The cosmic evolution of binary black holes in young, globular, and nuclear star clusters: rates, masses, spins, and mixing fractions

The growing population of binary black holes (BBHs) observed by gravitational wave (GW) detectors is a potential Rosetta stone for understanding their formation channels. Here, we use an upgraded version of our semi-analytical codes FASTCLUSTER and COSMOR ATE to investigate the cosmic evolution of four different BBH populations: isolated BBHs and dynamically formed BBHs in nuclear star clusters (NSCs), globular clusters (GCs), and young star clusters (YSCs). With our approach, we can study different channels assuming the same stellar and binary input physics. We find that the merger rate density of BBHs in GCs and NSCs is barely affected by stellar metallicity (Z), while the rate of isolated BBHs changes wildly with Z. BBHs in YSCs behave in an intermediate way between isolated and GC/NSC BBHs. The local merger rate density of Nth-generation black holes (BHs), obtained by summing up hierarchical mergers in GCs, NSCs, and YSCs, ranges from similar to 1 to similar to 4 Gpc(-3) yr(-1) and is mostly sensitive to the spin parameter. We find that the mass function of primary BHs evolves with redshift in GCs and NSCs, becoming more top-heavy at higher z. In contrast, the primary BH mass function almost does not change with redshift in YSCs and in the field. This signature of the BH mass function has relevant implications for Einstein Telescope and Cosmic Explorer. Finally, our analysis suggests that multiple channels contribute to the BBH population of the second GW transient catalogue.

Automated summary

This study investigates the cosmic evolution of different populations of binary black holes (BBHs) using upgraded semi-analytical codes. The results show that the merger rate density of BBHs in globular clusters (GCs) and nuclear star clusters (NSCs) is not significantly affected by stellar metallicity, while the rate of isolated BBHs changes with metallicity. The behavior of BBHs in young star clusters (YSCs) is intermediate between isolated and GC/NSC BBHs. The local merger rate density of Nth-generation black holes is mostly influenced by the spin parameter. The primary black hole mass function evolves with redshift in GCs and NSCs but remains constant in YSCs and in the field.