Transient rotation of photospheric vector magnetic fields associated with a solar flare

As one of the most violent eruptions on the Sun, flares are believed to be powered by magnetic reconnection. The fundamental physics involving the release, transfer, and deposition of energy have been studied extensively. Taking advantage of the unprecedented resolution provided by the 1.6 m Goode Solar Telescope, here, we show a sudden rotation of vector magnetic fields, about 12–20° counterclockwise, associated with a flare. Unlike the permanent changes reported previously, the azimuth-angle change is transient and cospatial/temporal with Hα emission. The measured azimuth angle becomes closer to that in potential fields suggesting untwist of flare loops. The magnetograms were obtained in the near infrared at 1.56 μm, which is minimally affected by flare emission and no intensity profile change was detected. We believe that these transient changes are real and discuss the possible explanations in which the high-energy electron beams or Alfve′n waves play a crucial role.


Introduction
It is well accepted that many solar flares, and other violent eruptions such as coronal mass ejections (CMEs), result from magnetic reconnection occurring in the corona. However, many manifestations are visible in the lower solar atmospheres, i.e. the chromosphere and photosphere. In addition to the radiation, significant changes of the magnetic fields have been observed in the literature 1;2;3;4;5;6 . Most of them are permanent changes, while transient changes are rarely reported, and are suspected of being instrumental artifacts. Permanent magnetic changes are irreversible phenomena of photospheric fields in reaction to the flare impacts, usually during strong flares greater than M-class. Shear flows measure horizontal motions of magnetic features along both sides of the magnetic polarity inversion line (PIL). Previous observations show the spatial correlation between strong shear flow and flare emission 2;7 . More importantly, shear flow can drop significantly after the flare 3;8;5 , indicating that a certain amount of magnetic free energy has been released. Tilt angle, also known as inclination angle, is determined by the ratio between vertical and horizontal magnetic components. During flares, the reconnection rearranges the topology of magnetic loops and the tilt changes consequently. Direct measurements of vector fields have shown that horizontal fields increase near the PIL and decrease in the nearby penumbral regions during flares 9;8;6 . As a consequence, sudden intensity changes of magnetic features (usually the penumbra) are observed 1;10;11;12 . Bodily rotation is one of the intrinsic properties of sunspots or sunspot groups first observed by Evershed (1910) 13 , which are usually gradual and continue during the entire lifetime. On the other hand, rapid rotations associated with X-class flares were reported 14;5 and attributed to the torque introduced by the change of horizontal Lorentz force 15 . Using the data with higher spatiotemporal resolution obtained by the 1.6 m Goode Solar Telescope (GST, formerly known as the New Solar Telescope 16 ) at Big Bear Solar Observatory (BBSO, 17 ), the sudden rotation is found to be nonuniform and synchronous with the flare ribbon propagation 18 .
In contrast to the stepwise temporal profile in permanent changes, the characteristic profile of a transient change is more like a δ function in time. Transient changes were rarely observed in the literature. An example is the magnetic anomaly or magnetic transient, a temporal reversal of magnetic polarities measured simultaneously with flare emission, first reported by 19;20 using BBSO data. The plausible explanation is that the profile of the Fe i line at 5324Å, used for the magnetic measurements, turned from absorption to emission due to the flare heating at lower layers of solar atmosphere 19 . From space-based observations, magnetic anomalies were reported during an X5.6 flare observed by the Michelson Doppler Imager on board Solar and Heliospheric Observatory (SOHO/MDI) 21 and an X2.2 flare observed by the Helioseismic and Magnetic Imager on board Solar Dynamics Observatory (SDO/HMI) 22 . The authors drew similar conclusions that the polarity reversal is a consequence of the line profile change. Thus, the magnetic anomaly/transient is not intrinsic to the Sun, but an artifact in magnetic measurements due to the change of line profile.
In this paper, we present 1.56 µm vector magnetograms with the highest cadence and resolution ever obtained, which are much less subject to line profile changes, yet reveal a sudden increase of the azimuth angle. An M6.5 flare was well observed on June 22, 2015 with BBSO/GST using multiple channels, including the Visible Imaging Spectrometer (VIS) tuned to the Hα line, a Broadband Filter Imager (BFI) tuned to a continuum near the TiO line at 7057Å, and the Near InfraRed Imaging Spectropolarimeter (NIRIS) providing vector magnetograms using the Fe i line at 1.56 µm. The image scale of vector magnetograms is about 0 ′′ .083 pixel −1 and the cadence is about 90 s for a full set of Stokes measurements. The Fe i Stokes profiles are measured at 40 different spectral positions, which is much higher than that on space-based spectropolarimeters, such as MDI and HMI, and permits a check of possible changes in line profile due to enhanced emission, which are not seen.
The flare started around 17:39 UT and peaked at 18:23 UT in GOES 1-8Å soft X-rays. It lasted for several hours and our interest in this study focuses on the initial phase within the core region of the flaring areas. The host active region NOAA 12371 was close to the solar disk center at that time and therefore the geometric projection effect is small and was corrected easily. From the time sequence of azimuth maps, we clearly see a ribbon-like structure moving co-spatially and co-temporally with the flare emission in the Hα line. On average, the azimuth angles increased by about 12 • -20 • , indicating the local magnetic fields rotated counterclockwise. In contrast to the permanent changes of magnetic field, the azimuth change is a transient variation, which restored quickly to its original value after the flare ribbons swept through. By reviewing the existing models, such as Alf vén waves and induced magnetic fields, we found that they may play important roles but can not solely explain the observation.

Results
Overview of the Flare Two major flare ribbons are identified in the core area of the flare. The eastward-moving ribbon resides in the area of positive magnetic polarity and the westward-moving ribbon propagates in the region with negative magnetic polarity. We focus on the eastern ribbon, where azimuth angle increases are much more obvious. A change of azimuth angle can also be identified associated with the conjugate flare ribbon within negative magnetic fields, but it is dispersed and too weak to be precisely measured. The elongated flare ribbons represent multiple footpoints of parallel flare loops. For each individual loop, the change of azimuth angle on its footpoints indicates a twisting or untwisting of the loop. To determine whether the twist of the loop is increased or decreased, the difference between the azimuth angles of the measured magnetic field and that of the extrapolated potential fields are calculated, in which the latter was extrapolated with the Fourier transformation method 23;24 . As we will see below, the vertical component of magnetic field (B z ) and the extrapolated potential field (B p , derived from B z ), remains nearly constant during the flare. Therefore, the comparison of transverse components of observed and extrapolated fields, represented by the azimuth angle, can in principle indicate the variation of the twist.

Characteristics of the Azimuth Angle Variation
The Supplementary Movie S1 shows the time sequence of azimuth angle within a field of view (FOV) of the flare core region, running from 17:32:35 UT to 18:58:19 UT. It is clear that a ribbon-like feature propagates from the right to the left. This disturbance of azimuth angle along a narrow ribbon is co-spatial and co-temporal with the flare emission seen in Hα. In the panel (d) of Figure 1, a running difference map of azimuth angle is shown at 18:00:12 UT. The dark feature indicated by the pink arrow represents the change of azimuth angle and the white contours show the leading front of the Hα emission, indicating a close relationship with precipitating electron beams 25 . The slight offset of about 300 ∼ 500 km could be a projection effect, because the formation height of Hα is about few thousand km higher than the formation height of the NIR line at 1.56 µm. Other panels show the SDO/HMI white light image (panel (a)), an running difference image of Hα blue wing (−1.0Å) (panel (b)) and LOS magnetogram derived from NIRIS data (panel (c)). All of the images are within the same FOV, where the ribbon of interest resides. To examine the azimuth change, we resolved the 180 • azimuthal ambiguity in the transverse field using the minimum-energy method 26 , and removed the projection effects by transforming the vector magnetogram from observational image plane to heliographic-cartesian coordinate. Panel (e) presents a time-distance diagram of the running-difference Hα images. The slit is 3-pixel wide and its position can be found in panel (b). The bright feature represents the ribbon front of Hα emission, similar to the one in panel (b). In Panel (f), we display the time-distance diagram of running-difference images of the azimuth angle.
The slit width is 9 pixels, because the cadence of the vector magnetogram is 90 s, about 3 times of the cadence of Hα images. The white contour indicates the location of Hα ribbons in panel (e). It shows a good correlation between Hα emission and azimuth-angle change at different times. Such a correlation does not vary much at different slit positions.
The characteristic sizes of ribbon-like features are fundamental parameters. For instance, the ribbon front, which is the precipitation site of electrons, is found to be very narrow 27;28 . We follow the method described in Xu et al. (2016) 25 and Jing et al. (2016) 27 to measure the width of the azimuth ribbon, as shown in Figure 2. We use sparse running difference maps (the reference image is taken several frames prior to the target) to minimize the background noise. On average, the width of the region of azimuth angle deviation is about 570 km, which is comparable to the size of the dark ribbon (340 -510 km) in helium 10830Å 25 . It is not easy to measure the ribbon length quantitatively as the ribbon is segmented and noisy near the two ends. We estimate the length manually using the image taken at 18:00:12 UT and the result is about 13300 km.

Temporal Evolution of the Azimuth Angle Change and Correlation with Hα Emission
In order to study the temporal evolution of the disturbance, three representative regions (R1, R2 and R3, marked using white color) are selected on the propagating path of the azimuth transient, as shown in panel (a) of Figure 3. These representative slits are selected in the middle of the ribbon and away from the sunspot boundary, where the magnetic fields are also affected by the sudden sunspot rotation 18 in a more gradual manner. The corresponding temporal profiles are plotted in panel (b). The uncertainties are estimated using the points prior to the initiation of the flare. For instance, the standard deviation of the first 12 points is used as the error in R1. Let us use R3 as an example. The average azimuth angle suddenly increases by about 20 • , from the pre-flare value of 11.7 • to the flare peak time value of 31.5 • , with an uncertainty of 6.6 • . Therefore, the azimuth peak is significant as it is about three times of the uncertainty. In particular, we see that the azimuth peak coincides with the Hα emission (dashed curve), based on the results shown in Figures 1 & 3. For the other two regions, R1 and R2, the horizontal field rotates by 12 • and 18 • , with uncertainties of 2.5 • and 5.2 • , respectively. Using the potential field extrapolation, the azimuth angle of potential field is determined and plotted as dot-dash curves in panel (b). We see that the potential field azimuth remains at a certain level above the azimuth angle of the vector fields. Only at the flare peak time, the measured azimuth angle becomes closer to that in the potential field due to the sudden rotation. This is a 2D comparison, but is a good proxy of the 3D configuration, because the extrapolated potential fields are based on the measured vertical component, which did not vary like the azimuth angle did during the flare. Therefore, the difference of the magnetic shear between the measured field and the potential field can be represented by the azimuth angle, which is determined by the horizontal components of B x and B y . In the panels (c) and (d) of Figure 3, the total magnetic strength and the inclination angle are plotted as a function of time, respectively. These curves contain noise-induced fluctuations and no impulsive peak is identified as in the azimuth transient. An area (white box) is selected far away from the flare ribbons and is used as a reference in comparison to the regions with significant azimuth angle changes. We see irregular fluctuations but certainly no obvious peak associated with flare emission.

Discussion
In summary, we present a clear transient change of azimuth angle, associated with propagating flare ribbons which are footpoints of 3D magnetic loops. The major results are as follows: 1) The local magnetic vectors rotated about 12 • to 20 • simultaneously with flare emission. 2) The strong correlation between the azimuth transient and flare ribbon front indicates that the energetic electron beams are very likely to be the cause.
3) The measured azimuth angle becomes closer to that in the potential field indicating a process of energy release (untwist) of the flare loop.
Firstly, the observed field change is different from the magnetic anomaly reported previously. In that scenario, the profile of the spectral line used to measure the magnetic fields has changed. In our case, the line profiles remain in absorption and unchanged during the flare as shown in Figure 4. It is not surprising as the spectral line used by NIRIS is the Fe i line at 1.56 µm, which is formed very deep in the photosphere where almost no flare heating can reach except in some extremely strong flares 29 . In addition, we investigate the polarized raw data before inversion is done. On the Stokes I, Q, U and V maps as shown in Figure 5, an area similar to R3 is selected and the corresponding profiles before and during the flare are plotted. As we can see, the Stokes I and V components, in which V represents the circular polarization and determines the LOS magnetic fields, remain almost identical. However, the Stokes Q and U components that determine the transverse fields, vary significantly. Therefore, we believe that azimuth change is real from Stokes Q and U components and not affected by either flare emission or circular polarizations. This is the first time that transient field rotation is observed. We attempt to explain the effect by considering several existing models, which are discussed below.
Magnetic field induced by the electron beams is the most straightforward and intuitive model. The basic idea is that the penetrating electrons produce induced magnetic fields, which act on the original fields such that the combined fields point to new directions. This is equivalent to a field rotation. The downward precipitation of electrons, with negative charges, is equivalent to a upward current. According to Ampère's circuit law, self-induced magnetic field is generated around the ribbon. The ribbon width is much smaller than its length, so the latter can be treated as a half infinite wall. Therefore, to the left side of the ribbon front, the self-induced magnetic field points to the south (in solar coordinates) and the overall field will rotate counterclockwise. To the right side, the overall field will rotate oppositely, which however will be balanced by the self-magnetic field of the trailing electron beams that have decreased but have not been turned off. We can estimate the required current I using Ampère's law, B • ds = µ 0 I, in which the integration loop is 2l (two times the ribbon length, which is about 2 × 10 7 m). In order to induce a magnetic field of order 100 G, the required current is about 1.6 × 10 11 A, or an electron flux of 10 30 s −1 , a tiny fraction of the total electron flux (∼ 10 35 ) with energy greater than 20 keV derived from the RHESSI HXR spectra. Whether the azimuth angles of the combined fields increase or decrease is determined by the relative orientation between the original fields and the flare ribbon. If this angle is larger than 90 • , an increase is seen in front of the flare ribbon. The rotation effect is cancelled out behind the flare ribbon by the following opposite rotation effect. Since the fields point outward from a sunspot center, when the ribbon passes through the sunspot, the relative orientation changes and the azimuth angle should decrease. However, such a increase-decrease pattern is not observed. Although the magnitude of induced field matches with observations, the direction does not match.
The second model considers the effect by downward-drafting plasma 30 , which in our case is the precipitating electron beams. The authors modeled a scenario in which the cooling plasma moving down from the top of hot granules amplifies the magnetic twist when entering into denser layers, which is similar to our case. However, we see the flare loops become less twisted. Nevertheless, this model suggests that the hydrodynamic effects may be coupled with electrodynamic effects to affect the pre-flare magnetic fields.
By analyzing and modeling the Hα and Hβ data, Hénoux and Karlický, (2013) 31 found that emission lines can be polarized linearly by multiple effects, such as electron beams, return current and filamentary chromospheric evaporation. They found the degree of linear polarizations was about 3 ∼ 9%. However, in our case, there was no emission detected in the NIR line at 1.56 µm. The NIR line intensity profile remains in absorption during the flare. In addition, the azimuth change, or say the enhanced linear polarization was only found in front of the propagating flare ribbons in our event. But the polarized signal was identified on both sides of the flare ribbons in Hénoux and Karlický, (2013) 31 . Therefore, again we cannot draw a conclusion based on their model.
Alf vén waves 32 also have impacts on the magnetic fields. They are well known in heating the corona 33 , accelerating electrons during flares 34 and solar winds 35 . Alf vén waves can be generated by magnetic reconnection during flares 36;34 . In open magnetic field regions, for instance in solar wind, Alf vén waves were found in untwisted field lines both in observations 37 and simulations 38 . For closed field regions, such as the flare loops, Fletcher et al. (2008) 34 presented the large-scale Alf vén wave pulses, which accelerate electrons locally. Within non-uniform plasma, Alf vén waves appear as torsional waves 39 , which can create rotational perturbations of the plasma and the magnetic fields frozen in the plasma 40 . The perturbations are usually torsional oscillations 41 , which should appear periodically but were not observed in our event. However, in the deep atmosphere, these waves can be damped locally by ion-neutral or resistive damping 42 and therefore only the effect of the initial pulse is observed as a transient event. Alf vén waves are plausible candidates, but most previous modeling was done for coronal flux tubes and no quantitatively description is available for their effects on photospheric magnetic fields.
In conclusion, the observed field change cannot be explained by existing models. The new, transient magnetic signature in the photosphere that we describe in this paper offers a new diagnostic for future modeling of magnetic reconnection and the resulting energy release. Such observations require high cadence and high resolution. Our results motivate further observations using GST and the Daniel K. Inouye Solar Telescope (DKIST) in probing the mystery of solar flares.

Magnetic Inversion
After dark and flat field correction, The crosstalk is removed by measuring the effect of optical elements from the telescope to the detector. Pure states of polarization are fed into the light path and their response at the detector tells how the incoming polarization from the Sun would be changed by the optics 43 (and references therein). After careful elimination of the crosstalk among Stokes Q, U, and V, the NIRIS data undergoes Milne-Eddington inversion to fit the Stokes line profiles based on an atmospheric model. The source function with respect to optical depth is simplified to a 1st order polynomial. As results, several key physical parameters can be extracted -B tot , azimuth angle, inclination, Doppler shift, and so forth. For successful fitting into ME-simulated profiles, initial parameters are pre-calculated to be in proximity to the observed Stokes profiles. This code was specifically designed for BBSO/NIRIS and written by Dr. Jongchul Chae using IDL language.

• Ambiguity Correction
In order to streamline the analysis of vector magnetogram data, data processing tools have been developed and implemented, including the 180 • ambiguity resolution and NLFF coronal magnetic field extrapolation. The 180 • azimuthal ambiguity in the transverse magnetograms is resolved using the minimum-energy algorithm that simultaneously minimizes both the electric current density J and the field divergence |∇ · B| 26 . Minimizing |∇ · B| gives a physically meaningful solution and minimizing J provides a smoothness constraint. A magnetogram is first broken into small subareas with which to compute a force-free α parameter. Then a linear force-free field is effectively constructed with which to infer the vertical gradients needed to minimize the divergence. Since the calculation of J and |∇ · B| involves derivatives of the magnetic field, the computation is not local, the number of possible solutions is huge and the solution space has many local minima. The simulated-annealing algorithm 44 is used to find the global minimum. This minimum-energy algorithm is the top-performing automated method among present state-of-art algorithms used for resolving the 180 • ambiguity 45 .