Solar active region flux fragmentation, subphotospheric flows, and flaring

We explore the properties of the fragmentation of magnetic flux in solar active regions. We apply gradient-based tessellation to magnetograms of 59 active regions to identify flux fragments. First, we find that the distribution function of flux fragments in these regions is highly consistent with lognormal form, which is the most direct evidence yet obtained that repeated random bifurcation dominates fragmentation and coalescence in all active regions. Second, we apply nonparametric statistical methods to the variance of the lognormal distribution of fragment flux, the flare X-ray energy output of the active regions, and kinetic helicity measurements in the upper convection zone to show that there is no significant statistical relationship between the amount of fragmentation of an active region's flux at photospheric levels and the amplitude of either its average kinetic helicity density in the upper convection zone or its X-ray flare energy output.