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Extremely magnetized neutron stars with magnetic fields as strong as $\sim10^{15-16}$ G, or magnetars, have received considerable attention in the lastdecade due to their identification as a plausible source for Soft GammaRepeaters and Anomalous X-ray Pulsars. Moreover, this class of compact objectshas been proposed as a possible engine capable of powering both Long and ShortGamma-Ray Bursts, if the rotation period in their formation stage is shortenough (~1 ms). Such strong fields are expected to induce substantialdeformations of the star and thus to produce the emission of gravitationalwaves. Here we investigate, by means of numerical modeling, axisymmetric staticequilibria of polytropic and strongly magnetized stars in full generalrelativity, within the ideal magneto-hydrodynamic regime. The eXtendedConformally Flat Condition (XCFC) for the metric is assumed, allowing us toemploy the techniques introduced for the X-ECHO code [Bucciantini & Del Zanna,2011, Astron. Astrophys. 528, A101], proven to be accurate, efficient, andstable. The updated XNS code for magnetized neutron star equilibria is madepublicly available for the community (seewww.arcetri.astro.it/science/ahead/XNS). Several sequences of models are hereretrieved, 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 thenon-perturbative regime.

Axisymmetric equilibrium models for magnetized neutron stars in General Relativity under the Conformally Flat Condition