The Cosmic Evolution of Binary Black Holes in Young, Globular and Nuclear Star Clusters: Rates, Masses, Spins and Mixing Fractions

TL;DR

This study models the cosmic evolution of binary black holes across different star cluster environments, revealing how formation channels influence merger rates, mass distributions, and spins, with implications for future gravitational wave observations.

Contribution

It introduces an upgraded semi-analytic framework to compare BBH populations across multiple formation channels using consistent physics, highlighting their distinct evolutionary signatures.

Findings

Merger rate density in GCs and NSCs is insensitive to metallicity.

Primary BH mass function becomes more top-heavy at higher redshift in GCs and NSCs.

Multiple formation channels contribute to the observed BBH population.

Abstract

The growing population of binary black holes (BBHs) observed by gravitational wave detectors is a potential Rosetta stone for understanding their formation channels. Here, we use an upgraded version of our semi-analytic codes {\sc fastcluster} and {\sc cosmo$\mathcal{R}$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 $\sim{1}$ to $\sim{4}$ 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 gravitational-wave transient catalog.