Predicting Stellar-Mass Black Hole Populations in Globular Clusters (1712.03979v3)

Abstract: 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.