We perform population synthesis simulations for Population III (Pop III) coalescing compact binary which merge within the age of the universe. We found that the typical mass of Pop III binary black holes (BH-BHs) is ∼ 30 M ⊙ 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) events/yr (SFR p /(10 −2.5 M ⊙ /yr/Mpc 3 )) · Err sys for the flat (Salpeter) initial mass function (IMF), respectively, where SFR p and 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. 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 ∼ 30 M ⊙ by the detections of gravitational waves if the merger rate of the Pop III massive BH-BHs dominates that of Pop I BH-BHs.
Using our population synthesis code, we found that the typical chirp mass defined by (m 1 m 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.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 yrThe minimum rate corresponds to the worst model which we think unlikely so that unless (SFR p /(10 −2.5 M ⊙ yr1, 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 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.
We study the formation of stellar mass binary black holes (BBHs) originating from Population III (PopIII) stars, performing stellar evolution simulations for PopIII binaries with MESA. We find that a significant fraction of PopIII binaries form massive BBHs through stable mass transfer between two stars in a binary, without experiencing common envelope phases. We investigate necessary conditions required for PopIII binaries to form coalescing BBHs with a semi-analytical model calibrated by the stellar evolution simulations. The BBH formation efficiency is estimated for two different initial conditions for PopIII binaries with large and small separations, respectively. Consequently, in both models, ∼ 10% of the total PopIII binaries form BBHs only through stable mass transfer and ∼ 10% of these BBHs merge due to gravitational wave emission within the Hubble time. Furthermore, the chirp mass of merging BBHs has a flat distribution over 15 < ∼ M chirp /M < ∼ 35. This formation pathway of PopIII BBHs is presumably robust because stable mass transfer is less uncertain than common envelope evolution, which is the main formation channel for Population II BBHs. We also test the hypothesis that the BBH mergers detected by LIGO originate from PopIII stars using the total number of PopIII stars formed in the early universe as inferred from the optical depth measured by Planck. We conclude that the PopIII BBH formation scenario can explain the mass-weighted merger rate of the LIGO's O1 events with the maximal PopIII formation efficiency inferred from the Planck measurement, even without BBHs formed by unstable mass transfer or common envelope phases.
Pre-DECIGO (DECihertz laser Interferometer Gravitational wave Observatory) consists of three spacecraft arranged in an equilateral triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be in the late 2020s.Pre-DECIGO has one clear target: binary black holes (BBHs) like GW150914 and GW151226. Pre-DECIGO can detect ∼ 30M ⊙ -30M ⊙ BBH mergers like GW150914 up to redshift z ∼ 30. The cumulative event rate is ∼ 1.8 × 10 5 events yr −1 in the Pop III origin model of BBHs like GW150914, and it saturates at z ∼ 10, while in the primordial BBH (PBBH) model, the cumulative event rate is ∼ 3 × 10 4 events yr −1 at z = 30 even if only 0.1% of the dark matter consists of PBHs, and it is still increasing at z = 30. In the Pop I/II model of GW150914-like BBHs, the cumulative event rate is (3-10) × 10 5 events yr −1 and it saturates at z ∼ 6. We present the requirements on orbit accuracy, drag-free techniques, laser power, frequency stability, and the interferometer test mass. For BBHs like GW150914 at 1 Gpc (z ∼ 0.2), SNR ∼ 90 is achieved with the definition of Pre-DECIGO in 0.01-100 Hz band. Since for z ≫ 1 the characteristic strain amplitude h c for a fixed frequency band weakly depends on z as z −1/6 , ∼ 10% of BBHs near face-on have SNR > 5 (7) even at z ∼ 30 (10). Pre-DECIGO can measure the mass spectrum and the z-dependence of the merger rate to distinguish various models of BBHs like GW150914, such as Pop III BBH, Pop II BBH and PBBH scenarios.Pre-DECIGO can also predict the direction of BBHs at z = 0.1 with an accuracy of ∼ 0.3 deg 2 and a merging time accuracy of ∼ 1 s at about a day before the merger so that ground-based GW detectors further developed at that time as well as electromagnetic follow-up observations can prepare for the detection of merger in advance like a solar eclipse. For intermediate mass BBHs such as ∼ 640M ⊙ -640M ⊙ at a large redshift z > 10, the quasinormal mode frequency after the merger can be within the Pre-DECIGO band so that the ringing tail can also be detectable to confirm the Einstein theory of general relativity with SNR ∼ 35.
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