Repeated mergers and ejection of black holes within nuclear star clusters

Current stellar evolution models predict a dearth of black holes (BHs) with masses $\gtrsim \! 50\, \rm M_\odot$ and $\lesssim \! 5\, \rm M_\odot$ , and intermediate-mass black holes (IMBHs; $\sim \! 10^2\!-\! 10^5\rm\, M_\odot$ ) have not yet been detected beyond any reasonable doubt. A natural way to form massive BHs is through repeated mergers, detectable via gravitational wave emission with current LIGO/Virgo or future LISA and ET observations. Nuclear star clusters (NSCs) have masses and densities high enough to retain most of the merger products, which acquire a recoil kick at the moment of merger. We explore the possibility that IMBHs may be born as a result of repeated mergers in NSCs, and show how their formation pathways depend on the NSC mass and density, and BH spin distribution. We find that BHs in the pair-instability mass gap can be formed and observed by LIGO/Virgo, and show that the typical mass of the ejected massive BHs is 400- $500\, \rm M_\odot$ , with velocities of up to a few thousand $\, \rm km\, s^{-1}$ . Eventually, some of these IMBHs can become the seeds of supermassive BHs, observed today in the centres of galaxies. In dwarf galaxies, they could potentially solve the abundance, core-cusp, too-big-to-fail, ultra-faint, and baryon-fraction issues via plausible feedback scenarios.