  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.
