Dynamical evolution of stellar-mass black holes in dense stellar
  clusters: estimate for merger rate of binary black holes originating from
  globular clusters
  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 ~ 10^6 due to its high calculation cost. We have simulated dynamical
evolution of small-N clusters (10^4 <~ N <~ 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 ~ 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 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 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.
