl}/r_{rm h}$ is the circular velocity in terms of initial cluster mass $M_{rm cl}$ and half-mass radius $r_{rm h}$. While this suggests IMBH formation is {em possible} even in typical clusters, we show that predicted IMBH masses for these systems are small, $sim 100-1000,M_{odot}$ or $sim 0.0003,M_{rm cl}$, below even the most conservative observational upper limits in all known cases. The IMBH mass could reach $gtrsim 10^{4},M_{odot}$ in the centers 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.
Establishing or ruling out, either through solid mass measurements or upper limits, the presence of intermediate-mass black holes (IMBHs) at the centers of star clusters would profoundly impact our understanding of problems ranging from the formation
For a sample of nine Galactic globular clusters we measured the inner kinematic profiles with integral-field spectroscopy that we combined with existing outer kinematic measurements and HST luminosity profiles. With this information we are able to de
Current theoretical models predict a mass gap with a dearth of stellar black holes (BHs) between roughly $50,M_odot$ and $100,M_odot$, while, above the range accessible through massive star evolution, intermediate-mass BHs (IMBHs) still remain elusiv
Collisions were suggested to potentially play a role in the formation of massive stars in present day clusters, and have likely been relevant during the formation of massive stars and intermediate mass black holes within the first star clusters. In t
We consider spherical stellar clusters with a broad mass function and a relaxation time short enough so that the segregation of massive stars toward the centre occurs before they have time to evolve off the main sequence. The relaxational and collisi