Classification of Magnetoatmospheric Modes in Sunspot Umbrae

Abstract

We examine the wave modes in a sunspot umbra. Assuming stratification, based on a model atmosphere in a sunspot, the normal mode spectrum is determined. The modes are classified using a scheme based on a Helmholtz decomposition of the displacement in to l(longitudinal) and t(transverse) components. In certain cases these can be related to the usual fast and slow MHD waves. We compute the theoretical eigenfrequencies and note the existence of umbral oscillations with periods in the range of 2-3 min, which are interpreted as slow and mixed modes. The frequencies of the Alfven waves are also calculated. It is suggested that these modes might also have been observed.