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Where is the solar dynamo located and what is its modus operandi? These arestill open questions in solar physics. Helio- and asteroseismology can helpanswer them by enabling us to study solar and stellar internal structuresthrough global oscillations. The properties of solar and stellar acoustic modesare changing with the level of magnetic activity. However, until now, theinference on subsurface magnetic fields with seismic measures has been verylimited. The aim of this paper is to develop a formalism to calculate theeffect of large-scale toroidal magnetic fields on solar and stellar globaloscillation eigenfunctions and eigenfrequencies. If the Lorentz force is addedto the equilibrium equation of motion, stellar eigenmodes can couple. Inquasi-degenerate perturbation theory, this coupling, also known as the directeffect, can be quantified by the general matrix element. We present theanalytical expression of the matrix element for a superposition of subsurfacezonal toroidal magnetic field configurations. The matrix element is importantfor forward calculations of perturbed solar and stellar eigenfunctions andfrequency perturbations. The results presented here will help to ascertainsolar and stellar large-scale subsurface magnetic fields, and their geometricconfiguration, strength, and their change over the course of activity cycles.

The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element