The statistical relationship between the photospheric magnetic parameters and the flare productivity of active regions

Using line-of-sight Michelson Doppler Imager (MDI) magnetograms of 89 active regions and Solar Geophysical Data (SGD) flare reports, we explored, for the first time, the magnitude scaling correlations between three parameters of magnetic fields and the flare productivity of solar active regions. These parameters are (1) the mean value of spatial magnetic gradients at strong-gradient magnetic neutral lines, (∇̄B_z) _NL; (2) the length of strong-gradient magnetic neutral lines, L _GNL; and (3) the total magnetic energy, J ∈(B_z) dA, dissipated in a layer of 1 m during 1 s over the active region's area. The MDI magnetograms of active regions used for our analysis are close to the solar central meridian (within ± 10°). The flare productivity of active regions was quantified by the soft X-ray flare index for different time windows from the time interval of the entire disk passage down to +1 day from the time of the analyzed magnetogram. Our results explicitly indicate positive correlations between the parameters and the overall flare productivity of active regions, and imminent flare production as well. The correlations confirm the dependence of flare productivity on the degree of nonpotentiality of active regions.