Magnetized Neutron Stars: Perturbative Versus Fully Numerical Approaches

(1) Background: For the study of highly magnetized neutron stars observed as magnetars and to quantify the effect of this intense magnetic field on the star’s structure and shape, which can be particularly relevant for the study of the emission of continuous gravitational waves, both numerical and perturbative approaches have been developed. (2) Methods: We compare these two approaches in General Relativity with the limitation to the case where the magnetic field has a purely poloidal structure. The perturbative one assumes that the deformation induced by the magnetic field is small and that this field arises only from dipole currents. The fully numerical one is based on the lorene library. (3) Results: We used both approaches to compute the magnetic-field distribution and the deformation of the star, varying the value of the magnetic field at the pole, the compactness of the star and its equation of state. (4) Conclusions: Whereas the perturbative approach breaks down for very high polar magnetic-field values (typically above a few times 1016 G), it achieves very good results for observed values, even in magnetars. On the contrary, the numerical code exhibits resolution problems for relatively low magnetic-field values (typically 1010 G), which translates into imprecise computation of the star’s deformation and mass quadrupole moment.