Predicting Stellar-Mass Black Hole Populations in Globular Clusters

Recent discoveries of black hole (BH) candidates in Galactic and extragalactic globular clusters (GCs) have ignited interest in understanding how BHs dynamically evolve in a GC and the number of BHs ($N_{\rm{BH}}$) that may still be retained by today's GCs. Numerical models show that even if stellar-mass BHs are retained in today's GCs, they are typically in configurations that are not directly detectable. We show that a suitably defined measure of mass segregation ($\Delta$) between, e.g., giants and low-mass main-sequence stars, can be an effective probe to indirectly estimate $N_{\rm{BH}}$ in a GC aided by calibrations from numerical models. Using numerical models including all relevant physics we first show that $N_{\rm{BH}}$ is strongly anticorrelated with $\Delta$ between giant stars and low-mass main-sequence stars. We apply the distributions of $\Delta$ vs $N_{\rm{BH}}$ obtained from models to three Milky Way GCs to predict the $N_{\rm{BH}}$ retained by them at present. We calculate $\Delta$ using the publicly available ACS survey data for 47 Tuc, M 10, and M 22, all with identified stellar-mass BH candidates. Using these measured $\Delta$ and distributions of $\Delta$ vs $N_{\rm{BH}}$ from models as calibration we predict distributions for $N_{\rm{BH}}$ expected to be retained in these GCs. For 47 Tuc, M 10, and M 22 our predicted distributions peak at $N_{\rm{BH}}\approx20$, $24$, and $50$, whereas, within the $2\sigma$ confidence level, $N_{\rm{BH}}$ can be up to $\sim150$, $50$, and $200$, respectively.