Evolution of a magnetic field in a differentially rotating radiative zone

TL;DR

This study investigates the evolution and stability of magnetic fields in differentially rotating radiative stellar zones, revealing conditions under which magnetic configurations remain stable or become unstable, and linking these findings to observed stellar magnetic dichotomies.

Contribution

It provides a detailed numerical analysis of magnetic field evolution in stellar radiative zones, introducing a stability criterion based on the ratio of toroidal to poloidal fields and connecting it to observed stellar magnetic properties.

Findings

Toroidal-to-poloidal magnetic field ratio peaks after an Alfvén crossing time.

High-density contrasts lead to an asymptotic ratio applicable to real stars.

Toroidal-dominated configurations are unstable if shear exceeds a critical threshold.

Abstract

Recent spectropolarimetric surveys of main-sequence intermediate-mass stars have exhibited a dichotomy in the distribution of the observed magnetic field between the kG dipoles of Ap/Bp stars and the sub-Gauss magnetism of Vega and Sirius. We would like to test whether this dichotomy is linked to the stability versus instability of large-scale magnetic configurations in differentially rotating radiative zones. We computed the axisymmetric magnetic field obtained from the evolution of a dipolar field threading a differentially rotating shell. A full parameter study including various density profiles and initial and boundary conditions was performed with a 2D numerical code. We then focused on the ratio between the toroidal and poloidal components of the magnetic field and discuss the stability of the configurations dominated by the toroidal component using local stability criteria and insights from recent 3D numerical simulations. The numerical results and a simple model show that the ratio between the toroidal and the poloidal magnetic fields is highest after an Alfv\'en crossing time of the initial poloidal field. For high density contrasts, this ratio converges towards an asymptotic value that can thus be extrapolated to realistic stellar cases. We then consider the stability of the magnetic configurations to non-axisymmetric perturbations and find that configurations dominated by the toroidal component are likely to be unstable if the shear strength is significantly higher than the poloidal Alfv\'en frequency. An expression for the critical poloidal field below which magnetic fields are likely to be unstable is found and is compared to the lower bound of Ap/Bp magnetic fields.