Research on the dynamic variation characteristics of the granule number of the solar photosphere

Context. Solar granules can be categorized into different classes based on their size. Granules of varying sizes exhibit distinct characteristics. Throughout their brief life cycle, granules continually form, split, and dissipate, constituting a dynamic process. However, within this dynamic process, our understanding of the overall changes in granules of different sizes in quiet and active regions, as well as the relationships and differences between these changes, remains insufficient. Aims. Using continuous high-resolution solar granule observation data from the Big Bear Solar Observatory (BBSO), we studied the continuous changes in the number of granule groups with three different equivalent diameter sizes–(d1 ≤ 265 km, 265 km < d2 < 1420 km, and d3 ≥ 1420 km) –in active and quiet regions, as well as the interrelationships among these changes. Methods. For research purposes, we propose an automatic granule segmentation method that combines grayscale remapping with the knee point of the grayscale probability curve. This method has excellent control capabilities over granule edges, significantly ameliorating the insufficient granule segmentation issues in current methods and enhancing the accuracy of granule segmentation. Moreover, it can effectively cope with fluctuations in the quality of consecutive images and the blurring of granule edges, enabling the proper segmentation of granules of different sizes. In addition, to analyze the subtle differences in the variation process of the granule counts across different sizes, we employed the variational mode decomposition method to decompose the variation process into five frequency components ranging from low to high frequencies. These components represent the variation characteristics of granules on different timescales. The mutual relationships among these components were also calculated and analyzed. Results. The characteristics of the changes in the number of granule groups of three different sizes in active and quiet regions exhibit similarities and differences. In both regions, the overall proportion of the number of granules follows the order d2 > d1 > d3. However, in the active region, the number of granules of size d2 is higher, while the number of granules of size d3 is lower. Within both regions, the number of granules of sizes d1 and d2, and of d2 and d3, show a negative correlation, whereas a positive correlation is observed between d1 and d3. These correlations are stronger in the active region, where the fluctuations in the number of granules are also more stable. Furthermore, analysis indicates that the decomposition rate of granules of size d3 in this region is faster and more stable, which may be related to magnetic field activity and the influence of surrounding sunspots.