A Study of Magnetic Active Regions: An Information Theory Approach

The evolution of the active regions in the sun is closely associated with the underlying dynamics of the solar dynamo. In this study, we use the sequence of Carrington rotation magnetograms to study the dyanmcs of active regions over several solar cycles. This study explores the information retained throughout time in active solar regions using the information theory approach. In order to measure the system memory, the mutual information between active regions in two different Carrington magnetograms separated by a time lag is determined. To ensure that we are able to track coherent structures effectively, we employ an entropy filter to identify active regions and partition the Carrington map so that the mutual information is based on a comparison of the sets of partitions in each magnetogram. We identify two key timescales. The first is a sharp drop in information content after approximately 20 Carrington rotations, which seems to be the coherence time of the active regions. The mutual information also peaks in multiples of 140 Carrington rotations, which is approximately a solar cycle indicating a similarity in the typical structures separated by a solar cycle. Long-term memory across multiple solar cycles was explored using conditional mutual information. The results suggest that the future solar cycle not only depends on the current solar cycle, but also on the prior solar cycle. This result is consistent with a time series analysis using the Hilbert-Huang transform to identify key frequencies including a weak mode with a period of two solar cycles in addition to the strong mode at the period of the solar cycle. We are currently exploring the relationship between the meridional flow and the active regions to see if the meridional flow may play a causal role in the decoherence of the active regions.