Correlation Functions of Photospheric Magnetic Fields in Solar Active Regions

We used magnetograms acquired with the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to calculate and analyze spatial correlation functions and the multifractal spectra in solar active regions (ARs). The analysis was performed for two very different types of ARs: i) simple bipolar magnetic structures with regular orientation (the magnetomorphological class A1), and ii) very complex multipolar ARs (the magnetomorphological class B3). All ARs were explored at the developed phase during flareless periods. For correlation functions, the power-law and exponential approximations were calculated and compared. It was found that the exponential law holds for the correlation functions of both types of ARs within spatial scales of 1 - 36 Mm, while the power law failed to approximate the observed correlation functions. The property of multifractality was found in all ARs, being more pronounced for the complex B3-class ARs. Our results might imply that the photospheric magnetic field of an AR is a self-organized system, which, however, does not exhibit properties of self-organized criticality (SOC), and its fractal properties are an attribute of a broader (than SOC only) class of nonlinear systems.