Relationship between Magnetic Power Spectrum and Flare Productivity in
Solar Active Regions

Valentyna Abramenko(1), Alexei Pevtsov(2), Paolo Romano(2)  and Vasyl
Yurchyshyn(1)

(1) Big Bear Solar Observatory, USA
(2) National Solar Observatory, USA
(3) Universita di Catania, Italy

Power spectra of the high resolution MDI line-of-sight magnetograms were
calculated for 16 active regions of different flare activity. 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. Tthe power
index, α, of the magnetic power spectrum, E(k)~k-α, 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 α>2.0, while flare-quiet active regions with low magnitude
of A displayed a Kolmogorov-type spectrum of α~5/3. Observational data suggest
that the flare index A may be determined from the power index α by
A(α)=409.5(α-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.

We then compared the soft X-ray luminosity of the solar corona, measured by the
Yohkoh spacecraft for 104 well developed and decaying active regions, to the
magnetic field parameters such as power index and the magnetic energy
dissipation rate, which are a proxy for the energy of random footpoint motions
induced by turbulent convection in the photosphere and below. Here we report
that the area-normalized soft X-ray flux correlates well with both the power
index and the magnetic energy dissipation rate. Our results present strong
observational support to those coronal heating models that rely on random
footpoint motions as an energy source to heat the corona above active regions.