Flares and magnetic non-potentiality of NOAA AR 11158

Magnetic non-potentiality is important for understanding flares and other solar activities in active regions （ARs）. Five non-potential parameters, i.e. electric current, current helicity, source field, photospheric free energy, and angular shear, are calculated to quantify the non-potentiality of NOAA AR 11158. Benefitting from the high spatial resolution, high cadence and continuous temporal coverage of vector mag- netograms from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, both the long-term evolution of the AR and the rapid change during flares are studied. We confirm that, compared with the magnetic flux, the magnetic non-potentiality has a closer connection with the flare, and the emerging flux regions are important for understanding the magnetic non-potentiality and flares. The main re- suits are as follows. （1） The vortex in the source field directly displays the deflection of the horizontal magnetic field. The deflection corresponds to the fast rotating sunspot with a time delay, which suggests that the sunspot rotation leads to an increase in the non-potentiality. （2） Two areas that have evident changes in the azimuth of the vector magnetic field are found near the magnetic polarity inversion line. The change rates of the azimuth are about 1.3° h-1 and 3.6° h-1, respectively. （3） Rapid and prominent increases are found in the variation of helicity during four flares in the regions where their initial brightening occurs. The recovery of the increases takes 3-4 h for the two biggest flares （X2.2 and M6.6）, but only takes about 2 h for the two other smaller flares （M2.2 and M1.6）.