Improving the Γ-functions method for vortex identification

¹ National Key Laboratory of Deep Space Exploration, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China
² CAS Center for Excellence in Comparative Planetology/CAS Key Laboratory of Geospace Environment/Mengcheng National Geophysical Observatory, University of Science and Technology of China, Hefei 230026, China
³ Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S3 7RH, UK
⁴ Department of Astronomy, Eötvös Loránd University, Budapest, Pázmány P. sétány 1/A H-1117, Hungary
⁵ Gyula Bay Zoltan Solar Observatory (GSO), Hungarian Solar Physics Foundation (HSPF), Petőfi tér 3., Gyula H-5700, Hungary

^⋆ Corresponding author: jiajialiu@ustc.edu.cn

Received: 14 March 2025
Accepted: 20 May 2025

Abstract

Context. Vortices have been observed at various heights within the solar atmosphere and are suggested to play a significant role in heating the solar upper atmosphere. Multiple automated vortex detection methods have been developed and applied to identify vortices.

Aims. We aim to improve the Γ-functions method for vortex identification by optimizing the value of Γ_1min and the approach to calculate Γ₁ and Γ₂, used to determine the center and edge of the vortex. This optimization enhances detection accuracy and enables statistical studies to improve our understanding of vortex generation and evolution in the solar atmosphere.

Methods. We applied the automated swirl detection algorithm (ASDA, a representative of the Γ-functions method) with different parameters to various synthetic datasets, each containing 1000 Lamb-Oseen vortices, to identify the optimal Γ_1min and kernel size when calculating Γ₁ and Γ₂. We also compared another detection method using simulation and observational data to validate the results obtained from the synthetic datasets.

Results. We achieve the best performance with the Optimized ASDA, which combines different kernel sizes (5, 7, 9, and 11) to calculate Γ₁ and Γ₂ with Γ_1min fixed at 0.63 for vortex center detection. We find that more vortices can be detected by the optimized ASDA with improved accuracy in location, radius, and rotation speed. These results are further confirmed by comparing vortices detected by the Optimized ASDA and the SWirl Identification by Rotation-centers Localization (SWIRL) method on CO5BOLD numerical simulation data and Swedish 1-m Solar Telescope observational data.