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We have performed N-body simulations of globular clusters (GCs) in order toestimate a detection rate of mergers of Binary stellar-mass Black Holes (BBHs)by means of gravitational wave (GW) observatories. For our estimate, we haveonly considered mergers of BBHs which escape from GCs (BBH escapers). BBHescapers merge more quickly than BBHs inside GCs because of their smallsemi-major axes. N-body simulation can not deal with a GC with the number ofstars N ~ 10^6 due to its high calculation cost. We have simulated dynamicalevolution of small-N clusters (10^4 <~ N <~ 10^5), and have extrapolated oursimulation results to large-N clusters. From our simulation results, we havefound the following dependence of BBH properties on N. BBHs escape from acluster at each two-body relaxation time at a rate proportional to N.Semi-major axes of BBH escapers are inversely proportional to N, if initialmass densities of clusters are fixed. Eccentricities, primary masses, and massratios of BBH escapers are independent of N. Using this dependence of BBHproperties, we have artificially generated a population of BBH escapers from aGC with N ~ 10^6, and have estimated a detection rate of mergers of BBHescapers by next-generation GW observatories. We have assumed that all the GCsare formed 10 or 12Gyrs ago with their initial numbers of stars N_i=5 x 10^5 --2 x 10^6 and their initial stellar mass densities inside their half-mass radii\rho_h,i=6 x 10^3 -- 10^6M_sun pc^-3. Then, the detection rate of BBH escapersis 0.5 -- 20 yr^-1 for a BH retention fraction R_BH=0.5. A few BBH escapers arecomponents of hierarchical triple systems, although we do not consider secularperturbation on such BBH escapers for our estimate. Our simulations have shownthat BHs are still inside some of GCs at the present day. These BHs maymarginally contribute to BBH detection.

monthly notices of the royal astronomical society

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