Witnessing magnetic twist with high-resolution observation from the 1.6-m New Solar Telescope

Magnetic flux ropes are highly twisted, current-carrying magnetic fields. They are crucial for the instability of plasma involved in solar eruptions, which may lead to adverse space weather effects. Here we present observations of a flaring using the highest resolution chromospheric images from the 1.6-m New Solar Telescope at Big Bear Solar Observatory, supplemented by a magnetic field extrapolation model. A set of loops initially appear to peel off from an overall inverse S-shaped flux bundle, and then develop into a multi-stranded twisted flux rope, producing a two-ribbon flare. We show evidence that the flux rope is embedded in sheared arcades and becomes unstable following the enhancement of its twists. The subsequent motion of the flux rope is confined due to the strong strapping effect of the overlying field. These results provide a first opportunity to witness the detailed structure and evolution of flux ropes in the low solar atmosphere.

M agnetic flux ropes are a group of twisted magnetic fields writhing about each other and rotating around a common axis. The importance of these helical, current-carrying magnetic flux systems was demonstrated long ago in plasma physics laboratories, such as in the experimental and modelling research with the tokamak 1,2 . As the toroidal plasma current in a tokamak produces a hoop force that expands the twisted fields along the major radius, the tokamak and similar experiments were designed to constrain this expansion by adding a strapping field, reducing the effect of the torus instability. Twisted flux ropes are also subject to kink instability 3 , where the rope axis itself can evolve into a helical structure when the flux rope twist reaches a certain threshold 4 . The structure of magnetic flux ropes associated with solar eruptions and interplanetary activities have received significant attention with the application of basic plasma physics. For example, the linkage between the solar plasma and tokamaks was discussed recently 5 . In the large scale, magnetic flux ropes are found in the interplanetary magnetic clouds 6 , which may interact with Earth's magnetic field to generate geomagnetic storms. Near the solar surface, there are evidences that different branches of magnetic loops could reconnect and form a flux rope during the eruption process [7][8][9] . On the other hand, some studies also suggest that flux ropes are built gradually and may already exist before eruptions 10,11 . Solar magnetic configurations prone to eruptions have been of great importance for space weather, which increasingly affects the modernization of human activities. There are a number of models that describe the initiation mechanism of solar eruptions, such as catastrophe or instability 12 and magnetic breakout 13 . One of the eruptive magnetic field configuration related to flux ropes is the so-called sigmoid 14 : an S-or inverse S-shaped magnetic field structure as seen in soft X-rays 15 and extreme ultraviolet 16 . In a qualitative cartoon picture 17 , the onset of a sigmoid eruption begins when the highly sheared inner legs of the two branches of the sigmoidal fields are joined via magnetic reconnection 18 . This initial stage of eruption produces a low-lying shorter loop across the magnetic polarity inversion line (PIL) and a longer twisted flux rope linking the two far ends of the sigmoid. The next stage proceeds when the formed flux rope becomes unstable (due to, for example, the torus instability) and erupts outward to become a coronal mass ejection. However, the insufficient spatial resolution of coronal images predominantly used by previous observational studies of flux ropes seriously hampers an unambiguous and detailed identification of flux ropes and their relation to eruptions. Moreover, the evolution of flux ropes has not been observed in the low solar atmosphere such as the chromosphere.
Here we report on clear observational evidence of a flaring twisted flux rope, taking advantage of H-alpha and He I 10,830 Å images at high resolution (60 and 100 km, respectively) obtained by the recently built 1.6 m New Solar Telescope 19,20   high time cadence (B15 s), thus providing a unique opportunity for a fine-scale assessment of evolving structures in the low atmosphere. An overall inverse S-shaped flux bundle (SFB) is initially observed to lie along the magnetic PIL, from which a set of loops appear to peel off and grow upward into a multi-stranded twisted flux rope within about 2 min. In the meantime, compact brightenings at the footpoints of the loop threads extend to form two elongated flare ribbons. These observations are supplemented by a nonlinear force-free field (NLFFF) extrapolation model 21 based on the surface vector magnetogram taken by the Helioseismic and Magnetic Imager (HMI) telescope 22 on board the Solar Dynamic Observatory. Hard X-ray (HXR) observation of the flare recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) telescope 23 is also used to reveal the likely energy release sites. We suggest that in this event, a low-lying single flux rope is embedded in sheared arcades. Following the enhancement of its twists, possibly driven by sub-surface motion, the flux rope becomes unstable. It is also possible that the two groups of the closely lying sheared arcades could reconnect to contribute to the active flux rope. The subsequent motion of the flux rope is, however, confined because of the strong strapping effect of the overlying field. These significant results provide a first opportunity to witness the detailed structure and evolution of flux ropes in the low solar atmosphere.

Results
BBSO/NST observation. On 11 August 2013, we observed an active magnetic flux rope and its associated GOES-class C2.1 flare around 19:30 UT in NOAA Active Region 11817. We present in Fig. 1 the H-alpha line-centre images at selected instances and a corresponding magnetic field on the surface. Owing to the unprecedented high resolution of NST, great details can be visualized. The full dynamics of evolution can be better seen in Supplementary Movie 1. It can be easily recognized that initially there is an overall inverse SFB lying along the PIL (the white dotted line in Fig. 1f). This SFB mainly consists of two branches of sheared arcade loops that seemingly cross and join near the centre (Fig. 1a). From about 19:15 UT (12 min before the event), the outside of these two branches of arcades (especially the eastern one; pointed to by the white arrows) appear to become weakened, while the inner loops (pointed to by the orange arrow) are enhanced (cf. Fig. 1a,b). At the beginning of the event, a bunch of long loop threads start to peel off from the SFB (pointed to by the yellow arrows in Fig. 1c,d). These threads seem to wrap around the entire SFB, with obvious brightenings seen at their two footpoints (pointed to by the red arrows) near the two ends of the SFB. In about 2 min, the threads rapidly expand and rise upward, and grow into a multi-stranded field structure with apparent twist and writhe clearly representing a flux rope (traced by the yellow dashed line in Fig. 1e). As clearly witnessed by  Magnetic field structure. Disentangling the topology of the SFB as observed with BBSO/NST in projection is crucial for understanding the nature and properties of the flux rope. However, vector magnetic fields of higher atmosphere (for example, chromosphere and corona) are not routinely measured with the present instrument. To shed light on the three-dimensional magnetic field structure, we thus construct a NLFFF model at the pre-event time and plot some selected representative field lines in Fig. 3. Obviously, the extrapolated field lines coloured blue bear a reasonable resemblance to the morphology of the SFB seen in H-alpha (see Fig. 1b), showing in general two branches of arcade loops (AB and CD) that are highly sheared when passing each other along the PIL (we note that there may not exist a clear separation between the AB and CD domains). Importantly, we also find that below the blue field lines, there lies a group of longer field lines (coloured red) that directly connect the two ends of the SFB from A to D. These field lines AD might correspond to the loops observed in He I 10,830 Å as well as H-alpha offbands at a lower height (see Fig. 2a-c), as also clearly demonstrated in Fig. 4a. A side view of the red field lines AD is presented in Fig. 3b. On the basis of the force-free field extrapolations, we can  further derive the magnetic twist number of a field line as 1 4p aL, where a is the force-free parameter and L is the field line length. It is obtained that the mean twist number of loops AB and CD is about 0.8 turns and that of AD is about 1.1 turns. Therefore, we speculate that the configuration of the SFB may represent a transition from twisted loops or flux ropes (for example, AD) to sheared arcades (for example, AB and CD). This may also be implied by the high-resolution BBSO/NST H-alpha images. We caution, however, that the NLFFF approach has limitations. These include that it does not take account of the plasma, and that it cannot be used to model the process of magnetic reconnection that involves non-force-free field.
Confined motion. It is worth mentioning that the aforementioned flux rope activity was not observed to develop into a coronal mass ejection. This suggests that the flux rope motion may be confined or failed. To shed light on this phenomenon, we calculate the decay index, defined by n ¼ À dlog(B)/dlog(h), which can gauge the likelihood of eruption in the torus instability model. Here B is the strength of the horizontal component of the overlying potential field, h is the height above the surface and n41.5-2.0 is the critical instability condition 24 . The calculation is performed above locations of the central portion of the PIL (the white dotted line in Fig. 3) underlying the flux rope. From the result plotted in Fig. 5, we can see that a flux rope would experience a decay index of the critical value at about 18 Mm, which is much higher than the maximum height (B4 Mm) of the present flux rope of interest. This means that the magnetic field overlying the flux rope may have a strong strapping effect that prevents a full flux rope eruption. Nevertheless, the twisted flux rope may reconnect with the ambient field and reform as a less twisted field 25,26 .

Discussion
On the basis of the BBSO/NST images and the NLFFF model result, we infer possible scenarios for this flux rope activity. The most likely explanation is that the twisted flux rope (modelled as loops AD underlying the SFB structure) may become unstable due to kink instability. Justifications for this view are discussed as follows. First, we show in Fig. 6 the maps with a larger field of view of twist number obtained by integrating the force-free parameter a along field lines. Note that a transient enhancement in the twist number at the footpoint regions (within the dotted ellipses) of the field lines similar to AD occurred at 19:10:24 UT, for a period before the onset of the event. Therefore, the subphotospheric motion may play a significant role in enhancing the twist and destabilizing the flux rope. Second, the NLFFF model indicates the existence of such a flux rope, with a twist number comparable to that visualized in the high-resolution BBSO/NST observation. Third, it is found that on the surface, the opposite magnetic polarities of this active region exhibit an overall converging and shearing motions, which may be favourable for the gradual build-up of flux ropes 27 . These motions are obvious when observing the TiO time sequence images (see Fig. 4b and Supplementary Movie 4) and are clearly shown in the derived flow field (see Fig. 4c). Fourth, the interaction between this rising flux rope and the SFB can explain the brightenings of the flare ribbons with the standard two-ribbon flare model. However, it is also possible that the magnetic reconnection between the sheared arcades contributes to the active flux rope. Specifically, a magnetic reconnection may occur between sheared arcades 17,27 loosely denoted here as AB and CD. The main evidence is that the site of coronal magnetic reconnection, although not directly visible, may be manifested by a strong HXR-emitting source (the central contours in Fig. 1f) imaged by RHESSI around the flare peak. This source is located apparently between AB and CD, consistent with the speculated occurrence of reconnection. In the meantime, compact HXR emissions (left and right contours in Fig. 1f) are also produced near the two footpoints A and D, indicating enhanced precipitating electrons around the flare maximum. The weakening of the arcade structure before the flare, as shown in Fig. 1a,b, is also consistent with this view. Nevertheless, the sheared arcades still have a maximum height (B6 Mm) well below the torus instability regime (see Fig. 5).
In conclusion, high-resolution images obtained by BBSO/NST make it possible to witness, for the first time, the detailed structure and evolution of a twisted flux rope in the low solar atmosphere. Observations with such a high resolution are invaluable in the studies of flux ropes, a magnetic structure important for energetic solar and interplanetary phenomena.

Methods
Observations and data processing. The essential observational evidence of the magnetic flux rope is provided by BBSO/NST. The telescope has gone through a few upgrades for its focal plane instrument and adaptive optics system. The latest upgrade of the high-order adaptive optics system uses 308 sub-apertures, which means that the telescope aperture is divided into 308 small telescopes so as to compensate and correct the atmospheric disturbances. Together with the speckle image reconstructions 28 , diffraction-limited imaging can thus be achieved. Here we use data (as shown in Fig. 1a-e, Fig. 2a,b, Fig. 4a and Supplementary Movies 1-3) from the Visible Imaging Spectrometer (VIS) at BBSO, which saw its first light with NST in the summer of 2013. This Fabry-Pérot filter-based system scans cross spectral lines in the range of 5,500-7,000 Å with millisecond steps. The H-alpha images have a spatial resolution of B0.068 00 (50 km), and the cadence is 15 s for VIS to complete a scan at a 0.2 Å step from À 1.0 to þ 1.0 Å around the H-alpha line centre. In addition, we also use He I 10830 Å images (as shown in Fig. 2c-f) taken by the InfraRed Imaging vector Magnetograph 29,30 (IRIM) at BBSO and the broadband TiO (a proxy for the photosphere at 7,057 Å) images (as shown in Fig. 4b and Supplementary Movie 4). The cadence is 15 s and the spatial resolution is about 120 km for 10,830 Å and 65 km for the TiO data. While H-alpha off-bands and line-centre images cover a wide height range (B1,500-3,000 km), the He I 10,830 Å line is formed around 2,000 km above the photosphere. The time sequence of TiO images can help to examine the photospheric flows (as shown in Fig. 4c), which are traced with the differential affine velocity estimator 31 , with the window size set to 19 pixels for feature tracking. Moreover, context information on the magnetic field structure of the solar photosphere (as shown in Fig. 1f) is provided by the vector magnetograms taken by the HMI instrument on the Solar Dynamic Observatory.
Signatures of magnetic reconnection can be revealed using the HXR emission due to the accelerated electrons, which was recorded for this flare event by RHESSI. The image of HXR sources, presented as contours in Fig. 1f, is reconstructed with the PIXON algorithm 32 using detectors 1 and 3-8, and is integrated from 19:29:45 to 19:30:45 UT in the 25-50 keV energy band.
Magnetic field modelling. The magnetic field model, as presented in Figs 3 and 4a, is constructed using the NLFFF extrapolation technique 21 . To obtain a chromospheric-like boundary data satisfying the force-free condition, a pre-processing procedure 33 is first applied to the 2 Â 2 rebinned Space-Weather HMI Active Region Patches 34 data. Then the three-dimensional magnetic field is extrapolated using a 'weighted optimization' method 35,36 . The extrapolation calculation is performed within a box of 584 Â 248 Â 256 uniform grid points, which corresponds to about 426 Â 181 Â 187 Mm 3 . 36. Wiegelmann, T. Optimization code with weighting function for the reconstruction of coronal magnetic fields. Sol. Phys. 219, 87-108 (2004).