Magnetic fields in axisymmetric neutron stars

TL;DR

This paper develops a formalism and computational method to model equilibrium configurations of rotating, magnetized neutron stars with various magnetic field geometries, analyzing their distortions and validity regimes.

Contribution

It introduces a general set of equations for axisymmetric Newtonian MHD and a code to compute neutron star equilibria with mixed magnetic fields, including bounds on the toroidal component.

Findings

Toroidal magnetic field component is less than 7%.

Perturbative formulas are accurate within 10% for ellipticity less than 0.15.

Magnetic and rotational distortions vary with polytropic index.

Abstract

We derive general equations for axisymmetric Newtonian MHD and use these as the basis of a code for calculating equilibrium configurations of rotating magnetised neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism the toroidal component appears to be bounded at less than 7%. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10% of the nonlinear results if the ellipticity is less than 0.15 or the average field strength is less than $10^{17}$ G. We also consider how magnetised equilibrium structures vary for different polytropic indices.