Sunspot Shearing and Sudden Retraction Motion Associated with the 2013 August 17 M3.3 Flare^*

Ever since the discovery made by Carrington (1859) and Hodgson (1859), solar flares have received intensive research for the striking scene of rapid energy release as well as their close relationship with disastrous space weather (Priest & Forbes 2002; Fletcher et al. 2011; Lin et al. 2003). It is now confirmed that the energy required for flares comes from the coronal magnetic field directly (Shibata & Magara 2011; Toriumi & Wang 2019). But how the energy is accumulated in the corona and how flares are triggered are still not very clear. Generally speaking, magnetic field lines in the corona move in both random and organized behavior primarily because of dragging the field line footpoints by photospheric motions, which builds up a highly stressed magnetic field in the corona (Forbes 2000; Chen 2011). Flares occur when magnetic energy in the corona accumulates to some extent and encounters some kind of triggering mechanism. The shearing motion of the photosphere is believed to play a key role in powering active regions and even triggering flares, creating a richness of magnetic shear in flare-prolific sites.

Over several decades, various trigger mechanisms have been proposed conceptually or via magnetohydrodynamics (MHD) simulations to explain the concrete initiation processes of certain kinds of flares, all summarizing magnetic shear as the key feature from observations. Moore et al. (2001) came up with the tether-cutting mechanism conceptually from a sheared core magnetic field. That is, a filament is supported by dips of the magnetic field nearly aligned with a magnetic polarity inversion line (PIL), below which a current sheet is formed between the two oppositely curved elbow regions of the sheared core field. As the magnetic shear increases, magnetic reconnection commences, leading to a long concave-upward flux rope, which pulls up the filament to rise and make it erupt (Song et al. 2021). A resembling model was proposed by van Ballegooijen & Martens (1989), who pointed out that successive magnetic flux cancellation along the PIL of a sheared magnetic arcade would create the helical fields which can hold a filament. The helical rope could get higher and higher as flux cancellation goes on, which is quite an analogy to a filament eruption (Amari et al. 2003). The flux cancellation could develop the twist of coronal fields, which can also cause filament eruption via MHD instability (Sakurai 1976; Török & Kliem 2005; Fan & Gibson 2007; Démoulin & Aulanier 2010). The so-called breakout model could be regarded as the external tether-cutting mechanism (Chen 2011), where the upper part of the core magnetic region reconnects with the overlying magnetic field, which erases the downward magnetic tension force of the background field (Antiochos et al. 1999; Aulanier et al. 2000; Archontis & Török 2008). All of the triggering mechanisms mentioned above are made in the framework of a sheared magnetic field, which is supposed to be produced by photospheric shearing motion, especially sunspot shearing motion. However, to our knowledge, unambiguous evidence for the eruption of a flare driven by the direct shearing motion of a sunspot is still rare in the literature.

The lower solar atmosphere often has an immediate signature during the eruption of a sheared magnetic field, like the unshearing motion in two-ribbon flares, often shown as the decrease of the centroid distance of Hα or hard X-ray kernels (the so-called converging motion) during the rising phase of solar flares (Ji et al. 2004; Liu et al. 2009b; Su et al. 2007). In addition to the converging motion, there is a simultaneous decrease in the height of loop-top sources or flaring loops, so the unshearing motion may also reflect the rapid shrinkage of the volume of the sheared magnetic field in the flare energy-releasing site (Ji et al. 2006, 2007; Simões et al. 2013; Liu et al.2009a). On the other hand, the shrinkage of the core magnetic field and the opening of the peripheral magnetic field, the restructuring or reconfiguration, will have an impact on the lower atmosphere. One kind is the stepwise and permanent flare-related changes of the photospheric magnetic fields or magnetic shear as reported by Wang (1992) and Cameron & Sammis (1999). Another is the backreaction of the flare to the photosphere that seems to provide Lorentz force to it as first formulated by Hudson et al. (2008). Fisher et al. (2012) further formulated both horizontal and vertical Lorentz forces changes implied by the observed changes in the vector magnetic fields related to flares and extended the discussion to the backreaction of the photosphere under the condition of momentum and energy conservation. The force and the associated torque will change the state of the photosphere's horizontal motion, and thus the theory can be verified with observations. Several verifications have been made with the nice spatiotemporal correlation (Wang et al. 2014; Bi et al. 2016), though they are far from enough; we should seek further quantitative analysis.

Here, we report on an M3.3 flare powered and even triggered by pure sunspot shear motion that started suddenly after being in a quasi-stationary state from the time it was formed. The energy accumulation and triggering processes are distinct from the gradual long-term evolutionary process of active regions often shown as flux emergence/cancellation and/or photospheric motion such as the rotation of a sunspot or network magnetic fields (Deng et al. 2001; Tan et al. 2009; Kumar et al. 2010; Sun et al. 2012; Vemareddy et al. 2012; Liu et al. 2013; Bi et al. 2016; Yan et al. 2018; Dai et al. 2021). The sunspot was suddenly pulled back in the opposite direction immediately after about the flare's peak time, and, to our knowledge, this kind of rapid backward motion has not been reported before. The entire evolution is investigated from long-term aspects, and we will also pay attention to the rapid changes during the flaring period in the HMI and AIA data sets. We describe the data analysis in Section 2. The results are presented in Section 3. The discussion and summary are given in Section 4.

The data used here were recorded by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) and the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012). AIA takes full-disk EUV images in 94, 131, 171, 193, 211, 304, and 335 Å with a time cadence of 12 s and UV images in 1600 and 1700 Å of 24 s. The photospheric line-of-sight (LOS) magnetograms and continuum intensities are obtained from HMI with a cadence of 45 s. HMI has also mapped the photospheric vector magnetic field every 720 s. For our research, the product of vector magnetograms was remapped to heliographic coordinates. All of the images were reconstructed in a resolution of 05.

The hosting active region NOAA 11818, exhibiting a magnetic δ configuration, was located in the southwest of the solar disk (S07W30) when the M3.3 flare occurred on 2013 August 17. The flare started at 18:16 UT, peaked at 18:24 UT, and ended at 18:35 UT as observed in the GOES 1–8 Å flux curve. Figure 1 presents four typical moments of the active region as observed with photospheric continuum intensities (top panels) and vertical magnetic field (B_z ) (bottom panels). The blue and red arrows in the lower panels represent the horizontal local velocity derived from the DAVE4VM method based on the magnetic features with positive (negative) B_z greater (lower) than 1000 (–1000) G (Schuck 2008). The target sunspot S1 appeared days before the flare at about 19:00 on August 15 and remained quasi-stationary relative to the main sunspot S0 of the AR until 08:27 UT on August 17. Two other sunspots, S2 and S3, existed, as shown in panels (a) and (e). At about 08:27 UT on August 17, sunspot S1 suddenly separated into two sunspots, and we label the sunspot in the east still as S1 and the western one S4. Sunspot S2 also split off a smaller sunspot labeled S5 at about the same period as displayed in panels (b). Soon after, the target sunspot S1 started on and remained in a distinct northeastward motion along the PIL until about the peak time of the flare. Meanwhile, sunspot S4 remained stationary relative to the main sunspot S0 as shown in panels (c) and (g). When the flare came to its apex, i.e., about 18:24 UT, the direction of movement of sunspot S1 underwent a sudden retraction from northeast to southwest, and at the same time, sunspot S4 suddenly moved, as displayed in panel (h). An associated animation is available to show the evolution more vividly.

To investigate the evolution of the target sunspot movement more comprehensively, we plot a time profile for the displacement of the target sunspot in Figure 2(a) by using the center of mass (CoM) (Anwar et al. 1993) to estimate its position. The x and y displacements of the sunspot at each moment in the CoM method are defined as

$$\begin{eqnarray}&&{X}_{d}=\displaystyle \frac{\sum {X}_{i}{I}_{i}}{\sum {I}_{i}}-\displaystyle \frac{\sum {X}_{i0}{I}_{i0}}{\sum {I}_{i0}},{Y}_{d}=\displaystyle \frac{\sum {Y}_{i}{I}_{i}}{\sum {I}_{i}}-\displaystyle \frac{\sum {Y}_{i0}{I}_{i0}}{\sum {I}_{i0}},\end{eqnarray} \tag{ 1 }$$

where X_i and Y_i are the x and y coordinates of each pixel in the sunspot at one moment, I_i is the corresponding continuum density, and the subscript i0 represents either the point of 17:00 UT on August 16 or 10:00 UT on August 17. We use a threshold of 52% of the quiet region (displayed by the dotted rectangle in Figure 1(a)) intensity in the calculation. The reason for the two starting points is that sunspot S4 was disjointed from S1 completely around 10:00 UT on August 17. The AR had no detectable enhancement in HMI continuum intensity during the flare. Therefore, there was no white-light emission that would bias the treatment of the sunspot position.

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In this way, the centroid of the sunspot before and after this point of time was subtracted from its centroid at 17:00 UT on August 16 and 10:00 UT on August 17. The second time profile was shifted to connect with the first time profile to form a complete one in order to demonstrate the whole moving process. The connection is smooth because of the same slope. Clearly, the whole time profile is characterized by four stages with different speeds, including the last horizontal one that is almost stationary. The three time nodes are 08:27, 18:22, and 18:48 UT on August 17. We mainly focus on the first three stages, which can be termed the quasi-stationary, shearing, and retraction states. The moving pattern is depicted by the red arrows in Figures 1(e), (g), and (h), while those in Figure 1(f) depict the separation process. The displacement of the first three stages is 2.1, 6.8, and −17 with periods of about 15.5, 10.0, and 0.4 hr. Their linear speeds are 22, 138, and −772 m s⁻¹, respectively. As a comparison, the average speeds of the target sunspot represented by the arrows in Figures 1(e), (g), and (h) are calculated, which are 39, 107, and −182 m s⁻¹. It can be seen that the speed in the second stage is over 100 m s⁻¹ as derived from the two methods, which is regarded to be the theoretical limit of the shear flow that can lead to effective heating and cause flares (Heyvaerts & Priest 1984).

The trajectories of all sunspot centroids obtained by the CoM are plotted in Figure 3. The portion of each curve shaded from white to dark blue represents the trajectory from 17:00 UT on August 16 to the flare starting time linearly, while the red portion outlines the track during the flaring time until 19:30 UT on August 17. It should be noted that the starting color of the curve of sunspot S4/S5 is light blue rather than white, which is due to the centroid of the two sunspots being measured from 10:00 UT on August 17. From the movement of sunspots S0, S2, and S3, we can clearly see that the entire active region had a general trend moving toward the north. The movement of sunspots S1 and S4 were significantly affected by the flare while other sunspots were less affected, as shown by the red trajectories.

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Figure 2(b) further presents the time profiles of the flux of the AR in AIA 94, 131, 171, 304, and 1600 Å. Comparing the first two stages, we can clearly see that the curves of the latter one contain more spikes. It means that the active region has been effectively activated in this period. All of these spikes are confined eruptions that can be considered as a series of precursors of the M3.3 flare.

Like most M- and X-class flares (Yan et al. 2011; Zhang et al. 2022), the M3.3 flare was also associated with a filament eruption as shown in Figure 4. A bright twisting or braided structure appeared on the central part of the filament around 18:00 UT, which can be seen clearly in the right subfigure of panel (b). At the same time, two brightening points (BP1 and BP2 in panel (a)) showed up in the chromosphere just below the center part of the filament, and one of them (BP1) was in contact with sunspot S1. The temporal and spatial consistency between BP1 and BP2 in the chromosphere and the braided structure on the filament hints that these two kinds of structures are manifestations at different heights of just one magnetic reconnection process. The spatial overlap between sunspot S1 and BP1 suggests that the magnetic fields of S1 might be involved in the reconnection. Starting at about 18:16 UT, the filament was activated and partially erupted out entangled with the braided structure, eventually forming a two-ribbon flare as shown in panels (e) and (h).

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After filament eruption, the side loops appeared to contract. We present AIA 171 Å observations for this event in the third column of Figure 4. Two coronal loop systems (Loops1 and Loops2) are visible in the south and northwest of the filament before the flare, as exhibited in panel (c). At about 18:21 UT, Loops1 suddenly moves inward to the center of the flare core region as shown by the auxiliary lines plotted in panels (c) and (i), while the majority of Loops2 bursts out with the filament. The contraction lasts about 20 minutes, even throughout the flare decaying phase. It should be noted that the reversal of the moving direction of the target sunspot also occurred at this time. Two slits are placed across Loops1 and the filament to construct time–distance diagrams (Figure 5). The inward motion shows an apparent speed of about 10 km s^–1, and the projected speed of filament is on the order of tens of kilometers per second. The starting time of the filament eruption (about 18:18 UT) was about three minutes ahead of that of the contraction of Loops1 (18:21 UT), which is consistent with the theoretical prediction that a smaller magnetic pressure gradient will be caused by the depletion of magnetic energy and overlying magnetic fields must contract to strike a new balance.

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In addition, a sudden and permanent enhancement of the photospheric horizontal field (B_h ) ensued from the beginning of the flare at 18:12 UT. In the top panels of Figure 6, a core region (enclosed by the dashed rectangle) along the PIL is identified to show the noticeable change before, during, and after the flare. The background maps are the vertical photospheric magnetic field (B_z ) while B_h is highlighted by the arrows aligned to the field direction, with varying colors proportional to the different field strengths as manifested by the color bar. Furthermore, the time profile of the average B_h , calculated from the dashed rectangle region, is plotted in panel (d). Before the flare, the strengths experienced an increase of 340 G in 14 hr and a reduction of 165 G in 11 hr, which should be due to the gradual evolution of the photospheric magnetic field. A sharp increment of 230 G can be observed 36 minutes into the flaring time, with the changeover cotemporal with the impulsive phase of the AIA curves in Figure 2(b). This suggests a more horizontal photospheric magnetic field around the PIL after the flare. Considering the coronal loop contraction, both pictures endorse the magnetic implosion scenario (Hudson 2000; Hudson et al. 2008; Wang & Liu 2010; Fisher et al. 2012).

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To investigate the possible reasons for the response of the photosphere to the flare, the Lorentz force changes on the photosphere are further derived by applying the method proposed by Fisher et al. (2012). The background maps of the top panels of Figure 7 are the running-difference maps of the vertical Lorentz force (δ F_z ) with the dark/bright features exhibiting the force directed downward/upward. The running-difference horizontal Lorentz force (δ F_h ) is highlighted by the golden arrows in the contours for B_z = −1000 G, with varying lengths proportional to the different force strengths. Panel (d) presents the time profiles of the mean δ F_h in the contour and δ F_z in the dotted rectangle, which is the same as that in Figure 6. Obviously, both δ F_h and δ F_z are nearly zero at most times, except for an impulse signal during the flaring time, with the values of 3.9 × 10¹⁹ dynes for δ F_h and −1.3 × 10¹⁹ dynes for δ F_z . It means that F_z , which should be interpreted as the magnetic pressure, strengthened and resulted in the enhancement of B_h . It stands for the downward collapse of the magnetic fields to the photospheric flare core region, contrasting with the upward component of the flare according to the magnetic implosion idea (Hudson 2000; Fisher et al. 2012). On the other hand, F_h also strengthened mainly on sunspots S1 and S4 along the direction of the retracting motion, that is, the direction toward the core region. Similarly, it contrasts with the laterally outward component of the flare considering the conservation of momentum in the horizontal direction. The change in both F_z and F_h during the flaring time depicts the process in which the magnetic fields erupt outward and then collapse inward.

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To support the picture, the bottom panel of Figure 7 gives the time profile for the mean angle formed between the horizontal local Lorentz force and the horizontal local velocity field, averaged in the region enclosed by the blue contours in the upper panels of Figure 7. We see that there is a sudden drop in the mean angle, showing that the horizontal Lorentz force was pulling the sunspot backward during the flare period. The tight temporal and spatial correlations between the above variations and flare eruption strongly imply that the retracting motion of the sunspot could result from Lorentz force change induced by the flare (Fisher et al. 2012).

For an order-of-magnitude estimation, we compare the momentum change of the sunspots S1 and S4 with the impulse of F_h during the rapid change in sunspot velocity. The linear fitting results 138 m s⁻¹ and −772 m s⁻¹ are used as the velocity at the start and end times of the period, respectively. The average F_h in flaring time, ∼2.5 × 10²² dyne, is taken as the average F_h in this process. The surface area of the sunspots S1 and S4 (B_z smaller than −1000 G) is about 2.2 × 10⁷ Mm², and the density is taken to be 4 × 10⁻⁷ g cm⁻³ (Wang et al. 2014). Under the assumption that the sunspot is a thin flux tube (Spruit 1974, 1981), the depth is taken to be 1.0 Mm (Anwar et al. 1993; Bi et al. 2016). Then, the mass of sunspots S1 and S4 is estimated to be ∼8.8 × 10¹⁵ kg, and the change in the sunspot's momentum is about 8.0 × 10¹⁸ kg m s⁻¹. Based on momentum conservation, these figures lead to the estimates of the timescale of ∼32 s. If the viscosity is taken into account, the timescale will be longer, possibly up to several minutes, which is consistent with our observations and previous reports (Anwar et al. 1993; Wang et al. 2014; Bi et al. 2016).

In this Letter, we give a detailed analysis of the M3.3 flare of 2013 August 17 (SOL2013-08-17T18:16), showing the well-defined associations between the rapid sunspot shearing motion of the small sunspot and the activation of the filament tied to the sunspot before the flare, between the sudden retracting motion of the same sunspot and the deduced Lorentz force from the rapid reconfiguration of the coronal magnetic field upon the flare onset.

By using HMI intensity images and vector magnetograms, we find that the flare was powered and triggered by a rapid sunspot shear motion that lasts ∼10 hr until the flare onset. Compared with previous reports in the literature that photospheric shearing motions were generally characterized by long-term gradual evolution along PILs and were often accompanied by other photospheric phenomena like flux emergence/cancellation, sunspot rotation, etc. (Deng et al. 2001; Yang et al. 2004; Kumar et al. 2010; Sun et al. 2012; Vemareddy et al. 2012; Liu et al. 2013; Yan et al. 2018), the shearing motion in this event and its association with flares are simple and neat as observed from the small moving sunspot. It started its shearing motion abruptly from the quasi-stationary state and underwent an abrupt retraction motion when the flare started, though it seems that pure shear motion cannot provide all of the energy for filament eruption/flare in a limited time from a potential state (Chen & Shibata 2000). In this case, AR 11818 might have already accumulated plenty of free magnetic energy, and further input will occur as the sunspot keeps its shearing motion along the PIL. The shear motion was followed by an increased number of brightening spikes noticeable in AIA flux curves, indicating the contributing processes of magnetic energy to the corona. The contribution is made via either the formation of sheared magnetic configuration resembling the process proposed by van Ballegooijen & Martens (1989) or the formation of unstable hot channels as observed by Wang et al. (2018). In this event, the shearing motion can be linked with the twisted magnetic structure of the filament. Therefore, the picture is similar to the shear reconnection model proposed by van Ballegooijen & Martens (1989), where shear flow along with the PIL transfers the arcade field in corona to the helical field by reconnection, which is capable of holding a filament. As the reconnection goes on, the magnetic flux in the helical field becomes too large to keep its equilibrium, which leads to the helical field erupting out with the filament in it (Sun et al. 2012).

The more important and interesting observation is that the small sunspot S1 underwent a sudden retraction motion with a much larger speed after the impulsive phase of the flare. Because the time for the direction reversal is too short for a turnover of the photospheric convection (Bi et al. 2016), the phenomenon can be explained with the Lorentz force produced during "magnetic implosion" (Hudson 2000; Hudson et al. 2008; Wang & Liu 2010; Fisher et al. 2012) under the condition of momentum and energy conservation. It is shown that the direction of the impulse of δ F_h in the flaring time is consistent with that of the sunspot reversal, thus we believe that the sudden retraction motion results from the horizontal Lorentz force produced by the coronal magnetic field reconfiguration rather than photospheric convective flows. The backreaction on the photospheric shear motion has various forms (Tan et al. 2009; Wang et al. 2014; Liu et al. 2016; Xu et al. 2017), but none of them showed a 180° change of direction. There still existed a vertical (downward) Lorentz force exerted on the photosphere manifested by the rapid and irreversible increase of the photospheric horizontal magnetic field. It should be noted that the two patterns of Lorentz force play different roles in the photosphere complex. That is, the vertical (downward) Lorentz force acts to increase the photospheric shear while the horizontal one decreases the shear (Petrie 2013).

In summary, the M3.3 solar flare in AR 11818 on 2013 August 17 is a rare and valuable event, showing sunspot motions before, during, and after the flare. Thus, it can serve as a good example of magnetic coupling across different layers of the solar atmosphere during a solar flare. It provides direct evidence that the shearing motion of a sunspot can power and trigger a solar flare. It especially confirms how the fast relaxation or restructuring of coronal fields can have an impact on the photosphere, resulting in a sudden Lorentz force as well as an enhanced horizontal magnetic field. Magnetic coupling processes across the solar atmosphere in other flares may take different forms, like the rotation of sunspots or network magnetic fields, and the emergence, cancellation, and rapid changes of magnetic fields, but the signature is vague in most flares. This may be due to insufficient spatiotemporal resolution and low accurate polarimetry (Keil et al. 2003; Rimmele et al. 2020). Further similar systematic research with the aid of well-observed cases will provide further insight into the coupling between the photosphere and corona during solar flares.

The authors are grateful to the anonymous referee and colleagues in Purple Mountain Observatory and Yunnan Observatories for their constructive suggestions and comments. SDO is a mission of NASA's Living With a Star Program. AIA and HMI data are courtesy of the NASA/SDO science teams. This work is supported by the National Key R&D Program of China 2021 YFA1600500 (2021YFA1600502), NSFC grants (Nos. 11790302, 11790300, 12173084, 12073072), CAS Key Laboratory of Solar Activity, and the Strategic Priority Research Program on Space Science, CAS (XDA15052200, XDA15320301), China Postdoctoral Science Foundation 2020M671639, and Yunnan Key Laboratory of Solar Physics and Space Exploration 202205AG070009.