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

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 as little as 1% of the energy, i.e. that the toroidal field can be – and is likely to be – significantly stronger the poloidal. 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.