Nonideal evolution of nonaxisymmetric, force-free magnetic fields in a magnetar

TL;DR

This paper models the resistive evolution of nonaxisymmetric, force-free magnetic fields in magnetars, showing how they relax into linked poloidal-toroidal configurations and exploring the implications for magnetic field decay and reorganization.

Contribution

It provides an analytical model of magnetar magnetic field evolution, extending numerical results to include nonaxisymmetric, force-free states and helicity exchange mechanisms.

Findings

Magnetic fields relax to linked poloidal-toroidal configurations over time.

Field inflation and increased toroidality occur during evolution.

End states depend on helicity exchange mechanisms.

Abstract

Recent numerical magnetohydrodynamic calculations by Braithwaite and collaborators support the `fossil field' hypothesis regarding the origin of magnetic fields in compact stars and suggest that the resistive evolution of the fossil field can explain the reorganisation and decay of magnetar magnetic fields. Here, these findings are modelled analytically by allowing the stellar magnetic field to relax through a quasistatic sequence of nonaxisymmetric, force-free states, by analogy with spheromak relaxation experiments, starting from a random field. Under the hypothesis that the force-free modes approach energy equipartition in the absence of resistivity, the output of the numerical calculations is semiquantitatively recovered: the field settles down to a linked poloidal-toroidal configuration, which inflates and becomes more toroidal as time passes. A qualitatively similar (but not identical) end state is reached if the magnetic field evolves by exchanging helicity between small and large scales according to an $\alpha$-dynamo-like, mean-field mechanism, arising from the fluctuating electromotive force produced by the initial random field. The impossibility of matching a force-free internal field to a potential exterior field is discussed in the magnetar context.