We have performed N -body simulations of globular clusters ( GCs ) in order to estimate a detection rate of mergers of Binary stellar-mass Black Holes ( BBHs ) by means of gravitational wave ( GW ) observatories .
For our estimate , we have only considered mergers of BBHs which escape from GCs ( BBH escapers ) .
BBH escapers merge more quickly than BBHs inside GCs because of their small semi-major axes . N -body simulation can not deal with a GC with the number of stars N \sim 10 ^ { 6 } due to its high calculation cost .
We have simulated dynamical evolution of small- N clusters ( 10 ^ { 4 } \lesssim N \lesssim 10 ^ { 5 } ) , and have extrapolated our simulation results to large- N clusters .
From our simulation results , we have found the following dependence of BBH properties on N .
BBHs escape from a cluster at each two-body relaxation time at a rate proportional to N .
Semi-major axes of BBH escapers are inversely proportional to N , if initial mass densities of clusters are fixed .
Eccentricities , primary masses , and mass ratios of BBH escapers are independent of N .
Using this dependence of BBH properties , we have artificially generated a population of BBH escapers from a GC with N \sim 10 ^ { 6 } , and have estimated a detection rate of mergers of BBH escapers by next-generation GW observatories .
We have assumed that all the GCs are formed 10 or 12 Gyrs ago with their initial numbers of stars N _ { i } = 5 \times 10 ^ { 5 } – 2 \times 10 ^ { 6 } and their initial stellar mass densities inside their half-mass radii \rho _ { h,i } = 6 \times 10 ^ { 3 } – 10 ^ { 6 } M _ { \odot } \mbox { pc } ^ { -3 } .
Then , the detection rate of BBH escapers is 0.5 – 20 yr ^ { -1 } for a BH retention fraction R _ { BH } = 0.5 .
A few BBH escapers are components of hierarchical triple systems , although we do not consider secular perturbation on such BBH escapers for our estimate .
Our simulations have shown that BHs are still inside some of GCs at the present day .
These BHs may marginally contribute to BBH detection .