On obliquely magnetized and differentially rotating stars

TL;DR

This study explores how differential rotation interacts with misaligned magnetic fields in stars, revealing how initial magnetic strength influences the evolution towards axisymmetry or uniform rotation, with implications for binary star systems.

Contribution

It provides a numerical analysis of the nonlinear interaction between differential rotation and oblique magnetic fields in stars, extending understanding beyond previous kinematic predictions.

Findings

Weak fields tend to become axisymmetric over time.

Stronger fields maintain non-axisymmetry and enforce uniform rotation.

The observed scaling of field decay differs from theoretical predictions.

Abstract

We investigate the interaction of differential rotation and a misaligned magnetic field. The incompressible magnetohydrodynamic equations are solved numerically for a free-decay problem. In the kinematic limit, differential rotation annihilates the non-axisymmetric field on a timescale proportional to the cube root of magnetic Reynolds number ($Rm$), as predicted by R\"adler. Nonlinearly, the outcome depends upon the initial energy in the non-axisymmetric part of the field. Sufficiently weak fields approach axisymmetry as in the kinematic limit; some differential rotation survives across magnetic surfaces, at least on intermediate timescales. Stronger fields enforce uniform rotation and remain non-axisymmetric. The initial field strength that divides these two regimes does not follow the scaling $Rm^{-1/3}$ predicted by quasi-kinematic arguments, perhaps because our $Rm$ is never sufficiently large or because of reconnection. We discuss the possible relevance of these results to tidal synchronization and tidal heating of close binary stars, particularly double white dwarfs.