The Effect of Toroidal Magnetic Fields on Solar Oscillation Frequencies

TL;DR

This study investigates how toroidal magnetic fields inside the Sun influence helioseismic oscillation frequencies, revealing that certain internal magnetic configurations do not account for observed solar cycle frequency shifts, but surface magnetic effects may contribute.

Contribution

The paper introduces a theoretical framework using quasi-degenerate perturbation theory to quantify the impact of toroidal magnetic fields on solar oscillation frequencies, considering both direct and indirect effects.

Findings

Strong tachocline fields are unlikely to cause observed p-mode frequency shifts.

Surface magnetic fields may explain part of the surface effect in helioseismic frequencies.

The theory applies to solar-like stars, aiding magnetic field inference from oscillation data.

Abstract

Solar oscillation frequencies change with the level of magnetic activity. Localizing subsurface magnetic field concentrations in the Sun with helioseismology will help us to understand the solar dynamo. Because the magnetic fields are not considered in standard solar models, adding them to the basic equations of stellar structure changes the eigenfunctions and eigenfrequencies. We use quasi-degenerate perturbation theory to calculate the effect of toroidal magnetic fields on solar oscillation mean multiplet frequencies for six field configurations. In our calculations, we consider both the direct effect of the magnetic field, which describes the coupling of modes, and the indirect effect, which accounts for changes in stellar structure due to the magnetic field. We limit our calculations to self-coupling of modes. We find that the magnetic field affects the multiplet frequencies in a way that depends on the location and the geometry of the field inside the Sun. Comparing our theoretical results with observed shifts, we find that strong tachocline fields cannot be responsible for the observed frequency shifts of p modes over the solar cycle. We also find that part of the surface effect in helioseismic oscillation frequencies might be attributed to magnetic fields in the outer layers of the Sun. The theory presented here is also applicable to models of solar-like stars and their oscillation frequencies.