The <sc>dragon-II</sc> simulations - III. Compact binary mergers in clusters with up to 1 million stars: mass, spin, eccentricity, merger rate, and pair instability supernovae rate

Compact binary mergers forming in star clusters may exhibit distinctive features that can be used to identify them among observed gravitational-wave sources. Such features likely depend on the host cluster structure and the physics of massive star evolution. Here, we dissect the population of compact binary mergers in the DRAGON-II simulation data base, a suite of 19 direct N-body models representing dense star clusters with up to 10(6) stars and <33 per cent of stars in primordial binaries. We find a substantial population of black hole binary (BBH) mergers, some of them involving an intermediate-mass BH (IMBH), and a handful mergers involving a stellar BH and either a neutron star (NS) or a white dwarf (WD). Primordial binary mergers, similar to 30 per cent of the whole population, dominate ejected mergers. Dynamical mergers, instead, dominate the population of in-cluster mergers and are systematically heavier than primordial ones. Around 20 per cent of DRAGON-II mergers are eccentric in the Laser Interferometer Space Antenna (LISA) band and 5 per cent in the LIGO band. We infer a mean cosmic merger rate of R similar to 30(4.4)(1.2) yr(-1) Gpc(-3) for BBHs, NS-BH, and WD-BH binary mergers, respectively, and discuss the prospects for multimessenger detection of WD-BH binaries with LISA. We model the rate of pair-instability supernovae (PISNe) in star clusters and find that surveys with a limiting magnitude m(bol) = 25 can detect similar to 1-15 yr(-1) PISNe. Comparing these estimates with future observations could help to pin down the impact of massive star evolution on the mass spectrum of compact stellar objects in star clusters.