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.

The effect of the density dependence of the nucleonic equation of state and the hyperon meson couplings on the star properties, including strangeness content, mass and radius, are studied within a relativistic mean field formalism. It is shown that there is still lacking information on the nucleonic equation of state at supra-saturation densities and on the hyperon interactions in nuclear matter that will allow a clear answer to the question whether the mass of the pulsar J1614-2230 could rule out exotic degrees of freedom from the interior of compact stars. We show that some star properties are affected in a similar way by the density dependence of the symmetry energy and the hyperon content of the star. To disentangle these two effects it is essential to have a good knowledge of the equation of state at supra-saturation densities. A linear correlation between the radius and the strangeness content of a star with a fixed mass is obtained.

The effect of strong magnetic fields on the equation of state (EoS) for compact stars described with density dependent relativistic hadronic models is studied. A comparison with other mean-field relativistic models is done. It is shown that the largest differences between models occur for low densities and that the magnetic field affects the crust properties of star, namely its extension. PACS numbers: 26.60.-c 26.60.Kp 97.60.Jd 24.10.Jv I. INTRODUCTIONThe study of very asymmetric nuclear matter is presently an important issue due to the radioactive beams which will be operating in the near future and which will allow the investigation of a region of the nuclear matter phase space unaccessible till recently. Asymmetric nuclear matter is of particular interest for the description of stellar matter of compact stars.Compact star properties depend a lot on the model used to describe the hadronic equation of state (EoS). In particular relativistic nuclear mean-field models [1,2] are very popular to describe stellar matter because causality will always be satisfied. The imposition of constraints, both coming from measured star properties or from relativistic heavy ion collisions in the laboratory, is essential to test the different models [3].Magnetars are neutron stars which may have surface magnetic fields larger that 10 15 G [4-6] and which were discovered at the x-ray and γ-ray energies (for a review refer [7]). They are identified with the anomalous x-ray pulsars (AXP) and soft γ-ray repeaters. Taking as reference the critical