Dynamical evolution of stellar mass black holes in dense stellar clusters: estimate for merger rate of binary black holes originating from globular clusters

Abstract

We have performed N-body simulations of globular clusters (GCs) in order to\nestimate a detection rate of mergers of Binary stellar-mass Black Holes (BBHs)\nby means of gravitational wave (GW) observatories. For our estimate, we have\nonly considered mergers of BBHs which escape from GCs (BBH escapers). BBH\nescapers merge more quickly than BBHs inside GCs because of their small\nsemi-major axes. N-body simulation can not deal with a GC with the number of\nstars N ~ 10^6 due to its high calculation cost. We have simulated dynamical\nevolution of small-N clusters (10^4 <~ N <~ 10^5), and have extrapolated our\nsimulation results to large-N clusters. From our simulation results, we have\nfound the following dependence of BBH properties on N. BBHs escape from a\ncluster at each two-body relaxation time at a rate proportional to N.\nSemi-major axes of BBH escapers are inversely proportional to N, if initial\nmass densities of clusters are fixed. Eccentricities, primary masses, and mass\nratios of BBH escapers are independent of N. Using this dependence of BBH\nproperties, we have artificially generated a population of BBH escapers from a\nGC with N ~ 10^6, and have estimated a detection rate of mergers of BBH\nescapers by next-generation GW observatories. We have assumed that all the GCs\nare formed 10 or 12Gyrs ago with their initial numbers of stars N_i=5 x 10^5 --\n2 x 10^6 and their initial stellar mass densities inside their half-mass radii\n\\rho_h,i=6 x 10^3 -- 10^6M_sun pc^-3. Then, the detection rate of BBH escapers\nis 0.5 -- 20 yr^-1 for a BH retention fraction R_BH=0.5. A few BBH escapers are\ncomponents of hierarchical triple systems, although we do not consider secular\nperturbation on such BBH escapers for our estimate. Our simulations have shown\nthat BHs are still inside some of GCs at the present day. These BHs may\nmarginally contribute to BBH detection.\n