Information Horizon of Solar Active Regions

Information theory is used to characterize the solar active region periodicities and memories from the Carrington map images 1974-2021. The active regions typically evolve and move from one map to the next. In order to track these active region structures in sequences of images, an innovative method based on information theory is developed. Image entropy provides a measure of the organization of structures in the images. The entropy can also be used as a filter to identify structures and partition the active regions, which are then registered for each image. The partitions are used to compute the mutual information and measure the information flow from the active regions from one image to the next. Finally, conditional mutual information is used to give a measure of the information flow from one image to another given the third image. The results suggest the following: (1) there is a long-term memory of two cycles or more; (2) the coherence time of the active regions is similar to 2 yr; and (3) the average active region structure scale size carrying the most information is approximately 118 x 10(3)-236 x 10(3) Mm(2). The study has implications to the short- and long-term predictability of active regions and sunspots as well as the nature of flux transport at the Sun. Finally, our innovative method can be similarly applied to stellar data to determine the dynamics of the active regions of stars.