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

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 ∼10¹³M_⊙ 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.