Relativistic models of magnetars: structure and deformations

We find numerical solutions of the coupled system of Einstein-Maxwell equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass M = 1.4 M-circle dot and surface magnetic fields of the order of 10(15) G, a quadrupole ellipticity of the order of 10(-6) to 10(-5) should be expected. Low-mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10(-3) in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.