Improving the Γ-functions method for vortex identification

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 Γ1min 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 Γ1min 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 Γ1min 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.