ABSTRACT
We find that a sunspot with positive polarity had an obvious counterclockwise rotation and resulted in the formation and eruption of an inverse S-shaped filament in NOAA Active Region 08858 from 2000 February 9 to 10. The sunspot had two umbrae which rotated around each other by 195° within about 24 hr. The average rotation rate was nearly 8° hr−1. The fastest rotation in the photosphere took place during 14:00 UT to 22:01 UT on February 9, with a rotation rate of nearly 16° hr−1. The fastest rotation in the chromosphere and the corona took place during 15:28 UT to 19:00 UT on February 9, with a rotation rate of nearly 20° hr−1. Interestingly, the rapid increase of the positive magnetic flux occurred only during the fastest rotation of the rotating sunspot, the bright loop-shaped structure, and the filament. During the sunspot rotation, the inverse S-shaped filament gradually formed in the EUV filament channel. The filament experienced two eruptions. In the first eruption, the filament rose quickly and then the filament loops carrying the cool and the hot material were seen to spiral counterclockwise into the sunspot. About 10 minutes later, the filament became active and finally erupted. The filament eruption was accompanied with a C-class flare and a halo coronal mass ejection. These results provide evidence that sunspot rotation plays an important role in the formation and eruption of the sigmoidal active-region filament.
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1. INTRODUCTION
Sunspot rotational motions have been observed by many authors for many decades (Evershed 1910; Maltby 1964; Gopasyuk 1965). Stenflo (1969) and Barnes & Sturrock (1972) suggested that the rotational motion of a sunspot may be involved with energy buildup and the buildup energy is later released by a flare.
With the high spatial and temporal resolution of recent satellite-borne telescopes, observations of rotating sunspots are easily obtained (Nightingale et al. 2002). Using white-light images from TRACE, Brown et al. (2003) analyzed the rotation speed of the umbrae and penumbrae of several rotating sunspots. They found that the average rotation speed of the penumbrae of the rotating sunspots was larger than that of the umbrae of the rotating sunspots. Through the method of time–distance helioseismology, Zhao & Kosovichev (2003) found evidence of structural twist beneath the visible surface of a rotating sunspot. Rotating sunspots related to other magnetic structures were also identified by many authors. Régnier & Canfield (2006) found that the slow rotation of the sunspot in NOAA Active Region (AR) 8210 enabled the storage of magnetic energy and allowed for the release of magnetic energy as C-class flares. Tian & Alexander (2006) found that the sunspot and the sunspot group exhibited a counterclockwise rotation. The twist of the active-region magnetic fields was dominantly left-handed. The vertical current and the current helicity were predominantly negative. Later, Yan & Qu (2007) reported that sunspot rotation resulted in the appearance of the Ω magnetic loop in the corona and finally the Ω magnetic loop erupted as an M-class flare. Zhang et al. (2007) reported that a flare was caused by the interaction between a fast rotating sunspot and ephemeral regions. In addition, Schrijver et al. (2008) used nonlinear force-free modeling to show the evolution of the coronal field associated with a rotating sunspot and suggested that the flare energy comes from an emerging twisted flux rope. Detailed information about the polarities, rotation directions, and helicities of rotating sunspots in cycle 23 was presented by Yan et al. (2008b). The active regions with rotating sunspots were classified into six types by Yan et al. (2008a). They also found that several types have higher flare productivity. Using multi-wavelength observations of Hinode, Yan et al. (2009) and Min & Chae (2009) studied the rapid rotation of a sunspot in NOAA AR 10930 in detail. They found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. Moreover, the sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. From a series of vector magnetograms, Yan et al. (2009) found that magnetic force lines are highly sheared along the neutral line accompanying the sunspot rotation. By analyzing the buildup of the energy and the helicity associated with the eruptive flare on 2005 May 13, Kazachenko et al. (2009) found that sunspot rotation alone can store sufficient energy to power a very large flare. Sunspot rotation may be the primary driver of helicity production and injection into the corona (Zhang et al. 2006, 2008; Kumar et al. 2010; Park et al. 2010; Ravindra et al. 2011).
Sigmoid structures were often observed to be precursors to coronal mass ejections (CMEs; Sterling & Hudson 1997; Sterling et al. 2000; Pevtsov 2002; Liu et al. 2007; Jiang et al. 2007; Green & Kliem 2009; Bi et al. 2011) and were statistically more likely to erupt (Hudson et al. 1998; Canfield et al. 1999, 2007). Eruptions of sigmoid structures or filaments are usually involved with flares and CMEs (Jing et al. 2004; Wang et al. 2007; Yan et al. 2011). Amari et al. (2000) reported that the shearing motion resulted in the formation of an S-shaped flux rope by MHD simulation. The emergence of the flux tube can also exhibit a sigmoid structure (Magara & Longcope 2001; Fan 2001; Gibson et al. 2004). A double-J loop pattern can be merged into full S-shaped loops by a slip-running tether-cutting reconnection in the coronal hyperbolic flux tube (Moore et al. 2001; Aulanier et al. 2010). Tripathi et al. (2009) found the coexistence of a pair of J-shaped hot arcs at temperature T > 2 MK with an S-shaped structure at somewhat lower temperature (T ≈ 1–1.3 MK). Some observational findings provide strong evidence to support the bald-patch separatrix surface model (Titov & Démoulin 1999) for the sigmoid (McKenzie & Canfield 2008). Other observations and simulations supposed that the X-ray sigmoid appears at the quasi-separatrix layer between the flux rope and external fields (Gibson et al. 2002; Low & Berger 2003; Kliem et al. 2004; Savcheva & van Ballegooijen 2009). Liu et al. (2002) reported that the sigmoid structure was formed by the reconnection of the emerging flux and the pre-existing field. Green et al. (2011) showed that the flux cancellation at the internal polarity inversion line resulted in the formation of a soft-X-ray sigmoid along the inversion line and a CME. By using a reconstructed three-dimensional coronal magnetic field, Régnier & Amari (2004) found that the sigmoid was higher than the filament in the corona, while the filament and the sigmoid had the same orientation. Consequently, the formation of the sigmoid structure remains an interesting open question.
In this paper, we present a clear case for S-shaped active-region filament formation and eruption caused by the sunspot rotation in NOAA AR 08858 on 2000 February 10.
2. OBSERVATIONS
The NOAA AR 08858 was observed by several spacecrafts from 2000 February 9 to 10. The active region was located at N28E01 with β field configuration of the sunspot group on 2000 February 9. This active region was a very productive active region. It produced 13 C-class, 3 M-class, and 1 X-class flares during its journey over the whole solar disk.
The observation of Transition Region and Coronal Explorer (TRACE) covered the whole process of this event from white light to EUV wavelength. The data of TRACE white light, 1600 Å, and Fe ix/x 171 Å images have a cadence of about 30 s to 1 minute and a pixel size of 0
5 (Handy et al. 1999). Full-disk line-of-sight magnetograms are used to show the magnetic fields in the photosphere. The magnetograms were taken by the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO; Scherrer et al. 1995) with a 96 minute cadence and a spatial resolution of 2'' pixel−1. In addition, we also use the data of soft-X-ray flux observed by Geostationary Operational Environmental Satellite (GOES) to identify flare occurrence. The data from Large Angle and Spectrometric Coronagraph (LASCO; Brueckner et al. 1995) C2 on board SOHO (Domingo et al. 1995) are used to identify the CME.
3. SUNSPOT ROTATION AND THE MAGNETIC FIELD EVOLUTION
3.1. Sunspot Rotation
Figure 1 shows the whole NOAA AR 08858 observed by TRACE white light (left panel) and the SOHO/MDI magnetogram (right panel). The rotating sunspot is marked by the red box and the black arrows in Figure 1. The areas of the red and yellow boxes are used to calculate the positive and negative magnetic flux, respectively. The rotating sunspot with positive polarity had two umbrae labeled by Umbra 1 and Umbra 2. This active region contains 12 sunspots. The rotating sunspot was the largest one and was located in the southeast of the active region.
Figure 1. NOAA AR 08858 observed by TRACE acquired at white light (left panel) and SOHO/MDI magnetogram (right panel). The rotating sunspot is marked by the red boxes and the black arrows. The rotating sunspot with positive polarity has two umbrae labeled Umbra 1 and Umbra 2. The areas of the red and yellow boxes are used to calculate the positive and negative magnetic flux, respectively.
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Standard image High-resolution imageFigure 2 shows the evolution of the rotating sunspot acquired at white light, 1600 Å, and 171 Å by TRACE. The left column of Figure 2 shows the white-light images observed by TRACE. We mark the two umbrae as "U1" and "U2." From 00:00:22 UT to 02:40:36 UT on February 9, the rotating sunspot was almost quiet. Later, the two umbrae began to rotate counterclockwise. The detailed motion in the photosphere can be seen from the change of the positions of "U1" and "U2." Following the sunspot rotation, the loop-shaped structure first appeared in the chromosphere and then formed an arch-shaped structure. In the corona, the filament was gradually formed in the filament channel. The filament connecting the rotating sunspot was also found to rotate counterclockwise around the center of the rotating sunspot.
Figure 2. Evolution of the rotating sunspot acquired at white light, 1600 Å, and 171 Å observed by TRACE. "U1" and "U2" denote the two umbrae of the rotating sunspot. The arrows in the middle column and right columns indicate the bright loop-shaped structure in the chromosphere and the active-region filament in the corona. The white dotted lines indicate the filament channel. The red dotted lines indicate the filament.(An animation and a color version of this figure are available in the online journal.)
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Standard image High-resolution imageFigure 3 shows the three images acquired at white light, 1600 Å, and 171 Å on February 9. The circles in the images contain two umbrae of the rotating sunspot and are used to calculate the rotational angle. The white brackets denote the rotational angles. The arrows denote the features which are used to calculate the rotational angle. We calculated the rotational angle of umbra "U2" around the center of the circle. The front of umbra "U2" (see the arrow in the left panel of Figure 3) that moved along the circle is used to evaluate the rotational angle (see the left panel of Figure 3). From a series of the TRACE images, we can get the coordinates of the center of the circle and the points. We adopt the average values of three repeated measurements of the angles. The measurement uncertainty is about 1°. Moreover, the rotational angles of both the bright loop-shaped structure marked by the arrows in the TRACE 1600 Å images and the filament marked by the arrows in the TRACE 171 Å images were also calculated. The emitting structure is identified as a filament whereas the absorptive dark structure is identified as a filament channel in the right panel of Figure 2. We use part of the bright loop-shaped structure (see the arrow in the middle panel of Figure 3) and the filament that connected the umbrae of the rotating sunspot (see the arrow in the right panel of Figure 3) to calculate the rotational angle. We trace the evolution of the features from a series of TRACE 1600 Å and 171 Å images to determine the positions of the features. Note that the angle is defined as the angle between the line connecting the point where the bright loop-shaped structure is situated on the circle with the center of the circle and the radius of the circle at 0°. Because the bright features have a certain width, we adopt the center point of the bright features to do the measurement, which is located on the circle. The radius of the circle is 5 arcsec. The coordinates can be seen from Figure 3. It is worth pointing out that the bright loop-shaped structure in the chromosphere and the filament are three-dimensional and the projection effect has to be taken into account when measuring apparent motion of a feature in general. It is hard to reconstruct the real shape of the loops from the single spacecraft observations. Our observations are based on the evolution of the magnetic loop topology from two-dimensional data.
Figure 3. Three images acquired at white light, 1600 Å, and 171 Å (from left to right) on 2000 February 9. The circles in the images contain the umbrae of the rotating sunspot and are used to calculate the rotational angles. The bright brackets denote the rotational angles. The arrows denote the features which are used to calculate the rotational angle.
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Standard image High-resolution imageFigure 4 shows the rotational angle of umbra "U2" (red line), the bright loop-shaped structure in the TRACE 1600 Å images (blue line), the filament in the 171 Å images (green line), and the evolution of the magnetic flux (negative: dashed line; positive: dotted line). The umbra "U2" rotated by 195°. The average rotation rate was about 8° hr−1 for 24 hr. The fastest rotation in the photosphere took place during 14:00 UT to 22:01 UT on February 9, with a rotation rate of nearly 16° hr−1. The bright loop-shaped structure in the chromosphere and the filament in the corona rotated by 142° and 116°, respectively. From 15:28 UT to 19:00 UT, the bright loop-shaped structure in the chromosphere and the filament in the corona rotated by 65° and 85°, respectively, with rotation rates of nearly 19° hr−1 and 24° hr−1, respectively. The diamonds (green line), asterisks (blue line), and pluses (red line) respectively denote the rotational angles of the filament in the corona, the bright loop-shaped structure in the chromosphere, and umbra "U2" in the photosphere. The rotational angle decreased from the photosphere to the corona. This is evidence that the sunspot rotation transfers the magnetic twist from the sub-surface to the corona.
Figure 4. Rotational angles measured from umbra "U2," the bright loop-shaped structure in the TRACE 1600 Å image, and the filament in the 171 Å image. The red, blue, and green lines indicate the rotational angle of umbra "U2," the bright loop-shaped structure in the TRACE 1600 Å image, and the filament in the TRACE 171 Å image, respectively. We adopt the average values of the three repeated measurements of the angles. The evolution of the negative (dashed line) and the positive (dotted line) magnetic flux calculated from the two regions marked by the yellow and red boxes in Figure 1 (right panel) is also shown.
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Standard image High-resolution image3.2. The Magnetic Field Evolution
The dashed line and the dotted line in Figure 4 show the evolution of magnetic flux (right axis) calculated from the regions marked by the yellow (negative magnetic flux) box and the red (positive magnetic flux) boxes in Figure 1 (right panel). From the evolution of the magnetic flux, there was a slow decrease in the negative magnetic flux from 11:15 UT to 20:47 UT on February 9 and then the negative magnetic flux increased a little. For the positive magnetic flux, there was a slow increase from 23:59 UT on February 8 to 14:27 UT on February 9 and then the positive magnetic flux increased rapidly from 16:03 UT to 19:11 UT on February 9. Interestingly, the rapid increase of the positive magnetic flux occurred only during the fastest rotation of the rotating sunspot, the bright loop-shaped structure, and the filament. At the beginning of the sunspot rotation, the magnetic flux was very stable. In addition, there was no eruption within about 5 hr from the GOES observation before the sunspot rotation. The disturbance from eruptions in this active region can also be excluded.
4. THE FORMATION AND ERUPTION PROCESS OF THE FILAMENT
4.1. The Formation Process of the Filament
From 02:49:36 UT on 2000 February 9 to 02:49:45 UT on 2000 February 10, the two umbrae rotated counterclockwise by 195°. The middle column of Figure 2 shows the 1600 Å images observed by TRACE. There was a small bright loop-shaped structure marked by the white arrows at 02:40:32 UT in the TRACE 1600 Å images. The loop-shaped structure was followed by the sunspot rotation and rotated counterclockwise around the center of the rotating sunspot. From 16:19:54 UT to 20:35:48 UT on February 9, the loop-shaped structure formed an arch shape. Finally, it disappeared after the flare. The right column of Figure 2 shows the 171 Å images observed by TRACE. The dotted lines in the first two images of the right column denote the EUV filament channel. The red dotted lines indicate the filament. Until 12:17:46 UT on February 9, a curved loop-shaped filament marked by the white arrows and outlined by the red dotted line appeared. The filament also rotated counterclockwise around the center of the sunspot. The filament was formed as a dark structure initially, and then part of it was brightened. This brightened part connecting the rotating sunspot was identified and measured. The change of the filament can be seen from the positions marked by the white arrows in the right column. Following the sunspot rotation, the part of the filament that connected the umbra of the rotating sunspot met the left part of the filament channel (see the position marked by the black arrow in the right panel of Figure 2), then the rotational motion stopped, and the filament finally erupted. The field of view of the left and the middle column images is 50'' × 50''. In order to show the formation process of the active-region filament, the field of view of the right column images is adjusted to 150'' × 150''. The detailed formation process of the filament can be seen from the movie (filamentformation.mpg) linked to Figure 2 in the online journal.
4.2. The First Failed Eruption of the Filament
Figure 5 shows a sequence of 171 Å images during the first failed filament eruption on 2000 February 10. The dashed line in Figure 5(a) indicates the filament channel and the white line in Figure 5(a) denotes the position of the time slice of Figure 6. From a sequence of TRACE 171 Å images, one can see that the filament gradually rose from the EUV filament channel after the sunspot underwent tens of hours of rotation motion. The filament is marked by the dotted lines in Figures 5(b) and (c). Moreover, the filament exhibited a swirling shape. The white arrows in Figures 5(b) and (c) point to the hot material of the filament. Before the filament eruption, the filament loops carrying the hot material can be seen to be moving counterclockwise. After about 90 s, the hot plasma moved to the position shown by the white arrow in Figure 5(c). At 01:14:38 UT, the filament rose rapidly and formed a fan-shaped structure. The two dotted lines outline the outer and the inner boundary of the filament in Figure 5(d). Note that the filament is composed of many bright loops. The white arrow and the black arrow in Figures 5(d) and (e) denote the lower and the upper parts of the filament. During the rise of the filament, we observe apparent counterclockwise motion of hot and cool material along the filament loops. The black arrows in Figures 5(f)–(i) denote the change of the position of the cool material. The white arrows denote the hot material which gradually fell into the umbrae of the sunspot. It is worth pointing out that the movement of the cool and hot material is not the true movement of the material. In fact, the movement of the filament loops carried the cool and hot material. At 01:26:48 UT on 2000 February 10, the loops of the whole filament were contracted and later were seen to spiral into the sunspot umbrae. The dotted lines in Figures 5(e)–(l) outline the outer boundary of the filament. From 01:14:38 UT to 01:26:48 UT on February 10, the filament loops gradually contracted (see the dotted lines in Figure 5). The detailed process of the first filament eruption can be seen from the movie (firsteruption.mpg) linked to Figure 5 in the online journal.
Figure 5. Sequence of 171 Å images showing the process of the first failed filament eruption. The dashed line in panel (a) indicates the filament channel. The white line denotes the position of the time slice of Figure 6. The dotted lines outline the filament in panels (b) and (c). The other dotted lines and the arrows are described in the text.(An animation of this figure is available in the online journal.)
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Figure 6. Time slice at the position marked by the white line in Figure 5(a). The two dotted lines denote the lower and the upper boundary of the filament.
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Standard image High-resolution imageFigure 6 shows the time slice at the position marked by the white line in Figure 5(a). The bright structure shows the trajectory of the filament. The two dotted lines denote the lower and the upper boundary of the filament. From the evolution of the filament intensity, one can see that the filament first expanded outward and then fell down.
4.3. The Second Successful Eruption of the Filament
After the first failed eruption, the filament gradually became active. At 01:36:16 UT on February 10, a small part of the filament began to erupt. From the observation of TRACE 1600 Å (see Figure 9), the two flare ribbons began to form at 01:40 UT as a signature of magnetic reconnection upon the filament eruption. Figure 7 shows a sequence of 171 Å images from 01:38:24 UT to 02:39:05 UT on 2000 February 10. At 01:38:24 UT on February 10, the right part of the filament became active again. The white arrow points to the same loop of the filament in Figures 7(a)–(c). At 01:39:59 UT, another bright loop marked by the black arrow in Figure 7(b) appeared. Subsequently, the bright loop marked by the black arrow first disappeared and then the other bright loop marked by the white arrow vanished. The disappearance of the features may be a temperature effect. After the eruption of the two bright loops, the bright material of the filament was found to flow from right to left. The white arrows in Figures 7(d)–(g) indicate the positions of the hot plasma from 01:43:39 UT to 01:48:23 UT on February 10. The filament loops carrying the hot plasma gradually moved along the loop from west to east. At 01:48:56 UT, another part of the filament enclosing the rotating sunspot also erupted. Next, the filament exhibited clearly an inverse S-shaped structure marked by the dotted lines in Figures 7(i) and (j). There was a data gap from 02:08:05 UT to 02:35:22 UT on February 10. However, comparing the change of the magnetic structure, it is easy to find that the inverse S-shaped filament disappeared. The post-flare loops marked by the white arrows in Figures 7(k) and (l) can be seen clearly. The detailed process of the second filament eruption can be seen from the movie (seconderuption.mpg) linked to Figure 7 in the online journal.
Figure 7. Sequence of 171 Å images showing the second successful eruption of the filament from 01:38:42 UT to 02:39:05 UT on 2000 February 10. The dashed lines denote the inverse S-shaped filament. The arrows are described in the text.(An animation of this figure is available in the online journal.)
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Standard image High-resolution image4.4. The Associated Flare and CME
Figure 8 shows the evolution of GOES soft-X-ray emission for the C7.3 flare on 2000 February 10. The C7.3 flare started at 01:40 UT, peaked at 02:08 UT, and ended at 02:39 UT. Figure 9 shows the evolution of the flare ribbons from 01:41:39 UT to 02:35:28 UT on February 10. The two white arrows in Figures 9(a) and (b) indicate the two flare ribbons. The two flare ribbons gradually brightened. The left flare ribbon along the dotted lines in Figures 9(c)–(g) expanded toward the southwest of the following sunspot. The flare ribbons swept across the umbra of the following sunspot while this did not happen to the leading rotating sunspot. Finally, the flare ribbon swept completely across the following sunspot. Li & Zhang (2009) suggested that the emergence, rotation, and shear motion of the following and leading sunspots caused flare ribbons to sweep across sunspots completely. In this event, the flare ribbon did not sweep across the rotating sunspot unlike those examples that Li & Zhang (2009) investigated. After the inverse S-shaped filament erupted, SOHO/LASCO observed a halo CME.
Figure 8. Evolution of GOES soft-X-ray emission for the C7.3 flare on 2000 February 10 (solid line: 1–8 Å; dashed line: 0.5–4 Å).
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Figure 9. Evolution of the flare ribbons from 01:41:39 UT to 02:35:28 UT on 2000 February 10. The two arrows in panels (a) and (b) indicate the two flare ribbons. The dotted lines denote the direction of the left flare ribbon expansion from the north of the following sunspot to the southwest.
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5. CONCLUSION AND DISCUSSION
We investigate the relationship between sunspot rotation and the formation and eruption of an active-region filament associated with a C7.3 flare and a halo CME in NOAA AR 08858 on 2000 February 10 using the GOES12 soft-X-ray flux, TRACE white light, 1600 Å, and 171 Å images, SOHO/MDI 96 minute magnetograms, and SOHO/LASCO C2 images. We find that the formation of the active-region filament in the EUV filament channel was followed by sunspot rotation. The sunspot rotated counterclockwise and the active-region filament exhibited an inverse S-shaped structure. The filament experienced two eruptions. In the first eruption, part of the filament rose and much of the material warmed up (becoming bright). The filament loops carrying the material were seen to spiral into the sunspot counterclockwise in the middle as it fell back toward the solar surface. In the second eruption, the inverse S-shaped filament fully erupted and produced a C-class flare and a halo CME. Before the second eruption, the filament loops carrying the hot material moved clockwise along the magnetic loop.
This event is a clear case of the formation of the sigmoidal active-region filament caused by sunspot rotation. According to the sunspot rotational direction (counterclockwise) and the shape of the filament (the inverse S-shaped filament), we can determine that the sunspot had negative helicity. The inverse S-shaped filament followed the hemisphere helicity rule. From the topology evolution of the magnetic loops in the corona, one can see that the sunspot rotation resulted in the upper magnetic field rotation and made the magnetic fields trend to a non-potential field. It is evident that sunspot rotation is a means of magnetic energy storage. The energy was later released via flares and a CME.
During the observation, no obvious magnetic flux emergence was found before the sunspot rotation. But there was a slow increase in the positive magnetic flux from 23:59 UT on February 8 to 14:27 UT on February 9 and then the positive magnetic flux increased rapidly from 16:03 UT to 19:11 UT on February 9. It is interesting that the rapid increase in the positive magnetic flux occurred only during the fastest rotation of the rotating sunspot, the bright loop-shaped structure, and the filament. The observation provides evidence that the sunspot rotation could be regarded as a result of the transfer of additional magnetic twist from the subsurface to the corona. The investigation of Zhao & Kosovichev (2003) also showed evidence that there was a strong subsurface vortical flow below a rotating sunspot. Magara & Longcope (2001) and Fan (2009) presented a simulation on the emergence of a twisted flux tube into the solar atmosphere. During the emergence, the regions of opposite polarity separated and rotated toward a more axial orientation. Fan (2009) concluded that the rotation in the two polarities is a result of propagation of nonlinear torsional Alfvén waves along the flux tube, which transports significant twist from the tube's interior portion to its expanded coronal portion. In some events, the sunspot rotation was obviously accompanied by the emergent flux and polarity separation (Zhang et al. 2007; Jiang et al. 2012). However, in this event, none of these characteristics is found. We assume that sunspot rotation can originate in two ways. It needs more observations to confirm these results.
When the total twist of the field exceeds a little over one turn, or 2.5π (Hood 1991; Vršnak et al. 1991; Rust et al. 1994; Török, & Kliem 2003), the flux rope becomes unstable. Leamon et al. (2003) measured the total twist of 191 X-ray sigmoids and found that most of the sigmoids have a total twist less than one turn. In this event, the sunspot rotated by 195° and the twist was less than the critical value obtained by former authors. However, the filament also erupted finally. We assume that the eruption of the flux rope is relative to not only the twist caused by sunspot rotation but also self-twist before sunspot rotation.
The authors thank the referee for very constructive comments and suggestions. The authors thank the TRACE, SOHO, and GOES consortia for their data. SOHO is a project of international cooperation between ESA and NASA. This work is sponsored by National Science Foundation of China (NSFC) under the grant numbers 10903027, 11078005, 10943002, Yunnan Science Foundation of China under number 2009CD120, and China's 973 project under the grant number G2011CB811400.