Relativistic models of magnetars: the twisted-torus magnetic field configuration

TL;DR

This paper develops general relativistic models of magnetar magnetic fields, specifically twisted-torus configurations, using the relativistic Grad-Shafranov equation, and explores their stability and multipolar structure.

Contribution

It extends previous Newtonian models to general relativity, providing equilibrium solutions with confined toroidal fields and coupled multipoles, enhancing understanding of magnetar magnetic configurations.

Findings

Equilibrium solutions with confined toroidal fields are obtained.

Twisted-torus configurations are more stable than other magnetic field arrangements.

Higher order multipoles are included and coupled to the dipolar field.

Abstract

We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. (2008). Our method is based on the solution of the relativistic Grad-Shafranov equation, to which Maxwell's equations can be reduced in some limit. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted-torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.