Merger rate density of Population III binary black holes below, above, and in the pair-instability mass gap

TL;DR

This study estimates the merger rate density of Population III binary black holes, including those in and around the pair-instability mass gap, highlighting their potential contribution to future gravitational wave detections.

Contribution

It provides the first detailed merger rate estimates for Pop. III BH binaries across the entire mass spectrum, including the pair-instability gap, using extended binary population synthesis models.

Findings

Merger rate density for low-mass BHs is ~0.1 yr$^{-1}$ Gpc$^{-3}$.

High-mass BH mergers in the pair-instability gap occur at ~0.01 yr$^{-1}$ Gpc$^{-3}$.

Pop. III BH mergers tend to have low effective spins and high mass ratios.

Abstract

We present the merger rate density of Population (Pop.) 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: $5-50 M_\odot$) but also high-mass BHs (hBHs: $130-200 M_\odot$), where lBHs and hBHs are below and above the pair-instability mass gap ($50-130 M_\odot$), respectively. Pop. III BH-BHs can be categorized into three subpopulations: BH-BHs without hBHs (hBH0s: $m_{\rm tot} \lesssim 100 M_\odot$), with one hBH (hBH1s: $m_{\rm tot} \sim 130-260 M_\odot$), and with two hBHs (hBH2s: $m_{\rm tot} \sim 270-400 M_\odot$), where $m_{\rm tot}$ is the total mass of a BH-BH. Their merger rate densities at the current universe are $\sim 0.1$ yr$^{-1}$ Gpc$^{-3}$ for hBH0s, and $\sim 0.01$ yr$^{-1}$ Gpc$^{-3}$ for the sum of hBH1s and hBH2s, provided that the mass density of Pop. III stars is $\sim 10^{13} M_\odot$ 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 near future. They have low effective spins $\lesssim 0.2$ in the current universe. The number ratio of the hBH2s to the hBH1s is high, $\gtrsim 0.1$. We also find BHs in the mass gap (up to $\sim 85 M_\odot$) merge. These merger rates can be reduced to nearly zero if Pop. III binaries are always wide ($\gtrsim 100 R_\odot$), and if Pop. III stars always enter into chemically homogeneous evolution. The presence of close Pop. III binaries ($\sim 10 R_\odot$) are crucial for avoiding the worst scenario.