Evolution of Magnetic Field and Energy in a Major Eruptive Active Region Based on SDO/HMI Observation

We report the evolution of the magnetic field and its energy in NOAA active region 11158 over five days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated nonlinear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with a sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6 × 10³² erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3 × 10³² erg within 1 hr of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: the horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion" and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic.