Our current understanding of the stellar initial mass function and massive star evolution suggests that young globular clusters may have formed hundreds to thousands of stellar-mass black holes, the remnants of stars with initial masses from $sim 20 - 100, M_odot$. Birth kicks from supernova explosions may eject some black holes from their birth clusters, but most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of globular clusters containing large numbers of stellar black holes. We describe numerical results for 42 models, covering a range of realistic initial conditions, including up to $1.6times10^6$ stars. In almost all models we find that significant numbers of black holes (up to $sim10^3$) are retained all the way to the present. This is in contrast to previous theoretical expectations that most black holes should be ejected dynamically within a few Gyr. The main reason for this difference is that core collapse driven by black holes (through the Spitzer mass segregation instability) is easily reverted through three-body processes, and involves only a small number of the most massive black holes, while lower-mass black holes remain well-mixed with ordinary stars far from the central cusp. Thus the rapid segregation of stellar black holes does not lead to a long-term physical separation of most black holes into a dynamically decoupled inner core, as often assumed previously. Combined with the recent detections of several black hole X-ray binary candidates in Galactic globular clusters, our results suggest that stellar black holes could still be present in large numbers in many globular clusters today, and that they may play a significant role in shaping the long-term dynamical evolution and the present-day dynamical structure of many clusters.
Globular clusters should be born with significant numbers of stellar-mass black holes (BHs). It has been thought for two decades that very few of these BHs could be retained through the cluster lifetime. With masses ~10 MSun, BHs are ~20 times more massive than an average cluster star. They segregate into the cluster core, where they may eventually decouple from the remainder of the cluster. The small-N core then evaporates on a short timescale. This is the so-called Spitzer instability. Here we present the results of a full dynamical simulation of a globular cluster containing many stellar-mass BHs with a realistic mass spectrum. Our Monte Carlo simulation code includes detailed treatments of all relevant stellar evolution and dynamical processes. Our main finding is that old globular clusters could still contain many BHs at present. In our simulation, we find no evidence for the Spitzer instability. Instead, most of the BHs remain well-mixed with the rest of the cluster, with only the innermost few tens of BHs segregating significantly. Over the 12 Gyr evolution, fewer than half of the BHs are dynamically ejected through strong binary interactions in the cluster core. The presence of BHs leads to long-term heating of the cluster, ultimately producing a core radius on the high end of the distribution for Milky Way globular clusters (and those of other galaxies). A crude extrapolation from our model suggests that the BH--BH merger rate from globular clusters could be comparable to the rate in the field.
