Alpha effect due to buoyancy instability of a magnetic layer

TL;DR

This study investigates the magnetic buoyancy instability in a rotating, stratified system, revealing an inhomogeneous, nonlocal alpha effect that increases with magnetic field strength, using 3D simulations and the test-field method.

Contribution

It provides a detailed analysis of the alpha effect caused by buoyancy instability, including its dependence on magnetic field strength and rotation angle, with new insights into its nonlocal and anti-quenched nature.

Findings

Alpha effect increases with initial magnetic field strength.

The growth rate of instability varies with thermal conductivity to magnetic diffusivity ratio.

Alpha effect is nonlocal, requiring multiple Fourier modes for accurate reconstruction.

Abstract

A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. We calculate the alpha effect due to helical motions caused by a disintegrating magnetic layer in a rotating density-stratified system with angular velocity Omega making an angle theta with the vertical. We also study the dependence of the alpha effect on theta and the strength of the initial magnetic field. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent EMF due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting alpha effect is inhomogeneous and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around 8--16 Fourier modes to reconstruct the actual EMF based on the actual mean field.