2018ApJ...864...13W

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_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 (Δ) between, e.g., giants and low-mass main-sequence stars, can be an effective probe to indirectly estimate N_BH in a GC aided by calibrations from numerical models. Using numerical models, including all relevant physics, we first show that N_BH is strongly anticorrelated with Δ between giant stars and low-mass main-sequence stars. We apply the distributions of Δ versus N_BH obtained from models to three Milky Way GCs to predict the N_BH retained by them at present. We calculate Δ using the publicly available Advanced Camera for Surveys' survey data for 47 Tuc, M10, and M22, all with identified stellar-mass BH candidates. Using these measured Δ and distributions of Δ versus N_BH from models as calibration we predict distributions for N_BH expected to be retained in these GCs. For 47 Tuc, M10, and M22 our predicted distributions peak at N_BH ≃ 20, 24, and 50, whereas, within the 2σ confidence level, N_BH can be up to ∼150, 50, and 200, respectively.