FREE MAGNETIC ENERGY AND FLARE PRODUCTIVITY OF ACTIVE REGIONS

In this study, the photospheric vector magnetograms, obtained with the Spectro-Polarimeter of the Solar Optical Telescope on board Hinode, are used as the boundary conditions to extrapolate the three-dimensional nonlinear force-free (NLFF) coronal magnetic fields. The observed non-force-free photospheric magnetic fields are preprocessed toward the nearly force-free chromospheric magnetic fields. The performance of the preprocessing procedure is evaluated by comparing with chromospheric magnetic fields obtained by the Vector SpectroMagnetograph instrument located on the Synoptic Optical Long-term Investigations of the Sun Tower. Then, the weighted optimization method is applied to the preprocessed boundary data to extrapolate the NLFF fields with which we are able to estimate the free magnetic energy stored in the active regions. The magnitude scaling correlation between the free magnetic energy and the soft X-ray flare index (FI) of active regions is then studied. The latter quantifies the impending flare production of active regions over the subsequent 1, 2, and 3 day time windows. Based on 75 samples, we find a positive correlation between the free energy and the FI. We also study the temporal variation of free magnetic energy for three active regions, of which two are flare-active and one is flare-quiet during the observation over a period of several days. While the magnitude of free magnetic energy unambiguously differentiates between the flare-active and the flare-quiet regions, the temporal variation of free magnetic energy does not exhibit a clear and consistent pre-flare pattern. This may indicate that the trigger mechanism of flares is as important as the energy storage in active regions.