Kilonova modelling: from binary neutron star merger microphysics to population properties

The detection of a gravitational wave (GW) signal from a binary neutron star (BNS) merger by the LIGO and Virgo interferometers, together with its broad-band electromagnetic (EM) counterpart signals from gamma to radio which happened in 2017, marked the birth of multi-messenger astronomy with GWs. The successful detection of the EM signals was made possible by a follow-up strategy able to coordinate GW detectors and space-born and ground-based telescopes. This epochal discovery showed the majestic potential of multi-messenger astronomy in unveiling the nature of neutron stars (NSs) and the physics governing the extremely energetic phenomena associated with their tidal disruption during the last phase of the coalescence. In particular, photometric and spectroscopic observations enabled the detection of the optical signal AT2017gfo, which revealed the signature of r-process nucleosynthesis characteristic of kilonova (KN) emission powered by the sub-relativistic neutron-rich ejecta. This detection solved the mystery of the nucleosynthesis of heavy elements in the Universe, indicating NS mergers as one of the major channels. The detection of a gamma-ray burst (GRB) together with the X-ray, optical, and radio afterglow emission answered the long-standing question about short-GRB progenitors, demonstrating that BNS mergers can power structured relativistic jets. Many years of theoretical investigations and numerical simulations have played a crucial role in achieving these breakthroughs, by providing reliable predictions about the properties and time evolution of the GW and EM signals, enabling the interpretation of the collected data, and constraining the merger microphysics. However, the wealth of observational data has opened up new enigmas, raising new questions about the physics underlying BNS mergers and the production of EM emissions. Improving our prediction and interpretation capabilities through more accurate theoretical models and numerical simulations is a critical step to addressing these questions in light of upcoming detections. Moreover, it is now imperative to get prepared for next-generation GW interferometers, such as the Einstein Telescope (ET). Next-generation interferometers are unprecedented resources to enhance the chances of detecting EM counterparts, significantly enlarging the horizon of detectable BNS mergers and dramatically improving the source parameter estimation. My thesis project aims at 1) improving the microphysical modelling of single BNS mergers, 2) improving the modelling of the KN emission (light curves and spectra), and 3) providing reliable predictions about detection prospects of multi-messenger emission from populations of BNS mergers. This is pivotal to develop observational strategies, optimise multi-messenger instrument designs and operations, and evaluate the multi-messenger science potential. My research wants to set the basis to interpret a larger set of observations expected with the advent of the next-generation detectors, which will provide increasingly precise data. Considering that the characteristics of KN emission strongly depend on the progenitor properties and the merger microphysics, which is not yet fully understood, this thesis develops two main themes. Firstly, I improve the modelling of the merger microphysics within numerical simulations, by exploring the impact of muons on the post-merger remnant. Secondly, I assess the prospects for KN multi-messenger detections by next-generation observatories, considering how current uncertainties in the NS population properties and NS microphysics might affect the KN emission. Motivated by the fact that state-of-the-art numerical simulations of BNS mergers do not include muons, despite their relevant role in the microphysics of cold NSs and favourable production conditions during mergers, I study how muons affect the post-merger remnant and its trapped neutrino component. My work demonstrates that the presence of muons and trapped neutrinos modifies the internal composition of the merger aftermath and has a discernible impact on the remnant pressure. Modifications of the remnant pressure might affect the collapse time of the central object and dynamical matter ejection, with possible implications for the KN emission. Exploring perspectives for KN multi-messenger detections requires handling many uncertainties concerning both the merger microphysics and the population properties of BNS mergers. Starting with improving the modelling of the KN light curves, I calibrate them on the outcome of BNS merger numerical-relativity simulations, including not only the results of GW170817-targeted simulations but also the ones targeted to the properties of second LIGO and Virgo BNS detection, GW190425. The KN emission modelling takes also into account the effects of prompt collapse on the KN emission. Then, using BNS merger populations with different local merger rates, NS mass distribution, and NS equation of state (EOS), I evaluate GW/KN joint detections for different configurations and designs of ET, operating alone or in a network of present and next-generation GW detectors, and working in synergy with the Vera Rubin Observatory. ET alone will enable the detection of about ten to hundred KNe per year by the Rubin Observatory, with an improvement of a factor ∼ 10 if operating in a network of GW detectors. Ac- cessing low frequencies is crucial for ET operating as a single observatory to maximise the chances of KN detection and constrain cosmological parameters. This work quantifies several theoretical uncertainties underlying current predictions on KN multi-messenger detections, showing that these uncertainties are dominated by the poorly constrained local BNS merger rate and depend to a lesser extent on NS mass distribution and EOS.