Modeling the (proto)neutron star crust: toward a controlled estimation of uncertainties

The main aim of this thesis is to make realistic predictions and to investigate the sources of uncertainties in the observables of non-accreting cold neutron stars and warm protoneutron stars, using the present day constraints provided by nuclear experiments, developments in chiral effective field theory, and astrophysical observations. A unified metamodeling approach was introduced to calculate the stellar composition and equation of state of cold non-accreting neutron stars for any functional of nuclear matter. A Bayesian determination of the equation of state parameters was carried out, leading to realistic predictions for neutron star observables. At finite temperature, a full statistical equilibrium of ions in the crust was considered, allowing in particular for the computation of the impurity parameter. The results are compatible with constraints inferred from GW170817, and suggest that a full crustal origin of pulsar glitches should be excluded. Deviations in the crust composition from cold catalyzed matter are observed at the crystallization temperature. Results show that the contribution of impurities is nonnegligible, thus potentially having an impact on transport properties in the crust. Higher precision in the determination of high-order isovector empirical parameters through nuclear experiments or low-density effective field theory predictions, and in the experimental and/or theoretical knowledge of the surface energy at extreme isospin ratios are needed to reduce the uncertainties of crustal observables. The numerical framework developed during this thesis can be used as a basis for future studies. (author)