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Using our population synthesis code, we found that the typical chirp mass ofPop III BH-BHs is $\sim30~\msun$ with the total mass of $\sim60~\msun$ so thatthe inspiral chirp signal as well as quasi normal mode (QNM) of the merging BHare interesting targets of KAGRA. The detection rate of the coalescing Pop IIIBH-BHs is $\sim$180 $\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun\rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$ in our standardmodel where $\rm SFR_{p},~f_b$ and $\rm Err_{sys}$ are the peak value of thePop III star formation rate, the binary fraction and the systematic error with$\rm Err_{sys}=1$ for our standard model, respectively. To evaluate therobustness of chirp mass distribution and the range of $\rm Err_{sys}$, weexamine the dependence of the results on the unknown parameters and thedistribution functions. We found that the chirp mass has a peak at $\sim 30~\msun$ in most of parameters and distribution functions as well as $\rmErr_{sys}$ ranges from 0.046 to 4. The minimum rate corresponds to the worstmodel which we think unlikely so that unless $ {\rm~(SFR_p/(10^{-2.5}~\msun~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33) \ll 0.1}$,we expect the Pop III BH-BHs merger rate of at least one event per year byKAGRA. Nakano, Tanaka \& Nakamura (2015) show that if S/N of QNM is larger than35, we can confirm or refute the General Relativity (GR) more than 5 sigmalevel. In our standard model, the detection rate of Pop III BH-BHs whose S/N islarger than 35 is $3.2~\rm events~yr^{-1}$$(\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 isa good chance to check whether GR is correct or not in the strong gravityregion.

monthly notices of the royal astronomical society

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