Spatial distribution and physical characteristics of decomposed sunspot wave modes

¹ Korea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of Korea
² Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
³ Astronomy and Space Science, University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea
⁴ National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁵ Research Institute of Natural Sciences, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea
⁶ Astronomy Research Center, Seoul National University, Gwanak-gu, Seoul 08826, Republic Korea

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 February 2026
Accepted: 21 April 2026

Abstract

Sunspot oscillations consist of multiple wave modes, making it challenging to isolate individual physical processes. To decompose these multi-modal oscillations, we apply empirical mode decomposition (EMD) to Hα Doppler velocity data obtained with the Fast Imaging Solar Spectrograph. By avoiding arbitrary frequency filtering, EMD resolves the oscillations into four distinct modes with unique periodicities and spatial distributions: c₁ in the umbra (periods of ∼2 min); c₂ in the umbra and penumbra (2.5 − 4 min); c₃ in the outer penumbra (4 − 6 min); and c₄ in the superpenumbra (∼10 min). We find that all modes, including the high-frequency 1-minute oscillations, coexist in the superpenumbral fibrils and represent potential candidates for transverse waves. Analysis of the c₁ and c₂ modes reveals the coexistence of umbra-trapped body waves and running penumbral waves within the umbra. Meanwhile, the c₃ and c₄ modes demonstrate that sunspot waves undergo significant nonlinear evolution as they propagate through the stratified atmosphere. Our results indicate that EMD effectively classifies dispersive oscillations into distinct groups based on their intrinsic timescales and underlying physical natures.