Binary black hole mergers from Population III star clusters

Binary black holes (BBHs) that are born from the evolution of Population III (Pop. III) stars are one of the main high-redshift targets for next-generation ground-based gravitational-wave (GW) detectors. Their predicted initial mass function and lack of metals make them the ideal progenitors of black holes above the upper edge of the pair-instability mass gap, that is, with a mass higher than ~134 (241) M_⊙ for stars that become (or do not become) chemically homogeneous during their evolution. We investigate the effects of cluster dynamics on the mass function of BBHs that are born from Pop. III stars by considering the main uncertainties on the mass function of Pop. III stars, the orbital properties of the binary systems, the star cluster mass, and the disruption time. In our dynamical models, at least ~5% and up to 100% BBH mergers in Pop. III star clusters have a primary mass m₁ above the upper edge of the pair-instability mass gap. In contrast, only ≲3% isolated BBH mergers have a primary mass above the gap, unless their progenitors evolved as chemically homogeneous stars. The lack of systems with a primary and/or secondary mass inside the gap defines a zone of avoidance with sharp boundaries in the plane of the primary mass-mass ratio. Finally, we estimate the merger rate density of BBHs. In the most optimistic case, we find a maximum of ℛ ~ 200 Gpc^-3 yr^-1 at ɀ ~ 15 for BBHs that formed via dynamical capture. For comparison, the merger rate density of isolated Pop. III BBHs is ℛ ≤ 10 Gpc^‑3 yr^‑1 for the same model of Pop. III star formation history.