How can large-scale twisted magnetic structures naturally emerge from buoyancy instabilities?

B Favier,L Jouve,M R E Proctor,L J Silvers,W Edmunds

doi:10.1111/j.1365-2966.2012.21920.x

Abstract

We consider the three-dimensional instability of a layer of horizontal magnetic field in a polytropic atmosphere where, contrary to previous studies, the field lines in the initial state are not unidirectional. We show that if the twist is initially concentrated inside the unstable layer, the modifications of the instability reported by several authors (see e.g. Cattaneo et al. (1990)) are only observed when the calculation is restricted to two dimensions. In three dimensions, the usual interchange instability occurs, in the direction fixed by the field lines at the interface between the layer and the field-free region. We therefore introduce a new configuration: the instability now develops in a weakly magnetised atmosphere where the direction of the field can vary with respect to the direction of the strong unstable field below, the twist being now concentrated at the upper interface. Both linear stability analysis and non-linear direct numerical simulations are used to study this configuration. We show that from the small-scale interchange instability, large-scale twisted coherent magnetic structures are spontaneously formed, with possible implications to the formation of active regions from a deep-seated solar magnetic field.

Highlights

Active regions at the surface of the Sun are believed to be the visible manifestation of deep-seated intense magnetic fields
We sought to examine the instability of a layer of horizontal magnetic field in a polytropic atmosphere, where the direction of the field lines is depth-dependent
We showed that the initial idea of building large-scale coherent magnetic structures from the buoyancy instability of a sheared magnetic layer, as studied by Cattaneo et al (1990a) and Kusano et al (1998), seemed limited to two-dimensional geometry

Summary

Introduction

Active regions at the surface of the Sun are believed to be the visible manifestation of deep-seated intense magnetic fields. The purpose of this paper is to investigate the simplest model that allows us to consider the buoyancy instability of a toroidal magnetic field in a weakly magnetised atmosphere above. The instability of a sheared magnetic field has already been studied (Cattaneo et al (1990a,b); Kusano et al (1998); Nozawa (2005)) In this case, the twist is uniformly distributed inside the unstable slab and the atmosphere above is field-free. The twist is uniformly distributed inside the unstable slab and the atmosphere above is field-free To our knowledge, this type of instability has only been considered in published papers using two-dimensional numerical simulations. The interchange instability in a weakly magnetised atmosphere is considered in section 4, using both linear stability analysis and non-linear numerical simulations in three dimensions

Model and governing equations

Initial conditions and parameters

Numerical method

Sheared magnetic field

Instability in a magnetised atmosphere

Discussion