  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.
