Stellar-mass black holes in young massive and open stellar clusters. VII. Comparisons with gravitational-wave events until LVK-O4a and Gaia compact binaries

Gravitational-wave (GW) detections from the LIGO-Virgo-KAGRA (LVK) GW observatories suggest multiple formation channels contributing to the GW coalescence of compact binaries in the Universe. In this study, I assess the contribution of young massive clusters (YMCs) evolving into old open clusters (OCs)---the YMC/OC channel---to the GW-merger population. To that end, a homogeneous grid of 90 N-body evolutionary model star clusters, spanning initial masses of ${10}^{4}{M}_{\ensuremath{\bigodot}}\ensuremath{\le}{M}_{\mathrm{cl}}(0)\ensuremath{\le}{10}^{5}{M}_{\ensuremath{\bigodot}}$, half-mass radii of 1--3 pc, and metallicities between 0.0002 and 0.02 is computed with the direct, star-by-star, post-Newtonian N-body code nbody7. The N-body simulations include primordial binaries, delayed stellar-remnant masses forming stellar-remnant black holes (BHs) and neutron stars (NSs), BH-spin prescriptions, and general-relativistic recoil kicks. The model clusters are evolved until they lose most of the retained BHs. The majority of the GW mergers from the cluster models are dynamically assembled binary black holes (BBHs) that merge within their host clusters, while the rarer escaped mergers are commonly primordially paired. Merger mass ratios reach down to 0.1--0.2 despite an overall bias toward nearly symmetric pairs of $q\ensuremath{\approx}0.8$. The GW-merger efficiency varies nonmonotonically with cluster mass, peaking around ${M}_{\mathrm{cl}}(0)=7.5\ifmmode\times\else\texttimes\fi{}{10}^{4}{M}_{\ensuremath{\bigodot}}$ and also for ${M}_{\mathrm{cl}}(0)\ensuremath{\le}3.0\ifmmode\times\else\texttimes\fi{}{10}^{4}{M}_{\ensuremath{\bigodot}}$. The computed mergers reproduce some of the key features of the latest observed GW event catalog, including asymmetric low-mass mergers, misaligned events among highly spinning, massive BHs, and an excess of $30{M}_{\ensuremath{\bigodot}}$ primaries, though they underproduce $10{M}_{\ensuremath{\bigodot}}$ primaries, hinting at contributions from other channels. The merger rate density from the model grid at redshift $z=0.2$ accounts for a fiducial 25%--33% of the observed rate depending on cosmic metallicity evolution; it increases with redshift somewhat more steeply than the cosmic star formation rate, consistent with the overall growth of the LVK-inferred merger rate. Some of the apparent low-redshift features of the observed BBH mergers' effective spin distribution, e.g., the positive asymmetry at $z=0$ and the broadening with redshift, are also qualitatively reproduced, after applying a postprocessing prescription to the model mergers. The model clusters also yield field BH- and NS-main sequence star binaries with parameters consistent with the Gaia-discovered candidates.