Spectral properties of oscillatory and non-oscillatory {\alpha}^2-dynamos

TL;DR

This paper analyzes the spectral properties of { extalpha}^2-dynamos, showing how oscillatory solutions emerge from sign changes in extalpha, and explores how symmetry breaking influences dynamo modes, with implications for magnetic polarity reversals.

Contribution

It provides a detailed spectral analysis of { extalpha}^2-dynamos, highlighting the role of sign changes and symmetry breaking in mode behavior and reversals, including the impact of inner core properties.

Findings

Oscillatory solutions occur with radial sign changes in extalpha.

Symmetry breaking leads to hemispherical dynamo modes.

Inner core properties have little impact on dominant modes.

Abstract

The eigenvalues and eigenfunctions of a linear {\alpha}^{2}-dynamo have been computed for different spatial distributions of an isotropic \alpha-effect. Oscillatory solutions are obtained when \alpha exhibits a sign change in the radial direction. The time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue as an oscillatory eigenfunction with conjugate complex eigenvalues. The close proximity of oscillatory and non-oscillatory solutions may serve as the basic ingredient for reversal models that describe abrupt polarity switches of a dipole induced by noise. Whereas the presence of an inner core with different magnetic diffusivity has remarkable little impact on the character of the dominating dynamo eigenmodes, the introduction of equatorial symmetry breaking considerably changes the geometric character of the solutions. Around the dynamo threshold the leading modes correspond to hemispherical dynamos even when the symmetry breaking is small. This behavior can be explained by the approximate dipole-quadrupole degeneration for the unperturbed problem. More complicated scenarios may occur in case of more realistic anisotropies of \alpha- and \beta-effect or through non-linearities caused by the back-reaction of the magnetic field (magnetic quenching).