THE FORMATION OF AN INVERSE S-SHAPED ACTIVE-REGION FILAMENT DRIVEN BY SUNSPOT MOTION AND MAGNETIC RECONNECTION

Solar prominences (or filaments) are common features in the solar atmosphere and are one hundred times cooler and denser than the coronal material (Vršnak et al. 1988; Tandberg-Hanssen 1995). When they are viewed on the solar disk, they show strong absorption in Hα and in the Extreme Ultraviolet (EUV) continuum, and are called "filaments." When they are seen above the solar limb, they are bright features against a dark background, and are called "prominences." Often, the terms "filament" and "prominence" are used interchangeably. Prominence plasma is embedded in special magnetic structures and thermally isolated from the surrounding environment. It is formed in "filament channels," which are the regions in the chromosphere surrounding a Polarity Inversion Line (PIL) where chromospheric fibrils are aligned with the PIL (Martin et al. 1994; Gaizauskas et al. 1997, 2001; Mackay et al. 1997, 2010; Martin 1998a; Kong et al. 2015). When they appear in active regions, at the border of active regions, and on the quiet Sun, they are classified as active-region filaments, intermediate filaments, and quiescent filaments, respectively (Parenti 2014). High resolution observations reveal that prominences consist of many thin threads with various material flows (Engvold 1998; Lin et al. 2005; Berger et al. 2008; Lin 2011; Yan et al. 2015b). In general, the height of quiescent filaments is larger than that of active-region filaments. But the difference in the physical nature between quiescent filaments and active-region filaments is not clear.

What is fascinating about prominences is their role as a crucially important component of solar activity. Generally, eruptions of prominences are associated with flares and coronal mass ejections (Shen et al. 2011; Deng et al. 2013; Kumar et al. 2013; McCauley et al. 2015). Several observational precursors of filament eruptions have been found and several models have been proposed (see e.g., Priest 2014), but our focus here is on the formation process.

The formation of prominences (filaments) is still a challenging problem in solar physics. To address this issue, researchers have suggested models (based on observations and simulations) that are broadly divided into two types: one is surface effects that reconfigure coronal fields; the other is subsurface effects. Surface effects include shear flows along the PILs, differential rotation, converging flows toward PILs, and magnetic cancellation (van Ballegooijen & Martens 1989; DeVore & Antiochos 2000; Cheng et al. 2015). Subsurface effects involve the emergence of a twisted flux tube by magnetic buoyancy through the convective layer and its emergence into the photosphere, chromosphere, and corona, dragging cool dense material with it (Low 1994; Rust & Kumar 1996). Active-region filaments are short lived and low lying compared with quiescent prominences. Observations of quiescent prominences tend to support surface flow mechanisms (Litvinenko & Somov 1994; Chae et al. 2001; Wang & Muglach 2007). Although an emergence mechanism has been proposed for active-region prominences (Lites & Low 1997; Okamoto et al. 2008, 2009), we here present observational evidence for a combination of surface motions and magnetic cancellation being responsible for its appearance.

Observations of the formation of solar filaments are relatively rare. Gaizauskas et al. (1997) have observed the early stages in the development of a filament channel and the subsequent formation of a filament in it. They found that the filament formed after the filament channel was created and filament formation was associated with convergence between opposite magnetic polarities in a filament channel. Chae et al. (2001) have found that shear motion, converging motion, and magnetic cancellation were closely related to the formation of a filament in active region NOAA 8688. Cancellation of small bipolar magnetic regions in a filament channel was also observed during the formation of solar filaments (Schmieder et al. 2004). For three case studies, Wang & Muglach (2007) found that magnetic cancellation is the dominant process in the formation of filaments and their channels. Martin (1998b) has presented several observations relevant to the conditions for filament formation, such as their location at a boundary between opposite polarity magnetic fields, the convergence of opposite polarity network magnetic fields toward their common boundary within the channel, and cancellation of magnetic flux at the common polarity boundary. Recently, high-resolution observations from the New Vacuum Solar Telescope (NVST) have revealed that two successive active-region filaments were formed by shear flow between opposite polarity magnetic fields and the rotation of a small sunspot in which one foot of the filaments was rooted (Yan et al. 2015a). A similar result was also presented by Yang et al. (2015). They found that a rotating magnetic field in the quiet Sun resulted in the formation of a circular filament. Yang et al. (2016) have also presented a case of filament formation, in which rapid formation of the filament was due to magnetic reconnection between two sets of dark threadlike structures. In addition, converging flows and continual flux cancellation have played important roles in filament formation.

In this paper, we study the formation of an S-shaped active-region filament (in AR NOAA 11884), which erupts soon afterwards, by using multi-wavelength observational data. Observations and methods are presented in Section 2. The results are shown in Section 3. The discussion are given in Section 4.

Active-region NOAA 11884 produced several C-class and M-class flares during the period from 2013 October 31 to November 2. During its evolution, an inverse S-shaped filament was observed to form in this active region. Observations by the NVST (Liu et al. 2014) and the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) covered the whole process of this formation.

The Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the SDO provides multiple, simultaneous high-resolution full-disk images from the transition region to the corona. Full-disk UV and EUV images are taken by the AIA with a 12 s cadence and a spatial resolution of 06 per pixel (Lemen et al. 2012). The 304 Å (He ii), 171 Å (Fe ix), and 193 Å (Fe xii, xxiv) images observed by SDO/AIA were used to show the formation of the active-region filament. We also used full-disk line-of-sight magnetograms at 45 s cadence with a precision of 10 G and vector magnetic fields in the photosphere observed by the Helioseismic and Magnetic Imager (HMI; Schou et al. 2012; Bobra et al. 2014; Centeno et al. 2014). The vector magnetograms, which have a pixel scale of about 05 and a cadence of 12 minutes, came from the Space Weather HMI Active Region Patch (SHARP) series. They were derived using the Very Fast Inversion of the Stokes Vector algorithm (Borrero et al. 2011). The minimum energy method (Metcalf 1994; Metcalf et al. 2006; Leka et al. 2009) was used to resolve the 180° azimuthal ambiguity. The images were remapped using Lambert (cylindrical equal area) projection centered on the midpoint of the AR, which is tracked at the Carrington rotation rate (Sun 2013).

The NVST is a vacuum solar telescope with a 985 mm clear aperture and is located in Fuxian Lake, in China. It is a multi-channel high-resolution imaging system (one channel for the chromosphere (6563 Å) and two channels for the photosphere (TiO 7058 Å and G-band 4300 Å) and spectrometer systems (a multi-band spectrometer and a high-dispersion spectrometer). The Hα images used in this paper from the NVST were taken at Hα center (6563 Å) with a bandwidth of 0.25 Å. They have a pixel size of 0163 and a cadence of 12 s. The data are calibrated from Level 0 to Level 1 with dark current subtracted and flat field corrected, and then the calibrated images are reconstructed to Level 1+ by speckle masking (Weigelt 1977; Lohmann et al. 1983). We used a cross-correlation method to co-align the Hα images. The method is divided into three steps. One is to remove the motion of the full-field images from one frame to the next by using a cross-correlation method and the next is to divide the full-field images into a number of sub-images, with the sub-images co-aligned using the cross-correlation method. Moreover, the sub-images were reconstructed from subsequent images. Finally, all the reconstructed sub-images are combined to form the whole high-resolution image (see Liu et al. 2014; Xiang et al. 2016).

Moreover, we used vector magnetic fields from SDO/HMI as boundary conditions to extrapolate the magnetic fields from photosphere to corona. The optimization algorithm proposed by Wheatland et al. (2000) and implemented by Wiegelmann (2004) was employed to extrapolate the three-dimensional NLFFF structure. We applied a preprocessing procedure (fff_temp_pre.pro in SSW) to the bottom boundary vector data before extrapolation. This procedure ensures the observational vector magetograms fulfill the following conditions: (i) the data coincide with the photospheric observations within measurement errors; (ii) the data are consistent with the assumption of a force-free magnetic field; (iii) the data are smooth. This removes most of the net force and torque that produce an inconsistency between the observed photospheric magnetic field and the force-free assumption (see Wiegelmann et al. 2006 for details).

The AIA and HMI data were calibrated to Level 1.5 by using the standard procedure in SSW, and rotated differentially to a reference time (at 04:30:07 UT on 2013 November 1). Then, we co-aligned the SDO and NVST images using the subpixel registration algorithm, respectively (Feng et al. 2012; Yang et al. 2014; Ji et al. 2015). Because the 304 Å and Hα images have similar structures, we used a cross-correlation method to align the two images and then the other wavelength images of AIA were co-aligned with the 304 Å images. The error of co-alignment is estimated to be about 06.

3.1. The Formation of the Inverse Active-region Filament

3.2. Magnetic Cancellation

In order to show more clearly the change in the magnetic fields, their evolution in the green box in Figure 1(a3) is shown in Figure 3 from 08:00:00 UT on 2013 October 31 to 23:36:00 UT on November 2. The two blue boxes marked 1 and 2 are used to show the cancellation of two strings of opposite polarity, the moving magnetic flux with negative polarity, and the sunspot with positive polarity, respectively. The yellow lines indicate positive polarities, while the green lines indicate negative polarities. The blue boxes 1 and 2 are the same as those in Figure 1(a3). During the formation of the filament, the two opposite polarities approached each other. The string with negative polarity exhibited an arcade shape around the trailing sunspot. Ultimately, they cancelled and the positive polarities disappeared completely. Figure 4(a) shows the movement of two opposite polarities along the red line marked in Figure 3(a). The positive polarity moved a little with a speed of 16 m s⁻¹. The velocity of the negative polarity approaching the positive polarity was 126 m s⁻¹. The change in the magnetic flux in box 1 is shown in Figure 4(b). The red and blue lines indicate the change in the positive and negative magnetic flux, respectively. The two vertical dashed lines show the duration of cancellation, which began at about 16:00 UT on 2013 November 1. The positive polarity was completely cancelled with the negative polarity by 20:00 UT on 2013 November 2. The region in box 2 also experienced cancellation (see Figures 3(b)–(f)). From 13:12:00 UT on 2013 November 1 to 00:12:00 UT on November 2, the negative polarity cancelled with the sunspot with positive polarity. The change in the magnetic flux in box 2 is shown in Figure 4(c). The red and blue lines indicate the change in the positive and negative magnetic flux, respectively. During the magnetic cancellation (the period marked by the two vertical dashed lines in Figure 4(c)), the cancellation site exhibited brightening in the chromosphere. Figure 4(d) shows the change in the 304 Å normalized intensity in the blue box 2 in Figure 1(b3). There are several discontinuous changes in the emission in the 304 Å images during magnetic cancellation (see the period between the two vertical dashed lines in Figure 4(d)). The cancellation process can be seen in the animated version of Figure 3. The two blue boxes mark the two regions that exhibited significant magnetic cancellation. The white and black patches indicate positive and negative polarity magnetic fields. Magnetic fields between –800 and 800 G are presented in Figure 3.

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3.3. NLFFF Extrapolation

The vector magnetograms and NLFFF extrapolation are shown in Figure 5. The left panel shows the evolution of the vector magnetic fields from 2013 October 31 to November 1, while the right panel shows the resulting NLFFF extrapolation. The blue arrows represent transverse magnetic fields in Figures 5(a1)–(a3). The structure of the filament during its formation can be seen in Figures 5(b1)–(b3). The filament gradually formed a curved structure (CD) (see Figures 5(b1)–(b2)). Then it reconnected with the arcade fibrils (AB). Finally, an inverse S-shaped filament (AD) was formed (see Figure 5(b3)). The curved filament (CD) and the inverse S-shaped filament (AD) both exhibited a twisted flux rope structure.

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The presence of twist in a flux rope before eruption is highly likely on theoretical grounds, since an increase in twist adds magnetic energy in excess of the potential to a flux tube and makes it more likely to become unstable and erupt (e.g., Priest 2014). Furthermore, in the present example, there are several ways of building up the twist. First, vortex motions associated with the rotation of the small positive spot around the main negative one will tend to add twist to the flux rope. Second, the two cancellation locations are likely to add twist by three-dimensional reconnection, during which the total magnetic helicity is conserved, so that mutual magnetic helicity can be converted into self-magnetic helicity. Wang & Muglach (2007) considered the formation of filaments by flux cancellation acting on a succession of pairs of loops, and suggested that this could produce a sheared field without twist. The newly formed loops in the model proposed by Wang & Muglach (2007) have increased shear, whereas the model proposed by van Ballegooijen & Martens (1989) suggests that the reconnected loops are twisted. Both of these cartoon models are possible formation mechanisms using flux cancellation, but detailed modeling is needed to determine which is more appropriate in the present case.

Observationally, twist is often seen in erupting prominences, but is notoriously difficult to detect in filaments before eruption and even more difficult to quantify, partly because of the lack of resolution of the dark filamentary structure. In our case, there are suggestions of twist in the filament in the early stages in Figures 1(b1)–(b3) and (c3) and Figures 2(a2) and (a3) and also in the later stages after cancellation in Figures 6(b4) and 7(a4) and (b4). But we cannot be certain from the observations that the pre-eruptive filament is twisted.

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3.4. Plasma Injection

3.5. Lengthening the Filament by Reconnection

A simple model to show how reconnection can lengthen a filament is as follows. Suppose a flux tube of flux F stretches from a point A(0, 0) to a point B(2, 0) on the x-axis, and that another flux tube also of flux F stretches between C(c, 0) and D(4, 0), so that we are measuring lengths in terms of twice the distance between A and B. Reconnection between the two tubes to create a longer tube joining A and D may be modeled by considering evolution through a series of two-dimensional potential fields as the parameter c decreases from 4 to 2 (Figure 8).

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The magnetic field components may be written

$$\begin{eqnarray}&&{B}_{r}=\displaystyle \frac{\partial A}{r\partial \theta },\ \ \ \ \ \ {B}_{\theta }=-\displaystyle \frac{\partial A}{\partial r}\ \end{eqnarray} \tag{ 1 }$$

in terms of the flux function (A). For a point source at the origin that produces a flux F in the upper half-plane, the magnetic field is B_r = F/(πr), while the flux function is A = Fθ/π.

Suppose there are sources of fluxes +F, −F, +F, and −F at A, B, C, and D, respectively. Then, using the notation in Figure 8(a), the magnetic field components are

$$\begin{eqnarray}&&{B}_{x}=\displaystyle \frac{F}{\pi }\left(\displaystyle \frac{\cos \theta }{r}-\displaystyle \frac{\cos {\theta }_{B}}{{r}_{B}}+\displaystyle \frac{\cos {\theta }_{C}}{{r}_{C}}-\displaystyle \frac{\cos {\theta }_{D}}{{r}_{D}}\right),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{B}_{y}=\displaystyle \frac{F}{\pi }\left(\displaystyle \frac{\sin \theta }{r}-\displaystyle \frac{\sin {\theta }_{B}}{{r}_{B}}+\displaystyle \frac{\sin {\theta }_{C}}{{r}_{C}}-\displaystyle \frac{\sin {\theta }_{D}}{{r}_{D}}\right),\end{eqnarray} \tag{ 3 }$$

where $\cos \theta =x/r$, $\cos {\theta }_{B}=(x-2)/{r}_{B}$, $\cos {\theta }_{C}=(x-c)/{r}_{C}$, $\cos {\theta }_{D}=(x-4)/{r}_{D}$, $\sin \theta =y/r$, $\sin {\theta }_{B}=y/{r}_{B}$, $\sin {\theta }_{C}\ =y/{r}_{C}$, $\sin {\theta }_{D}=y/{r}_{D}$, ${r}^{2}={x}^{2}+{y}^{2}$, ${r}_{B}^{2}={(x-2)}^{2}+{y}^{2}$, ${r}_{C}^{2}={(x-c)}^{2}+{y}^{2}$, ${r}_{D}^{2}={(x-4)}^{2}+{y}^{2}$.

There is a null point (N) where the magnetic field vanishes at (x_N, y_N), say, given by setting B_x = B_y = 0 in Equations (2) and (3), namely,

$$\begin{eqnarray}&&\displaystyle \frac{x}{{x}^{2}+{y}^{2}}-\displaystyle \frac{x-2}{{(x-2)}^{2}+{y}^{2}}+\displaystyle \frac{x-c}{{(x-c)}^{2}+{y}^{2}}\\ &&\quad -\displaystyle \frac{x-4}{{(x-4)}^{2}+{y}^{2}}=0,\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\displaystyle \frac{1}{{x}^{2}+{y}^{2}}-\displaystyle \frac{1}{{(x-2)}^{2}+{y}^{2}}+\displaystyle \frac{1}{{(x-c)}^{2}+{y}^{2}}\\ &&\quad -\displaystyle \frac{1}{{(x-4)}^{2}+{y}^{2}}=0.\end{eqnarray} \tag{ 5 }$$

The way in which the coordinates of N change as c decreases from c = 4 to c = 2 and C moves from D to B is shown in Figure 8(b). Combining Equations (4) and (5), we find x_N and y_N to be

$$\begin{eqnarray}&&{x}_{N}=\displaystyle \frac{8}{6-c},\ \ \ \ \ {y}_{N}=\displaystyle \frac{2\sqrt{2}}{6-c}\sqrt{| {c}^{2}-6c+8| }.\end{eqnarray} \tag{ 6 }$$

The value of the magnetic flux going from C to B is

$$\begin{eqnarray}&&{F}_{{CB}}={\displaystyle \int }_{0}^{{y}_{N}}| {B}_{x}{| }_{x={x}_{N}}{dy}.\end{eqnarray} \tag{ 7 }$$

Then, since the total magnetic flux entering B is F, the magnetic flux that joins A and B is ${F}_{{AB}}=F-{F}_{{CB}}$. Also, since the flux leaving A is F, the flux joining A and D is F_AD = F_CB (Figure 8(c)). The way in which F_AB decreases from F to zero, while F_AD increases from 0 to F as c decreases from 4 to 2 is shown in Figure 9(c). The curves of the relationship between x_N, y_N, and c can be seen in Figures 9(a) and (b).

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3.6. Changing the Twist of a Filament by Reconnection

The way in which the reconnection of a filament can change its twist may be illustrated as follows. If two flux tubes are in the same line, their twists just add together when they reconnect. However, when they are inclined at some angle, then the net twist after reconnection may be different, due to the conversion of mutual helicity into self-helicity. Our example may be modeled by comparing the configurations just before and just after reconnection.

Suppose the long flux tube (AB) of twist Φ_AB and flux F has length 2 and is inclined π/4 to the other tube (CD) of Φ_CD, flux F, and length 1, as indicated in Figure 10 and suppose C is just about to coincide with B and create one long tube (AD) of twist Φ_AD. The initial self-helicities of AB and CD are Φ_ABF²/(2π) and Φ_CDF²/(2π), respectively, and their mutual helicity is $({\theta }_{2}-{\theta }_{1}){F}^{2}/(2\pi )$. After reconnection a single tube AD is created with self-helicity Φ_ADF²/(2π), so that conservation of helicity during reconnection implies that the sum of the self-helicities of AB and CD and their mutual helicity must equal the final self-helicity of AD, so that

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{{AD}}={{\rm{\Phi }}}_{{AB}}+{{\rm{\Phi }}}_{{CD}}+{\theta }_{2}-{\theta }_{1},\end{eqnarray} \tag{ 8 }$$

where θ₂ = π/4 and ${\theta }_{1}={\tan }^{-1}(\sqrt{2}/(1+\sqrt{2}))\approx (2\pi )/25$. The measured twist values of the two parts in the nonlinear force-free extrapolation are 0.38 and 0.6 (Figure 5(b2)). Therefore, Φ_AD equals 1.15. The final twist of the filament calculated from the nonlinear force-free extrapolation in Figure 5(b3) is 1.49. The twist value of the model is consistent with that of the extrapolation.

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One important effect of flux rope lengthening is too much increase in the height of its summit that it may become unstable to torus instability, which occurs when the summit height exceeds a critical value. Another effect is to increase its twist, so that the rope may become unstable to kink instability.

During the evolution of active region NOAA 10484, it was found that a sunspot with positive polarity rotated around a trailing sunspot with negative polarity. Chromospheric fibrils connecting the sunspot with positive polarity were dragged to form a curved filament. After the positive sunspot cancelled with the moving magnetic flux of negative polarity, the curved filament and arched fibrils combined together through magnetic cancellation and formed an inverse S-shaped filament. During the formation of the sigmoid filament, flux with opposite polarity moved together and cancelled below the upper part of the filament. According to NLFFF extrapolation, the formation of the sigmoid filament can be obtained from the evolution of the magnetic structures. Moreover, a twisted magnetic structure for the filament is present in the extrapolation. In addition, hot plasma was found to be injected into the filament from the cancellation site.

Two means for forming solar filaments have been suggested by previous researchers. One is the building of magnetic structures through photospheric flux cancellation and/or coronal magnetic reconnection (van Ballegooijen & Martens 1989; DeVore & Antiochos 2000; Mackay et al. 1998; Yang et al. 2015). The other is the emergence of a flux rope from below the photosphere (Low 1994; Rust & Kumar 1996; Fan & Gibson 2006; Magara 2006; Xu et al. 2012). The observations of Martin (1998b) and Wang & Muglach (2007) suggested that shearing motion, convergence, and cancellation of magnetic flux play a critical role in the formation of filaments. The emergence of a horizontal flux rope from below the photosphere was also observed by Lites & Low (1997) and Okamoto et al. (2009). Moreover, more and more observations provide evidence that active-region filaments have twisted magnetic structures (Wang et al. 1996; Yan et al. 2013, 2014; Yang et al. 2014; Bi et al. 2015; Hou et al. 2016) as well as extrapolations (Guo et al. 2010; Cheng et al. 2013; Xia et al. 2014; Wang et al. 2015). However, there is still controversy regarding the structures of filaments (Ouyang et al. 2015). Our observation is a little different from previous ones. First, the formation of the curved filament was closely related to the rotation of a sunspot, which stretched out and twisted the field lines. The filament later evolved into a longer inverse S-shaped filament through magnetic reconnection with arcade fibrils. Reconnection was evidenced by magnetic cancellation in the photosphere. The simple cartoon in Figure 11 shows the formation of the inverse S-shaped active-region filament. Minus and plus symbols indicate negative and positive polarities.

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Formation of the curved filament was due to sunspot rotation around the trailing sunspot. The convergence and cancellation of two opposite polarities started under the curved filament. The filament also exhibited movement toward the west. The negative polarity followed the movement of the filament. The cancellation of two opposite polarities continued after the formation of the inverse S-shaped filament. When the positive flux was cancelled completely, the filament began to erupt. The filament formation studied in this paper is consistent with a surface-effect mechanism, in which sunspot motion and magnetic cancellation play important roles. From the observations, we cannot deduce that the filament has a twisted magnetic structure. The later eruption needs to be studied in more detail to deduce whether it is due to torus or kink instability, which requires a twisted magnetic structure, or due to mechanisms that do not need a twisted structure like breakout or tether cutting. However, the mechanism of flux emergence can be excluded in this event, since the data clearly show flux cancellation before filament eruption.

There is a debate about the magnetic topology of solar filaments. One possibility is a twisted flux rope (Demoulin & Priest 1989; Priest et al. 1989; Amari et al. 2000; Gibson & Fan 2006; Jiang et al. 2014; Li & Zhang 2015; Su et al. 2015) and the other is a sheared arcade structure (Amari et al. 1991; Antiochos et al. 1994; DeVore & Antiochos 2000; Welsch et al. 2005). For this event, the nonlinear force-free extrapolation suggests that the filament has a twisted magnetic structure, but such a twisted structure cannot be seen clearly in the observations at present.

The authors thank the referee for constructive suggestions and comments that helped to improve this paper. SDO is a mission of NASA's Living With a Star Program. The authors are indebted to the SDO and NVST teams for providing the data. The authors thank Yongyuan Xiang for high-resolution reconstruction of H-alpha images. This work is supported by the National Science Foundation of China (NSFC) under grant numbers 11373066, 11503080, 11603071, and 11633008; Yunnan Science Foundation of China under number 2013FB086; CAS "Light of West China" Program; Key Laboratory of Solar Activity of CAS under number KLSA201603, KLSA201303; and Youth Innovation Promotion Association CAS (No. 2011056).