Non-rigid precession of magnetic stars

Stars are, generically, rotating and magnetized objects with a misalignment between their magnetic and rotation axes. Since a magnetic field induces a permanent distortion to its host, it provides effective rigidity even to a fluid star, leading to bulk stellar motion that resembles free precession. This bulk motion is, however, accompanied by induced interior velocity and magnetic field perturbations, which are oscillatory on the precession time-scale. Extending previous work, we show that these quantities are described by a set of second-order perturbation equations featuring cross-terms scaling with the product of the magnetic and centrifugal distortions to the star. For the case of a background toroidal field, we reduce these to a set of differential equations in radial functions, and find a method for their solution. The resulting magnetic field and velocity perturbations show complex multipolar structure and are strongest towards the centre of the star.