Stellar mass black holes in star clusters: gravitational wave emission and detection rates

TL;DR

This study uses direct N-body simulations to explore how stellar-mass black holes in star clusters form binaries and merge via gravitational waves, predicting detection rates for advanced GW detectors.

Contribution

It provides the first detailed dynamical modeling of BH-BH binary formation and merging in star clusters, estimating GW detection rates for the first time.

Findings

BHs rapidly segregate into cluster cores forming dense sub-clusters.

Most BH binaries escape, but some merge within clusters or after escape within a Hubble time.

Estimated GW detection rate of about 30 per year for Advanced LIGO.

Abstract

We investigate the dynamics of stellar-mass black holes (BH) in star clusters focusing on the dynamical formation of BH-BH binaries, which are very important sources of gravitational waves (GW). We examine the properties of these BH-BH binaries through direct N-body computations of Plummer clusters, having initially N(0) <= 10^5 low mass stars and a population of stellar mass BHs, using the state-of-the-art N-body integrator "NBODY6". We find that the stellar mass BHs segregate rapidly into the cluster core to form a central dense sub-cluster of BHs in which BH-BH binaries form via 3-body encounters. While most of the BH binaries finally escape from the cluster by recoils due to super-elastic encounters with the single BHs, we find that for clusters with N(0) >= 5 X 10^4, typically a few of them dynamically harden to the extent that they can merge via GW emission within the cluster. Also, for each of such clusters, there are a few escaped BH binaries that merge within a Hubble time, most of the mergers happening within a few Gyr of cluster evolution. These results imply that the intermediate-aged massive clusters constitute the most important class of star clusters that can produce dynamical BH-BH mergers at the present epoch. The BH-BH merger rates obtained from our computations imply a significant detection rate (~ 30/yr) for the "Advanced LIGO" GW detector that will become operative in the near future. Finally, we briefly discuss our ongoing development on this work incorporating the formation of BHs in star clusters from stellar evolution. In particular, we highlight the effect of stellar metallicity on the BH sub-cluster driven expansion of a star cluster's core.