Temporal evolution of free magnetic energy associated with four X-class flares

We study the temporal variation of free magnetic energy E_free around the time of four X-class flares. The highcadence photospheric vector magnetograms obtained by the digital vector magnegograph system at the Big Bear Solar Observatory are used as the boundary conditions to reconstruct the three-dimensional nonlinear forcefree (NLFF) coronal field. In order to remove the effect of the net Lorentz force and torque acting in the photosphere, the vector magnetograms are preprocessed using the method devised by Wiegelmann et a!.. Then a well-tested multigrid-like optimization code by Wiegelmann is applied to the preprocessed boundary data to extrapolate the NLFF coronal field with which we are able to estimate the free energy E_free. In all the four events, we find a significant drop of E_free starting ∼15 minutes before the peak time of the associated nonthermal flare emission, although long-term, trend varies from, event to event. We discuss the physical implication of the result, i.e., the magnetic relaxation is already going on in the corona well before the flare reconnection.