Gravitational-Wave Emission from Binary Black Holes Formed in Open Clusters

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.