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 (NBH) that may still be retained by todays GCs. Numerical models show that even if stellar-mass BHs are retained in todays GCs, they are typically in configurations that are not directly detectable. We show that a suitably defined measure of mass segregation (Δ) between, e.g., giants and low-mass main-sequence stars, can be an effective probe to indirectly estimate NBH in a GC aided by calibrations from numerical models. Using numerical models, including all relevant physics, we first show that NBH is strongly anticorrelated with Δ between giant stars and low-mass main-sequence stars. We apply the distributions of Δ versus NBH obtained from models to three Milky Way GCs to predict the NBH retained by them at present. We calculate Δ using the publicly available Advanced Camera for Surveys survey data for 47Tuc, M10, and M22, all with identified stellar-mass BH candidates. Using these measured Δ and distributions of Δ versus NBH from models as calibration we predict distributions for NBH expected to be retained in these GCs. For 47Tuc, M10, and M22 our predicted distributions peak at NBH≈20, 24, and 50, whereas, within the 2σ confidence level, NBH can be up to ∼150, 50, and 200, respectively.