Axisymmetric equilibrium models for magnetized neutron stars in General   Relativity under the Conformally Flat Condition
  Extremely magnetized neutron stars with magnetic fields as strong as $\sim 10^{15-16}$ G, or magnetars, have received considerable attention in the last decade due to their identification as a plausible source for Soft Gamma Repeaters and Anomalous X-ray Pulsars. Moreover, this class of compact objects has been proposed as a possible engine capable of powering both Long and Short Gamma-Ray Bursts, if the rotation period in their formation stage is short enough (~1 ms). Such strong fields are expected to induce substantial deformations of the star and thus to produce the emission of gravitational waves. Here we investigate, by means of numerical modeling, axisymmetric static equilibria of polytropic and strongly magnetized stars in full general relativity, within the ideal magneto-hydrodynamic regime. The eXtended Conformally Flat Condition (XCFC) for the metric is assumed, allowing us to employ the techniques introduced for the X-ECHO code [Bucciantini & Del Zanna, 2011, Astron. Astrophys. 528, A101], proven to be accurate, efficient, and stable. The updated XNS code for magnetized neutron star equilibria is made publicly available for the community (see www.arcetri.astro.it/science/ahead/XNS). Several sequences of models are here retrieved, from the purely toroidal (resolving a controversy in the literature) or poloidal cases, to the so-called twisted torus mixed configurations, expected to be dynamically stable, which are solved for the first time in the non-perturbative regime. 
A. G. Pili, N. Bucciantini, L. Del Zanna
astro-ph.HE