Merging hierarchical triple black hole systems with intermediate-mass black holes in population III star clusters

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(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 O(100)M-circle dot, and as a result, their merger rate could be up to 0.1Gpc(-3)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 O(0.1)Hz to 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 the formation channels of merging BBHs, whether through isolated evolution or dynamical interaction, by examining eccentricities.