The Topology of Background Magnetic Fields and Solar Flare Activity

We investigate the topological properties and evolution of background magnetic fields on synoptic maps from Wilcox Solar Observatory using mathematical morphology methods in terms of the Minkowski functionals. The total length of the neutral line, the total areas occupied by positive and negative polarities, and the Euler characteristics of background magnetic fields vary over an eleven-year cycle. Changes in the length of the neutral line that separates the polarities of the background magnetic field correlate well with flare activity. A time–longitude analysis of solar flare activity revealed a complicated organization and rotation of the entire flare ensemble. On the time–longitude diagram, flare activity is organized into the patterns which follow the rearrangements in background magnetic field and exhibit coexisting and alternating modes of rigid rotation. The character of rotation of the entire flare ensemble is similar to the rotation of background magnetic fields. The emergence of background magnetic fields and changes in their topology and rotation are often accompanied by enhancements in flare activity. A comparative analysis of the topological changes in background magnetic fields and flare activity reveals their causal relation.