Core-crust transition in neutron stars with finite-range interactions: The dynamical method

Abstract

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.

New Gogny interaction suitable for astrophysical applications

“…It is obtained as E sym (ρ) = 1 2 ∂ 2 E b (ρ, δ)/∂δ 2 | δ=0 from the energy per particle E b (ρ, δ) in asymmetric nuclear matter of density ρ = ρ n + ρ p and isospin asymmetry δ = (ρ n − ρ p )/ρ, where ρ n and ρ p are the neutron and proton densities. In the Gogny interaction, the symmetry energy becomes [14]:…”

“…The mass-radius (M-R) relation in neutron stars is dictated by the corresponding EOS, which is the essential ingredient to solve the Tolman-Oppenheimer-Volkov (TOV) equations [1]. The EOS (total pressure against density) of β-stable, globally charge-neutral NS matter [13,14] calculated with the given functionals is displayed in Fig. 1b.…”

“…For instance, Skyrme-HFB models [8] have reached a high degree of accuracy in predicting experimental masses and are at the same time well suited for astrophysical studies [9,10]. More occasionally, also Gogny forces have been applied in NS calculations [11][12][13][14]. Due to the complexity of modeling the inner crust, there are few EOSs that describe the whole NS from the crust to the core in a unified manner.…”

“…Unfortunately, the extrapolation to the domain of neutron stars with the Gogny parametrizations works less well. It has been found [12][13][14] that the most successful Gogny forces for describing finite nuclei, namely D1S, D1N and D1M, are unable to reach NS masses of about 2M , as required by recent astrophysical observations [23,24]. Moreover, only few Gogny forces, including D1M but not D1N nor D1S, achieve a NS mass above the canonical 1.4M value [13,14].…”

“…It has been found [12][13][14] that the most successful Gogny forces for describing finite nuclei, namely D1S, D1N and D1M, are unable to reach NS masses of about 2M , as required by recent astrophysical observations [23,24]. Moreover, only few Gogny forces, including D1M but not D1N nor D1S, achieve a NS mass above the canonical 1.4M value [13,14]. Therefore, the aim of this work is to introduce a new Gogny force, which we call D1M * , that retaining a similar quality to D1M for finite nuclei, may be used to study NS physics at a level of the most successful Skyrme forces.…”