BAYESIAN INFERENCE ON NUCLEAR DATA AND NEUTRON STAR OBSERVATIONS FOR THE NUCLEAR EQUATION OF STATE

Nuclear matter is defined as a uniform infinite system composed of neutrons and protons at zero temperature interacting only through the nuclear force. Although an idealisation, it is achieved, to a good extent, in the interior of nuclei, where the density is roughly constant and the interaction is dominated by the nuclear force, and in neutron stars, where the high densities in their interior exceed the nuclear ones. Finite nuclei deliver information only on symmetric or quasi-symmetric matter, i.e., when the proton and neutron densities are similar; neutron stars deliver information on highly asymmetric matter instead, since they are mostly composed of neutrons. Hence, low-energy nuclear physics has the potential of imposing tight constraints into the physics of the star, and in turn neutron star observations can inform us on the behaviour of nuclear matter at densities unachievable here on Earth. Recently, two nuclear physics observables that are thought to be intimately connected to the physics of a neutron star have challenged nuclear theory. These observables are the nuclear electric dipole polarizability –in a sense analogous to the tidal deformability in a star– and the parity violating asymmetry –that is very sensitive to the pressure felt among neutrons in the surface of the atomic nucleus. No model to date is able to describe these two observables (within 1 standard deviation). The aim of this project is to study the nuclear Equation of State (EoS) using a the EDF formalism that properly describe the above mentioned observables and that includes statistically sound theoretical errors, and then bridge this information to the study of neutron stars. Within the standard Skyrme functional ansatz, we build a reliable probability distribution for a combination of nuclear matter parameters (NMP) and Skyrme parameters (which are needed to constrain all the terms of the functional) using a combined Bayesian inference of a large set of EoS-sensitive nuclear structure data. Beyond the usual ground state properties like binding energies and charge radii, we also included the above mentioned polarizabilities and parity-violating asymmetries of 208Pb and 48Ca. The result is a multivariate probability distribution for the NMPs and Skyrme parameters. One of the most delicate aspects of the analysis was handling the uncertainties associated with each measurement, as Skyrme energy density functionals cannot always reproduce experimental data within experimental errors, particularly for binding energies. This led us to discover an interplay between the binding energies and the polarizabilities of 208Pb and 48Ca, which favours a soft nuclear equation of state. Furthermore, the posterior distribution can be used as a prior distribution in a successive Bayesian analysis, this time using astrophysical observations as constraints. This way, this second posterior distribution of NMPs will be informed by both nuclear physics and astrophysics. We will show that the constraints from nuclear experiments are well compatible with the theoretical predictions for infinite pure neutron matter from ab initio modelling, and those constraints additionally indicate the existence of interesting structures in the EoS of neutron stars. We will discuss the final predictions on some selected static properties of neutron stars, which can be computed from the distribution of NMPs. We will devote further attention to the composition of the star crust, which is computed consistently with the star EoS within the extended Thomas-Fermi formalism.