A Statistical Study of the Magnetic Imprints of X-class Solar Flares

Magnetic imprints, the rapid and irreversible evolution of photospheric magnetic fields as a feedback from flares in the corona, have been confirmed by many previous studies. These studies showed that the horizontal field will permanently increase at the polarity inversion line (PIL) after eruptions, indicating that a more horizontal geometry of photospheric magnetic field is produced. In this study, we analyze 20 X-class flares since the launch of the Solar Dynamics Observatory (SDO) in 15 active regions (ARs) with heliographic angle no greater than 45 degrees. We observe clear magnetic imprints in 16 flares, whereas 4 flares are exceptional. The imprint regions of the horizontal field are located not only at the PIL but also at sunspot penumbra with strong vertical fields. Making use of the observed mass and speed of the corresponding coronal mass ejections (CMEs) , we find that the CMEs with larger momenta are associated with stronger magnetic imprints. Furthermore, a linear relationship, with a Kendall's Tau-b coefficient 0.54, between the CME momentum and the change of Lorentz force is revealed. Based on that, we quantify the back reaction time to be around 70 s, with a 90% confidence interval from about 50 s to 90 s.