The detection rates of merging binary black holes originating from star clusters and their mass function

Advanced LIGO (Laser Interferometer Gravitational Wave Observatory) observations achieved the first detection of the gravitational wave, which was from a merging binary black hole (BBH). In the near future, more merger events will be observed, and the mass distribution of them will become available. The mass distribution of merger events reflects the evolutionary path of BBHs: dynamical formation in dense star clusters or common envelope evolution from primordial binaries. In this paper, we estimate the detection rate of merging BBHs which dynamically formed in dense star clusters by combining the results of N-body simulations, modeling of globular clusters, and cosmic star-cluster formation history. We estimate that the merger rate density in the local universe within the redshift of 0.1 is 13-57 Gpc^-3 yr^-1. We find that the detection rate is 0.23-4.6 per year for the current sensitivity limit and that it would increase to 5.1-99 per year for the designed sensitivity which will be achieved in 2019. The distribution of merger rate density in the local universe as a function of redshifted chirp mass has a peak close to the low-mass end. The chirp mass function of the detected mergers, on the other hand, has a peak at the high-mass end, but is almost flat. This difference is simply because the detection range is larger for more massive BBHs.