A New Approach to Identifying MHD Wave Modes in Sunspots and Pores

Observations of sunspots and pores provide us with unique information on magnetohydrodynamic (MHD) wave mode excitation, propagation and conversion. High resolution observations show the complex temporal and special structure of associated with these wave motions. To help untangle this complexity we apply the techniques of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) which in combination identify the dominant MHD wave modes from the intensity time series. The POD method was used to find modes that are spatially orthogonal whereas DMD identifies temporal orthogonality. While POD offers a clear ranking criteria, based on the contribution of the modes to the variance of the signal, DMD does not rank the modes in any way. If it is assumed that solar modes are temporally orthogonal, i.e., different modes cannot have identical frequencies, then DMD with a search criteria offers an optimal methodology to identify coherent mode structure from, for example, intensity snapshots. Based on our analysis we were able successfully identify previously undetected wave modes in sunspot observation data and analyse their power spectra. This approach has great potential in answering the many, as yet, still unresolved questions about properly identifying MHD wave modes in magnetically dominated solar atmospheric features such as sunspots and pores which mostly have irregular cross-sectional shape. Even if these magnetic features have close to circular cross-sections the proper identification of slow/fast sausage (m=0), kink (m=1) and fluting (m=2, 3, 4, ….) modes is still not trivial. Here we show that the combined POD and DMD approach has been very successful in identifying both kink and fluting modes in a sunspot umbra with an approximately circular cross-section.