# Black Hole Binaries Dynamically Formed in Globular Clusters

## TL;DR

This study uses N-body simulations to analyze how black hole mass functions influence the properties and merger rates of dynamically formed black hole binaries in globular clusters, highlighting their potential contribution to gravitational-wave detections.

## Contribution

It provides new insights into the effects of black hole mass functions on binary properties and merger rates, focusing on dynamical formation processes in globular clusters.

## Key findings

- Most BH binary mergers occur after ejection from clusters.
- Mass ratios of formed binaries are typically close to one or less than 2:1.
- Estimated merger rate from globular clusters is at least 6.5 per year per Gpc^3.

## Abstract

We investigate properties of black hole (BH) binaries formed in globular clusters via dynamical processes, using direct N-body simulations. We pay attention to effects of BH mass function on the total mass and mass ratio distributions of BH binaries ejected from clusters. Firstly, we consider BH populations with two different masses in order to learn basic differences from models with single-mass BHs only. Secondly, we consider continuous BH mass functions adapted from recent studies on massive star evolution in a low metallicity environment, where globular clusters are formed. In this work, we consider only binaries that are formed by three-body processes and ignore stellar evolution and primordial binaries for simplicity. Our results imply that most BH binary mergers take place after they get ejected from the cluster. Also, mass ratios of dynamically formed binaries should be close to one or likely to be less than 2:1. Since the binary formation efficiency is larger for higher-mass BHs, it is likely that a BH mass function sampled by gravitational-wave observations would be weighed toward higher masses than the mass function of single BHs for a dynamically formed population. Applying conservative assumptions regarding globular cluster populations such as small BH mass fraction and no primordial binaries, the merger rate of BH binaries originated from globular clusters is estimated to be at least 6.5 per yr per Gpc^3. Actual rate can be up to more than several times of our conservative estimate.