The detection rate of inspiral and quasi-normal modes of Population 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 defined by (<it>m</it><inf>1</inf><it>m</it><inf>2</inf>)3/5/(<it>m</it><inf>1</inf> + <it>m</it><inf>2</inf>)1/5 of Population III (Pop III) binary black holes (BH–BHs) is ∼30 M<inf>⊙</inf> with the total mass of ∼60 M<inf>⊙</inf> so that the inspiral chirp signal as well as quasi-normal mode (QNM) of the merging black hole (BH) are interesting targets of KAGRA. The detection rate of the coalescing Pop III BH–BHs is ∼180 events yr− 1 (<it>SFR</it><inf>p</inf>/(10−2.5 M<inf>⊙</inf> yr−1 Mpc−3))([<it>f</it><inf>b</inf>/(1 + <it>f</it><inf>b</inf>)]/0.33)<it>Err</it><inf>sys</inf> in our standard model, where <it>SFR</it><inf>p</inf>, <it>f</it><inf>b</inf> and <it>Err</it><inf>sys</inf> are the peak value of the Pop III star formation rate, the binary fraction and the systematic error with <it>Err</it><inf>sys</inf> = 1 for our standard model, respectively. To evaluate the robustness of chirp mass distribution and the range of <it>Err</it><inf>sys</inf>, we examine the dependence of the results on the unknown parameters and the distribution functions in the population synthesis code. We found that the chirp mass has a peak at ∼30 M<inf>⊙</inf> in most of parameters and distribution functions as well as <it>Err</it><inf>sys</inf> ranges from 0.046 to 4. Therefore, the detection rate of the coalescing Pop III BH–BHs ranges about 8.3-720 events yr− 1(<it>SFR</it><inf>p</inf>/(10− 2.5 M<inf>⊙</inf> yr− 1 Mpc− 3))([<it>f</it><inf>b</inf>/(1 + <it>f</it><inf>b</inf>)]/0.33). The minimum rate corresponds to the worst model which we think unlikely so that unless (<it>SFR</it><inf>p</inf>/(10− 2.5 M<inf>⊙</inf> yr− 1 Mpc− 3))([<it>f</it><inf>b</inf>/(1 + <it>f</it><inf>b</inf>)]/0.33) ≪ 0.1, we expect the Pop III BH–BHs merger rate of at least one event per year by KAGRA. Nakano, Tanaka & Nakamura show that if signal-to-noise ratio (S/N) of QNM is larger than 35, we can confirm or refute the general relativity (GR) more than 5σ level. In our standard model, the detection rate of Pop III BH–BHs whose S/N is larger than 35 is 3.2 events yr− 1 (<it>SFR</it><inf>p</inf>/(10− 2.5 M<inf>⊙</inf> yr− 1 Mpc− 3))([<it>f</it><inf>b</inf>/(1 + <it>f</it><inf>b</inf>)]/0.33)<it>Err</it><inf>sys</inf>. Thus, there is a good chance to check whether GR is correct or not in the strong gravity region.