Oscillations in a complex sunspot: From theory to data

Abstract: Sunspot oscillations, intricate three-dimensional wave-like motions in the solar atmosphere, result from the complex interplay between plasma and magnetic fields. This study delves into the behaviour of these oscillations, exploring their simultaneous excitation and evaluating their impact on solar phenomena like coronal heating, energy transport, and solar flares. Utilising magnetohydrodynamic models, my work replicates and extends a computational study by Stangalini et al. I confirm the existence of multiple resonant modes inside the sunspot's umbra in active region AR 12546, characterised by a powerful magnetic field. I also demonstrate the model's sensitivity to the sunspot umbra's shape as it influences the physical characteristics of eigenfunctions. An extension of the study involves introducing an inhomogeneous distribution of the sound and Alfvén speed while assuming a vertical magnetic field. This advancement from a previously constant model yields substantial variations in results, notably distinguishing between slow and fast modes. The sound speed towards the sunspot centre notably constrains the slow modes. Additionally, analysing the power spectral density of vertical velocity in sunspots verifies the presence of five-minute oscillations, with more vital occurrences in the quiet sun and diminishing towards the centre of the sunspot. Examination of active region evolution over time reveals apparent magnetic polarity changes. This research significantly contributes to our understanding of sunspot dynamics. It introduces a novel model incorporating an inhomogeneous sound distribution and Alfvén speed, an advancement from prior approaches. This innovation adds depth to the comprehension of solar phenomena, paving the way for further investigations.