Where is the solar dynamo located and what is its modus operandi? These are
still open questions in solar physics. Helio- and asteroseismology can help
answer them by enabling us to study solar and stellar internal structures
through global oscillations. The properties of solar and stellar acoustic modes
are changing with the level of magnetic activity. However, until now, the
inference on subsurface magnetic fields with seismic measures has been very
limited. The aim of this paper is to develop a formalism to calculate the
effect of large-scale toroidal magnetic fields on solar and stellar global
oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added
to the equilibrium equation of motion, stellar eigenmodes can couple. In
quasi-degenerate perturbation theory, this coupling, also known as the direct
effect, can be quantified by the general matrix element. We present the
analytical expression of the matrix element for a superposition of subsurface
zonal toroidal magnetic field configurations. The matrix element is important
for forward calculations of perturbed solar and stellar eigenfunctions and
frequency perturbations. The results presented here will help to ascertain
solar and stellar large-scale subsurface magnetic fields, and their geometric
configuration, strength, and their change over the course of activity cycles.Comment: 20 pages, accepted for publication in The Astrophysical Journa
