Magnetized neutron stars: perturbative versus fully-numerical approaches

TL;DR

This study compares perturbative and fully numerical methods for modeling highly magnetized neutron stars, highlighting their respective ranges of validity and limitations in the context of gravitational wave emission.

Contribution

It provides a detailed comparison between perturbative and numerical approaches for modeling magnetized neutron stars with purely poloidal magnetic fields.

Findings

Perturbative approach is accurate for observed magnetic fields in magnetars.

Numerical approach faces resolution issues at low magnetic field strengths.

Perturbative method fails at very high magnetic fields (above a few times 10^{16} G).

Abstract

(1) Background: for the study of highly magnetized neutron stars observed as magnetars, and to quantify the effect of this intense magnetic field onto the star's structure and shape which can be particularly relevant for the study of 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 (Konno-99) assumes that the deformation induced by the magnetic field is small and that this field arises only from dipole currents. The full numerical one is based on the library LORENE. (3) Results: we have 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 $10^{16}$ G), it gives 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 $10^{10}$ G), which translates into imprecise computation of the star's deformation and mass quadrupole moment.