Merging Hierarchical Triple Black Hole Systems with Intermediate-mass Black Holes in Population III Star Clusters

TL;DR

This study explores the evolution and merger rates of hierarchical triple black hole systems with intermediate-mass black holes in Population III star clusters, highlighting their gravitational wave signatures and detection prospects.

Contribution

It provides the first detailed analysis of hierarchical triple black hole mergers in Population III clusters, including their eccentricities and implications for gravitational wave detection.

Findings

Inner BBHs often contain IMBHs of around 100 solar masses.

Merger rate could reach 0.1 Gpc^{-3} yr^{-1}.

High eccentricities near 1 in mHz GW bands.

Abstract

Theoretical predictions suggest that very massive stars have the potential to form through multiple collisions and eventually evolve into intermediate-mass black holes (IMBHs) within Population III star clusters embedded in mini dark matter haloes. In this study, we investigate the long-term evolution of Population III star clusters, including models with a primordial binary fraction of $f_{\rm b}=0$ and 1, using the $N$-body simulation code PETAR. We comprehensively examine the phenomenon of hierarchical triple black holes in the clusters, specifically focusing on their merging inner binary black holes (BBHs), with post-Newtonian correction, by using the TSUNAMI code. Our findings suggest a high likelihood of the inner BBHs containing IMBHs with masses on the order of $\mathcal{O}(100)M_{\odot}$, and as a result, their merger rate could be up to $0.1{\rm Gpc}^{-3}{\rm yr}^{-3}$. The orbital eccentricities of some merging inner BBHs oscillate over time periodically, known as the Kozai-Lidov oscillation, due to dynamical perturbations. Detectable merging inner BBHs for mHz GW detectors LISA/TianQin/Taiji concentrate within $z<3$. More distant sources would be detectable for CE/ET/LIGO/KAGRA/DECIGO, which are sensitive from $\mathcal{O}(0.1)$Hz to $\mathcal{O}(100)$Hz. Furthermore, compared with merging isolated BBHs, merging inner BBHs affected by dynamical perturbations from tertiary BHs tend to have higher eccentricities, with a significant fraction of sources with eccentricities closing to 1 at mHz bands. GW observations would help constrain formation channels of merging BBHs, whether through isolated evolution or dynamical interaction, by examining eccentricities.