Relationship between Magnetic Field Properties and an X-class Flare in Active Region NOAA 9077

Abstract: The magnetic field plays a key role in producing solar flares, so that the investigation on the relationship between the magnetic field properties and flares is significant. In this paper, based on the magnetic field extrapolated from the photospheric vector magnetograms of the active region NOAA 9077 obtained at Huairou Solar Observing Station, the magnetic field parameters including the height of field lines, force-free factor, free magnetic energy and inclination angle were studied with respect to an X-class flare in this region. We found that the magnetic field lines became lower and the ratio of number of closed field lines to those of open field lines increased after the flare. The force-free factor ($\alpha$) attained a large value before the flare and then decreased after the flare for the closed field lines, while the open field lines showed the opposite tendency. Free energy reach to maximum before flare, then decrease after flare. The magnetic inclination angles showed opposite change trends after the flare for closed and open field lines. Therefore, we may conclude that non-potential energy released by flare mostly contained in the closed magnetic field lines.