Stellar-mass black holes in young massive and open stellar clusters V: comparisons with LIGO-Virgo merger rate densities

I study the contribution of young massive star clusters (YMCs) and open star clusters (OCs) to the present-day intrinsic merger rate density of dynamically-assembled binary black holes (BBHs). The BBH merger event rate is estimated based on a set of 65 state-of-the-art evolutionary models of star clusters, as presented in Banerjee (2021). These relativistic direct many-body computed models incorporate up-to-date stellar mass loss and remnant formation ingredients. The merger-event rates are obtained by constructing a cluster population of the Universe, out of the models, taking into account mass distribution of clusters and cosmic star formation and enrichment histories, as per observations. The model BBH merger rate density ranges from a pessimistic to a reference value of $0.5{\rm~yr}^{-1}{\rm Gpc}^{-3}-37.9{\rm~yr}^{-1}{\rm Gpc}^{-3}$, for a LIGO-Virgo-like detector horizon. The reference rate well accommodates the BBH merger rate densities estimated from GWTC-1 and GWTC-2 merger-event catalogues. The computed models also yield differential BBH merger rate densities that agree reasonably with those from GWTC-1 and, as well, with the much more constrained ones from GWTC-2. These results suggest that dynamical interactions in YMCs and OCs can, in principle, alone explain the BBH merger rate density and its dependence on the merging-binary properties, as inferred from to-date gravitational-wave (GW) events. The cosmic evolution of merger rate density from the computed models is also studied. The models predict a rate of $\approx5{\rm~yr}^{-1}{\rm Gpc}^{-3}$ for eccentric LIGO-Virgo mergers from YMCs and OCs. The improving constraints on BBH merger rate density with mounting GW events will help constraining scenarios of star cluster formation across cosmic time and as well the relative contributions of the various compact binary merger channels.