Gravitational Waves and Intermediate-mass Black Hole Retention in Globular Clusters

TL;DR

This paper models the evolution and merger rates of intermediate-mass black holes in globular clusters, predicting detectable gravitational wave signals for upcoming observatories like LISA and the Einstein Telescope.

Contribution

It introduces a semi-analytical model for IMBH formation and merger rates in globular clusters, providing predictions for gravitational wave detections.

Findings

Approximately 1000 IMBHs within 1 kpc of the Galactic Center.

IMBH-SBH merger rate density varies from 1000 Gpc$^{-3}$ yr$^{-1}$ at high redshift to 1-10 Gpc$^{-3}$ yr$^{-1}$ locally.

Future GW detectors may observe these IMBH-SBH mergers, especially LISA and the Einstein Telescope.

Abstract

The recent discovery of gravitational waves has opened new horizons for physics. Current and upcoming missions, such as LIGO, VIRGO, KAGRA, and LISA, promise to shed light on black holes of every size from stellar mass (SBH) sizes up to supermassive black holes which reside in galactic nuclei. The intermediate mass black hole (IMBH) family has not been detected beyond any reasonable doubt neither directly nor indirectly. Recent analyses suggest observational evidence for the presence of IMBHs in the centers of two Galactic globular clusters. In this paper, we investigate the possibility that globular clusters were born with a central IMBH, which undergo repeated merger events with SBHs in the cluster core. By means of a semi-analytical method, we follow the evolution of the primordial cluster population in the galactic potential and the Gravitational Wave (GW) mergers of the binary IMBH-SBH systems. Our models predict $\approx 1000$ IMBHs within $1$ kpc from the Galactic Center. Our results show that the IMBH-SBH merger rate density changes from $\mathcal{R}\approx 1000$ Gpc$^{-3}$ yr$^{-1}$ beyond $z\approx 2$ to $\mathcal{R}\approx 1-10$ Gpc$^{-3}$ yr$^{-1}$ at $z\approx 0$. The rates at low redshifts may be significantly higher if young massive star clusters host IMBHs. The merger rates are dominated by IMBHs with masses between $10^3$ and $10^4\,\mathrm{M}_{\odot}$. Currently there are no LIGO/VIRGO upper limits for GW sources in this mass range, but our results show that at design sensitivity these instruments may detect these IMBH-SBH mergers in the coming years. \textit{LISA} and the Einstein Telescope will be best suited to detect these GW events. The inspirals of IMBH-SBH systems may also generate an unresolved GW background.