The Effect of Toroidal Magnetic Fields on Solar Oscillation Frequencies

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.

28 pages, 14 figures. Accepted for publication in The Astrophysical Journal

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• Core magnetic field imprint in the non-radial oscillations of red giant stars
• Sensitivity kernels for inferring Lorentz stresses from normal-mode frequency splittings in the Sun
• What Seismic Minimum Reveals About Solar Magnetism Below the Surface?
• Sensitivity of low-degree solar p modes to active and ephemeral regions: frequency shifts back to the Maunder Minimum
• Recipe for inferring sub-surface solar magnetism via local mode-coupling using Slepian basis functions
• The impact of rotation on the stochastic excitation of stellar acoustic modes in solar-like pulsators
• Empirical Relations for the Sensitivities of Solar-like Oscillations to Magnetic Perturbations
• Solar radius and luminosity variations induced by the internal dynamo magnetic fields
• Probing the internal magnetism of stars using asymptotic magneto-asteroseismology