Nuclear Physics in Neutron Stars: Study of Superfluidity in Hypernuclei and Constraining the Nuclear Equation of State

In this thesis, we first investigated the effect of Lambda pairing on the ground state properties of hypernuclei within the Hartree-Fock-Bogoliubov formalism. The SLy5 Skyrme functional is used in the NN channel, while for N-Lambda channel we employ three functionals fitted from microscopic Brueckner-Hartree-Fock calculations: DF-NSC89, DF-NSC97a and DF-NSC97f. These functionals reproduce the sequence of single-Lambda experimental binding energies from light to heavy hypernuclei. For the Lambda-Lambda channel, we used the empirical prescription EmpC, calibrated to 1 MeV on the experimental bond energy in ⁶He_ΛΛ. Based on this density-functional approach, several nuclei have been studied with nucleon closed-shells and Lambda open-shells. A Lambda-Lambda pairing interaction is introduced, which magnitude is calibrated to be consistent with the maximum BCS predictions for the Lambda pairing gap in hypernuclear matter. In this way, we provide an upper bound for the prediction of the Lambda pairing gap and its effects in hypernuclei. We have shown that the effects of the Lambda-Lambda pairing depends on hypernuclei. The condensation energy is predicted to be about 3 MeV as a maximum value, yielding small corrections on density distributions and shell structure. Generally, we found that Lambda-Lambda pairing could be active if the energy gap between shells is smaller than 3 MeV. Under this condition, Lambda pairing could impact densities and binding energies. Since only a weak spin-orbit interaction is expected in the Lambda channel, Lambda states are highly degenerated and usually levels are distant by more than 3 MeV in energy. In summary, it is shown that the Lambda-related pairing effect can usually be neglected in most of hypernuclei, except for hypernuclei which have a single particle gap lower than 3 MeV around the Fermi level. In addition, conditions on both Fermi energies and orbital angular momenta are expected to quench the nucleon-Lambda pairing for most of hypernuclei. The second part of the thesis is devoted to equation of states in neutron stars. We confronted the tidal deformability values extracted from the gravitational event GW170817 to nuclear physics constraints within a semi-agnostic approach for the dense matter equation of state. We used Bayesian statistics to combine together low density nuclear physics data, such as the ab-initio predictions based on chiral EFT interactions or the isoscalar giant monopole resonance, and astrophysical constraints from neutron stars, such as the maximum mass of neutron stars or the probability density function of the tidal deformability obtained from the GW170817 event. The posteriors probability distribution functions are marginalized over several nuclear empirical parameters (L_sym, K_sym, Q_sat and Q_sym), as well as over observational quantities such as the 1.4 Msun radius R_1.4 and the pressure at twice the saturation density P(2n_sat). The correlations between L_sym and K_sym and between K_Sat and Q_sat are also further analyzed. It is found that there is a marked tension between the gravitational wave observational data and the nuclear physics inputs for the L_sym and R_1.4 marginal probability distributions. This could be a hint for nucleons to more exotic particles phase transition inside of the core of neutron stars. We also conclude that increasing the accuracy on the determination of tidal deformability from the gravitational wave, as well as Mc from the isoscalar giant monopole resonance, will lead to a better determination of K_Sat and Q_sat