Cluster formation in compact stars: Relativistic versus Skyrme nuclear models

Abstract

We present various properties of nuclear and compact-star matter, comparing the predictions from two kinds of phenomenological approaches: relativistic models (with both constant and density-dependent couplings) and nonrelativistic Skyrme-type interactions. We mainly focus on the liquid-gas instabilities that occur at subsaturation densities, leading to the decomposition of the homogeneous matter into a clusterized phase. Such study is related to the description of neutron-star crust (at zero temperature) and supernova dynamics (at finite temperature).

Light clusters, pasta phases, and phase transitions in core-collapse supernova matter

“…In Ref. [43], it is shown that the behavior of the symmetry energy, and its derivatives with respect to density for relativistic nuclear models with density-dependent couplings, is much closer to the behavior of Skyrme forces.…”

Low density instabilities in asymmetric nuclear matter within the quark-meson coupling (QMC) model with the δ meson

“…This means that highly asymmetric matter is less bound in NL3 and QMC than in NL3δ and QMCδ. A mere inspection of the symmetry energy is not enough to account for the differences in the instability region if different models are considered [23]. With the introduction of the δ-meson the scalar channel is not affected, and therefore we are essentially changing the isovector channel.…”

“…This is possibly due to the σ contribution in the Lagrangian for QMC (both with and without δ): the fields here attain magnitudes so as to minimize the bag energy, whereas in hadron models their meanfield values are determined by solving the relevant set of equations where nonlinearities show explicitly or through density dependent couplings. The extension of the spinodal for ρ p = ρ n defines the density ρ s , corresponding to the density value for which the pressure of symmetric nuclear matter has a minimum and the incompressibility is zero [23]. We have included the values of this density for the different models in Table I.…”

“…We also notice that at ρ p = ρ n the curvature of the QMC spinodal is intermediate between NL3 and TW. As shown in [23] this curvature is defined by the symmetry energy and its first and second derivatives.…”

Phase transition toward strange matter

“…For this reason the convexity analysis of the thermodynamical potential in the extensive variable space has been often employed to spot the presence of phase transitions, e.g. for the neutron-proton system [42,43]. At zero temperature, one thermodynamic potential is given by the total energy…”