Binary Black Hole Mergers from Globular Clusters: the Impact of Globular Cluster Properties

The dense environment of globular clusters (GCs) can facilitate the formation of binary black holes (BBHs), some of which can merge with gravitational waves (GW) within the age of the Universe. We have performed a survey of Monte-Carlo simulations following the dynamical evolution of GCs with different masses, sizes and binary fractions and explored the impact of the host GC properties on the formation of BBH mergers. We find that the number of BBH mergers from GCs is determined by the GC's initial mass, size and primordial binary fraction. We identify two groups of BBH mergers: a primordial group whose formation does not depend on cluster's dynamics and a dynamical group whose formation is driven by the cluster's dynamical evolution. We show how the BBH origin affects the BBH mergers' main properties such as the chirp mass and merging time distributions. We provide analytic expressions for the dependence of the number of BBH mergers from individual GCs on the main cluster's structural properties and the time evolution of the merger rates of these BBHs. These expressions provide an essential ingredient for a general framework allowing to estimate the merger rate density. Using the relations found in our study, we find a local merger rate density of 0.18$-$1.8 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ for primordial BBH mergers and 0.6$-$18 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ for dynamical BBH mergers, depending on the GC mass and size distributions, initial binary fraction and the number density of GCs in the Universe.