Rotating Magnetic Structures Associated with a Quasi-circular Ribbon Flare

It is generally accepted that sigmoids are highly twisted and sheared magnetic structures in the solar corona that are often observed as forward or inverse S-shaped coronal loops in soft X-ray (SXR) (Rust & Kumar 1996; Gibson et al. 2002). They provide the storage of free magnetic energy in the solar corona and are the best proxies for various solar activities, such as flares and filament/flux rope eruptions (Gibson et al. 2002; Canfield et al. 2007; Green et al. 2007; Savcheva et al. 2014). It has been revealed that solar flares are often associated with the emergence of new magnetic flux from below the photosphere (Kundu & Woodgate 1986; Kurokawa 1989). In many previous works, shear and emergence of magnetic flux have been shown to be an important way of building up magnetic energy in the coronal field, which might be released in subsequent flares (Schrijver et al. 2005; Sun et al. 2012; Deng et al. 2013; Chen et al. 2015). Chen & Shibata (2000) performed two-dimensional magnetohydrodynamic (MHD) numerical simulations based on the flux rope model, proposing an emerging flux trigger mechanism for the onset of eruptions. In a unipolar region, newly emerging flux, carrying opposite-polarity magnetic fields, may also be responsible for triggering solar flares (Zirin 1874; Wang & Shi 1993; Fletcher et al. 2001; Masson et al. 2009; Wang et al. 2014). In addition, the shearing motion driven by the rotation of sunspots may be an efficient mechanism for injecting magnetic helicity or magnetic energy into the solar atmosphere, which plays a key role in flare onset (Tian & Alexander 2006; Zhang et al. 2008; Jiang et al. 2012; Ruan et al. 2014).

The emergence of twisted flux ropes can lead to magnetic instabilities, interacting with the overlying fields and eventually resulting in the flare and the associated eruption (Jiang et al. 2013, 2014; Yang et al. 2015). Furthermore, circular ribbon flares frequently take place at a complex fan-spine magnetic configuration (Schmieder et al. 1997; Masson et al. 2009; Liu et al. 2010; Reid et al. 2012; Wang & Liu 2012; Deng et al. 2013; Jiang et al. 2013, 2014; Sun et al. 2013; Vemareddy & Wiegelmann 2014; Joshi et al. 2015; Yang et al. 2015; Zhang et al. 2015, 2016). Recently, Jiang et al. (2013, 2014) analyzed the eruption of a sigmoid below a fan dome and the triggering of a circular ribbon flare. Vemareddy & Wiegelmann (2014) also investigated a quasi-circular ribbon that occurred with two remote ribbons. Joshi et al. (2015) studied null-type reconnection triggered by an erupting sigmoid, which led to the formation of a large quasi-circular ribbon. The interaction between the rising filament/flux and ambient field can produce circular flare ribbons and Hard X-ray (HXR) sources (Liu et al. 2010; Yang et al. 2015). These types of reconnection may be associated with the magnetic null point (Pariat et al. 2009).

Besides the magnetic null point, magnetic reconnection may occur in separators (Gorbachev et al. 1988; Mandrini et al. 1991) and quasi-separatrix layers (QSLs; Démoulin et al. 1996, 1997). These are preferential sites for the occurrence of magnetic reconnection (Démoulin et al. 1996; Aulanier et al. 2006; Janvier et al. 2013). Thus, flare ribbons can be used to identify properties of the reconnection site. Particularly, QSL reconnection has been observed at the intersection of the fan and the lower boundary corresponding to flare ribbons (Démoulin et al. 1997; Aulanier et al. 2006; Masson et al. 2009; Reid et al. 2012; Wang & Liu 2012; Sun et al. 2013). The successive restructuring of field lines along the QSLs can lead to continuous apparent field line footpoint motions (Aulanier et al. 2006). As the flux rope emerges rigidly into the corona, separator field lines appear below the flux tube (Titov & Demoulin 1999). The separator is called a bald patch (BP), which is a separatrix surface touching the photosphere along sections of the polarity inversion line (PIL) with a large magnetic gradient. Accompanied with the eruption of flux rope, flares associated with strong current layers will be formed. Two J-shaped flare ribbons are often regarded as evidence for the presence of a twisted flux rope (Savcheva et al. 2012, 2015).

In this work, we present an eruption of a sigmoid under a fan spine topology that produced a quasi-circular ribbon on 2015 February 3. The event was driven by an emerging bipole with a rotation motion. We mainly focus on understanding the relation between magnetic bipole rotation and the major eruption associated with quasi-circular ribbon. The paper is structured as follows. Observations and magnetic field modeling are presented in Section 2. Section 3 includes the active region (AR) description and coronal field structure morphology (fan-spine). In Section 4, we describe the observational details of the sigmoid eruption associated with a C3.9 flare. In Section 5, we present the evolution of magnetic field and analyze the triggering mechanism of the eruption. In the last section, we discuss the results and draw the conclusions.

Sigmoid eruption under a fan spine system was clearly observed by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012). There are seven EUV filters and two UV filters to cover a wide temperature range. Their cadence is up to 12 s, and the pixel resolution is 06. The magnetic field with a cadence of 45 s and a spatial sampling of 05 pixel⁻¹ is measured by the Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) on board SDO. Based on the differential affine velocity estimator (DAVE) method (Schuck 2006), the photospheric velocity field was calculated. The data observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI; Lin et al. 2002) were provided for the analysis of the flare by using the Clean reconstruction algorithm (Hurford et al. 2002). In this study, we also used Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014) slit-jaw images (SJIs) in the filter of 2796 Å. The pixel size is 033 pixel⁻¹ for SJIs. To track the evolution of the event, the above mentioned data were then differentially rotated to a reference time at 11:00 UT.

To better understand the magnetic connectivities within the jet's eruption region, we utilized the "weighted optimization" method to derive a nonlinear force-free field (NLFFF) (Wiegelmann & Inhester 2010; Wiegelmann et al. 2012) by using the vector magnetic field data (HMI; Schou et al. 2012). Before the processing, the data selected for the NLFFF extrapolation were remapped using the Lambert equal area projection. The 180° ambiguity of the transverse components of the magnetic field was resolved with the minimum energy code (Metcalf 1994; Metcalf et al. 2006; Leka et al. 2009). To best suit the force-free condition, a procedure developed by Wiegelmann et al. (2006) was applied to minimize the net force and torque in the observed photospheric field. The calculation was performed within a box of 416 × 233 × 256 uniform grid points whose photospheric FOV is about 250 × 140 Mm⁻². Furthermore, we calculated squashing factor Q by using the code of Liu et al. (2016). To achieve a map with a high precision of Q, the photospheric computational grid was refined 16 times and magnetic field lines were traced with a fourth-order RungeKutta method, point by point. The squashing factor associated with the field lines is defined as slog Q ≡ sign(B_r) × log₁₀ Q (Titov et al. 2011).

A small jet was ejected from the western part of AR 12277 (N06°W03°). Figure 1 shows the general appearance of the AR and the morphology of the jet eruption in the AIA 131 Å running difference image. The image in panel (a) is the vertical magnetic field saturated at ±300 G, with the positive field in white and the negative in black. In particular, the small positive field is surrounded by negative magnetic patches. The horizontal photospheric field is represented with arrows, indicating that the new bipole has a strong horizontal field parallel to the PIL. Panel (b) shows a topological configuration of the fan spine derived from the observations. The AIA 131 Å image (panel (b)) shows that the jet was ejected along the western leg of the coronal loop system, and a remote brightening also appeared at the other end of the coronal loops. By means of NLFFF extrapolation, we compared the extrapolated coronal magnetic configuration with the associated EUV image as shown in Figure 1(b). Some basic structures for the topology of the magnetic field can be found in Figure 2. A null point is measured by the trilinear method (Haynes & Parnell 2007), and is situated ∼24 Mm above the positive magnetic polarity. By using the Jacobian field matrix, we can find the spine and the fan structure near the singularity (null point) (Parnell et al. 1996). The inner spine is rooted in the positive polarity that is surrounded by the negative polarities and the outer spine extends east (a remote place on the solar surface). A twisted field line is located underneath the fan dome with a width of ∼28 Mm. Such a magnetic configuration has already been reported by Liu et al. (2010) and Zhang et al. (2015).

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Figures 3(a)–(b) show a sigmoid structure observed 30 min before the eruption. The structure consists of bright envelope loops in hotter 94 Å and low-lying darker material in cooler 304 Å, with a projected length of about ∼23 Mm. By overlaying a simultaneous HMI magnetogram on the EUV image, we note that the sigmoid is rooted in a single magnetic bipole (see Figure 3(b)). At 10:36 UT, we can see that initial brightening appeared around one end of the sigmoid structure (Figure 3(c)), which may imply that magnetic reconnection occurred and it became unstable. With the increase of brightening intensities, the material contained by the sigmoid rose slowly at a constant projected velocity of about 110 km s⁻¹ (Figure 3(j)), squeezing the overlying arcade field lines. One may observe the rising material with enhancement of the brightenings at 10:49 UT (Figure 3(d)), meaning that the cool plasma was significantly heated by magnetic reconnection. The sigmoid interacted with the spine-like field, as indicated by brightening feature in IRIS 2796 Å (see Figure 3(f)). Moreover, in the 171 Å image, the morphology of the null point resembles the observed inverse-Y structure, as shown in Figure 3(e). Such a cusp structure is believed to be evidence for the existence of a Y-type magnetic reconnection region where the energy release occurred. Another notable feature is that a quasi-circular ribbon flare progressively brightened around the sigmoid in the chromosphere in an counterclockwise direction (Figures 3(g)–(i)). It has an apparent slipping velocity of about 51 km s⁻¹ (see Figure 3(k)). The flare ribbon strongly indicates the presence of a magnetic null point configuration (Masson et al. 2009; Wang & Liu 2012) (see Figure 3(e)). In Figure 3(i), the RHESSI X-ray contours at the 6–12 and 12–25 keV energy channels are overlaid at the selected AIA 1600 Å image. The contours show the co-spatial X-ray source with the brightening in the chromosphere where the position of the sigmoid structure during the flare impulsive phase can be seen.

Accompanied with the quasi-circular ribbon flare, the cool material carried by the sigmoid structure was ejected as a jet. As shown in Figures 4(a)–(d) in the AIA 304 and 193 Å images, the material of the jet scattered and moved along the spine-like loops. To investigate the jet's dynamic structures more clearly, time–distance diagrams of 304 and 193 Å along the longer arrow are displayed in Figures 4(f) and (g). The launching of the jet material began at 10:48 UT with a projected speed of 80 km s⁻¹. In this period, the material was heated to brightenings by magnetic reconnection. At 11:00 UT, the material began to flow back along the coronal loops, and the velocity was about 84 km s⁻¹. Accompanied with the eruption, there was a C3.9 flare, which began at 10:45 UT and peaked at 10:51 UT. Figure 4(e) displays GOES SXR flux and a height–time plot of the sigmoid eruption that was tracked in the stack plot shown in Figure 3(j). We note that the rising of the sigmoid began at 10:46 UT and ended at 10:49 UT, which coincides well with the rise phase in GOES soft X-ray flux.

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HMI magnetograms were used to follow the evolution of magnetic fields at the jet base. The negative and positive polarities are indicated by black and white, respectively. We note that a magnetic bipole, "p" and "n," was encircled by some diffusion negative magnetic field (Figure 5). The new emergence started at 01:36 UT (Figure 5(a)). As a common practice of emerging flux, "p" and "n" separated from each other and increased in size after they appeared (Figures 5(a)–(d)). The changes of magnetic flux covering the emergence region have been displayed in Figure 6(a). Given the diffusion negative magnetic field surrounding the emerging bipole is almost stable in this process of magnetic field evolution, the selected region containing the neighboring field is used to calculate the variation of magnetic flux for the emerging bipole. Before the flare, both the positive and negative magnetic flux show a slow increase from 03:00 to 10:40 UT, which implies that the bipole was emerging (Figure 6(a)). This is consistent with the evolution of the bipole size (Figures 5(a)–(d)). However, magnetic flux decreased after the flare, suggesting that magnetic canceling may play a key role in leading the eruption of the sigmoid.

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In the process of the emergence, the negative polarity shows an counterclockwise rotation around the positive one, while the positive moved northward (Figures 5(b)–(d)). Therefore, the total rotation for the positive polarity had a significant counterclockwise direction until 12:00 UT. In order to obtain the rotation angle, the centers of the opposite polarity were traced. The measured rotation angle as a function of time is displayed in Figure 6(b). The rotation angle increased fast at first and then slowly. A strong peak and a weak peak appeared in the recording rotation speeds before the eruption. The accumulated rotation angle was a total of 120° before the flare onset. The average rotation speed was about 107 h⁻¹. During the rotating of the two poles, the polarity separation also increased slowly with time after they started emerging (Figure 6(c)). Compared the AIA 94 and 304 Å images with the overlaid magnetogram, the footpoints of the emerged loop system were anchored in the emerged opposite polarity (Figures 3(a)–(b)). Following the rotation, the coronal magnetic field between the two magnetic polarities around the magnetic inversion line seemed to form a twisted field configuration (Figure 3(b)), which may be related to the rotation of the magnetic bipole.

To confirm magnetic flux motion, which is important for understanding the flare energy build-up, we measured the photospheric horizontal flow pattern about the emerging bipole in the active region. Via the DAVE method (Schuck 2006), we present a transverse velocity field vector with an integration time of 12 min, superposed on the HMI magnetogram at 10:46 UT (see Figure 5(d)). The flow map showed an counterclockwise rotation spiral pattern of photospheric magnetic field, in which maximum flow speed is about 0.5 km s⁻¹. Opposite flows were found in the emerging bipole. The positive polarity moved toward the neighboring negative polarity field region in the north-east direction (indicated in Figure 5(d)) where the sigmoid activity and brightening occurred (see Figure 3(b)), whereas the negative polarity moved oppositely in the south-west direction. This motion may develop the twisted field lines in the emerging bipole and accumulate magnetic energy for the sigmoid eruption.

Using the code of Liu et al. (2016), we calculated the quashing factor Q to emphasize some complex topology structure under the fan sipne. In Figure 7(a), the distribution of the squashing factor Q in the x–y plane for z = 0 is displayed clearly. For a better comparison, the intensity contours of the AIA 1600 Å images during the sigmoid initial rising are overplotted on the Q map. At 10:46 UT, three brightenings of ribbon appeared below the sigmoid structure, which match the strong squashing factor Q. At 10:48 UT, however, only part of ribbon resembles Q values in the region of the sigmoid, suggesting the complex structure of the flux rope. In Figures 7(c)–(d), the extrapolated twist magnetic structure associated with the rotating magnetic bipole is in line with the sigmoid structure (Figure 3(b)). The green field lines show the flux rope system, while purple field lines are the overlying sheared arcades (less sheared arcades). The NLFFF extrapolation about the sigmoid may contribute to the understanding of the formation mechanism of the central flare ribbon associated with the activity of the sigmoid. Another compared structure is that of the quasi-circular ribbon. We can note that the flare ribbons do not exactly match the QSLs. The northern part of the QSLs only correspond to the weaker part of the flare ribbon. Compared with the center ribbon, the quasi-circular flare ribbon is thinner and weaker in intensity corresponding to the fan footprint, which traces the inner edge of surrounding negative field and lies along the PIL (plotted in Figure 7(b)).

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In this paper, high-resolution observations from IRIS and SDO/AIA were utilized to study a sigmoid eruption under a fan spine magnetic topology. The sigmoid structure was initially located below the fan dome. It was related to a new emerging bipole, which was encircled by negative polarity. The footpoints of the sigmoid were rooted in the emerged bipole. The negative of the bipole rotated around the positive. Regarding the sigmoid structure, some brightening features appeared around its northern end of footpoints. To some extent, this process may initiate the magnetic structure and promote it to rise. The stored magnetic free energy was released rapidly by the onset of instability. The RHESSI X-ray source was also formed above the sigmoid during the flare impulsive phase. In particular, the rising magnetic rope got close to the null point, producing a null point magnetic reconnection. The process of magnetic reconnection may be similar to null point reconnection (Liu et al. 2010; Sun et al. 2013; Joshi et al. 2015). The energetic electrons generated by magnetic reconnection of the null-point were not only accelerated and propagated downward along the field lines to the lower level of the atmosphere, generating a quasi-circular flare ribbon at the fan footprint, but also created a remote brightening at the outer spine footprint. The flare can be regarded as a confined flare that is triggered by reconnection at the null point.

Our attention is focused on the rotation of the magnetic bipole that was a prominent feature associated with the eruption. We calculated the horizontal velocity of the magnetic field on the photosphere, and furthermore obtained the temporal evolution of the rotation speed and the accumulated rotation angle of the magnetic bipole. This may be related to the magnetic flux emergence of an encircling unipolar region. The rotation may be caused by a pre-twisted magnetic flux tube emerging from below the photosphere (Brown et al. 2003; Tian & Alexander 2006; Min & Chae 2009). We conjecture that the rotation of the magnetic bipole generated a sheared PIL, which created the twisted magnetic field structure in the corona. The build up of the flux rope may be driven by shear flows on the photosphere. Therefore, the rotational motion was closely related to the flare triggering. We suggest that the bipolar flux tube was somehow connected to the magnetic bipole beneath the surface. With the eruption of the sigmoid, the helicity may be injected into the coronal region. Similar to sunspot rotating motion, the accumulated twist in the flux rope is transferred to the ambient open field, and the corona may be sufficiently heated by the energy stored in the twisted flux tubes (Tian & Alexander 2006; Jiang et al. 2012; Yan et al. 2012).

The overall topology of the present sigmoid is quite complex, but is a key ingredient for understanding where the flare occurred. The central flare ribbon associated with the sigmoid activation may be related with the separator of the flux rope touching the photosphere at the PIL, in which the free magnetic energy of configuration was released in the form of a flare. The model proposed by Titov & Demoulin (1999) provides important clues to the mechanism of solar flares in twisted configurations. It suggests that the presence of the segments below the flux rope touching the photosphere forms a separatrix surface, where the field line connectivity suffers a jump (Titov & Demoulin 1999). There, a strong current sheet can form and produce enhanced heating along the surface, which manifests itself as the X-ray or EUV sigmoid. In our case, our observation can fit the theoretical explanation that the flare under the sigmoid in the chromosphere corresponds to a higher squashing factor Q, displaying irregular shape. However, in some cases observed by Savcheva et al. (2012, 2015), the bald patch separatrix surface bifurcates gradually and transforms into the double J-shaped QSL. These results suggest that the structure of flux rope are quite complex.

The interaction between the sigmoid and the null point under the fan spine structure can be regarded as the triggering mechanism of the quasi-circular ribbon flare (Jiang et al. 2013, 2014; Sun et al. 2013; Vemareddy & Wiegelmann 2014; Joshi et al. 2015). Jiang et al. (2013, 2014) studied the eruption of a flux rope underneath the fan dome and found that the magnetic reconnection of the sigmoid caused the initial expulsion, which finally triggered the reconnection at the magnetic null point. In our case, the erupting sigmoid also caused a quasi-circular ribbon flare associated with the null point reconnection. Indeed, the positive polarity of the bipole was pushed toward a nearby negative polarity field, which triggered the sigmoid to rise. Furthermore, the null point in the 171 Å image was examined, and is in line with the NLFFF extrapolation. Such an inverse-Y structure has never been reported in other examples flux rope/filament eruption (e.g., Sun et al. 2012). This site is favorable for reconnection between different flux components in a fan spine structure. After experiencing magnetic reconnection, the magnetic flux rope structure was destroyed, and some material flowed along the spine-like loops in the form of the jet. As proposed by Moore et al. (2010), this event can be described as a blowout jet phenomenon. When the emerging field with appreciable shear or twist interacts with the ambient field, the core field containing a filament may erupt violently. Previous research has already demonstrated that small-scale filament eruption can lead to a blowout jet when erupting under ambient field lines (e.g., Shen et al. 2011, 2012; Sterling et al. 2015, 2016; Hong et al. 2016). Meanwhile, a quasi-circular ribbon was clearly observed clearly. It showed a fast drift of the emission along the direction of the magnetic bipole rotation. This process can be interpreted as a slip-running magnetic reconnection, which is similar to counterclockwise brightening motions observed by Masson et al. (2009), Wang & Liu (2012), and Sun et al. (2013).

No exact mechanism has been proposed for the triggering of a quasi-circular ribbon associated with the rotation of a magnetic bipole in a fan spine structure. In order to understand the exact mechanism, more detailed work is required to understand this kind of flare. In the future, we would expect a reconnection model to interpret our observations, i.e., a quasi-circular ribbon flare via magnetic bipole rotation.

We thank the anonymous referee for providing detailed suggestions and comments that significantly improved the presentation of this paper. We are grateful to the AIA, HMI, and IRIS teams for data support. This work is supported by the Natural Science Foundation of China (11333007, 11403098, 11473065, 11573012, 11503081, 11503082, and 11633008) and the CAS "Light of West China" and "QYZDJ-SSW-SLH012" Programs.