Scaling behavior of structure functions of the longitudinal magnetic field in active regions on the sun

In the framework of a refined Kolmogorov hypothesis, the scaling behavior of the B_z-component of the photospheric magnetic field is analyzed and compared with flaring activity in solar active regions. We use Solar and Heliospheric Observatory Michelson Doppler Imager, Huairou (China), and Big Bear measurements of the B_z-component in the photosphere for nine active regions. We show that there is no universal behavior in the scaling of the B_z-structure functions for different active regions. Our previous study has shown that scaling for a given active region is caused by intermittency in the field, ε^(B)(x), describing the magnetic energy dissipation. When intermittency is weak, the B_z field behaves as a passive scalar in the turbulent flow, and the energy dissipation is largely determined by the dissipation of kinetic energy in the active regions with low flare productivity. However, when the field ε^(B)(x) is highly intermittent, the structure functions behave as transverse structure functions of a fully developed turbulent vector field, and the scaling of the energy dissipation is mostly determined by the dissipation of the magnetic energy (active regions with strong flaring productivity). Based on this recent result, we find that the dissipation spectrum of the B_z-component is strongly related to the level of flare productivity in a solar active region. When the flare productivity is high, the corresponding spectrum is less steep. We also find that during the evolution of NOAA Active Region 9393, the B _z dissipation spectrum becomes less steep as the active region's flare activity increases. Our results suggest that the reorganization of the magnetic field at small scales is also relevant to flaring: the relative fraction of small-scale fluctuations of magnetic energy dissipation increases as an active region becomes prone to producing strong flares. Since these small-scale changes seem to begin long before the start of a solar flare, we suggest that the relation between scaling exponents, calculated by using only measurements of the B_z-component, and flare productivity of an active region can be used to monitor and forecast flare activity.