Non-rigid precession of magnetic stars

TL;DR

This paper investigates how magnetic stars undergo non-rigid precession due to magnetic and rotational distortions, revealing complex internal velocity and magnetic field perturbations with multipolar structures.

Contribution

It extends previous models by deriving second-order perturbation equations for magnetic and velocity perturbations in precessing stars, especially for toroidal magnetic fields.

Findings

Perturbations exhibit complex multipolar structures.

Perturbations are strongest near the star's center.

Derived a method to solve the differential equations for these perturbations.

Abstract

Stars are, generically, rotating and magnetised 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 which resembles free precession. This bulk motion is however accompanied by induced interior velocity and magnetic field perturbations, which are oscillatory on the precession timescale. 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.