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.
