  In order to investigate the formation rate of binary black holes (BBHs) in
stellar clusters with a mass comparable to open clusters, we performed a series
of direct $N$-body simulations of open clusters with a mass of $2.5\times10^3$
(Model A) and $10^4 M_{\odot}$ (Model B). Since such low-mass clusters would
have been more populous than globular clusters when they were born, low-mass
clusters are also candidates as the origin of BBHs which are the source of the
gravitational waves. In model A, most of BBHs merged within 10 Gyr formed via
dynamically formed main-sequence binary stars and stable and unstable mass
transfer between them since open clusters collapse within the main-sequence
life-time of massive stars. These binaries, therefore, have little
eccentricities. The fraction of such binaries among all merging BBHs increases
as the cluster mass decrease due to the shorter relaxation time. In our
simulations, $4.0\times10^{-5}$ and $1.7\times10^{-5}$ BBHs per solar mass
merged within 10 Gyr for models A and B, respectively. These values correspond
to $\sim$ 20-50% of the number of mergers per solar mass originated from
globular clusters with a mass of $10^5$-$10^6M_{\odot}$. Thus, the contribution
of BBHs originated from open clusters is not negligible. The estimated mergers
rate density in the local universe is about 0.3 yr$^{-1}$ Gpc$^{-3}$ assuming a
cluster mass function with a power of $-$2.
