Gravitational waves from merging intermediate-mass black holes : II Event rates at ground-based detectors

Abstract

Based on a dynamical formation model of a supermassive black hole (SMBH), we estimate the expected observational profile of gravitational wave at ground-based detectors, such as KAGRA or advanced LIGO/VIRGO. Noting that the second generation of detectors have enough sensitivity from 10 Hz and up (especially with KAGRA owing to its location at less seismic noise), we are able to detect the ring-down gravitational wave of a BH with the mass $M < 2\times 10^3 M_\odot $. This enables us to check the sequence of BH mergers to SMBHs via intermediate-mass BHs. We estimate the number density of galaxies from the halo formation model and estimate the number of BH mergers from the giant molecular cloud model assuming hierarchical growth of merged cores. At the designed KAGRA (and/or advanced LIGO/VIRGO), we find that the BH merger of its total mass $M\sim 60M_\odot$ is at the peak of the expected mass distribution. With its signal-to-noise ratio $ρ=10 (30)$, we estimate the event rate $R \sim 200 (20)$ per year in the most optimistic case, and we also find that BH mergers in the range $M < 150 M_\odot$ are $R>1$ per year for $ρ=10$. Thus, if we observe a BH with more than $100 M_\odot$ in future gravitational-wave observations, our model naturally explains its source.