  We study the properties of plasma oscillations in the solar tachocline using
shallow-water magnetohydrodynamic equations. These oscillations are expected to
correlate with solar activity. We find new qualitative features in the
equatorial spectrum of magnetohydrodynamic oscillations associated with
magneto-Rossby and magneto-Yanai waves. By studying this spectrum in terms of
band theory, we find that magneto-Kelvin and magneto-Yanai waves are
topologically protected. This highlights the important role of these two
classes of waves, as robust features of the plasma oscillation spectrum, in the
interpretation of helioseismological observations.
