Observing Formation of Flux Rope by Tether-cutting Reconnection in the Sun

A magnetic flux rope is a distinctive helical structure that contains magnetic field lines wrapping more than one turn around the central axis. From theories and observations, they have been confirmed to exist in the solar corona (e.g., Forbes 2000; Fan & Gibson 2004; Török & Kliem 2005; Cheng et al. 2011; Zhang et al. 2012; Li & Zhang 2013). Magnetic flux ropes can usually be reconstructed using nonlinear force-free field models based on vector magnetic field observations (Régnier & Amari 2004; Canou & Amari 2010; Guo et al. 2010; Jiang et al. 2014). Magnetic flux ropes play an important role in solar activities, such as filament/prominence eruptions and coronal mass ejections (Dere et al. 1999; Patsourakos et al. 2013; Yan et al. 2014). Filaments seen in Hα and sigmoids in hot channels are often considered to be the observational features of magnetic flux ropes (Yang et al. 2014). So far, it is not quite clear where and how magnetic flux ropes form in the solar atmosphere. There are two accepted theories to explain the formation of magnetic flux ropes supported by numerical simulations and observations. One theory is the emergence model that flux ropes form in the convection zone and emerge into the corona due to the magnetic buoyancy effect (Fan 2001; Manchester et al. 2004; Okamoto et al. 2008, 2009). The other one is the reconnection model that flux ropes can be directly formed in the corona by the reconnections between coronal arcades due to convergence and vortex motions (Moore et al. 2001; Aulanier et al. 2010; Amari et al. 2011).

Magnetic reconnection is a fundamental physical process through which magnetic energy can be released as thermal and kinetic energy, and thus it is usually related to solar activities and eruptions (e.g., Xue et al. 2016a). Tether-cutting reconnection, one theoretical model proposed by Moore & LaBonte (1980) and developed by Sturrock (1989), Moore & Roumeliotis (1992), and Moore et al. (2001), is used to explain the formations of magnetic flux ropes and the triggering mechanism of eruptions. In this model, a single, highly sheared magnetic bipole is involved, and overlying envelope magnetic arcades may also be present but are not necessarily required. Magnetic reconnection occurs between the inner legs of the sheared core fields, often under a filament. And then a longer twisted flux rope connecting the far ends of the core fields and shorter newly loops are formed over the polarity inversion line (PIL). Because of the destabilization of the system, the reconnection may result in two possible processes. Either the flux rope erupts successfully or its eruption is confined. van Ballegooijen & Martens (1989) proposed a similar model named "flux cancelation" to show the formations and eruptions of solar prominences. So far, tether-cutting reconnections have been investigated in many papers (e.g., Sterling & Moore 2003; Kim et al. 2008; Taftery et al. 2010; Liu et al. 2013; Chen et al. 2014, 2016).

The New Vacuum Solar Telescope (NVST; Liu et al. 2014) is a one-meter ground-based vacuum telescope in the Fuxian Solar Observatory (FSO) of the Yunnan Observatories, Chinese Academy of Sciences (CAS). It is mainly composed of four instrumentations: the adaptive optics system, the polarization analyzer, the imaging system, and the spectrometers. The main goal of NVST is to observe fine structures and their activities/eruptions in lower atmospheres simultaneously. The high-resolution image can be reconstructed using at least 100 short exposure images (see Xiang et al. 2016). Since commencing operations, many fine-scale and small-scale solar events are studied using the NVST data, for example, magnetic reconnections (Yang et al. 2015; Xue et al. 2016a), filaments/prominences (Shen et al. 2015; Yan et al. 2015a, 2015b; Xue et al. 2016b), Ellerman bombs (Tian et al. 2016), flux ropes (Yan et al. 2016), and jets (Hong et al. 2016). In this Letter, using high-resolution and multi-wavelength data obtained by the NVST and Solar Dynamic Observatory (SDO; Pesnell et al. 2012), we present the detailed observations of tether-cutting reconnection between two sets of highly sheared arcades and its resulting in the formation of a flux rope in NOAA AR 11967 on 2014 February 2.

The Hα images, observed by the NVST at line-center channel (6562.8 Å, corresponding to chromosphere), are used to present the process of the tether-cutting reconnection and fine structure of the newly formed flux rope. The NVST observations are chosen from 03:30 UT to 06:26 UT on 2014 February 2, and they have a cadence of ∼12 s. The full field of view (FOV) of the Hα observations is 154'' × 154'' with a spatial resolution of 033. The extreme ultraviolet (EUV) images observed by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012), including the 304 Å (He ii, 0.05 MK), 171 Å (Fe ix, 0.6 MK), 193 Å (Fe xii, 1.3 MK and Fe xxiv, 20 MK), 335 Å (Fe xvi, 2.5 MK), 211 Å (Fe xiv, 2 MK), 94 Å (Fe xviii, 7 MK), and 131 Å (Fe viii, 0.4 MK and Fe xxi, 11 MK) channels, show the reconnection at higher temperatures. The photospheric magnetograms obtained by the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) are also used to study the evolution of the magnetic fields of AR 11967 and connectivities of the arcades and the flux rope.

On 2014 February 2, NVST observes a part of NOAA AR 11967 (see Figure 1(a)) that is located at S13E04 with a βγδ magnetic configuration (Figure 1(b); an HMI line-of-sight (LOS) magnetogram). The AR is very active and produces a lot of C- and M-class flares. The region that we focus on in this Letter is marked with a red rectangle in Figure 1(a), which represents the FOV of Figures 1(c)–(e). Two sets of magnetic arcades can be observed clearly in the NVST Hα and AIA 304 Å images (Figures 1(c)–(d)). One set of arcades shows a shorter C-shaped structure, labeled by L1 and marked by a cyan dotted line and arrows. Another set displays a longer arch-shaped structure, labeled by L2 and marked by a blue dotted line and arrows. The high-resolution observations of the NVST show that the arcades are composed of many fine threads along their axes. Figure 1(e) displays the magnetogram overlaid by the positions of L1 and L2 (the cyan and blue dotted lines, respectively). It is found that the southern footpoint of L1 is anchored in the main negative polarity (N) and the northern footpoint in a smaller positive polarity (P1); L2 connects N and another positive polarity (P2). Although the magnetic configuration is not a simple bipole, the two sets of arcades are highly sheared across the PIL. This magnetic field configuration is in agreement with that required by the tether-cutting model before reconnection (Moore & LaBonte 1980; Moore et al. 2001). To investigate the evolution of the magnetic fields in detail, along slice S1 indicated by the yellow line in Figure 1(e), a time-slice map is computed and shown in Figure 1(f) in which the polarity P1 is marked by a red dotted curve. It is found that before and during the reconnection, P1 moves from the southeast to the northwest, and this movement leads L1 to be more sheared (see the animation of Figure 1). It is also shown that P1 moves most quickly in the period from about 03:40 UT to about 05:25 UT with a mean velocity of 0.30 ± 0.02 km s⁻¹. During the reconnection, the polarity P1 undergoes magnetic cancelation with a portion of the main negative polarity N. We calculate the positive flux of P1 in the area marked by a green rectangle in Figure 1(e) and display the result in Figure 1(g). It shows that the magnetic flux starts to decrease at ∼04:13 UT. Then it decreases from 3.1 × 10¹⁹ Mx (∼04:13 UT) to 1.5 × 10¹⁹ Mx (∼05:34 UT) with a rate of 3.2 × 10¹⁵ Mx s⁻¹.

Figure 2 displays the evolutions of the tether-cutting reconnection and the formation of the flux rope observed by the NVST in Hα channel (see the animation of Figure 2). Before the reconnection, the northern leg of L1 is close to the eastern leg of L2, and the footpoints of these legs are rooted in the opposite polarities: the northern footpoint of L1 in the positive polarity and the eastern footpoint of L2 in the negative polarity (Figure 2(a)). L1 and L2 begin to reconnect at ∼04:07 UT. Several Hα images with smaller FOV are displayed in Figures 2(b)–(g) to show the reconnection in detail. The reconnection site, marked by the red circle in Figure 2(b), is close to the northern leg of L1 and eastern leg of L2 (Figure 2(b)), between which the reconnection occurs. Before about 04:25 UT, a part of L2's magnetic arcades reconnect and disappear quickly (indicated by the black arrow in Figures 2(b)–(c)). Meanwhile, the reconnection produces many newly formed longer loops and shorter loops indicated by the pink and red lines in Figure 2(d). The longer loops connect P2 and N, and the shorter loops connect P1 and N. A brightening region, marked by white arrows, appears below the longer loops, indicating that the plasma is heated to a higher temperature due to the reconnection. Then, the reconnection continues to occur, and the magnetic field lines connecting P2 and N increase gradually, and the brightening exists continuously beneath the longer loops that is consistent with the tether-cutting model. Meanwhile, during the reconnection, a lot of hot plasma are observed to propagate along the arcades from the reconnection site to the footpoints, especially in the EUV channels (see the next paragraphs). It may be caused by the magnetic energy being released into thermal and kinetic energy of particles accelerated at the reconnection site, and the plasma is heated to a higher temperature due to the reconnection (e.g., Xue et al. 2016a). However, the outflowing plasma is very weak in Hα images (see the animation of Figure 2). At the end, a flux rope with an M-shaped helical structure is formed. It connects far footpoints, P2 and N (Figure 2(h)). It is found that the flux rope consists of many twisted threads wrapping around a central core. Two clear threads are indicated by the black and white dotted lines in Figure 2(g). One can see that they intertwine with each other, indicating that the flux rope has a left-handed twisted structure (Martin 1998). In the NVST Hα images (Figures 2(a) and (h)), it also shows that the two legs of the flux rope are similar to the southern part of L1 and the western part of L2. However, the dip part of the flux rope rises slowly, probably owing to unbalance between the upward magnetic pressure force and downward magnetic tension force. Based on the time-slice map along the slice S2 marked by the black dotted line in Figure 2(f), the rising velocity of the flux rope is calculated to be 0.61 ± 0.07 km s⁻¹ (Figure 2(i)). This is consistent with the observational characteristics of the tether-cutting reconnection and further confirms the occurrence of magnetic reconnection (see also Sterling et al. 2011). At about 07:53 UT, another magnetic reconnection takes place between the flux rope and the ambient magnetic loops, and leads to the eruption of the flux rope finally. NVST observes the eruption of the flux rope, but the eruption is not analyzed here.

The process of the tether-cutting reconnection and the formation of the flux rope are also shown in the EUV images taken by SDO/AIA (see the animation of Figure 3). In the 304 Å images (Figures 3(a)–(f)), in addition to the brightening (white arrows) appearing beneath the newly formed flux rope (black arrows) and the clear twisted threads of the flux rope (see Figure 3(f)), many hot outflows propagating from the reconnection site to the footpoints along the magnetic arcades are observed intermittently. They show elongated brightening plasma flows. When they move away from the reconnection region, they become darker and darker and disappear gradually. It should be noted that, in this event, the outflows propagating in three directions to the footpoints N and P2 are observed at the same time (indicated by the green arrows in Figure 3(d)). Theoretically, the outflows moving from the reconnection site to P1 should exist. However, due to the projection effects and obscuration by surrounding material, it is not observed by NVST and SDO/AIA. Here, the outflows are similar to another phenomena, double-sided jets whose arms point in opposite directions caused by reconnections (e.g., Wang & Muglach 2013). Figures 3(g)–(l) display the images observed with SDO/AIA in hot channels (171, 193, 211, 335, 94, and 131 Å, respectively) at 04:57 UT. They show that the brightenings and the outflows are observed in all six channels, suggesting that the brightenings are multi-temperature and heated to higher temperature by the reconnection. The newly formed flux rope is not observed in the higher-temperature channels (e.g., 94 and 131 Å), indicating the flux rope has a lower-temperature structure.

To study the dynamic characteristics of the outflows, along the three slices S3, S4, and S5 from the reconnection site to the footpoints as indicated by green dotted lines in Figure 3(e), three time-slice maps are obtained using AIA 304 Å images and displayed in Figures 4(a)–(c), respectively. The outflows along S3 move farthest from the reconnection site to the polarity P2. Here, we choose six typical outflows marked by the green dotted lines in Figure 4(a) and calculate their velocities through fitting the motion with linear functions, and the resulting velocities are from 24 ± 1 km s⁻¹ to 49 ± 2 km s⁻¹ with an average velocity of 27 ± 1 km s⁻¹. Along S4, the outflows propagate from the reconnection site to the polarity N (Figure 4(b)). Using the same method, the velocities of the outflows along S4 are calculated to be from 45 ± 8 km s⁻¹ to 69 ± 5 km s⁻¹ resulting in an average velocity of 57 ± 3 km s⁻¹, which are the fastest motions of the hot plasma. The outflows propagating from the reconnection site to the polarity N along S5 are the shortest ones, less than about 5 Mm (Figure 4(c)), and their velocities are from 34 ± 3 km s⁻¹ to 49 ± 8 km s⁻¹ with an average value of 39 ± 2 km s⁻¹.

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Although the tether-cutting model has been proposed for more than 30 years, there are few observations confirming the formation of a flux rope due to tether-cutting reconnection (e.g., Kumar et al. 2015; Yang et al. 2016). Here, thanks to the high-resolution data of NVST and SDO, we observe a very good case of the formation of a left-handed twisted flux rope caused by the tether-cutting reconnection. Some solid observational evidence for the tether-cutting reconnection is obtained from the observations of NVST and SDO: (1) changes of magnetic connection between two sets of highly sheared arcades; (2) brightening in multiple wavelengths; (3) hot outflows from the reconnection site with velocities from 24 ± 1 km s⁻¹ to 69 ± 5 km s⁻¹; (4) the formation of a longer flux rope; (5) slow-rise motion of the flux rope with a velocity of 0.61 ± 0.07 km s⁻¹; (6) flux cancelation between P1 and N with a rate of 3.2 × 10¹⁵ Mx s⁻¹. Additionally, the flux rope and reconnection are observed most clearly in the Hα channel; we deduce that the reconnection may occur in the lower atmosphere (e.g., the chromosphere), similar to that predicted by the models. Moore & LaBonte (1980) and Moore et al. (2001) proposed that tether-cutting reconnections occur at low altitudes below filaments along the PIL. In another similar model, "flux cancelation," van Ballegooijen & Martens (1989) suggest that reconnection takes place at a height of only a few times H_p above the base of the photosphere, where the H_p (=kT_e/mg) is the local pressure scale height of the photosphere.

To better illustrate the process of the tether-cutting reconnection and the formation of the flux rope, we sketch several cartoons in Figure 5 from different views: the actual observed view (Figures 5(a)–(d)) and the view paralleling to the solar surface (Figures 5(e)–(h)). Two sets of highly sheared magnetic arcades are shown in Figures 5(a) and (e) using cyan and blue lines that connect different magnetic polarities. The reconnection occurs between the two closer legs. At first, the inner arcades interact and reconnect and form a longer loop indicated by a pink line connecting far footpoints (P2 and N2) and a shorter loop indicated by a red line (Figures 5(b) and (f)). Then, the outer arcades start to reconnect, and other longer and shorter loops appear (Figures 5(c) and (g)). Meanwhile, the newly formed longer loop intertwines with that formed previously, and they form a twisted structure. With the reconnection, the outermost arcades reconnect with each other (Figures 5(d) and (h)). Finally, the flux rope forms with a concave-up-shape structure in the middle (see also Figure 2(h)). One possible way to produce the quasi-steady concave-up-shape structure in the middle of the flux rope is that there are overlying arcades. However, the middle part of the flux rope still rises slowly with a velocity of 0.61 ± 0.07 km s⁻¹ accompanied by the formation of more and more magnetic field lines connecting P2 and N due to the reconnection.

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In the "flux cancelation" model, van Ballegooijen & Martens (1989) suggested that flux cancelation at the neutral line of sheared arcades may drive magnetic reconnection and leads to the formation of helical field lines. Moore & Roumeliotis (1992) found that tether-cutting reconnection is accompanied by flux cancelation in the sheared core. In our observations, because of the movement of P1, L1 becomes more and more sheared before and during the reconnection, and this may trigger the tether-cutting reconnection. At the same time, we find that the magnetic fluxes start to cancel between P1 and a part of N at about 04:13 UT after the onset of the reconnection. We proposed that a set of shorter arcades appear at the lower atmosphere produced by the reconnection and then are pulled down through the lower atmosphere and submerge under the photosphere due to unbalances of the upward and the downward forces. This process exhibits magnetic cancelation in the magnetic field evolution. During tether-cutting reconnections, magnetic cancelations are frequently seen in the observational events (Kumar et al. 2015; Yang et al. 2016; Kumar et al. 2017).

We gratefully acknowledge insightful and constructive comments and suggestions by the anonymous referee that led to significant improvements of this Letter. We thank the NVST and SDO teams for providing high-resolution data. This work is sponsored by the National Science Foundation of China (NSFC) under grant numbers 11503080, 11373066, 11633008, 11573012, 11373065; CAS Key Laboratory of Solar Activity, National Astronomical Observatories under number KLSA201612, CAS "Light of West China" Program, and Youth Innovation Promotion Associated CAS (No. 201156).