On magnetic instabilities and dynamo action in stellar radiation zones

TL;DR

This study investigates MHD instabilities in stellar radiation zones, focusing on the Pitts & Tayler instability, its effects on magnetic fields, and the conditions under which dynamo action may or may not occur.

Contribution

It provides detailed simulations of the Pitts & Tayler instability in stellar radiation zones, highlighting its characteristics and the absence of dynamo action up to high magnetic Reynolds numbers.

Findings

Pitts & Tayler instability is present with m=1 azimuthal dependence.

The poloidal field remains unaffected by the instability, undergoing Ohmic decline.

No dynamo action observed up to magnetic Reynolds number of 10^5.

Abstract

We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field. We focus on the non-axisymmetric instability that affects the toroidal magnetic field in a rotating star, which was first studied by Pitts and Tayler in the non-dissipative limit. According to Spruit, it could also drive a dynamo. The Pitts & Tayler instability is manifestly present in our simulations, with its conspicuous m=1 dependence in azimuth. But its analytic treatment used so far is too simplified to be applied to the real stellar situation. Although the instability generated field reaches an energy comparable to that of the mean poloidal field, that field seems unaffected by the instability: it undergoes Ohmic decline, and is neither eroded nor regenerated by the instability. The toroidal field is produced by shearing the poloidal field and it draws its energy from the differential rotation. The small scale motions behave as Alfven waves; they cause negligible eddy-diffusivity and contribute little to the net transport of angular momentum. In our simulations we observe no sign of dynamo action, of either mean field or fluctuation type, up to a magnetic Reynolds number of 10^5. However the Pitts & Tayler instability is sustained as long as the differential rotation acting on the poloidal field is able to generate a toroidal field of sufficient strength.