Evaluating the Merger Rate of Binary Black Holes from Direct Captures and Third-Body Soft Interactions Using the Milky Way Globular Clusters

TL;DR

This study estimates binary black hole merger rates in Milky Way globular clusters, highlighting the significance of third-body interactions over direct captures, and suggests these clusters could account for a substantial fraction of detectable gravitational wave events.

Contribution

It provides the first detailed merger rate estimates from direct captures and third-body interactions in globular clusters based on observational data.

Findings

Direct capture mergers occur at 0.3-5 x 10^{-11} yr^{-1} per cluster.

Third-body interactions lead to higher merger rates of 2-4 x 10^{-10} yr^{-1} per cluster.

Estimated global merger rate from clusters is about 100 per year up to redshift 1.

Abstract

The multitude of binary black hole coalescence detections in gravitational waves has renewed our interest on environments that can be the cradle of these mergers. In this work we study merger rates of binary black holes in globular clusters that are among the most dense stellar environments and a natural place for the creation of black hole binaries. To model these systems with all their variations we rely on the observational properties of the known Milky Way globular clusters. We consider direct capture events between black holes, as well as soft interactions of black hole binaries with stars as third bodies that accelerate the evolution of these binaries. We find that binary black holes from direct captures merge at an averaged rate of $0.3-5 \times 10^{-11}$ yr$^{-1}$ per cluster. Third body soft interactions are a much more prominent channel giving an averaged rate of $2-4 \times 10^{-10}$ yr$^{-1}$ per cluster. Those rates in globular clusters can lead to a cumulative merger rate of about 100 mergers per year up to redshift of 1, i.e. a significant fraction of the detectable in the near future binary black hole coalescence events. Further observations of cluster properties both in terms of their masses, profile properties, velocity dispersion of stars and their cosmological distribution, will allow us to better constrain the contribution of these environments to the detectable coalescence events rate.