Unified Equation of State for Neutron Stars Based on the Gogny Interaction

Abstract

The effective Gogny interactions of the D1 family were established by D. Gogny more than forty years ago with the aim to describe simultaneously the mean field and the pairing field corresponding to the nuclear interaction. The most popular Gogny parametrizations, namely D1S, D1N and D1M, describe accurately the ground-state properties of spherical and deformed finite nuclei all across the mass table obtained with Hartree–Fock–Bogoliubov (HFB) calculations. However, these forces produce a rather soft equation of state (EoS) in neutron matter, which leads to predict maximum masses of neutron stars well below the observed value of two solar masses. To remove this limitation, we built new Gogny parametrizations by modifying the density dependence of the symmetry energy predicted by the force in such a way that they can be applied to the neutron star domain and can also reproduce the properties of finite nuclei as good as their predecessors. These new parametrizations allow us to obtain stiffer EoS’s based on the Gogny interactions, which predict maximum masses of neutron stars around two solar masses. Moreover, other global properties of the star, such as the moment of inertia and the tidal deformability, are in harmony with those obtained with other well tested EoSs based on the SLy4 Skyrme force or the Barcelona–Catania–Paris–Madrid (BCPM) energy density functional. Properties of the core-crust transition predicted by these Gogny EoSs are also analyzed. Using these new Gogny forces, the EoS in the inner crust is obtained with the Wigner–Seitz approximation in the Variational Wigner–Kirkwood approach along with the Strutinsky integral method, which allows one to estimate in a perturbative way the proton shell and pairing corrections. For the outer crust, the EoS is determined basically by the nuclear masses, which are taken from the experiments, wherever they are available, or by HFB calculations performed with these new forces if the experimental masses are not known.

Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. III. Inclusion of microscopic corrections to pasta phases

“…Bigger differences with respect to the present paper might be expected with functionals based on finite-range Gognytype effective interactions. Recently a unified EoS using such functionals has been constructed by Mondal et al [36,37], with quantal corrections calculated by the SI method, but with the inner-crust calculations limited to spherical WS cells. There is a clear interest in generalizing these calculations to include pasta.…”

Crustal properties of a neutron star within an effective relativistic mean-field model

“…One may note that the Z = 40 is not a magic number in ordinary nuclei but corresponds to a filled proton sub-shell. Recent calculation by BCPM [7] and D1M [84] also indicated the same feature of inner crust.…”

“…1 for the various mass models. In addition to the HFB computed mass excess, we also show the result from most recent FRDM(2012) [83], BCPM [7] and D1M [84] Gogny interaction for a comparative analysis. The outermost layer is occupied by the 56 Fe nucleus accompanied by the layer of 28 Ni nucleus in the intermediate densities.…”

“…The unknown mass are taken from microscopic calculations HFB-14 [40], HFB-24 , HFB-26 [41] along with the FRDM(2012) mass table [83]. A comparison with BCPM [7] and D1M [84] is also shown. In addition the experimental mass of…”

Unified nuclear matter EOSs constrained by the in-medium balance in density-dependent covariant density functionals

“…Due to the lack of knowledge for the nuclear energy density functionals, the uncertainties in the EOSs and microscopic structures of neutron star matter are still significant [61][62][63][64][65][66][67][68][69][70][71][72]. Additional uncertainties will be introduced if the EOSs were not obtained in a unified manner [66,71].…”