A novel approach to decomposing and identifying individual magnetohydrodynamic wave modes in sunspots.

Abstract

High resolution solar observations show the complexity of the tem- poral and spatial structure of the magnetohydrodynamic (MHD) wave motion, that makes the identification of the nature and prop- erties of waves rather difficult. In general, observations of waves in solar magnetic structures are limited to the determination of one single wave that turns out to be the most energetic one, i.e. hav- ing the largest amplitude. Based on mechanical analogy of waves in elastic media, it would be natural to expect the appearance of other modes, too. However, these eluded the observers for many years. The present Thesis aims to address this shortcoming and propose new methods for wave identification. In particular, in this Thesis, we are applying both the Proper Or- thogonal Decomposition (POD) and Dynamic Mode Decomposi- tion (DMD) techniques on solar observational data. These tech- niques are well documented and validated in the areas of fluid me- chanics, hydraulics, and granular flows, yet are relatively new to the field of solar physics. While POD identifies modes based on orthogonality in space and it provides a clear ranking of modes in terms of their contribution to the total variance of the signal, DMD resolves modes that are orthogonal in time, i.e. different modes cannot have identical frequencies. The clear presence of the fundamental slow body sausage (n = 0) and kink (n = 1) modes, as well as the higher-order modes (n ≥ 2) has been evidenced based on the POD and DMD analysis of chromospheric Hα observation for sunspots with a circular and elliptical cross-sectional shapes. Additionally to the various slow body modes, evidence for the presence of the fast surface kink mode was found in the circular sunspot. Moreover, for a further analysis, the assumption of changing of the boundary’s shape with time is considered on a long time period of chromospheric HMI sunspot with a circular cross-sectional shape. All the MHD modes patterns recovered from observations were cross-correlated with their theoretically predicted counterparts and we demonstrated that the higher-order MHD wave modes were more sensitive to the changes in the umbral cross-sectional shape, hence this must be taken into account for more accurate modelling of the resonant modes of sunspots and pores.