Merger rates of intermediate-mass black hole binaries in nuclear star clusters

TL;DR

This study estimates the merger rates of intermediate-mass black hole binaries in nuclear star clusters and predicts detectable gravitational wave events across multiple observatories.

Contribution

It provides the first comprehensive analysis of IMBH merger rates considering various cluster parameters and predicts multi-band gravitational wave detections.

Findings

Merger rates range from 0.01 to 10 Gpc$^{-3}$ yr$^{-1}$.

A few IMBH merger events per year are detectable with current and future GW observatories.

Predicted detection rates vary with IMBH mass and observatory sensitivity.

Abstract

Repeated mergers of stellar-mass black holes (BHs) in dense star clusters can produce intermediate-mass black holes (IMBHs). In particular, nuclear star clusters at the centers of galaxies have deep enough potential wells to retain most of the BH merger products, in spite of the significant recoil kicks due to anisotropic emission of gravitational radiation. These events can be detected in gravitational waves (GWs), which represent an unprecedented opportunity to reveal IMBHs. In this paper, we analyze the statistical results of a wide range of numerical simulations, which encompass different cluster metallicities, initial BH seed masses, and initial BH spins, and we compute the merger rate of IMBH binaries. We find that merger rates are in the range $0.01$-$10$\,Gpc$^{-3}$\,yr$^{-1}$ depending on IMBH masses. We also compute the number of multi-band detections in ground-based and space-based observatories. Our model predicts that a few merger events per year should be detectable with LISA, DECIGO, ET, and LIGO for IMBHs with masses $\lesssim 1000\msun$, and a few tens of merger events per year with DECIGO, ET, and LIGO only.