The detection rate of Inspiral and Quasi-normal modes of Pop III binary black holes which can confirm or refute the General Relativity in the strong gravity region

Using our population synthesis code, we found that the typical chirp mass of Pop III BH-BHs is $\sim30~\msun$ with the total mass of $\sim60~\msun$ so that the inspiral chirp signal as well as quasi normal mode (QNM) of the merging BH are interesting targets of KAGRA. The detection rate of the coalescing Pop III BH-BHs is $\sim$180 $\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun \rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$ in our standard model where $\rm SFR_{p},~f_b$ and $\rm Err_{sys}$ are the peak value of the Pop III star formation rate, the binary fraction and the systematic error with $\rm Err_{sys}=1$ for our standard model, respectively. To evaluate the robustness of chirp mass distribution and the range of $\rm Err_{sys}$, we examine the dependence of the results on the unknown parameters and the distribution functions. We found that the chirp mass has a peak at $\sim 30 ~\msun$ in most of parameters and distribution functions as well as $\rm Err_{sys}$ ranges from 0.046 to 4. The minimum rate corresponds to the worst model which we think unlikely so that unless $ {\rm ~(SFR_p/(10^{-2.5}~\msun~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33) \ll 0.1}$, we expect the Pop III BH-BHs merger rate of at least one event per year by KAGRA. Nakano, Tanaka \& Nakamura (2015) show that if S/N of QNM is larger than 35, we can confirm or refute the General Relativity (GR) more than 5 sigma level. In our standard model, the detection rate of Pop III BH-BHs whose S/N is larger than 35 is $3.2~\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun \rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$. Thus, there is a good chance to check whether GR is correct or not in the strong gravity region.