Magnetic energy spectra in solar active regions

Line-of-sight magnetograms for 217 active regions (ARs) with different flare rates observed at the solar disk center from 1997 January until 2006 December are utilized to study the turbulence regime and its relationship to flare productivity. Data from the SOHO/MDI instrument recorded in the high-resolution mode and data from the BBSO magnetograph were used. The turbulence regime was probed via magnetic energy spectra and magnetic dissipation spectra. We found steeper energy spectra for ARs with higher flare productivity. We also report that both the power index, α, of the energy spectrum, E(k) ∼ k^-α, and the total spectral energy, W = ∫E(k)dk, are comparably correlated with the flare index, A, of an AR. The correlations are found to be stronger than those found between the flare index and the total unsigned flux. The flare index for an AR can be estimated based on measurements of α and Was A = 10^b(αW)^c, with b = - 7.92 ±0.58 and c = 1.85 ±0.13. We found that the regimeof the fully developed turbulence occurs in decaying ARs and in emerging ARs (at the very early stage of emergence). Well-developed ARs display underdeveloped turbulence with strong magnetic dissipation at all scales.