Gravitational wave quasinormal mode from Population III massive black hole binaries in various models of population synthesis

Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black hole mergers can be detected at the rate of 5.9-500 events yr(SFR/(10M yr Mpc))ṡ([f/(1+f)]/0.33) for various parameters and functions. This rate is estimated for events with SNR>8 for second-generation gravitational wave detectors such as KAGRA. Here, SFR and f are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only events with SNR>35, the event rate becomes 0.046-4.21 events yr(SFR/(10M yr Mpc))ṡ([f/(1+f)]/0.33). This suggest that for a remnant black hole spin of q>0.95 we have an event rate of quasinormal modes with SNR>35 of less than 0.037 events yr(SFR/(10M yr Mpc))ṡ([f/(1+f)]/0.33), while it is 3-30 events yr(SFR/(10M yr Mpc))ṡ([f/(1+f)]/0.33) for third-generation detectors such as the Einstein Telescope. If we detect many Population III binary black hole mergers, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.