Background: An accurate determination of the core-crust transition is necessary in the modeling of neutron stars for astrophysical purposes. The transition is intimately related to the isospin dependence of the nuclear force at low baryon densities.Purpose: To study the symmetry energy and the core-crust transition in neutron stars using the finite-range Gogny nuclear interaction and to examine the deduced crustal thickness and crustal moment of inertia. Methods:The second-, fourth-and sixth-order coefficients of the Taylor expansion of the energy per particle in powers of the isospin asymmetry are analyzed for Gogny forces. These coefficients provide information about the departure of the symmetry energy from the widely used parabolic law. The neutron star core-crust transition is evaluated by looking at the onset of thermodynamical instability of the liquid core. The calculation is performed with the exact Gogny EoS (i.e., the Gogny EoS with the full isospin dependence) for the β-equilibrated matter of the core, and also with the Taylor expansion of the Gogny EoS in order to assess the influence of isospin expansions on locating the inner edge of neutron star crusts.Results: The properties of the core-crust transition derived from the exact EoS differ from the predictions of the Taylor expansion even when the expansion is carried through sixth order in the isospin asymmetry. Gogny forces, using the exact EoS, predict the ranges 0.094 fm Conclusions:The finite-range exchange contribution of the nuclear force, and its associated non-trivial isospin dependence, is key in determining the core-crust transition properties. Finite-order isospin expansions do not reproduce the core-crust transition results of the exact EoS. The predictions of the Gogny D1M force for the stellar crust are overall in broad agreement with those obtained using the Skyrme-Lyon EoS.

We analyze the effects of including ∆(1232) isobars in an equation of state (EoS) for cold, β-stable neutron star matter, employing relativistic nuclear mean field theory. The selected EoS reproduces the properties of nuclear matter and finite nuclei and, in the astrophysical context, allows for the presence of hyperons in neutron stars having masses larger than 2M . We find that the composition and structure of neutron stars is critically influenced by the addition of the ∆ isobars, which allows us to constrain their interaction with the meson fields taking into account astrophysical information. Imposing that the EoS is stable and ensures the existence of 2M neutron stars, as well as requiring agreement with data of ∆ excitation in nuclei, we find that, in the absence of other mechanisms stiffening the EoS at high densities, the interaction of the ∆ isobars with the sigma and omega meson fields must be at least 10% stronger than that of the nucleons. Moreover, the neutron star moment of inertia turns out to be sensitive to the presence of ∆ isobars, whereas the inclusion of ∆ isobars in the EoS allows for smaller stellar radii and for a lower value of the tidal deformability consistent with the analysis of the GW170817 merger event.

The D1 family of parametrizations of the Gogny interaction commonly suffers from a rather soft neutron matter equation of state that leads to maximal masses of neutron stars well below the observational value of two solar masses. We propose a reparametrization scheme that preserves the good properties of the Gogny force but allows one to tune the density dependence of the symmetry energy, which, in turn, modifies the predictions for the maximum stellar mass. The scheme works well for D1M, and leads to a new parameter set, dubbed D1M * . In the neutron-star domain, D1M * predicts a maximal mass of two solar masses and global properties of the star in harmony with those obtained with the SLy4 Skyrme interaction. By means of a set of selected calculations in finite nuclei, we check that D1M * performs comparably well to D1M in several aspects of nuclear structure in nuclei.

The properties of the core-crust transition in neutron stars are investigated using effective nuclear forces of finite-range. Special attention is paid to the so-called dynamical method for locating the transition point, which, apart from the stability of the uniform nuclear matter against clusterization, also considers contributions due to finite-size effects. In particular, contributions to the transition density and pressure from the direct and exchange energies are carefully analyzed. To this end, finite-range forces of Gogny, Modified Gogny Interaction (MDI) and Simple Effective Interaction (SEI) types are used in the numerical applications. The results from the dynamical approach are compared with those from the popular thermodynamical method that neglects the surface and Coulomb effects in the stability condition. The dependence of the core-crust transition on the stiffness of the symmetry energy of the finite-range models is also addressed. Finally, we analyze the impact of the transition point on the mass, thickness and fraction of the moment of inertia of the neutron star crust. Prominent differences in these crustal properties of the star are found between using the transition point obtained with the dynamical method or the thermodynamical method. It is concluded that the core-crust transition needs to be ascertained as precisely as possible in order to have realistic estimates of the observed phenomena where the crust plays a significant role.

A set of equations of state obtained from finite-range Gogny forces and momentum-dependent interactions is used to investigate the recent observation of gravitational waves from the binary neutron star merger GW170817 event. For this set of interactions, we have calculated the neutron star tidal deformabilities (related to the second Love number), the mass-radius diagram, and the moment of inertia (I). The I-Love relation has been verified. We also have found strong correlations among the tidal deformability of the canonical neutron star, its radius, and the derivatives of the nuclear symmetry energy at the saturation density. Most of the obtained results are located within the constraints of the tidal deformabilities extracted from the GW170817 detection.