Merger rate density of stellar-mass binary black holes from young massive clusters, open clusters, and isolated binaries: comparisons with LIGO-Virgo-KAGRA results

I investigate the roles of cluster dynamics and massive binary evolution in producing stellar-remnant binary black hole (BBH) mergers over the cosmic time. To that end, dynamical BBH mergers are obtained from long-term direct N-body evolutionary models of $\sim10^4M_\odot$, pc-scale young massive clusters (YMC) evolving into moderate-mass open clusters (OC). Fast evolutionary models of massive isolated binaries (IB) yield BBHs from binary evolution. Population synthesis in a Model Universe is then performed, taking into account observed cosmic star-formation and enrichment histories, to obtain BBH-merger yields from these two channels observable at the present day and over cosmic time. The merging BBH populations from the two channels are combined by applying a proof-of-concept Bayesian regression chain, taking into account observed differential intrinsic BBH merger rate densities from the second gravitational-wave transient catalogue (GWTC-2). The analysis estimates an OB-star binary fraction of $f_{\rm Obin}\gtrsim90$% and a YMC formation efficiency of $f_{\rm YMC}\sim10^{-2}$, being consistent with recent optical observations and large scale structure formation simulations. The corresponding combined Model Universe present-day, differential intrinsic BBH merger rate density and the cosmic evolution of BBH merger rate density both agree well with those from GWTC-2. The analysis also suggests that despite significant 'dynamical mixing' at low redshifts, BBH mergers at high redshifts ($z_{\rm event}\gtrsim1$) could still be predominantly determined by binary-evolution physics. Caveats in the present approach and future improvements are discussed.