Flare differentially rotates sunspot on Sun's surface

Abstract

Sunspots are concentrations of magnetic field visible on the solar surface (photosphere). It was considered implausible that solar flares, as resulted from magnetic reconnection in the tenuous corona, would cause a direct perturbation of the dense photosphere involving bulk motion. Here we report the sudden flare-induced rotation of a sunspot using the unprecedented spatiotemporal resolution of the 1.6 m New Solar Telescope, supplemented by magnetic data from the Solar Dynamics Observatory. It is clearly observed that the rotation is non-uniform over the sunspot: as the flare ribbon sweeps across, its different portions accelerate (up to ∼50° h^-1 ) at different times corresponding to peaks of flare hard X-ray emission. The rotation may be driven by the surface Lorentz-force change due to the back reaction of coronal magnetic restructuring and is accompanied by a downward Poynting flux. These results have direct consequences for our understanding of energy and momentum transportation in the flare-related phenomena.

ARTICLE

Received 25 Mar 2016 | Accepted 2 Sep 2016 | Published 10 Oct 2016

Chang Liu1,2,3, Yan Xu1,2,3, Wenda Cao2,3, Na Deng1,2,3, Jeongwoo Lee1,4, Hugh S. Hudson5,6, Dale E. Gary3,

Jiasheng Wang1,2,3, Ju Jing1,2,3 & Haimin Wang1,2,3

Sunspots are concentrations of magnetic eld visible on the solar surface (photosphere).

It was considered implausible that solar ares, as resulted from magnetic reconnection in the tenuous corona, would cause a direct perturbation of the dense photosphere involving bulk motion. Here we report the sudden are-induced rotation of a sunspot using the unprecedented spatiotemporal resolution of the 1.6 m New Solar Telescope, supplemented by magnetic data from the Solar Dynamics Observatory. It is clearly observed that the rotation is non-uniform over the sunspot: as the are ribbon sweeps across, its different portions accelerate (up to B50 h 1) at different times corresponding to peaks of are hard X-ray emission. The rotation may be driven by the surface Lorentz-force change due to the back reaction of coronal magnetic restructuring and is accompanied by a downward Poynting ux. These results have direct consequences for our understanding of energy and momentum transportation in the are-related phenomena.

DOI: 10.1038/ncomms13104 OPEN

Flare differentially rotates sunspot on Suns surface

1 Space Weather Research Laboratory, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102-1982, USA. 2 Big Bear Solar Observatory, New Jersey Institute of Technology, 40386 North Shore Lane, Big Bear City, California 92314-9672, USA. 3 Center for Solar-Terrestrial Research, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102-1982, USA. 4 Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea. 5 School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK. 6 Space Sciences Laboratory, University of California, Berkeley, California 94720-5071, USA. Correspondence and requests for materials should be addressed to C.L. (email: mailto:[email protected]

Web End [email protected] ) or to H.W. (email: [email protected]).

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Sunspots on the solar surface are the most visible manifestation of solar magnetic eld1,2, which has a direct and critical inuence on space weather. Line-tied to the

dense (B10 7 g cm 3) photosphere with high plasma beta (ratio of gas to magnetic pressure, b41; bE1 in sunspots), magnetic elds of sunspots and the induced active regions (ARs) extend into the tenuous (B10 15 g cm 3) low-beta (boo1)

corona. Thus, the long-term (in days) evolution of photospheric magnetic eld, as driven by surface ows and new ux emergence, plays a key role in shaping coronal eld structure and, importantly, building up free energy in the corona that powers solar ares via magnetic reconnection3,4. For example, the gradual rotational motion of sunspots (generally up to a few degrees per hour) can, in principle, braid and twist the eld, leading to an increase of helicity and energy in the corona510. Sunspots frequently exhibit rotation and this has been linked in the past to the storage of free magnetic energy associated with currents owing through the corona1113.

Once triggered, solar ares give rise to a variety of emission signatures. It is generally accepted that accelerated particles can stream down from the magnetic reconnection site in the corona to the low atmosphere along newly formed magnetic loops, producing chromospheric H-alpha and hard X-ray (HXR) emissions14. The former usually appears in eruptive ares as two separating ribbons straddling the magnetic polarity inversion line15; the latter is thought to be due to thick-target bremsstrahlung of high-energy particles16, both reecting the reconnection process. Subsequently, the heated plasma evaporates to ll are loops, emitting soft X-rays (SXRs) and other wavelength emissions as it cools. As magnetic ux tubes in the corona are anchored in the dense photosphere, the possibility of a non-particle-related, impulsive (in tens of minutes) and permanent photospheric structure change has been ignored in almost all models of ares and the often associated coronal mass ejections (CMEs), which primarily focus on the coronal eld restructuring. Recently, a theory based on momentum conservation predicts that as a back reaction on the solar surface and interior, the photospheric magnetic eld would become more horizontal (that is, inclined to the surface) near aring magnetic polarity inversion lines after ares/CMEs17,18. This prediction has been conrmed in multiple observations (for example, see refs 1922). As the plasma beta within sunspot umbrae and inner penumbrae could be lower than unity2,23, the Lorentz-force change at and below the photosphere, as quantied by the above back reaction theory, may drive bulk plasma motions in sunspots; however, related supporting observations are extremely rare24,25. There is only one study reporting the rotation of a sunspot along with a are25, but a denite conclusion on its relationship with the are emission was hampered by insufcient image resolution.

To advance our understanding of the response of the photosphere to the are-associated coronal restructuring, here we study the 22 June 2015 M6.5 are (SOL2015-06-22T18:23) using TiO broadband (a proxy for the continuum photosphere near 7,057 ) and H-alpha red-wing ( 1 ) images with the

highest resolution (B60 km) ever achieved and rapid cadence (15 and 28 s, respectively). These data are obtained from the recently commissioned 1.6 m New Solar Telescope (NST)2629 at Big Bear Solar Observatory (BBSO), which is equipped with a high-order adaptive optics system (see Methods). The high spatiotemporal-resolution imaging capability of NST offers an unprecedented opportunity to investigate the low-atmosphere dynamics in detail. Also used are time proles of are HXR and SXR uxes from the Fermi Gamma-Ray Burst Monitor30 and the Geostationary Operational Environmental Satellite (GOES)-15, respectively, and photospheric vector magnetograms from the

Solar Dynamics Observatorys (SDOs) Helioseismic and Magnetic Imager (HMI)31. With these multiwavelength observations, we clearly see the sunspot in this aring AR rotating when the are ribbon propagates through it; more importantly, different portions of the spot accelerate (up to B50 h 1) at different times corresponding to the are HXR peaks. This fast rotation is distinct from the aforementioned slow sunspot rotation seen in the pre-are stage. As a comparison, the only other similar study25 used the SDO/HMI intensity data, of which the spatial (temporal) resolution is about 12 (3) times lower than that of the current BBSO/NST data. Our highest resolution makes it possible to resolve the differential sunspot rotation and uncover its intrinsic relationship with the are emission. We also analyse the are-related photospheric vector magnetic eld change and nd that the observed sunspot rotation may be driven by the Lorentz-force change due to the back reaction of coronal magnetic restructuring. Furthermore, we compute the temporal evolution of the energy (Poynting) and helicity uxes through the surface, and nd that they reverse sign during the are, suggesting that the energy source for the sudden rotation comes from the corona rather than from below the photosphere. These results have direct consequences for our understanding of energy and momentum transportation in the are-related phenomena.

ResultsEvent overview. The 22 June 2015 M6.5 are occurred in NOAA AR 12371 (8W, 12N) and was associated with a halo CME. The are starts at 17:39 universal time (UT), peaks at 18:23 UT and ends at 18:51 UT in GOES 1.612.4 keV SXR ux, and has three (IIII) main peaks in Fermi 2550 keV HXR ux at 17:52:31, 17:58:37 and 18:12:25 UT, respectively. The are core region was covered by the eld of view of BBSO/NST, showing two separating are ribbons in H-alpha (see Fig. 1a and also Supplementary Movie 1 of ref. 32). The ribbons in TiO are much weaker but still discernible. In particular, the eastern are ribbon sweeps through the regions of two sunspot umbrae f1 and f2 of positive magnetic polarity (Fig. 1a). From the movies constructed using the TiO and H-alpha images (Supplementary Movies 13), one can clearly nd that f1 and f2 (especially f1) exhibit a sudden rotational motion in the clockwise direction closely associated with the are. Such observation of a sudden sunspot rotation following a are, with great details revealed in high resolution, was never achieved. Notably, the TiO data are ideal for tracing the photospheric plasma ow motions, especially in sunspot umbrae. Figure 1b shows the ow patterns in f1 and f2 right before the are, derived using the differential afne velocity estimator (DAVE)33 (see Methods). It portrays ne-scale umbral ows, with a general pattern of inward motion34,35. The DAVE results allow us to examine the sunspot rotation in a comprehensive way, as described below.

Flare-induced sunspot rotation. We study the dynamics of the sunspot (with an emphasis on f1) through two data analysis approaches. We pay special attention to the relationship between the sunspot rotation and the are emission.

First, we evaluate the rotational motion of the whole sunspot in a simplied solid-body approximation. Considering its shape we t an ellipse to the f1 region determined based on the TiO intensity (for example, see Fig. 1c,d and Methods) and plot the temporal evolution of the angle between the derived major axis of the ellipse (for example, yellow and orange dashed lines in Fig. 1c,d) and the horizontal direction as the blue line in Fig. 2. The result shows that f1 begins to rotate clockwise as a whole from B17:56 UT (about 3.5 min after the HXR peak I) and the

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Figure 1 | Flaring region and sunspot dynamics observed with BBSO/NST. (a) H-alpha 1 image at the second main HXR peak time showing two

separating H-alpha ribbons, with are-related sunspot umbrae labelled as f1, f2, p1 and p2. The white (black) lines contour the 17:58:25 UTvertical magnetic eld from SDO/HMI at 1,100 ( 1,100) G. The box denotes the eld of view of bd. (b) Pre-are TiO image superimposed with arrows (colour-coded by

direction) representing the ow eld in f1/f2 derived with DAVE (averaged between 17:33:53 and 17:38:54 UT). (c) Pre-are TiO image with the white dashed line representing an ellipse t to the f1 region and the yellow dashed line (also plotted in d) the major axis. (d) Same as c but at a post-are time, with the major axis drawn in orange.

rotation lasts for about 2 h till B20:00 UT, covering a total angular range of B13. Clearly, the present case is distinct from almost all previously studied events, where sunspots undergo a rotation before the are initiation in SXR. It is also noteworthy that the time prole of the rotation angle can be well approximated by an acceleration function between 17:56 and 18:12:29 UT (around the HXR peak III) followed by a deceleration function (see Fig. 2 and Methods).

Second, a closer examination of the full-resolution movies (Supplementary Movies 2 and 3) unambiguously shows that as the are ribbon moves across, different portions of the sunspot start rotating at different times (meaning a differential rotation) corresponding to the peaks of HXR emission. To characterize in detail the non-uniform rotation, we resort to the tracking of photospheric plasma ows with DAVE throughout the event (see Fig. 3 and Supplementary Movie 4). Based on the derived velocity vectors, we also compute the ow vorticity (curl of the velocity; calculated by equation (1) in Methods) and examine the spatial and temporal evolution of the negative vorticity (corresponding to a clockwise rotation) in the sunspot region (see Figs 4 and 5, and Supplementary Movie 5). Furthermore, we remap TiO images to a polar coordinate system and trace several distinct features (see Methods and Fig. 6) for a precise

determination of the timing relationship between the sunspot rotation and are emission. Below, we divide the whole event into three phases and describe the characteristics of sunspot rotation in each phase.

Phase 1 (from HXR peak I at 17:52:31 UT to peak II at 17:58:37 UT): the are ribbon propagates towards f1/f2 and just enters into their regions from the west at the time of the HXR peak I (see Fig. 4a). Immediately, the sunspot umbrae underlying the ribbon begin to rotate southwestward. This is clearly exhibited by the space-time slice image (Fig. 6a) from the re-mapped TiO images along the circle C1 (in Fig. 3b), in which the northeastern portion of f1 (as represented by features 14, which are co-spatial with the are ribbon at this time; see Fig. 4a) starts rotating right after the HXR peak I, at a mean angular velocity of 50 h 1. Later, as the ribbon proceeds (Fig. 3a) the far western portion of f1/f2 seemingly forms a clockwise rotational pattern, which can be visualized by the average ow eld in this phase (Fig. 3b). The mean angular velocity of f1 reaches a maximum of B38 h 1 at 17:56:23 UT (Fig. 4b), about 4 min after the HXR peak I (Fig. 5).

It is pertinent to point out that the afore-described ellipse tting under a solid-body assumption shows a signicant rotation of f1 only after B17:56 UT. This highlights the differential nature of this sunspot rotation.

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Figure 2 | Overall sunspot rotation. Time proles of SXR ux (black line), HXR ux (gray shaded area; not available during 18:1919:19 UT) and orientation angle y of f1 (between the major axis and horizontal direction;

blue line) from an ellipse t (see, for example, Fig. 1c,d). The intensity threshold for delineating the f1 region was varied to evaluate the 1-s.d. error bars of y. Overplotted is the approximation of y evolution using a horizontal line between 17:00 and 17:56 UT (green), a second-order polynomial (acceleration) between 17:56 and 18:12:29 UT (yellow), and another second-order polynomial (deceleration) between 18:12:29 and 20:50 UT (red). See Methods for details. The vertical dashed lines mark the start and end times of the are in GOES 1.612.4 keV SXR ux and the dotted lines mark the three main Fermi 2550 keV HXR peaks IIII.

Phase 2 (from HXR peak II at17:58:37 UT to about peak III at 18:12:25 UT): the are ribbon, mainly its northern part, moves a signicant distance towards the east, across the main regions of f1/f2 (Figs 3c and 4cf). As can be seen in Fig. 6, the southern and eastern portions of f1, represented by features 57 and 810 marked in Figs 3b,d and 4ce, begin a rotation-like motion immediately following the HXR peak II, at a mean angular velocity of 52 and 30h 1, respectively. It can also be noticed that the northwestern portion of f1 (for example, features 14)

keeps rotating in this phase. As a result, the entire f1 and f2 display a rotational ow pattern in the clockwise direction (Fig. 3d). The mean angular velocity of f1 has the second maximum of 36 h 1 at about 4 min after the HXR peak II and sustains roughly this speed till about 18:08 UT. As for f2, its clockwise rotation keeps accelerating after the HXR peak I, and peaks at 45 h 1 about 3.5 min after the HXR peak II (see Fig. 5).

Phase 3 (from about HXR peak III at 18:12:25 UT): the are ribbon almost moves out of the sunspot region (Fig. 3e). The rotational ows involving both f1 and f2 diminish, as reected by the observations that the mean vorticity of f1/f2 largely returns to the pre-are level (Fig. 5), and that drifting features nearly attens in the re-mapped space-time slice images (Fig. 6). Interestingly, f1 shows overall westward and southwestward ows (Fig. 3f), and it continues to rotate clockwise as a whole (see Fig. 2 and Supplementary Movie 1).

Taken together, the exceptionally high-resolution observations from BBSO/NST make it possible to witness, for the rst time, a sudden sunspot differential rotation that exhibits an intrinsic spatiotemporal relationship with the coronal energy release process, manifested as are ribbon propagation and HXR emission prole. The measured angular velocity of rotation amounts up to B50 h 1, which is much higher than that of the reported pre-are rotating sunspots. These strongly indicate that the observed sunspot rotation on the photosphere is a result, not a cause, of the are magnetic reconnection in the corona, which challenges the conventional view of the photosphere-corona coupling.

It is worth noting that similar to the propagating ribbon, the negative vorticity feature also progresses from west to east across the sunspot (see Supplementary Movie 5, vorticity evolution). More exactly, the development of regions of intense negative vorticity follows the are ribbon motion and concentrates on the portion swept by the ribbon (see Fig. 4). This implies that the sunspot rotation is intimately linked to the aring process. The features 17 in the west start rotating as the are ribbon sweeps by and ensuing the peaks of the HXR emission (Figs 4a,c and 6). In contrast, features 810 in the east begin to move northeastward (with little rotation, that is, low vorticity) at the HXR peak II (Figs 4c and 6), when the ribbon has not spread to their locations. Enhancement of the negative vorticity in these regions occur only when the ribbon arrives B5 min later (Fig. 4d,e). These two movement stages of the eastern part of f1 are discernible in the time-lapse movie (Supplementary Movie 2). For simplicity, we still describe the earlier motions of features 810 as rotations. The umbrae f1/f2 gain maximum angular velocity in a few minutes after the initiation of rotation of sunspot features, consistent with the low Alfvn speed of the photospheric plasma (B10

20 km s 1 in sunspot umbrae). Unlike f1, no obvious internal rotations are observed within f2; in fact, together they present a coherent rotation (Fig. 3d), despite of the sunspot light bridge lying between them. This connotes that f1 and f2 may be parts of a unied magnetic structure. As the rotational motion of the whole sunspot shows a deceleration after 18:12:29 UT (Fig. 2), phase 3 could be an after-effect following phase 1 and phase 2 of the rapid rotation directly related to the are.

Flare-related magnetic evolution. As moving H-alpha ribbons are regarded as a mapping of the reconnecting coronal magnetic eld onto the low solar atmosphere14 and HXR emissions could gauge the magnitude of coronal magnetic reconnection3, the revealed correlation between the sunspot rotation and are emissions motivates us to explore the changes of magnetic eld and related quantities, which can shed light on the mechanism of the are-induced sunspot rotation. To analyse the photospheric magnetic eld and its evolution, we use vector magnetograms from SDO/HMI with 12 min cadence and 1 arcsec spatial resolution (see Methods). We observe that the are causes apparent changes of the sunspot (especially f1) structure, in terms of intensity and vector magnetic eld (see Supplementary Fig. 1). Here we mainly concern ourselves with the Lorentz-force change exerted at and below the surface by coronal magnetic eld from above, which is attributed to the restructuring of coronal magnetic eld in the back reaction theory17,18. There are two HMI measurements made during the main phases of sunspot rotation. At 18:00:44 UT (1.5 min into phase 2), the density map of the horizontal component of the Lorentz-force change dFh (calculated using equation (2) in Methods) is presented in Fig. 7a. It is remarkable that dFh forms a swirl in the western portion of f1 and also exhibits a coherent clockwise rotation over regions of f1/f2, resembling a combination of TiO ow patterns of phase 1 and phase 2 (see Fig. 3b,d). As shown in Fig. 7b, the dFh density map at 18:12:44 UT (beginning of phase 3) changes to an overall rotating structure also similar to the ow pattern of phase 3 (Fig. 3f). Intriguingly, similar to the ow vorticity (Fig. 4) the dFh distribution seems to evolve with the ribbon motion; however, this aspect needs to be further addressed when higher cadence vector magnetograms become available. In any case, these hint that the torque T produced by dFh may drive the sunspot rotation, a scenario also suggested by the only other related study25. For simplicity, ignoring the differential rotation but assuming a rigid rotation of the elliptical f1 around its centre (cross in Fig. 7), the time prole of T on f1, as plotted in Fig. 8a,

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Figure 3 | Solar are and induced sunspot rotation. BBSO/NST H-alpha 1 images (a,c,e) and the co-temporal TiO images (b,d,f), showing the

sunspot rotation in three phases (see text for details and Supplementary Movies 14 for animations). SDO/HMI vertical magnetic eld is contouredat 1,300 G on H-alpha images. In b,d,f, the superimposed arrows (colour-coded by direction) illustrate DAVE ows in f1/f2 averaged between 17:52:3817:58:38 UT (phase 1), 17:58:3818:12:29 UT (phase 2) and 18:12:2918:22:30 UT (in phase 3), respectively, subtracted by a pre-are ow eld averaged between 17:32:23 and 17:52:23 UT to better show the rotational motion. The overplotted white curves delineate the co-temporal H-alpha are ribbons. The plus in b (d) is the origin for the polar re-mapping, with the circle C1 (C2) denoting the constant radius for constructing the space-time slice image presented in Fig. 6a (6b). The angle starts at due South and increases anticlockwise. The beginning angle locations of features 110 along C1/C2 as seen in Fig. 6 are marked as solid dots.

shows impulsive T signals closely associated with the rotation of f1. A rough quantitative estimate also indicates that the amount of T on f1 is sufcient compared with that required for the measured rotation (see Methods). The torque rapidly decrease to zero soon after the beginning of phase 3. Thus, the torque evolution is also in line with the observed acceleration followed by deceleration of the overall sunspot rotation (Fig. 2).

With SDO/HMI vector magnetic eld data, we further track the photospheric plasma ows using the DAVE for vector

magnetograms (DAVE4VM)36 (see Methods), which can derive not only the horizontal but also the vertical component of ows. These vector photospheric velocity elds permit an accurate assessment of the Poynting ux _

E and helicity ux _

H transported through the photosphere, which are physical quantities intimately associated with rotating sunspots510, thus may help elucidate the essential physics needed to properly interpret our observations. The temporal evolution of _

E and _

H throughout the are (calculated by equations (3) and (4) in Methods) is drawn in

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Figure 4 | Spatial evolution of vorticity. Time sequence of vorticity maps during phase 1 (a,b) and phase 2 (cf) in the regions of umbrae f1 and f2, computed based on BBSO/NST TiO images (see Methods and Supplementary Movie 5 for an animation). The overplotted yellow line denotes the front edge of the co-temporal H-alpha are ribbon. The circles C1 and C2 and the associated features (crosses 110) are the same as those in Fig. 3b,d.

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o of f1

(red) and f2 (blue). The error bars (plotted every 1 min to better show the results) represent 1 s.d. calculated from the average

o over a pre-are period (17:00 to 17:39 UT), demonstrating the signicant are-related variations compared to that seen in the long-term evolution. The vertical dashed lines mark the start and end times of the are in GOES 1.612.4 keV SXR ux and the dotted lines mark the three main Fermi 2550 keV HXR peaks IIII.

Fig. 8b,c. The former is integrated over the regions of f1 and f2, considering the low cadence of HMI data and the fact that f1/f2 could make up a unied magnetic structure (see previous discussion). The latter is integrated over the entire AR. It can be seen that energy and negative helicity are injected upward from below the surface both before and after the are. The negative sign of helicity conforms with the measured left-handed twist of f1 and f2. However, during the are time interval, both _

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H reverse sign. In particular, there is a downward Poynting ux during the are time interval (with a total energy about1.6 1030 ergs), which could be the energy source driving the

photospheric motion. These point to a physical process associated

with the sunspot rotation (presumably the back reaction of coronal magnetic recongurations) that contrasts with that in the non-aring period.

DiscussionOur observations demonstrate that sunspots f1/f2 rotate as a response of the are energy release, and that the rotation is progressive and differential, ensuing the are emissions. We notice that f1 and f2 are at the footpoints of erupting ux loops, which develop into a halo CME accompanying the present are. These loops connect to two other sunspots p1 and p2 in negative eld regions (Fig. 1a), which vaguely show a similar are-related clockwise rotation in SDO/HMI data (details, however, are unknown as p1/p2 are out of the eld of view of BBSO/NST). This alludes to the possibility that on the large scale, the observed sunspot dynamics may be linked to the properties of a twisted ux tube. With related to sunspot rotation, let us consider theoretically the emergence of a vertical, twisted magnetic ux tube from the interior into the corona37,38. During its emergence, rapid expansion and stretching occur to the coronal portion of the tube, where the twist rate of the eld (a J B/B2) decreases rapidly. As a result,

along the eld lines a gradient of the twist rate gets established, and it drives torsional Alfvn waves that propagate twist from the interior into the corona, until a twist balance is reached on a time scale of a few days. This constitutes an explanation of rotating sunspots in emerging ux regions (for example, see refs 8,39). However, if an eruption suddenly happens that stretches out the coronal eld again, the gradient of twist rate and hence the torque on the photosphere would increase, which can consequently cause a sudden increase of the sunspot rotational motion in the same direction as before the eruption, as seen in the only other observation of a are-related sunspot rotation25. Under this scenario, it would be expected that the Poynting ux _

E and also

helicity ux _

H (with the same sign as that before the eruption) injected into the atmosphere by the emerging ux tube would also suddenly enhance40. However, we observe the exact opposite behaviours of _

E and _

H during this eruptive are event.

Therefore, we are led to conclude that the driving agent behind and the energy source of the observed sunspot rotation originates

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TiO intensity (data number)

0 0 20

Figure 6 | Space-time slice image for sunspot rotation. The results in a and b are constructed from TiO images re-mapped to a polar coordinate system, at a constant radius of 2.700 (C1 in Fig. 3b) and 4.100 (C2 in Fig. 3d), respectively. The shown angular range is 0180 for C1 and 230330 for C2, and these ranges are denoted using solid lines when drawing C1/C2 in Figs 3b,d and 4a,ce. The black dotted lines trace several distinct features 110 in f1 by a linear approximation. The numbers in bracket are the corresponding angular velocity (in degree per hour) from the linear t. The initial locations of these features are also indicated in Figs 3 and 4.

The vertical dashed lines mark the start and end times of the are in GOES 1.612.4 keV SXR ux and the dotted lines mark the three main Fermi 2550 keV HXR peaks IIII.

5

X (arcsec)

5 104 dyne cm2

(G)

Figure 7 | Horizontal Lorentz-force change. SDO/HMI vertical magnetic eld, with the white (black) colour representing positive (negative) polarity, superimposed with arrows (colour-coded by direction) displaying the horizontal Lorentz-force change vectors between 17:48:44 and 18:00:44 UT (a), and between 18:00:44 and 18:12:44 UT (b). The projected and re-mapped HMI data product is used. See Methods for details. Arrows are only shown at locations with vertical eld 41,200 G. The cross is the tted centre of the elliptical f1 for the torque calculation shown in Fig. 8a. The black line illustrates the front of the co-temporal H-alpha are ribbon.

from the corona rather than below the photosphere, most probably associated with the back reaction of the are-related restructuring of coronal magnetic eld. We also postulate that the torque produced by coronal transients might drive the low atmosphere down to a certain depth. Certainly, more observations of the low solar atmosphere in high resolution, together with simulations of photospheric sunspot dynamics41 and further understanding of the photosphere-corona coupling, are desired to tackle the problem of energy and momentum transportation in the are-related phenomenon.

Methods

Instrumentation and data. The broadband TiO and H-alpha red-wing images used in the present study, with a spatial resolution of B61 and 66 km and a cadence of 15 and 28 s, respectively, are obtained with the 1.6 m BBSO/NST, which is currently the largest-aperture ground-based solar telescope. It combines a high-order adaptive optics system using 308 sub-apertures and the post-facto

speckle image reconstruction techniques to achieve diffraction-limited imagingof the solar atmosphere. The H-alpha data are taken by the Visible Imaging Spectrometer, which is a FabryProt lter-based system that can scan in the wavelength range of 5,5007,000 . For this observation run, ve points were scanned around the H-alpha line centre at 1.0, 0.6 and 0.0 . For data processing, the images were aligned with sub-pixel precision and the intensity was normalized to that of a quiet-Sun area. The TiO and H-alpha images were co-aligned by matching sunspot and plage areas, with an alignment accuracy of about 0.2 Mm. All the images presented in this paper were registered with respect to 22 June 2015 17:38:54 UT.

For the analysis of photospheric magnetic eld, we use the observation from HMI on board SDO with 12 min cadence and 1 arcsec spatial resolution. Specically, for the context study in Figs 1 and 3, and Supplementary Fig. 1, we use the full-disk HMI vector magnetogram data product hmi.B_720s (refs 31,42). For the calculation of Lorentz-force change, tracking of plasma ows with DAVE4VM and computation of Poynting and helicity uxes, we use the Space-weather HMI Active Region Patches vector magnetogram data product hmi.sharp_cea_720s (ref. 43). The Space-weather HMI Active Region Patches data are re-mapped using Lambert (cylindrical equal area) projection centred on the studied AR.

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a

(s 1)) as:

Start II III End

I

o

@@x vy

0

(1030 dyne cm)

1

3

@@y vx; 1

where vx and vy are velocity vectors after a 5 min running average of the DAVE ow elds, which is to alleviate the effects of the atmospheric disturbances and photospheric 5 min oscillation contained in the observation. In this denition, vorticity is equal to twice the angular velocity.

Re-mapping of TiO images to a polar coordinate system is carried out with the centre of the rotational ow pattern (plus signs in Fig. 3b,d) as the origin, where the two axes of the re-mapped frames represent the polar angle around and the distance R from the origin. To construct the space-time slice images shown in Fig. 6, we stack one slice per frame, which is averaged for 11 pixels betweenR 0.1700 and R 0.1700, where R 2.700 (4.100) for the circle C1 (C2) drawn in Fig.

3b(3d). The size and location of these circles are determined in such a way that the right (left) half of C1 (C2) closely follows the rotational ows in the western (eastern) portion of f1 during phase 1 (phase 2).

Magnetic evolution analysis. The change of the horizontal Lorentz force exerted at and below the photosphere can be formulated as:

dFh

1 4p

2

b

5

0

(1026 ergs s1 )

Z dAd BrBh

; 2

where Br is the photospheric vertical magnetic eld and Bh is the horizontal eld vector17,18. Assuming that f1 has a geometry of rigid elliptical disk rotating about its centre, the torque T resulted from dFh can produce an angular accelerationa T/I T/{14rphab(a2 b2)}, where I is the moment of inertia relative to its

center, r is the photospheric density, h is the depth (a coherent depth of rotation is presumed), and a and b are the length of the semi-major and semi-minor axes of the ellipse that can be derived from the shape tting. Here we take rE(4

11) 10 7 g cm 3, hE270 km (a density scale height at the photosphere),

aE6.8 Mm and bE3.2 Mm. At 18:00:04 UT in phase 2, the clockwise torque exerted on f1 (relative to the centre marked as the cross in Fig. 7) produced by dFh (relative to a pre-rotation time 17:48:44 UT) amounts to TE3.1 1030 dyne cm

(Fig. 8a), which can produce an a of (1.13.0) 10 6 rad s 2. This is more than

sufcient compared to the observed aE2.3 10 7 rad s 2, when considering that

the angular velocity of f1 increases B6.8 10 5 rad s 1 from B17:51:30 to

17:56:23 UT in phase 1 (Fig. 5). In addition, if considering a total angular distance of B5 till the end of phase 2 (Fig. 2), the work done by the torque (that is, the rotational kinetic energy of f1) is roughly 3 1029 ergs. We caution that our

calculation has a large uncertainty due to the assumption of h and ignorance of the

differential rotation nature of f1.

The DAVE4VM technique based on the magnetic induction equation is employed to track both the horizontal and vertical components of the photospheric plasma ows. For this analysis, we use time series of SDO/HMI data with a window size of 19 pixels, which is selected according to previous studies44,45.

The vertical component of Poynting ux across the plane S at the photospheric level can be derived as46:

dE dt

S

5

10

Poynting flux (f1/f2)

16:00 18:00 20:00 22:00Start Time (22-Jun-15 15:00:00)

c

5

0

(1037 Mx2 s1 )

5

10

15 Helicity flux (AR)

Figure 8 | Temporal evolution of magnetic properties. (a) Torque on f1 resulted from horizontal Lorentz-force change. The error bars represent1 s.d. calculated from the provided uncertainty of HMI vector eld.(b) Poynting ux integrated over the rotating sunspots f1 and f2.(c) Magnetic helicity ux integrated over the whole aring AR. Error bars in b and c represent an uncertainty of 17% for energy ux and 23% for helicity ux due to noise in the HMI data. See Methods for details. The vertical dashed lines mark the start and end times of the are in GOES 1.612.4 keV SXR ux and the dotted lines mark the three main Fermi 2550 keV HXR peaks IIII.

Bt V?t

BndS; 3

where Bt and Bn are the tangential (horizontal) and normal (vertical) magnetic elds, and V>t and V>n are the tangential and normal components of velocity V>

(the velocity perpendicular to the magnetic eld lines, as the eld-aligned plasma ow is irrelevant44). Contributions from ux emergence and surface shearing motions are represented by the rst and second terms, respectively. According to ref. 44, V> V (V B)B/B2, where V is the velocity vector derived by

DAVE4VM. Similarly, the magnetic helicity ux across S can be expressed by the combination of an emerging and a shearing terms47:

dH dt

S

1 4p

Z

S

B2tV?ndS

1 4p

Z

S

Sunspot rotation analysis. To evaluate the overall rotation of f1, we (1) use the REGION_GROW function in IDL with a pre-set TiO intensity threshold to dene the region of f1, (2) conduct an ellipse t to the f1 region using the FIT_ELLIPSE function in IDL and (3) vary the intensity threshold from 3,900 to 4,000 data number and perform a total of 11 runs of calculation for error estimation. These threshold values are selected so that the umbra f1 can be well delineated throughout the studied time period. The temporal evolution of the angle y between the major axis of the tted ellipse and the horizontal direction, as shown in Fig. 2, is approximated using a least-squares t to a horizontal line between 17:00 and 17:56 UT, a second-order polynomial y 14.9 3.63 10 3t 1.84 10 6t2 between

17:56 and 18:12:29 UT where t is in units of second from 17:56 UT, and another second-order polynomial y 21.0 1.72 10 3t 1.11 10 7t2 between

18:12:29 and 20:50 UT (the end of this BBSO/NST observation run) where t is in units of second from 18:12:29 UT.

To track the photospheric plasma ows, we employ the DAVE method, which is a well-established, state-of-the-art technique using the advection (adopted here) or continuity equation and a differential feature tracking algorithm for ow detection. In this study, a 2 2 binning is applied to the TiO data to

increase the S/N ratio. The tracking window size is set to 23 pixels, which balances the needs for including enough structure information and a good spatial resolution. We then calculate the vorticity o (in units of

Z

S

2 Ap Bt

V?

ndS 2 Z

S

Ap V?t

B

ndS; 4

where Ap is the vector potential of the potential eld Bp. As the helicity ux density is not a gauge invariant quantity, we study the helicity ux integrated over the whole AR. The Poynting and helicity uxes derived with the DAVE4VM results based on SDO/HMI vector magnetograms have an uncertainty of 17% and 23%, respectively44,45. These were determined by ref. 44 using a Monte Carlo experiment where noises are randomly added to the HMI vector data. We also note that DAVE4VM has intrinsic method errors and may underestimate both Poynting and helicity uxes by 29 and 10%, respectively36,48.

Software availability. DAVE and DAVE4VM ow tracking codes as used in this study can be obtained from http://ccmc.gsfc.nasa.gov/lwsrepository/index.php

Web End =http://ccmc.gsfc.nasa.gov/lwsrepository/index.php .

Data availability. All the data used in the present study are publicly available. The BBSO/NST TiO and H-alpha images can be downloaded from http://bbso.njit.edu

Web End =http://bbso.njit.edu . The Fermi X-ray ux data can be downloaded from http://hesperia.gsfc.nasa.gov/fermi_solar

Web End =http://hesperia.gsfc.nasa.gov/ http://hesperia.gsfc.nasa.gov/fermi_solar

Web End =fermi_solar . The GOES X-ray ux data can be downloaded from http://www.ngdc.noaa.gov/stp/satellite/goes/dataaccess.html

Web End =http://

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13104 ARTICLE

http://www.ngdc.noaa.gov/stp/satellite/goes/dataaccess.html

Web End =www.ngdc.noaa.gov/stp/satellite/goes/dataaccess.html . The SDO/HMI vector magnetograms can be downloaded from http://jsoc.stanford.edu

Web End =http://jsoc.stanford.edu .

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Acknowledgements

We thank the BBSO, Fermi, GOES and SDO/HMI teams for providing the data. The BBSO operation is supported by NJIT, US NSF AGS 1250818 and NASA NNX13AG14G grants, and the NST operation is partly supported by the Korea Astronomy and Space Science Institute and Seoul National University, and by the strategic priority research programme of CAS with Grant Number XDB09000000. This work is supported by NASA under LWSTRT grants NNX13AF76G and NNX13AG13G, and HGI grants NNX14AC12G and NNX16AF72G, and by NSF under grants AGS 1250818, 1348513, 1408703 and 1539791. J.L. is supported by the BK21 Plus Program (21A20131111123) funded by the Ministry of Education (MOE, Korea) and National Research Foundation of Korea (NRF), and also by NRF-2012 R1A2A1A 03670387. This work uses the DAVE/DAVE4VM codes written and developed by P.W. Schuck at the Naval Research Laboratory.

Author contributions

C.L. discovered the differential nature of this sunspot rotation, performed all the data analysis and interpretation, and wrote and revised the manuscript. Y.X. was the PI of this NST observation run and helped with the analysis of overall sunspot rotation.

W.C. developed instruments of NST and coordinated the observation. N.D. contributed to the data processing and analysis, especially the ow tracking. J.L., H.S.H. and D.E.G. contributed to the result interpretation and presentation. J.W. and J.J. helped with the data processing. H.W. rst observed this sunspot rotation and directed the research. All authors commented on the manuscript.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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How to cite this article: Liu, C. et al. Flare differentially rotates sunspot on Suns surface. Nat. Commun. 7, 13104 doi: 10.1038/ncomms13104 (2016).

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