Abstract
Abstract It has been proposed that primordial black holes (PBHs) form binaries in the radiation dominated era. Once formed, some fraction of them may merge within the age of the universe by gravitational radiation reaction. We investigate the merger rate of the PBH binaries when the PBHs have a distribution of masses around , which is a generalization of the previous studies where the PBHs are assumed to have the same mass. After deriving a formula for the merger time probability distribution in the PBH mass plane, we evaluate it under two different approximations. We identify a quantity constructed from the mass distribution of the merger rate density per unit cosmic time and comoving volume , , which universally satisfies 0.97 ≲ α ≲ 1.05 for all binary masses independently of the PBH mass function. This result suggests that the measurement of this quantity is useful for testing the PBH scenario.
Highlights
Recent detections of gravitational wave events (GW150914, LVT151012, GW151226, GW170104, GW170608, and GW170814) by the LIGO-Virgo collaboration (Abbott et al 2016b, 2016c, 2017a, 2017b, 2017c) revealed the existence of binary black holes (BHs) in the mass range 8–35 M
We extend the formalism of previous studies (Nakamura et al 1997; Ioka et al 1998; Sasaki et al 2016) to compute the merger event rate to the case in which the primordial black holes (PBHs) mass function is not restricted to a single mass but extends over a mmax mmin 10.8 mass range We assume between that the mmin PBH
Previous studies (Sasaki et al 2016) showed that the BH binary merger event rate estimated by LIGO can be explained by the PBHs, which constitute only a tiny fraction of the entire dark matter
Summary
Recent detections of gravitational wave events (GW150914, LVT151012, GW151226, GW170104, GW170608, and GW170814) by the LIGO-Virgo collaboration (Abbott et al 2016b, 2016c, 2017a, 2017b, 2017c) revealed the existence of binary black holes (BHs) in the mass range 8–35 M. In Sasaki et al (2016), under the approximation that all PBHs have the same mass of 30 M , it was shown that the expected event rate of the PBH binary mergers is consistent with the one determined by the LIGO-Virgo collaboration after the announcement of GW150914 (Abbott et al 2016d), if the fraction of cold dark matter in PBHs is about 10−3 This fraction is consistent with existing observational upper limits We apply the derived formula to evaluate the mass dependence of the merger rate in the (m1, m2) BH mass plane and show that the special quantity constructed out of the event rate density becomes almost independent of the PBH mass function
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