The possibility to draw links between the isospin properties of nuclei and the structure of compact stars is a stimulating perspective. In order to pursue this objective on a sound basis, the correlations from which such links can be deduced have to be carefully checked against model dependence. Using a variety of nuclear effective models and a microscopic approach, we study the relation between the predictions of a given model and those of a Taylor density development of the corresponding equation of state: this establishes to what extent a limited set of phenomenological constraints can determine the core-crust transition properties. From a correlation analysis, we show that (a) the transition density ρt is mainly correlated with the symmetry energy slope L, (b) the proton fraction Yp,t with the symmetry energy and symmetry energy slope (J, L) defined at saturation density, or, even better, with the same quantities defined at ρ = 0.1 fm −3 , and (c) the transition pressure Pt with the symmetry energy slope and curvature (L, Ksym) defined at ρ = 0.1 fm −3 .

The theory of the nuclear energy-density functional is used to provide a unified and thermodynamically consistent treatment of all regions of cold non-accreting neutron stars. In order to assess the impact of our lack of complete knowledge of the density dependence of the symmetry energy on the constitution and the global structure of neutron stars, we employ four different functionals. All of them were precision fitted to essentially all the nuclear-mass data with the Hartree-Fock-Bogoliubov method and two different neutron-matter equations of state based on realistic nuclear forces. For each functional, we calculate the composition, the pressure-density relation, and the chemical potentials throughout the star. We show that uncertainties in the symmetry energy can significantly affect the theoretical results for the composition and global structure of neutron stars. To facilitate astrophysical applications, we construct analytic fits to our numerical results.

The equation of state and composition of the inner crust of neutron stars at zero temperature are calculated, using the T = 0 version of the TETFSI (temperature-dependent extended Thomas-Fermi plus Strutinsky integral) method, for each of a family of three functionals based on Skyrme-type forces BSk19, BSk20 and BSk21, which are characterized by different degrees of symmetry-energy stiffness, and also for the SLy4 functional. We also solve the Tolman-Oppenheimer-Volkoff equations to calculate the distribution of mass within the inner crust. Qualitatively similar results are found for all four functionals, and in particular the number of protons per Wigner-Seitz cell is in all cases equal to 40 throughout the inner crust.Comment: 35 pages, 13 figures, accepted for publication in Physical Review

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Because of the presence of a liquid-gas phase transition in nuclear matter, compactstar matter can present a region of instability against the formation of clusters. We investigate this phase separation in a matter composed of neutrons, protons and electrons, within a Skyrme-Lyon mean-field approach. Matter instability and phase properties are characterized through the study of the free-energy curvature. The effect of β-equilibrium is also analyzed in detail, and we show that the opacity to neutrinos has an influence on the presence of clusterized matter in finite-temperature proto-neutron stars.

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).

The slope of the nuclear symmetry energy at saturation density L is pointed out as a crucial quantity to determine the mass and width of neutron-star crusts. This letter clarifies the relation between L and the core-crust transition. We confirm that the transition density is soundly correlated with L despite differences between models, and we propose a clear understanding of this correlation based on a generalised liquid drop model. Using a large number of nuclear models, we evaluate the dispersion affecting the correlation between the transition pressure Pt and L. From a detailed analysis it is shown that this correlation is weak due to a cancellation between different terms. The correlation between the isovector coefficients Ksym and L plays a crucial role in this discussion.Stimulated by the development of exotic nuclear physics, the efforts to determine the nuclear equation of state (EOS) have focused in the last few years on the density dependence of the symmetry energy S(ρ) [1,2]. In particular, the symmetry-energy slope at saturation density, represented by the quantity L, has raised a great deal of interest [1-6]: while the different nuclear models widely disagree on the value of this basic quantity, increasing experimental data [5,[7][8][9][10][11][12] are expected to bring more and more stringent constraints, leading to a radical progress in our knowledge of the EOS of neutron-rich matter. Several experimental constraints on the slope L have already been proposed in the last decade. Such studies include information obtained from the mass formula [7], isospin diffusion [8], experimental double neutron to proton ratio [9], and isoscaling parameters in heavy ion collisions [10], pygmy dipole resonances [11], giant dipole resonances [12], neutron-skin thickness [5]. This impacts strongly on the physics of compact stars. In this letter, we will discuss the link between L and the transition from the liquid core to the solid crust of a neutron star. It has been claimed that a precise determination of L would give a tight indication of the density ρ t and pressure P t at the transition point [2], and consequently the mass and extension of the crust which play a crucial role in the interpretation of pulsar observations [13]. However, the role of L in the determination of the core-crust transition needs to be checked against model dependence and clarified, as mentioned in Ref. [14]. In the present work, we use a variety of nuclear models to address this issue. We verify and explain the strong correlation between L and ρ t . However, we show that when independent models are considered there is no real correlation between L and the pressure at the transition point. This behaviour results from a competition between opposite effects which destroy the correlation. This serious limitation has to be taken into consideration when drawing astrophysical consequences from the experimental determination of L.Catalyzed matter in compact stars satisfies the βequilibrium condition which favors very neutron-rich matter: the prot...

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