Axisymmetric magnetic fields in stars: relative strengths of poloidal and toroidal components

TL;DR

This paper investigates the stability of axisymmetric magnetic fields in stars, revealing that toroidal components can be significantly stronger than poloidal ones, with stability dependent on their energy ratio, impacting neutron star phenomena.

Contribution

It provides analytic predictions and numerical validation for the stable ratio of toroidal to poloidal magnetic field components in stars.

Findings

Poloidal field can be up to 80% of total energy.

Toroidal field is likely much stronger than poloidal.

Weaker overall fields allow even smaller poloidal components.

Abstract

In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and in particular at the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's (1973) stability conditions for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running numerical simulations. It is found that while the poloidal field can account for no more than approximately 80% of the total energy, it can account for a very small fraction of the energy, i.e. that the toroidal field can be -- and is likely to be -- significantly stronger than the poloidal. Furthermore, the weaker the field, the weaker the poloidal component can be in relation to the toroidal. The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron stars, free precession, and a `hidden' energy source for magnetars.