From Young Massive Clusters to Old Globular Clusters: Density Profile Evolution and IMBH Formation

The surface brightness profiles of globular clusters are conventionally described with the well-known King profile. However, observations of young massive clusters (YMCs) in the local Universe suggest that they are better fit by simple models with flat central cores and simple power-law densities in their outer regions (such as the Elson-Fall-Freeman, or EFF, profile). Depending on their initial central density, YMCs may also facilitate large numbers of stellar collisions, potentially creating very massive stars that will directly collapse to intermediate-mass black holes (IMBHs). Using Monte Carlo $N$-body models of YMCs, we show that EFF-profile clusters transform to Wilson or King profiles through natural dynamical evolution, but that their final $W_0$ parameters do not strongly correlate to their initial concentrations. In the densest YMCs, runaway stellar mergers can produce stars that collapse into IMBHs, with their final masses depending on the treatment of the giant star envelopes during collisions. If a common-envelope prescription is assumed, where the envelope is partially or entirely lost, stars form with masses up to $824\,M_{\odot}$, collapsing into IMBHs of $232\,M_{\odot}$. Alternatively, if no mass loss is assumed, stars as massive as $4000\,M_{\odot}$ can form, collapsing into IMBHs of $\sim 4000\,M_{\odot}$. In doing so, these runaway collisions also deplete the clusters of their primordial massive stars, reducing the number of stellar-mass BHs by as much as $\sim$ 40%. This depletion will accelerate the core collapse, suggesting that the process of IMBH formation itself may produce the high densities observed in some core-collapsed clusters.