Relationship between magnetic power spectrum and flare productivity in solar active regions

Power spectra of the line-of-sight magnetograms were calculated for 16 active regions of different flare activity. Data obtained by the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory in high-resolution mode were used in this study. For each active region, the daily soft X-ray flare index, A, was calculated. This index characterizes the flare productivity of an active region per day, being equal to 1 when the specific flare productivity is one C1.0 flare per day. The power index, alpha, of the magnetic power spectrum, E(k) similar to k(-alpha), averaged over all analyzed magnetograms for a given active region, was compared with the flare index. It was found that active regions, which produced X-class flares, possessed a steep power spectrum with alpha > 2.0, while flare-quiet active regions with low magnitude of A displayed a Kolmogorov-type spectrum of alpha approximate to 5/3. Observational data suggest that the flare index A may be determined from the power index alpha by A(alpha) 409.5(alpha - 5/3)(2.49). The magnitude of the power index at the stage of emergence of an active region seems not to be related to the current flaring level of this active region, but rather reflects its future flare productivity, when the magnetic configuration becomes well evolved. This finding shows the way to distinguish at the very early stage those solar active regions that are "born bad'' and have a potential to produce significant disturbances in the Earth magnetosphere.