Magnetic Energy Spectra in Active Regions

TL;DR

This study analyzes magnetic energy spectra in 217 solar active regions to understand turbulence and its link to flare activity, revealing correlations between spectral properties and flare productivity.

Contribution

It introduces a method to relate magnetic energy spectral parameters to flare productivity, showing stronger correlations than total unsigned flux.

Findings

Steeper energy spectra in highly flare-productive active regions.

Correlation between spectral index, total spectral energy, and flare index.

Turbulence regime varies with active region development stage.

Abstract

Line-of-sight magnetograms for 217 active regions (ARs) of different flare rate observed at the solar disk center from January 1997 until December 2006 are utilized to study the turbulence regime and its relationship to the flare productivity. Data from {\it 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 of higher flare productivity. We also report that both the power index, $\alpha$, of the energy spectrum, $E(k) \sim k^{-\alpha}$, and the total spectral energy $W=\int E(k)dk$ are comparably correlated with the flare index, $A$, of an active region. The correlations are found to be stronger than that found between the flare index and total unsigned flux. The flare index for an AR can be estimated based on measurements of $\alpha$ and $W$ as $A=10^b (\alpha W)^c$, with $b=-7.92 \pm 0.58$ and $c=1.85 \pm 0.13$. We found that the regime of the fully-developed turbulence occurs in decaying ARs and in emerging ARs (at the very early stage of emergence). Well-developed ARs display under-developed turbulence with strong magnetic dissipation at all scales.