Symmetry properties of the large-scale solar magnetic field

TL;DR

This paper analyzes the symmetry properties of the solar magnetic field using a dynamo model, revealing differences between dipole and quadrupole modes and predicting a dominant dipole configuration over time.

Contribution

The study maps the solar magnetic field problem onto a quantum double-well problem and provides analytical solutions for dipole and quadrupole modes using WKB approximation.

Findings

Dipole eigenvalue exceeds quadrupole eigenvalue.

A weak dynamo wave violating Hale's law exists.

Dipole mode dominates over quadrupole after long times.

Abstract

We investigate symmetry properties of the solar magnetic field in the framework of the linear Parker's migratory dynamo model. We show that the problem can be mapped onto the well-known quantum-mechanical double-well problem. Using the WKB approximation, we construct analytical solutions for the dipole and quadrupole configurations of the generated magnetic field. Our asymptotic analysis within the equatorial region indicates the existence of an additional weak dynamo wave which violates the Hale's polarity law. We estimate the spatial decay decrement of this wave. We also calculate explicitly the splitting of the eigenvalues corresponding to the dipole and quadrupole modes. The real part of the dipole eigenvalue is shown to exceed the quadrupole one. A sufficiently long time after generation the dipole mode should dominate the quadrupole one. The relevant observational evidences of the properties obtained are discussed.