Demography of compact-object binaries in the era of multi-messenger astronomy

The first direct detection of gravitational waves (GWs) opened the era of GW astronomy. Besides GW150914, ten other GW detections were reported during the first two observing runs. One of them, GW170817, is associated to the merger between two neutron stars (NSs). In addition, GW170817 was accompanied by the emission of electromagnetic radiation observed over a large range of wavelengths. Several pathways have been proposed for the formation of COBs and one of the most important ones is represented by the evolution of massive isolated binaries. Close binary stars undergo several complex processes, that may strongly affect the mass of the final compact objects and their orbital separation e.g. mass transfer and common envelope (CE). Some of these processes are only barely understood. The goal of my Thesis is to study the formation of COBs through the evolution of isolated massive binaries. In oder to study COBs I used population-synthesis simulations. In particular, I developed MOBSE ('Massive Objects in Binary Stellar Evolution') which is a customized and upgraded version of BSE (Hurley et al. 2002). MOBSE contains up-to-date equations for stellar winds and SN explosion mechanisms, essential ingredients to capture the evolution of massive stars. I used MOBSE to simulate the evolution of large grids of massive binary stars. I found that the most massive BHBs (~ 100Msun) can form only at low metallicity (Z< 0.1Zsun) and do not merger in a Hubble because of their large semi-major axis. Since the merging time due to GW emission also depends on the masses involved, metallicity even affects the number of mergers of both BHBs and BHNSs. I defined the merger efficiency (η) as the total number of mergers integrated over a Hubble time in a coeval population divided by the total mass of that population. I found that η for BHBs is about four order of magnitude higher at low metallicities than at high Z. From my simulations, it is also apparent that CE efficiency (α) plays an important role in the formation of merging COBs. One of the important quantities that the LVC can infer from GW detections is the local merger rate density (MRD). I adopted a data-driven approach to estimate MRD starting form my simulations. In practice, I combined η (from my simulations) with some prescriptions for the cosmological metallicity evolution and the star formation rate (SFR) density evolution. With this formalism, I have estimated a BHNS local merger rate density of up to few tens of mergers Gpc^-3 yr^-1 for all the different combinations of α, natal kicks, cosmological metallicity evolution and SFR I have considered, consistent with the upper limit inferred by the LVC (< 610 Gpc^-3 yr^-1). On the other hand, my prediction for the BHB merger rate density matches that inferred by the LVC ( 24-112 Gpc^-3 yr^-1) only for specific combinations of SFR, cosmological metallicity evolution and α. In particular, the merger rate density of BHBs is very sensitive to the cosmological metallicity evolution. Finally, I was able to match the LVC merger rate density for DNSs (110-3840 Gpc^-3 yr^-1) only if I considered high α and relatively low natal kicks. In particular, I proposed a new prescription for the treatment of natal kicks. The basic idea is that the strength of the natal kick is proportional to the mass ejected during the SN explosion as suggested by recent hydrodynamical studies. With respect to the other prescriptions currently adopted by population-synthesis codes, this new approach allows to match both the natal kick distribution of young Galactic pulsars and the local merger rate inferred by the LVC. Still, to match the LVC merger rate I needed to adopt an high CE efficiency (α >2).