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Magnetohydrodynamic wave mode identification in circular and elliptical sunspot umbrae: evidence for high order modes  

ABDULRAHMAN ALBIDAH   Submitted: 2022-02-10 05:12

In this paper we provide clear direct evidence of multiple concurrent higher order magnetohydrodynamic (MHD) modes in circular and elliptical sunspots by applying both Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) techniques on solar observational data. These techniques are well documented and validated in the areas of fluid mechanics, 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 variance of the signal, DMD resolves modes that are orthogonal in time. The clear presence of the fundamental slow sausage and kink body modes, as well as higher order slow sausage and kink body modes have been identified using POD and DMD analysis of the chromospheric Hα line at 6562.808 Å for both the circular and elliptical sunspots. Additionally, to the various slow body modes, evidence for the presence of the fast surface kink mode was found in the circular sunspot. All the MHD modes patterns were cross-correlated with their theoretically predicted counterparts and we demonstrated that ellipticity cannot be neglected when interpreting MHD wave modes. The higher-order MHD wave modes are even more sensitive to irregularities in umbral cross-sectional shapes, hence this must be taken into account for more accurate modelling of the modes in sunspots and pores.

Authors: A. B. Albidah, V. Fedun, A. A. Aldhafeeri, I. Ballai, W. Brevis, D. B. Jess, J. Higham, M. Stangalini, S. S. A. Silva and G. Verth
Projects: None

Publication Status: Accepted
Last Modified: 2022-02-11 09:27
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Proper Orthogonal and Dynamic Mode Decomposition of Sunspot Data.  

ABDULRAHMAN ALBIDAH   Submitted: 2020-11-12 02:29

High resolution solar observations show the complex structure of the magnetohydrodynamic (MHD) wave motion. We apply the techniques of POD and DMD to identify the dominant MHD wave modes in a sunspot using the intensity time series. The POD technique was used to find modes that are spatially orthogonal, whereas the DMD technique identifies temporal orthogonality. Here we show that the combined POD and DMD approaches can successfully identify both sausage and kink modes in a sunspot umbra with an approximately circular cross-sectional shape.

Authors: A. B. Albidah, W. Brevis, V. Fedun, I. Ballai, D. B. Jess, M. Stangalini, J. Higham and G. Verth
Projects: None

Publication Status: Accepted
Last Modified: 2020-11-16 16:41
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Magnetohydrodynamic wave mode identification in circular and elliptical sunspot umbrae: evidence for high order modes
Proper Orthogonal and Dynamic Mode Decomposition of Sunspot Data.

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