The star clusters that make black hole binaries across cosmic time

TL;DR

This paper combines cosmological models and dynamical prescriptions to identify star cluster properties that favor the formation and merger of black hole binaries over cosmic time, estimating merger rates and cluster characteristics.

Contribution

It introduces a combined cosmological and dynamical framework to predict which star clusters produce merging black hole binaries and estimates their cosmic merger rate evolution.

Findings

Black hole binaries ejected from clusters of ~10^{5.3} M_sun merge ex-situ.

In-situ merging binaries form in clusters of ~10^{5.7} M_sun.

Estimated cosmic merger rate of ~6 Gpc^{-3} yr^{-1} at z=0.

Abstract

We explore the properties of dense star clusters that are likely to be the nurseries of stellar black holes pairing in close binaries. We combine a cosmological model of globular cluster formation with analytic prescriptions for the dynamical assembly and evolution of black hole binaries to constrain which types of clusters are most likely to form binaries tight enough to coalesce within a Hubble time. We find that black hole binaries which are ejected and later merge ex-situ form in clusters of a characteristic mass $M_{\rm cl} \sim 10^{5.3}M_{\odot}$, whereas binaries which merge in-situ form in more massive clusters, $M_{\rm cl} \sim 10^{5.7}M_{\odot}$. The clusters which dominate the production of black hole binaries are similar in age and metallicity to the entire population. Finally, we estimate an approximate cosmic black hole merger rate of dynamically assembled binaries using the mean black hole mass for each cluster given its metallicity. We find an intrinsic rate of $\sim 6\,\mathrm{Gpc\,yr^{-1}}$ at $z=0$, a weakly increasing merger rate out to $z=1.5$, and then a decrease out to $z=4$. Our results can be used to provide a cosmological context and choose initial conditions in numerical studies of black hole binaries assembled in star clusters.