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
May 26, 201522 pages
Published in:
- Mon.Not.Roy.Astron.Soc. 456 (2016) 1, 1093-1114
- Published: Feb 11, 2016
e-Print:
- 1505.06962 [astro-ph.SR]
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Abstract: (Oxford University Press)
Using our population synthesis code, we found that the typical chirp mass defined by (m_1m_2)^3/5/(m_1 + m_2)^1/5 of Population III (Pop III) binary black holes (BH–BHs) is ∼30 M_⊙ with the total mass of ∼60 M_⊙ 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 (SFR_p/(10^−2.5 M_⊙ yr^−1 Mpc^−3))([f_b/(1 + f_b)]/0.33)Err_sys in our standard model, where SFR_p, f_b and Err_sys are the peak value of the Pop III star formation rate, the binary fraction and the systematic error with Err_sys = 1 for our standard model, respectively. To evaluate the robustness of chirp mass distribution and the range of Err_sys, 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_⊙ in most of parameters and distribution functions as well as Err_sys 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(SFR_p/(10^− 2.5 M_⊙ yr^− 1 Mpc^− 3))([f_b/(1 + f_b)]/0.33). The minimum rate corresponds to the worst model which we think unlikely so that unless (SFR_p/(10^− 2.5 M_⊙ yr^− 1 Mpc^− 3))([f_b/(1 + f_b)]/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 (SFR_p/(10^− 2.5 M_⊙ yr^− 1 Mpc^− 3))([f_b/(1 + f_b)]/0.33)Err_sys. Thus, there is a good chance to check whether GR is correct or not in the strong gravity region.Note:
- 29 pages, 24 figures, accepted to MNRAS
- black hole physics
- gravitational waves
- binaries: general
- stars: black holes
References(76)
Figures(35)