Abstract 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 $\sim{} 241~\mathrm{M}_\odot$. In Mestichelli et al. 2024, we investigated 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. To do so, we used the semi-analytical code $\text{FASTCLUSTER}$ (Mapelli et al. 2021, Torniamenti et al. 2024). In our dynamical models, at least $\sim 5\%$ and up to $100\%$ BBH mergers in Pop. III star clusters have a primary mass $m_1$ above the upper edge of the pair-instability mass gap. In contrast, only $\lesssim {} 3\%$ 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 estimated the merger rate density of BBHs. In the most optimistic case, we found a maximum of $\mathcal{R}\sim200\,{\rm Gpc^{-3}\,yr^{-1}}$ at $z\sim15$ for BBHs that formed via dynamical capture. For comparison, the merger rate density of isolated Pop. III BBHs is $\mathcal{R}\leq{}10\,{\rm Gpc^{-3}\,yr^{-1}}$ for the same model of Pop. III star formation history. Here we report the catalogs of BBH mergers and the merger rate densities as processed via $\text{COSMO}\mathcal{R}\text{ATE}$ (Santoliquido et al. 2020, 2021, 2023) obtained with the fiducial configuration from Mestichelli et al. 2024.

We report here the merger rate densities and BBH merger catalogs processed with $\text{COSMO}\mathcal{R}\text{ATE}$ (Santoliquido et al. 2020, 2021, 2023) for Pop. IIII clusters. The fiducial configuration (log1) corresponds to a log-flat initial mass function and orbital parameters from Sana et al. 2012. The catalogs of single and binary black holes were extracted with $\text{SEVN}$ (Iorio et al. 2023,Costa et al. 2023) and used as input of the dynamical semi-analytical code $\text{FASTCLUSTER}$ (Mapelli et al. 2021, Torniamenti et al. 2024), which follows the dynamical hardening of binaries and their gravitational-wave driven evolution while self-consistently modeling the main physical processes governing the host star cluster. We assume that our clusters can survive for a maximum of $300\,\rm Myr$; the evolution of BBH binaries is followed until z=0. 20_10 vs. 30_11 catalogs_20_10: fiducial configuration in Mestichelli et al. 2024. The parameter zMAX in cosmo_params.py is set to 20; catalogs_30_11: fiducial configuration used for the ETO paper. Here we put zMAX = 30 to be in accordance with Santoliquido et al. 2023 and with the star formation rate density from Hartwig et al. 2022. We show a comparison of the two configurations in m1_hm_lm_catalogs.png and mrd_hm_lm_catalogs.png, produced via make_plots.py. In particular: m1_hm_lm_catalogs. png shows the primary mass distributions of BBH mergers at $z=15$ for high-mass (HM) and low-mass (LM) clusters, considering original (orig) and dynamical (oleary) binaries; mrd_hm_lm_catalogs.png shows instead the merger rate density of BBHs from z = 0 to z = zMAX for HM and LM clusters. Files description All the information on the structure of catalogs_20_10 and catalogs_30_11 can be found in README.md