Merger Rate Density of Population III Binary Black Holes Below, Above, and in the Pair-instability Mass Gap

Abstract

Abstract We present the merger rate density of Population III binary black holes (BHs) by means of a widely used binary population synthesis code BSE with extensions to very massive and extreme metal-poor stars. We consider not only low-mass BHs (lBHs: 5–50M ⊙) but also high-mass BHs (hBHs: 130–200M ⊙), where lBHs and hBHs are below and above the pair-instability mass gap (50–130M ⊙), respectively. Population III BH–BHs can be categorized into three subpopulations: BH–BHs without hBHs (hBH0s: m tot ≲ 100M ⊙), with one hBH (hBH1s: m tot ∼ 130–260M ⊙), and with two hBHs (hBH2s: m tot ∼ 270–400M ⊙), where m tot is the total mass of a BH–BH. Their merger rate densities at the current universe are ∼0.1 yr−1 Gpc−3 for hBH0s, and ∼0.01 yr−1 Gpc−3 for the sum of hBH1s and hBH2s, provided that the mass density of Population III stars is ∼1013 M ⊙ Gpc−3. These rates are modestly insensitive to initial conditions and single star models. The hBH1 and hBH2 mergers can dominate BH–BHs with hBHs discovered in the near future. They have low effective spins ≲0.2 in the current universe. The number ratio of hBH2s to hBH1s is high, ≳0.1. We also find that BHs in the mass gap (up to ∼85M ⊙) merge. These merger rates can be reduced to nearly zero if Population III binaries are always wide (≳100R ⊙), and if Population III stars always enter into chemically homogeneous evolution. The presence of close Population III binaries (∼10R ⊙) is crucial for avoiding the worst scenario.