Abstract:
The nature of umbral oscillations is investigated using an empirical model for the sunspot umbra, based on the model of Maltby et al. (1986). Approximating the sunspot as a thick flux tube of circular cross section, the axisymmetric normal modes of magnetoatmospheric waves were determined, and a diagnostic diagram was generated for different field strengths. The diagram shows the existence of 'avoided crossings' in the solution of magnetoatmospheric modes in a sunspot atmosphere. It was found that, for low values of the radial wavenumber k, corresponding to observed oscillations, a simple global classification is not possible. The oscillations in the low photosphere and below are of either fast or mixed type, but tend to acquire a slow or acoustic character above the temperature minimum.