DOUBLE POWER-LAW DISTRIBUTION OF MAGNETIC ENERGY IN THE SOLAR CORONA OVER AN ACTIVE REGION

In this paper, we study the magnetic energy (ME) structure contained in the solar corona over the active region NOAA 11158. The time period is chosen as from 0:00 to 06:00 UT on 2011 February 15, during which an X-class flare occurred. The nonlinear force-free field (NLFFF) and the potential field extrapolation are carried out to model the coronal magnetic field over this active region, using high-quality photospheric vector magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory as boundary conditions. We find that the volume distribution for the density of the ME (B 2/8π) and the ohmic dissipation power (ODP, j 2/σ), in which j is the electric current density (c/4π∇ × B) and σ is the conductivity in the corona, can be readily fitted by a broken-down double-power law. The turn-over density for the spectrum of the ME and ODP is found to be fixed at ∼1.0 × 104 erg cm–3 and ∼2.0 × 10–15 W cm–3 (assuming σ = 105 Ω–1 m–1), respectively. Compared with their first power-law spectra (fitted below the corresponding turn-over value) which remain unchanged, the second power-law spectra (fitted above the corresponding turn-over value) for the NLFFF's ME and ODP show flare-associated changes. The potential field remains steady. These results indicate that a magnetic field with energy density larger than the turn-over energy density plays a dominant role in powering the flare.