The cell structure of clusters in the inner crust of a cold β-equilibrium neutron star is studied within a Thomas Fermi approach and compared with other approaches which include shell effects. Relativistic nuclear models are considered. We conclude that the symmetry energy slope L may have quite dramatic effects on the cell structure if it is very large or small. Rod-like and slab-like pasta clusters have been obtained in all models except one with a large slope L.

The crust of a neutron star is thought to be comprised of a lattice of nuclei immersed in a sea of free electrons and neutrons. As the neutrons are superfluid their angular momentum is carried by an array of quantized vortices. These vortices can pin to the nuclear lattice and prevent the neutron superfluid from spinning down, allowing it to store angular momentum which can then be released catastrophically, giving rise to a pulsar glitch. A crucial ingredient for this model is the maximum pinning force that the lattice can exert on the vortices, as this allows us to estimate the angular momentum that can be exchanged during a glitch. In this paper we perform, for the first time, a detailed and quantitative calculation of the pinning force per unit length acting on a vortex immersed in the crust and resulting from the mesoscopic vortexlattice interaction. We consider realistic vortex tensions, allow for displacement of the nuclei and average over all possible orientation of the crystal with respect to the vortex. We find that, as expected, the mesoscopic pinning force becomes weaker for longer vortices and is generally much smaller than previous estimates, based on vortices aligned with the crystal. Nevertheless the forces we obtain still have maximum values of order f pin ≈ 10 15 dyn/cm, which would still allow for enough angular momentum to be stored in the crust to explain large Vela glitches, if part of the star is decoupled during the event.

We discuss the thermalization process of the neutron star's crust described by solving the heat-transport equation with a microscopic input for the specific heat of baryonic matter. The heat equation is solved with initial conditions specific to a rapid cooling of the core. To calculate the specific heat of inner-crust baryonic matter, that is, nuclear clusters and unbound neutrons, we use the quasiparticle spectrum provided by the Hartree-Fock-Bogoliubov approach at finite temperature. In this framework, we analyze the dependence of the crust thermalization on pairing properties and on cluster structure of inner-crust matter. It is shown that the pairing correlations reduce the crust thermalization time by a large fraction. The calculations show also that the nuclear clusters have a non-negligible influence on the time evolution of the surface temperature of the neutron sta

The cell structure of β-stable clusters in the inner crust of cold and warm neutron stars is studied within the Thomas-Fermi approach by using relativistic mean-field nuclear models. The relative size of the inner crust and the pasta phase of neutron stars is calculated, and the effect of the symmetry energy slope parameter L on the profile of the neutron star crust is discussed. It is shown that, while the size of the total crust is mainly determined by the incompressibility modulus, the relative size of the inner crust depends on L. It is found that the inner crust represents a larger fraction of the total crust for smaller values of L. Finally, it is shown that, at finite temperature the pasta phase in β-equilibrium matter essentially melts above 5 to 6 MeV, and that the onset density of the rod-like and slab-like structures does not depend on the temperature.

22 pages, 5 figuresWe analyse how the structure of the inner curst is influenced by the pairing correlations. The inner-crust matter, formed by nuclear clusters immersed in a superfluid neutron gas and ultra-relativistic electrons, is treated in the Wigner-Seitz approximation. The properties of the Wigner-Seitz cells, i.e., their neutron to proton ratio and their radius at a given baryonic density, are obtained from the energy minimization at beta equilibrium. To obtain the binding energy of baryonic matter we perform Skyrme-HFB calculations with zero-range density-dependent pairing forces of various intensities. We find that the Wigner-Seitz cells have much smaller numbers of protons compared to previous calculations. For the dense cells the binding energy of the configurations with small proton numbers do not converge to a well-defined minimum value which precludes the determination of their structure. We show that for these cells there is a significant underestimation of the binding energy due to the boundary conditions at the border of the cells imposed through the Wigner-Seitz approximation

Abstract. In this work we study the effect of the symmetry energy on several properties of neutron stars. First, we discuss its effect on the density, proton fraction and pressure of the neutron star crust-core transition. We show that whereas the first two quantities present a clear correlation with the slope parameter L of the symmetry energy, no satisfactory correlation is seen between the transition pressure and L. However, a linear combination of the slope and curvature parameters at ρ = 0.1 fm −3 is well correlated with the transition pressure.In the second part we analyze the effect of the symmetry energy on the pasta phase. It is shown that the size of the pasta clusters, number of nucleons and the cluster proton fraction depend on the density dependence of the symmetry energy: a small L gives rise to larger clusters. The influence of the equation of state at subsaturation densities on the extension of the inner crust of the neutron star is also discussed. Finally, the effect of the effect of the density dependence of the symmetry energy on the strangeness content of neutron stars is studied in the last part of the work. It is found that charged (neutral) hyperons appear at smaller (larger) densities for smaller values of the slope parameter L. A linear correlation between the radius and the strangeness content of a star with a fixed mass is also found.PACS. 26.60.-c Nuclear matter aspects of neutron stars -21.65.-f Nuclear matter

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