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

Abstract: 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.