Mass and rate of hierarchical black hole mergers in young, globular and nuclear star clusters

TL;DR

This study introduces a semi-analytic model to simulate hierarchical black hole mergers across different star cluster types, revealing their frequency, mass distribution, and contribution to gravitational wave events.

Contribution

It provides a fast semi-analytic approach to model hierarchical black hole mergers in star clusters, highlighting differences among cluster types and environmental effects on black hole masses.

Findings

Hierarchical mergers are more common in nuclear star clusters due to higher escape velocities.

Black holes up to ~1000 solar masses can form in NSCs, with larger masses possible in high escape velocity environments.

The local BBH merger rate varies from 10 to 60 Gpc$^{-3}$ yr$^{-1}$, with NSCs contributing significantly.

Abstract

Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs, because of the different escape velocity. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitor's metallicity. In our fiducial model, we form black holes (BHs) with masses up to $\sim{}10^3$ M$_\odot$ in NSCs and up to $\sim{}10^2$ M$_\odot$ in both GCs and YSCs. When escape velocities in excess of 100 km~s$^{-1}$ are considered, BHs with mass $>10^3$ M$_\odot$ are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs, but only in metal-poor environments. The local BBH merger rate in our models ranges from $\sim{}10$ to $\sim{} 60$ Gpc$^{-3}$ yr$^{-1}$; hierarchical BBHs in NSCs account for $\sim{}10^{-2}- 0.2$ Gpc$^{-3}$ yr$^{-1}$, with a strong upper limit of $\sim{}10$ Gpc$^{-3}$ yr$^{-1}$. When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.