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.

Possible Indirect Confirmation of the Existence of Pop III Massive Stars by Gravitational Wave

We perform population synthesis simulations for Population III (Pop III) coalescing binary neutron stars (NS-NSs), neutron star - black hole binaries (NS-BHs), and binary black holes (BH-BHs) which merge within the age of the universe. We found that the typical mass of Pop III BH-BHs is $sim 30 rm{M}_{odot}$ so that the inspiral chirp signal of gravitational waves can be detected up to z=0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO network. Our simulations suggest that the detection rate of the coalescing Pop III BH-BHs is $140 (68) cdot ({rm SFR}_{rm p}/10^{-2.5} rm{M}_{odot} {rm yr}^{-1} {rm Mpc}^{-3}) cdot {rm Err}_{rm sys} ~{rm events} ~{rm yr}^{-1}$ for the flat (Salpeter) initial mass function (IMF), respectively, where $rm SFR_p$ and $rm Err_{sys}$ are the peak value of the Pop III star formation rate and the possible systematic errors due to the assumptions in Pop III population synthesis, respectively. $rm Err_{sys}=1$ correspond to conventional parameters for Pop I stars. From the observation of the chirp signal of the coalescing Pop III BH-BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH-BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass $sim 30~rm M_{odot}$ by the detections of gravitational waves if the merger rate of the Pop III massive BH-BHs dominates that of Pop I BH-BHs.