 11158. Wang et al. (2012) observed the same phenomenon associated with the X2.2 flare in this active region. These results suggested that the magnetic field near the polarity inversion line could become more horizontal after a flare.
In this study, we analyze the evolution of sunspots in NOAA AR 11429. We will explore the rotation of sunspots along with the flares, i.e., how do the flares and the rotation of sunspots affect each other. The magnetic transients induced by flares are studied in prior works. We further study the motion of the magnetic transients to understand how the flares influence sunspots. The paper is organized as follows. In Section 2 we describe the data used and the entire structure of the active region. Section 3 shows data processing. We summarize and discuss the results in Section 4.

OBSERVATIONAL DATA
The 45 s cadence and spatial sampling of 0 ′′.5 pixel −1 full-disk continuum intensity images and lineof-sight magnetograms observed by the Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) on board the Solar Dynamics Observatory ( SDO) are used to analyze the variation of sunspots in NOAA AR 11429. The images from the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board SDO are used to investigate the chromospheric and coronal context: AIA 304Å formed in transition region and chromosphere, and AIA 1600Å formed in upper photosphere and transition region.
AR 11429 appeared on the eastern limb on 3 March 2012, and then rapidly became complicated reverse-polarity βγδ active region. The evolution and development of AR 11429 from 5 March to 12 March are displayed in Figure 1. It is interesting to note that the sunspots in this active region were moving away from each other, i.e., the leading sunspots moving westward and the following sunspots moving eastward. Several major eruptions were clearly visible in this active region. Typically, three Xclass flares occurred: one (X1.1) on 5 March and two of interest (X5.4 and X1.3) on 7 March. The GOES soft X-ray flux ( Figure 3a) indicates that the X5.4 flare started at 00:02 UT, peaked at 00:27 UT, and ended at 00:40 UT, and the X1.3 flare started at 01:05 UT, peaked at 01:14 UT, and ended at 01:23 UT. The evolution of five prominent sunspots, two positive polarity sunspots (P1 and P2) and three negative polarity sunspots (N1, N2 and N3), were associated with these two flares, as be discussed in the next section.

Sunspots rotating associated with flares
To study the rotation, we take the rotation of individual sunspots as a simplified solid-body rotation (i.e., a sunspot rotates around its umbral center), and track the variation of the ellipses that best fit individual sunspots on time-series intensity images (see Bi et al. 2016). Take sunspot P1 as an example. The best-fit ellipses on the intensity images at 23:29:23 UT of 6 March and 01:28:38 UT of 7 March are shown in Figure 2(a) and Figure 2(b), respectively. Obviously, the major axis rotates counterclockwise about 7 •. In the present study, the changes of the angle between the major axis and the horizontal direction of the best-fit ellipses are used to describe the rotation of the sunspot. The results together with the GOES soft X-ray flux are shown in Figure 3. Figure 3(b) shows that P1 rotated mainly counterclockwise from ∼23:30 UT of 6 March to ∼01:30 UT of 7 March. Before the start of the X5.4 flare, the rotation was very fast with speed up to 7.92 • hr −1. From start to peak of the flare, the rotation speed decreased slowly to about 4.89 • hr −1 and the rotation trend kept counterclockwise. Just after the peak of the flare, the rotation trend reversed from counterclockwise to clockwise. Its speed was about 4.07 • hr −1. After the flare, the rotation direction returned to counterclockwise with the rotation speed of about 6.56 • hr −1, and the rotation speed increased gradually until the beginning of the X1.3 flare. Later, the rotation trend reversed to clockwise again with the rotation speed of about 6.44 • hr −1 and slowed down. These results indicate that the rotation of sunspot P1 was significantly affected by both flares. The relative mean intensity profiles in different AIA wavelengths, obtained from the co-aligned with HMI images, are also plotted in Figure 3. The intensity in the AIA wavelengths of 304Å (green curve) and AIA 1600Å (blue curve) started rising around 00:05 UT, peaked at about 00:07 UT, and then decreased during the impulsive phase of the X5.4 flare. At about 01:05 UT, the intensities started rising again and peaked at about 01:14 UT. It provides further support for the view that solar flares are often related to the rotation of sunspots.
The rotation of the sunspot N1 was complicated (Figure 3c). Before the peak of the X5.4 flare, the rotation trend was mainly counterclockwise, and then reversed to clockwise. The situation around the X1.3 flare was similar to that around the former flare. The intensity of AIA wavelengths increased and the rotation changed significantly during the impulsive phases of the X5.4 and X1.3 flares. As shown in Figure 3(d), sunspot N2 rotated clockwise from ∼00:15 UT to ∼00:40 UT. The relative mean intensity of 1600Å in this sunspot started rising at ∼00:05 UT and reached its maximum at ∼00:20 UT. The relative mean intensity of 304Å started rising at ∼00:05 UT and reached its maximum at ∼00:30 UT. So the X5.4 flare affected the rotation of sunspot N2. The sunspot N3 remained stable during the two flares ( Figure 3e). The rotation speed was poorly correlated with the intensity of AIA wavelengths, and therefore the X5.4 and X1.3 flares.

The motion of Magnetic Transient
Magnetic transients induced by flares have been well investigated by Patterson (1984) and Qiu & Gary (2003). They analyzed the cause, location and level of the magnetic transients. Here, we find that there are some magnetic transients moving through sunspots N1, N2 and N3, and there is no apparent magnetic transient motion in the sunspots P1 and P2. Because the polarity of the sunspots N1, N2 and N3 is negative (black regions in the magnetograms), the magnetic transients means that the polarity is reversed. Figure 4 shows the changes of the magnetic field in sunspot N1. At 01:09 UT of 7 March, the magnetic transients marked by red arrows in the umbra of the sunspot can be clearly seen. These magnetic transients (the positive magnetic field) moved toward the southeast direction. At 01:14 UT, the area with positive magnetic field became larger while the strength became weaker, as shown in Figure 4(a2). The green line in Figure 4(a3) indicates the moving trajectory of the positive polarity points. To investigate the kinematic evolution of the reversed polarity, the time-distance plots obtained along the green trajectory line are shown in Figure 4(d). A white streak is clearly visible. It started at ∼01:07 UT and ended at ∼01:16 UT, consistent with the time of the X1.3 flare. It might imply that the reversed magnetic polarity was caused by this flare. The distance corresponding to the streak was about 5 arcsec. Thus, the moving speed of the magnetic transients can be estimated to be about 6.59 km s −1. Similarly, some magnetic transients (i.e., the reversed magnetic field) were presented in sunspots N2 and N3, and probably associated with the X5.4 flare, as shown in Figures 5 and 6. They were moving toward southeast with speed about 3.69 km s −1 and 3.22 km s −1 respectively.
In order to check whether the magnetic transients were co-spatial with flare ribbons, we further examined the co-aligned AIA 304Å and AIA 1600Å images corresponding to HMI magnetograms, which are displayed in panels (b1)-(b3) and panels (c1)-c(3) in Figures 4, 5 and 6 respectively. The flare ribbons can be seen in these panels. They were separating from each other. The locations of sunspots N1, N2 and N3 in AIA images, marked by magnetogram contours at -800 G, were moving with flare ribbons. This implies the magnetic transients were co-spatial with flare ribbons.
We calculated magnetic flux of sunspots N1, N2 and N3 for the regions marked by the red rectangular boxes in Figure 1. The magnetic flux of sunspots with negative polarity together with GOES soft X-ray flux are shown in Figure 7. Before the start of the X5.4 flare, the absolute value of magnetic flux in sunspot N1 decreased slowly. From the start to peak of the flare, it decreased gradually. Then, the value kept almost unchanged. At the end of the flare, it increased slightly. During the period of the X1.3 flare, the absolute value of magnetic flux decreased first and then increased abruptly. These results suggest