Evolution of the Black Hole Mass Function in Star Clusters from Multiple Mergers

We investigate the effects of black hole (BH) mergers in star clusters on the black hole mass function (BHMF). As BHs are not produced in pair-instability supernovae, it is suggested that there is a dearth of high-mass stellar BHs. This dearth generates a gap in the upper end of the BHMF. Meanwhile, parameter fitting of X-ray binaries suggests the existence of a gap in the mass function under 5 solar masses. We show, through evolving a coagulation equation, that BH mergers can appreciably fill the upper mass gap, and that the lower mass gap generates potentially observable features at larger mass scales. We also explore the importance of ejections in such systems and whether dynamical clusters can be formation sites of intermediate-mass BH seeds.