The delay times of Neutron Star Mergers: from Europium to Gamma-Ray Bursts

The detailed characterization of neutron star binary systems has recently become a focal point of research, playing a pivotal role in advancing our understanding across diverse fields such as gravitational wave astronomy, gamma-ray bursts (GRBs), and the chemical evolution of galaxies. Regarding the chemical evolution of elements produced via rapid neutron captures two primary astrophysical sites have been proposed: core-collapse supernovae (CC SNe) and neutron star mergers (NSMs). While the exact contribution of these sources to the r-process enrichment remains a matter of debate, recent observations, particularly the gravitational wave event GW170817, have provided critical insights into the role of NSMs as prolific r-process element producers. The chemical evolution of galaxies offers a unique lens through which we can probe the timescales, yields, and astrophysical sites responsible for the enrichment of heavy elements. In this thesis, we conduct a comprehensive investigation into the characteristic delay time distribution (DTD) of NSMs. By integrating chemical evolution models with demographic studies, this work seeks to provide deeper insights into the astrophysical sites and timescales of r-process nucleosynthesis.\\ We begin with a stochastic chemical evolution model to test which astrophysical site, or combination of sources, can best explain the observed [Eu/Fe] versus metallicity trends in halo stars, using europium (Eu) as a tracer for r-process enrichment. Assuming a power-law DTD for NSMs, the chemical properties of halo stars indicate a preference for a DTD favouring fast mergers. However, an exclusive NSM scenario does not reproduce the observed spread in abundance ratios, especially at extremely low metallicities. A contribution from a secondary and fast source, e.g. magneto-rotationally driven supernovae (MRD SNe), mitigates this inconsistency. This suggests that r-process enrichment in the Galactic halo is driven by a dual contribution from both NSMs and MRD SNe.\\ To specifically address the presence of stars with sub-solar ratios ([Eu/Fe]$<0$) at very low metallicities ([Fe/H]$<-3$), we improve the initial modelling of the halo considering it as the result of subsequent mergers of smaller satellite galaxies. Each building block has its own star formation efficiency and timescale. In addition, this model includes inefficient enrichment of Eu from NSMs due to their individual dynamics. The results suggest that Eu-poor stars in the Galactic halo likely originate from smaller satellite galaxies, in which the produced Eu is only partially retained.\\ To characterize the DTD of NSMs, we investigate the demographics of SGRBs host galaxies as potential constraints. Using a more sophisticated DTD model rooted in stellar evolution theory, we estimate NSMs merger rate in a mock universe, that we developed based on galaxy templates obtained from observations. Our results suggest that the fraction of SGRBs in star-forming galaxies is highly sensitive to the assumed DTD model, providing a potential avenue for constraining NSM delay times with SGRBs. We find that current observational data are limited by poor statistics and estimate that a 5-10 times larger sample will allow us to derive firm conclusions on the DTD.\\ In summary, chemical evolution arguments indicate that a major component of r-process elements enrichment occurs on short time scales. of order of tens of Myr. Either this is due to a sizeable contribution of SNe from massive stars, or to a distribution of the delay times of NSMs with a very strong prompt component. The demographic of SGRBs host galaxies offers a very important tool to estimate the magnitude of this prompt component, helping to disentangle between these possibilities. Overall, this thesis underscores the importance of combining results from different studies to improve our knowledge on the chemical evolution of r-process elements and their production sites.