We study the effect of a strong magnetic field on the properties of neutron stars with a quarkhadron phase transition. It is shown that the magnetic field prevents the appearance of a quark phase, enhances the leptonic fraction, decreases the baryonic density extension of the mixed phase and stiffens the total equation of state, including both the stellar matter and the magnetic field contributions. Two parametrisations of a density dependent static magnetic field, increasing, respectively, fast and slowly with the density and reaching 2 − 4 × 10 18 G in the center of the star, are considered. The compact stars with strong magnetic fields have maximum mass configurations with larger masses and radius and smaller quark fractions. The parametrisation of the magnetic field with density has a strong influence on the star properties.

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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.

In-medium modifications of light cluster properties in warm stellar matter are studied within the relativistic mean-field approximation. In-medium effects are included by introducing an explicit binding energy shift analytically calculated in the Thomas-Fermi approximation, supplemented with a phenomenological modification of the cluster couplings to the σ meson. A linear dependence on the σ meson is assumed for the cluster mass, and the associated coupling constant is fixed imposing that the virial limit at low density is recovered. The resulting cluster abundances come out to be in reasonable agreement with constraints at higher density coming from heavy ion collision data. Some comparisons with microscopic calculations are also shown.

We examine the correlations of neutron star radii with the nuclear matter incompressibility, symmetry energy, and their slopes, which are the key parameters of the equation of state (EoS) of asymmetric nuclear matter. The neutron star radii and the EoS parameters are evaluated using a representative set of 24 Skyrme-type effective forces and 18 relativistic mean field models, and two microscopic calculations, all describing 2M⊙ neutron stars. Unified EoSs for the inner-crust-core region have been built for all the phenomenological models, both relativistic and non-relativistic. Our investigation shows the existence of a strong correlation of the neutron star radii with the linear combination of the slopes of the nuclear matter incompressibility and the symmetry energy coefficients at the saturation density. Such correlations are found to be almost independent of the neutron star mass in the range 0.6-1.8M⊙. This correlation can be linked to the empirical relation existing between the star radius and the pressure at a nucleonic density between one and two times saturation density, and the dependence of the pressure on the nuclear matter incompressibility, its slope and the symmetry energy slope. The slopes of the nuclear matter incompressibility and the symmetry energy coefficients as estimated from the finite nuclei data yield the radius of a 1.4M⊙ neutron star in the range 11.09-12.86 km.PACS numbers: 21.65.+f, 21.30.Fe, 26.60.+c The bulk properties of neutron stars are mainly governed by the behaviour of the equation of state (EoS) of highly asymmetric dense matter. The correlations of the various EoS parameters of asymmetric nuclear matter with the different properties of neutron star, such as the crust-core transition density and pressure, radii, maximum mass and cooling rate, have been studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The crust-core transition density is strongly correlated with the slope of the symmetry energy, L 0 , at saturation density (ρ 0 ∼ 0.16 fm −3 ) [5,6,11]. However, the transition pressure is found to be strongly correlated with a linear combination of the slope and curvature of the symmetry energy at the sub-saturation density (ρ = 0.1 fm −3 ) [7,11,12]. The simultaneous determination of mass and radius of low-mass neutron stars can better constrain the product of nuclear matter incompressibility and symmetry energy slope parameter [13].The correlations of the neutron star radii of different masses with the EoS parameters have been investigated extensively. The covariance analysis, based on a single model, suggests the existence of strong correlations of the radii of low-mass neutron stars (M NS ∼ 0.6-1.2M ⊙ ) with the symmetry energy slope parameter L 0 [10], the correlations becoming weaker with the increase of the neutron star mass. Similar analysis for the correlations of the radii with the symmetry energy slope over a wider range of densities was performed for two different models, having different behaviours on the density dependence of the symmetry energy, a...

The Vlasov equation is used to determine the dispersion relation for the eigenmodes of magnetized nuclear and neutral stellar matter, taking into account the anomalous magnetic moment of nucleons. The formalism is applied to the determination of the dynamical spinodal section, a quantity that gives a good estimation of the crust-core transition in neutron stars. We study the effect of strong magnetic fields, of the order of 10 15 -10 17 G, on the extension of the crust of magnetized neutron stars. The dynamical instability region of neutron-proton-electron (npe) matter at subsaturation densities is determined within a relativistic mean-field model. It is shown that a strong magnetic field has a large effect on the instability region, defining the crust-core transition as a succession of stable and unstable regions due to the opening of new Landau levels. The effect of the anomalous magnetic moment is non-negligible for fields larger than 10 15 G. The complexity of the crust at the transition to the core and the increase of the crust thickness may have direct impact on the properties of neutrons stars related with the crust.

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean-field models. Three different calculations are used for comparison: the Thomas-Fermi, the coexisting phases, and the compressible liquid drop approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy, pressure, entropy, and chemical potentials in the range of particle number densities and temperatures expected to cover the pasta region are calculated. Finally, a comparison with a finite-temperature Skyrme-Hartree-Fock calculation is drawn.

We study the effect of strong magnetic fields, of the order of 10 15 -10 17 G, on the extension of the crust of magnetized neutron stars. The dynamical instability region of neutron-proton-electron (npe) matter at subsaturation densities and the mode with the largest growth rate are determined within a relativistic mean-field model. It is shown that the effect of a strong magnetic field on the instability region is very sensitive to the density dependence of the symmetry energy, and that it is at the origin of an increase of the extension of the crust and of the charge content of clusters. DOI: 10.1103/PhysRevC.94.062801 Soft-γ -ray repeaters and some anomalous x-ray pulsars are strongly magnetized neutron stars known as magnetars [1][2][3]. These stars have strong surface magnetic fields of the order of 10 14 -10 15 G [4], and slow rotation with a period of ∼1-12 s. Recently, the time evolution of the magnetic field of isolated x-ray pulsars has been studied by Pons et al. [5]. The authors show that a fast decay of the magnetic field could explain the nonobservation of stars with periods above 12 s. The decay of the magnetic field was obtained by including a high electrical resistivity in the inner crust, attributed to the possible existence of an amorphous and heterogeneous layer at the bottom of the inner crust. The lack of isolated x-ray pulsars with a period higher than 12 s could, therefore, be a direct indication of the existence of an amorphous inner crust, possibly in the form of pasta phases [5].At low nuclear matter densities, a competition between the long-range Coulomb repulsion and short-range nuclear attraction will lead to the formation of clusterized matter, known as nuclear pasta [6], near the crust-core transition. These geometrical configurations are observed not only in nuclear matter, but also in a variety of amorphous solids, crystals, and magnetic and biological materials [7]. One of the main interests of the existence of these exotic structures in the crust of neutron stars is the effect that they might have on the neutrino transport and the subsequent cooling of the neutron star [8].Molecular dynamics simulations of the nuclear pasta have shown that topological defects in the pasta could increase electron scattering and reduce the electrical and the thermal conductivities [9]. Electron conductivity in magnetized neutron star matter was also studied in Ref. [10], and it was shown that the electron transport is strongly anisotropic, due to the presence of strong magnetic fields. The complexity introduced by the magnetic field suggests that both suppression and enhancement of the electron conduction in the presence of the pasta phases are possible, and further calculations are required.* jian-junfang@163.com † pais.lena@gmail.com ‡ sidney.avancini@ufsc.br § cp@teor.fis.uc.pt Stellar matter contains, besides neutrons and protons, also electrons, which neutralize the proton charge. The transition clusterized-homogeneous matter has been estimated by using different methods. In particular, ...