The influence of internal magnetic layers on the frequencies of solar p-modes

Buried magnetic fields at the base of the convection zone and in the anchoring zones of sunspots are presumed to vary over the solar activity cycle. Their effect on p-mode oscillations is explored in detail, through theoretical modelling. The helioseismic signature from a "tachocline" or "shallow" horizontal layer of magnetic field, buried in a plane-stratified model of the Sun, is explored by examining frequency shifts of various order and degree. p-modes propagating perpendicular to the magnetic field lines are found to yield the largest frequency shifts. However, frequency shifts due to buried magnetic fields are considerably smaller than observationally determined shifts over the solar cycle. Nonetheless, an analytical approach to the problem provides useful insight for solar and stellar applications.