Axisymmetric sunspot oscillations

A discussion of some elementary considerations encountered in the study of the oscillations of axisymmetric sunspot; equilibria is presented. An expansion method is proposed for converting the relevant oscillation equations to a form that is better suited to numerical computation. In so doing, it is demonstrated that thin flux tube and flat canopy approximations are capable of providing physical insight onto the morphology of the oscillations in the deep submerged root of the sunspot and the far-flung outlying penumbral canopy.