We investigate the merging rates of compact binaries in galaxies, and the related detection rate of gravitational wave (GW) events with AdvLIGO/Virgo and with the Einstein Telescope. To this purpose, we rely on three basic ingredients: (i) the redshift-dependent galaxy statistics provided by the latest determination of the star formation rate functions from UV+far-IR/(sub)millimeter/radio data; (ii) star formation and chemical enrichment histories for individual galaxies, modeled on the basis of observations; (iii) compact remnant mass distribution and prescriptions for merging of compact binaries from stellar evolution simulations. We present results for the intrinsic birthrate of compact remnants, the merging rates of compact binaries, GW detection rates and GW counts, attempting to differentiate the outcomes among BH-BH, NS-NS, and BH-NS mergers, and to estimate their occurrence in disk and spheroidal host galaxies. We compare our approach with the one based on cosmic SFR density and cosmic metallicity, exploited by many literature studies; the merging rates from the two approaches are in agreement within the overall astrophysical uncertainties. We also investigate the effects of galaxy-scale strong gravitational lensing of GW in enhancing the rate of detectable events toward high-redshift. Finally, we discuss the contribution of undetected GW emission from compact binary mergers to the stochastic background.

In this paper, we study the impact of different galaxy statistics and empirical metallicity scaling relations on the merging rates and properties of compact object binaries. Firstly, we analyze the similarities and differences of using the star formation rate functions versus stellar mass functions as galaxy statistics for the computation of cosmic star formation rate density. We then investigate the effects of adopting the Fundamental Metallicity Relation versus a classic Mass Metallicity Relation to assign metallicity to galaxies with given properties. We find that when the Fundamental Metallicity Relation is exploited, the bulk of the star formation occurs at relatively high metallicities, even at high redshift; the opposite holds when the Mass Metallicity Relation is employed, since in this case the metallicity at which most of the star formation takes place strongly decreases with redshift. We discuss the various reasons and possible biases giving rise to this discrepancy. Finally, we show the impact of these different astrophysical prescriptions on the merging rates and properties of compact object binaries; specifically, we present results for the redshift-dependent merging rates and for the chirp mass and time delay distributions of the merging binaries.