Stellar-mass black holes in star clusters: implications for
  gravitational wave radiation
  We study the dynamics of stellar-mass black holes (BH) in star clusters with
particular attention to the formation of BH-BH binaries, which are interesting
as sources of gravitational waves (GW). We examine the properties of these
BH-BH binaries through direct N-body simulations of star clusters using the
GPU-enabled NBODY6 code. We perform simulations of N <= 10^5 Plummer clusters
of low-mass stars with an initial population of BHs. Additionally, we do
several calculations of star clusters confined within a reflective boundary
mimicking only the core of a massive cluster. We find that stellar-mass BHs
with masses ~ 10 solar mass segregate rapidly into the cluster core and form a
sub-cluster of BHs within typically 0.2 - 0.5 pc radius, which is dense enough
to form BH-BH binaries through 3-body encounters. While most BH binaries are
ejected from the cluster by recoils received during super-elastic encounters
with the single BHs, few of them harden sufficiently so that they can merge via
GW emission within the cluster. We find that for clusters with $N \ga 5\times
10^4$, typically 1 - 2 BH-BH mergers occur within them during the first ~ 4 Gyr
of evolution. Also for each of these clusters, there are a few escaping BH
binaries that can merge within a Hubble time, most of the merger times being
within a few Gyr. These results indicate that intermediate-age massive clusters
constitute the most important class of candidates for producing dynamical BH-BH
mergers. Old globular clusters cannot contribute significantly to the
present-day BH-BH merger rate since most of the mergers from them would have
occurred earlier. In contrast, young massive clusters are too young to produce
significant number of BH-BH mergers. Our results imply significant BH-BH merger
detection rates for the proposed "Advanced LIGO" GW detector. (Abridged)
