Long-Range Correlations in 2D Structures of the Magnetic Field Dissipation in the Photosphere of Solar Active Regions

Vector-magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) were utilized to explore the spatial correlation functions of the dissipative structures, such as the vertical magnetic field dissipation, Ediss, the squared density of the vertical electric current, $$J_{z}^{2}$$ , the current helicity density, Hc. Six mature active regions (ARs) were explored, three of them belong to the magneto-morphological class (MMC) A1—regular ARs that follow the empirical rules of the Babcock-Leighton dynamo theory, and the rest three ARs belong to the MMC B3 class, irregular multipolar ARs. We found that, on the contrary to the vertical magnetic field structures (see (Abramenko, Suleymanova 2024)), all considered here dissipative structures reveal a range of the power law in the correlation function. Parameters of the power law vary significantly for different types of the considered structures and for different ARs of different classes. The most pronounced difference in the power law parameters between the AR’s classes was found for both $$J_{z}^{2}$$ and Hc: the B3-class ARs demonstrate a capability for longer correlations and shallower power law slope than the A1-class ARs do. As soon as the power law correlation function is thought to indicate the self-organized criticality (SOC) state, we might conclude that in the photosphere, the SOC is rather observable in the magnetic dissipative structures, than in the magnetic field itself; a signature of SOC seems to be stronger manifested in the complex irregular B3-class ARs with high flaring activity. The proposed approach can facilitate to find a connection between the photosphere and upper layers in setting up the critical state, which is necessary for eruptions of all scales.