Formation of a Double-decker Magnetic Flux Rope in the Sigmoidal Solar Active Region 11520
X. Cheng, M. D. Ding, J. Zhang, X. D. Sun, Y. Guo, Y. M. Wang, B. Kliem, Y. Y. Deng
OOnline-only material: animations, color figures
Accepted for publication in ApJ
Preprint typeset using L A TEX style emulateapj v. 08/13/06
FORMATION OF A DOUBLE-DECKER MAGNETIC FLUX ROPE IN THE SIGMOIDAL SOLAR ACTIVEREGION 11520
X. Cheng , , , M. D. Ding , , J. Zhang , , X. D. Sun , Y. Guo , , Y. M. Wang , B. Kliem , , & Y. Y. Deng School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China Key Laboratory for Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, VA 22030, USA W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam, Germany and Yunnan Observatory, Chinese Academy of Sciences, P. O. Box 110, Kunming, Yunnan 650011, China
Accepted for publication in ApJ
ABSTRACTIn this paper, we address the formation of a magnetic flux rope (MFR) that erupted on 2012 July 12and caused a strong geomagnetic storm event on July 15. Through analyzing the long-term evolutionof the associated active region observed by the Atmospheric Imaging Assembly and the Helioseismicand Magnetic Imager on board the
Solar Dynamics Observatory , it is found that the twisted field of anMFR, indicated by a continuous S-shaped sigmoid, is built up from two groups of sheared arcades nearthe main polarity inversion line half day before the eruption. The temperature within the twisted fieldand sheared arcades is higher than that of the ambient volume, suggesting that magnetic reconnectionmost likely works there. The driver behind the reconnection is attributed to shearing and convergingmotions at magnetic footpoints with velocities in the range of 0.1–0.6 km s − . The rotation of thepreceding sunspot also contributes to the MFR buildup. Extrapolated three-dimensional non-linearforce-free field structures further reveal the locations of the reconnection to be in a bald-patch regionand in a hyperbolic flux tube. About two hours before the eruption, indications for a second MFR inthe form of an S-shaped hot channel are seen. It lies above the original MFR that continuously existsand includes a filament. The whole structure thus makes up a stable double-decker MFR system forhours prior to the eruption. Eventually, after entering the domain of instability, the high-lying MFRimpulsively erupts to generate a fast coronal mass ejection and X-class flare; while the low-lying MFRremains behind and continuously maintains the sigmoidicity of the active region. Subject headings:
Sun: corona — Sun: coronal mass ejections (CMEs) — Sun: magnetic fields — Sun:filaments, prominences INTRODUCTION
A magnetic flux rope (MFR) is defined as a currentchannel with a set of magnetic field lines wrapping morethan once around the central axis. Such a structure oftenerupts from the Sun as a coronal mass ejection (CME;the largest-scale eruption in the solar system), which re-leases a large quantity of magnetized plasma into theinterplanetary space with a velocity of hundreds km s − ,even up to 3000 km s − (Yashiro et al. 2004; Zhang &Dere 2006; Chen 2011). The magnetized plasma is stillorganized frequently as a coherent MFR when arrivingat the Earth, as indicated by features such as the mag-netic field rotation, the drop of the solar wind densityand proton temperature, and the low plasma beta in thein situ observations (Burlaga et al. 1981).Several lines of evidence imply that the MFR exists inthe corona prior to the CME eruption. Sigmoid, a for-ward or reversed S-shaped emission pattern in soft X-ray(SXR) and extreme ultraviolet (EUV) passbands, oftenappears in CME-productive active regions (ARs) (Rust& Kumar 1996; Canfield et al. 1999). The straight sec-tion in the middle of the sigmoid is believed to be strongevidence of the MFR existing in the corona (e.g., Sterlinget al. 2000; Liu et al. 2007; McKenzie & Canfield 2008; Electronic address: [email protected]
Liu et al. 2010; Savcheva et al. 2012b). Filaments areanother piece of evidence of the existence of the MFR,which includes magnetic dips that are able to collect coolmaterial against gravity (Mackay et al. 2010; Guo et al.2010; Su et al. 2011; Su & van Ballegooijen 2012). Fil-ament channels are even thought to be the body of theMFR because rotation motions are often observed at thebottom of dark cavities, the cross sections of filamentchannels at the solar limb (Low & Hundhausen 1995;Guo & Wu 1998; Gibson et al. 2004; Wang & Stenborg2010; Li et al. 2012). Moreover, taking advantage of theobserved photospheric vector magnetic field at the bot-tom boundary, the MFR can be reconstructed by extrap-olation techniques using the assumption of a non-linearforce free field (NLFFF); this has also indicated preex-istence of the MFR (e.g., Yan et al. 2001; Canou et al.2009; Guo et al. 2010; Cheng et al. 2010, 2013b; Su et al.2011; Jiang et al. 2013, 2014; Inoue et al. 2013).If the MFR really exists in the corona prior to erup-tion, the question arises of when and where the MFRis built up. Two possibilities are proposed theoretically.One is that the MFR is generated in the convection zoneand partly emerges into the corona by buoyancy (Fan2001; Mart´ınez-Sykora et al. 2008). Manchester et al.(2004) noted that when the primary axis approaches thephotosphere, the MFR may split into two parts by the re- a r X i v : . [ a s t r o - ph . S R ] M a y connection with the surrounding fields, which only allowsthe upper part of the MFR to ascend to the corona (alsosee Magara 2006; Archontis & T¨or¨ok 2008; Leake et al.2013). The other possibility is that the MFR is builtup directly in the corona. Through imposing shearingand/or vortex motions to the different polarities, an ini-tial potential field is gradually sheared. Converging flowsthen initiate the reconnection near the polarity inversionline (PIL), which converts sheared fields into twisted ones(van Ballegooijen & Martens 1989; Amari et al. 2003).Depending on the specific locations of the reconnection,the MFR is created either through flux cancellation inthe photosphere prior to the eruption (Aulanier et al.2010; Amari et al. 2011; Xia et al. 2014) or via tether-cutting and flare reconnection in the corona during theeruption (Moore et al. 2001; Antiochos et al. 1999; Lynchet al. 2008; Karpen et al. 2012).Observationally, the MFR is also conjectured either tostem from emergence from below the photosphere or tobuild up in the corona. Lites (2005) studied the prop-erties of the vector magnetograms associated with twofilaments and found a concave up geometry underneaththe filaments. Okamoto et al. (2008) examined a se-quence of vector magnetograms of AR 10953 and foundthat two abutting opposite-polarity regions with hori-zontally strong but vertically weak magnetic fields grewlaterally and then narrowed. The directions of the hor-izontal magnetic fields along the PIL gradually reversedfrom a normal polarity to an inverse one. Both concaveup geometry and reversed polarity suggest that the MFRmay come from below the photosphere. However, Var-gas Dom´ınguez et al. (2012) recently provided an oppo-site interpretation for the photospheric evolution char-acteristics of the AR 10953. Through comparing withthe numerical results by MacTaggart & Hood (2010),they stated that magnetic cancellation is also able toproduce the lateral growing and then narrowing of theopposite polarities, as well as the reversal of the hori-zontal field direction. Moreover, through analyzing thetemperature structure of a sigmoid, Tripathi et al. (2009)discovered that the plasma in the J-shaped arcades canhave a higher temperature than that in the S-shaped fluxif both are simultaneously visible. They argued that itis most likely that the J-shaped arcades are reconnect-ing to the S-shaped flux. The reconnection at the sametime heats the plasma, which afterwards enters a coolingphase. Green & Kliem (2009) and Green et al. (2011)supported the conjecture that the reconnection is mostlyassociated with flux cancellation, although only part ofthe cancelled flux may be injected into the MFR. It isworth noting that the MFR can even be formed during aconfined flare and be destabilized in a subsequent majoreruption (Patsourakos et al. 2013; Song et al. 2014). Thisis similar to the conjecture of Guo et al. (2013), who ar-gued that the quasi-separatrix layer reconnection in theinterface between the MFR and the surrounding fields,indicated by a series of confined flares, has an importantrole in injecting self-helicity to the MFR.Although previous works have displayed elementary re-sults on the formation of the MFR, their objects for studyare filaments or sigmoids, not the MFR itself. Recently,using the data from the Atmospheric Imaging Assembly(AIA; Lemen et al. 2012) on board the Solar Dynam-ics Observatory ( SDO ), Zhang et al. (2012) and Cheng et al. (2013a) found that the MFR directly exists as anelongated EUV channel structure appearing in the hightemperature AIA passbands at 131 and 94 ˚A. In the im-pulsive acceleration phase, the MFR is further enhancedby flare reconnection, and the morphology evolves fromthe sigmoidal shape to the semicircular one. A num-ber of further observations have indicated that this hotchannel is actually the MFR that plays an importantrole in forming and accelerating the CME (Zhang et al.2012; Cheng et al. 2013a, 2014; Li & Zhang 2013). Inthis paper, we pay our attention to the long-term for-mation process of a hot channel in the sigmoidal ARNOAA 11520. We find that (1) the MFR is most likelyformed through coexisting reconnection at a bald patch(BP) and at a hyperbolic flux tube, driven by photo-spheric shearing and converging flows; (2) a second high-lying MFR (the hot channel) locates vertically above afilament-associated low-lying MFR; the whole structurethus constitutes a double-decker MFR system that sta-bly exists for about two hours prior to the eruption. Theinstruments are presented in Section 2. Observations ofthe MFR formation are displayed in Section 3, followedby the causes of the MFR formation in Section 4. InSection 5, we give our summary and discussions. INSTRUMENTS
The data used in this study are mainly from the AIA(Lemen et al. 2012) and the Helioseismic and MagneticImager (HMI; Schou et al. 2012), both of which are onboard the
SDO . The AIA includes ten passbands, six ofwhich image the solar corona almost simultaneously withan unprecedented high cadence (12 seconds) and highspatial resolution (1.2 (cid:48)(cid:48) ), covering the temperature rangefrom 0.06 MK to 20 MK (O’Dwyer et al. 2010). The HMIobserves the vector magnetic field of the full solar pho-tosphere with approximately the same spatial resolution(1.0 (cid:48)(cid:48) ) as the AIA but with a cadence of 12 minutes. TheX-Ray Telescope (XRT; Golub et al. 2007) aboard
Hin-ode (Kosugi et al. 2007) images the hot plasma in thecorona. The
Geostationary Operational EnvironmentalSatellite ( GOES ) and the
Reuven Ramaty High EnergySolar Spectroscopic Imager ( RHESSI ; Lin et al. 2002)spacecraft register the SXR and hard X-ray (HXR) fluxesof solar flares. In addition, the Large Angle and Spectro-metric Coronagraph (LASCO; Brueckner et al. 1995) onboard the
Solar and Heliospheric Observatory ( SOHO )and the Sun-Earth Connection Coronal and HeliosphericInvestigation (SECCHI; Howard et al. 2008) on boardthe
Solar Terrestrial Relations Observatory ( STEREO-A and
STEREO-B ) provide the EUV and white-lightimages of the CME. OBSERVATIONS OF THE MFR
Formation of double-decker MFR
On 2012 July 15, a magnetic cloud reached the Earthat ∼ ∼ ∼ a XRT Ti/poly 11-July 03:00UT d XRT Ti/poly 12-July 07:00UT b AIA 94 11-July 03:00UT e AIA 94 12-July 07:00UT c AIA 335 11-July 03:00UT f AIA 335 12-July 07:00UT
Fig. 1.—
Hinode /XRT Ti-poly (a and d) and
SDO /AIA 94 ˚A (b and e) and 335 ˚A images (c and f) showing the formation of the MFRin the sigmoidal AR 11520. The two J-shaped yellow dotted lines and the S-shaped one depict two bundles of strong sheared arcades andthe twisted field, respectively. (Animations this figure are available in the online journal.)
TABLE 1Phases of the formation and development of the double-decker MFR.
Time NoteJuly 7 00:00 UT The AR 11520 rotated from backside to the east limb.July 11 00:00 UT A sigmoidal structure appeared, the core field mainly consists of two sets ofhot sheared arcades (Figure 1a–1c, Figure 6g, and Figure 8a).July 11 00:00 – July 12 03:00 UT The sheared arcades transformed to the continuous S-shaped field lines (Fig-ure 1d–1f, Figure 6h, and Figure 8b) driven by the shear and convergenceflows near the main neutral line (Figure 7).July 12 14:00 UT A diffuse and elongated high-lying channel appeared (Figure 2a–2c and Figure3).July 12 16:10 UT The hot channel started to expand and rise (Figure 2g–2i), resulting in aCME (Figure 4) and X1.4 class flare, but the filament survived (Figure 5c).July 13 14:00 UT The low-lying MFR and associated filament could be identified with the dis-appearance of flare loops (Figure 5f and Figure 8d).July 15 06:00 UT The high-lying MFR-associated magnetic cloud arrived at the Earth.July 15 19:00 UT The Dst index peaks at −
127 nT .
UT, then rapidly increased from ∼ ∼ ∼ ≥ ∼ ∼ ∼ a XRT Al/thick 12-July 14:57UT b XRT Ti/poly 12-July 14:57UT
FR1FR2 c AIA 94 12-July 14:50UT d AIA 335 12-July 14:50UT e AIA 304 12-July 14:50UT
B (G) -1500-1000-500 0 500 1000 1500 f HMI 12-July 14:48UT
30 Mm g AIA 94 12-July 16:00UT h AIA 94 12-July 16:06UT i AIA 94 12-July 16:10UT
Fig. 2.—
Hinode /XRT and
SDO /AIA images displaying the double-decker MFR configuration before the eruption. a–f: XRT Al-thick,Ti-poly, the AIA 94 ˚A, 335 ˚A, 304 ˚A, and the HMI line-of-sight magnetogram. The two S-shaped dotted lines indicate the low-lying (yellow)MFR and the high-lying MFR (red), respectively. The field-of-view of the panel f is pointed out by the box in the panel c. g–i: AIA 94 ˚Aimages showing the expansion and rising of the over-lying MFR in the early eruption phase, as indicated by the red dotted lines.(Animations this figure are available in the online journal.) and the middle moving to the south. Because the channelis diffuse and less bright than the flare signatures, onlythe animation of the AIA 94 ˚A images that accompaniesFigure 2 permits a full appreciation of the hot channel’sshape and dynamics. While the hot channel erupted,the filament (as seen in Figure 2e) stayed in place; it didnot show any displacement larger than the slight changesin position seen during the preceding days. Such partialsigmoid eruptions are not uncommon (Pevtsov 2002) andhave been interpreted as a partial eruption of an MFR,whose top part has become unstable while the bottompart is tied to the photosphere in a BP (Gilbert et al.2001; Gibson & Fan 2006, 2008; Green & Kliem 2009).While this is a plausible scenario in general, here it runsinto difficulties because the HMI vector field data pre-sented below show a BP section of the PIL only under theshorter left part of the filament (see, e.g., Figure 9a be-low). Moreover, at least some motion of the filament waslikely to occur if it was part of the same erupting MFRas the hot channel; however, no motion in the southwarddirection of the eruption was seen. Next we considerthe arcade of loops that dominated the middle and leftpart of the sigmoid in the AIA 94 ˚A images prior to theeruption of the hot channel (marked by white arrows inFigure 2c). These loops did not show any systematicor significant change in position or shape while the hotchannel erupted (see Figure 2g–2i and the accompanyinganimation). Such a behavior is clearly at variance withthe interpretation that a single MFR erupted in part.Finally, we consider the perspective of
STEREO-B (Fig- ure 3a) and find that the filament was blocked behindthe solar limb, indicating it is low-lying; while the coun-terpart of the hot channel in the EUV 195 ˚A passband,probably from the emission of the Fe
XXIV line at 192˚A (Milligan & McElroy 2013), is located at a height of ∼
90 Mm above the limb in the period of 14:00–16:00UT, which is far above typical heights of active-regionfilaments (e.g., Tandberg-Hanssen 1995). Thus, we areled to conclude that the hot channel was independentof the magnetic flux of the filament-associated low-lyingMFR and constituted a double-decker MFR system al-ready prior to the onset of the impulsive phase of theeruption. Note that the identification of the structure ofthe filament with a low-lying MFR is further supportedby the NLFFF modeling in Section 4.3.
Partial Eruption of double-decker MFR
The explosive eruption of the high-lying MFR com-menced at ∼ ∼ ∼ ∼ a b c Fig. 3.— a: STEREO /EUVI-B 195 ˚A image from which no filament is seen. b and c:
STEREO /EUVI-B 195 ˚A running-differenceimages. The red arrows show the initial height of the high-lying MFR. The black lines display the optical solar limb.(Animation this figure is available in the online journal.) attached high cadence movies). After 16:10 UT, the foot-points brightenings extended along the direction of thePIL. At ∼ ORIGIN OF THE MFR
DEM Properties of MFR
Thanks to the multi-passband multi-temperatureimaging ability of AIA, differential emission measure(DEM) structures of the plasma in the AR can be con-structed. The observed flux F i for each AIA passband isgiven by F i = (cid:82) R i ( T ) × DEM( T ) d T , where R i ( T ) de-notes the temperature response function of passband i . In order to reduce the error of the DEM inversion,we first calibrate six near-simultaneous AIA EUV im-ages to the data level 1.5 using the SolarSoft routine“aia prep.pro” and then degrade the resolution to 2.4 (cid:48)(cid:48) by the routine “rebin.pro”, thus guaranteeing a goodcoalignment accuracy of 0.6 (cid:48)(cid:48) between the images in dif-ferent passbands (Aschwanden et al. 2013). Using the routine “xrt dem iterative2.pro” as proposed by Weberet al. (2004) and Golub et al. (2004), we reconstructthe DEM in each pixel. The validation of this inver-sion method and uncertainties of the DEM results canbe found in Cheng et al. (2012).With the DEM in each pixel, we calculate the emis-sion measure (EM) at the different temperature intervals(∆ T ) through the formula EM( T )= (cid:82) TT − ∆ T DEM( T (cid:48) )d T (cid:48) to construct the two-dimensional maps of the plasmaEM. Figure 6 shows the EM structure of the AR in threetemperature ranges. One can see that the emission in theambient volume of the AR is dominated by cool plasma(1–2 MK; upper row), whereas the emission of the sig-moidal structure is mostly from warm plasma (3–4 MK;middle row). Hot plasma (8–10 MK) contributes the sig-nificant emission in the sigmoid center (bottom row).The EM maps of the AR provide important clues forunderstanding the formation of the MFR. From the EMmaps in the early phase of the sigmoid, e.g., at 03:00UT on July 11 (Figure 6d), one can only see an indica-tion of the sigmoidal emission pattern at the warm tem-perature; while at the hot temperature, two groups ofclearly sheared sigmoidal arcades have already appeared.Their maximum EM is ∼ cm − , being comparable tothat of the loops in the warm temperature range. Withthe time elapsing, a clear sigmoidal emission pattern ap-peared at 07:00 UT on July 12 in the warm and hot tem-perature ranges, possibly due to the fact that magneticflux carrying heated plasma was added to the continu-ous S-shaped field (Figure 6h). This demonstrates thegradual pre-eruption evolution of the AR, forming anMFR by reconnection. The low-lying MFR is very wellcaptured in the EM maps, and a trace of the high-lyingMFR can be identified as well in Figure 6i by the cor-respondence with the diffuse S-shaped structure markedby the red line in the AIA 94 ˚A image in Figure 2c. Fi-nally, we note that the peak EM of the low-lying MFRat 10 MK decreased in Figure 6i (to ∼ cm − ); thismay correspond to the temporarily reduced rate of fluxcancellation (Figure 7a). Shearing and Converging Flows and SunspotRotation
In this section, we study the photospheric propertiesduring the MFR formation. We first plot the evolu-tion of the line-of-sight magnetic flux of the sigmoidal
Fig. 4.—
STEREO /COR1 and
SOHO /C2 white-light images of the CME on 2012 July 12. The white circles indicate the solar limb. b AIA 94 12-July 21:30UT e AIA 94 13-July 14:00UT c AIA 304 12-July 21:30UT f AIA 304 13-July 14:00UT
50 Mm a XRT Ti/poly 12-July 21:30UT d XRT Ti/poly 13-July 14:00UT
Fig. 5.—
Hinode /XRT Ti-poly and
SDO /AIA 94 ˚A and 304 ˚A images showing the post-flare loops (a–c) and the reappearance of thesigmoid after the eruption (d–f).
AR in Figure 7a. During 40 hours before the erup-tion, the positive flux increased from ∼ × Mx to ∼ × Mx, while the negative flux decreased slightlyfrom ∼ × Mx to ∼ × Mx. Overall, there isno significant flux emergence in the period of the MFRformation (Table 1 and Figure 7a). After the eruption,the positive flux approximately kept a constant valueof ∼ × Mx, whereas the negative flux quickly de-creased to ∼ × Mx at 00:00 UT on July 14. Thedecrease is most likely to be attributed to magnetic can-cellation along the main PIL as shown in Figure 7f–7i.In order to investigate the driver of the magnetic can-cellation, we calculate the transverse velocity of flux el-ements in the photosphere through applying the differ-ential affine velocity estimator (DAVE) to a temporalsequence of HMI line-of-sight magnetograms. This tech-nique assumes an affine velocity profile within a smallwindow and then executes variational principles to min-imize the deviations in the magnitude of the magneticinduction equation (Schuck 2005, 2006). The only freeparameter is the window size, which is set to 10 pixels inour calculation. According to the tests by Chae & Saku-rai (2008), this window size ensures a relative error lessthan 20%.We find that the MFR formation in the sigmoid is as-sociated with three main types of photospheric motions: shearing, converging, and rotational flows (see Figure 7f–7i and the accompanying movie). In the center of thesigmoid there are strong flows toward the PIL, mainlyfrom the positive-polarity side. These consist of the moatflow of the preceding sunspot and of the motion of thesunspot as a whole toward the PIL, both of which per-sist throughout the time range analyzed. These flowslead to strong magnetic cancellation in the middle of thesigmoid, between the straight legs of the initial double-J pair of arcades. Under the left part of the sigmoid,positive flux is intruding along the PIL toward the cen-ter of the AR with a velocity of ∼ − ; while theadjacent negative flux shows motions in the opposite di-rection at a velocity of ∼ − during part of thetime. This leads to strong shear flows at a section ofthe PIL that likely cause significant cancellation, sincethe polarities are closely butted against each other whilepossessing a strong relative motion. The shearing motionstretched the loops to form the two sets of J-shaped ar-cades (Figure 7b and 7f). The converging flows initiatedthe reconnection between their heads and tails, produc-ing the twisted field lines as suggested by Martens &Zwaan (2001). With the continuous photosphere-drivenreconnection, more and more J-shaped arcades are con-verted to the twisted flux and came into being the MFR(Figure 7c and 7g). l og E M ( c m - ) adg beh cfi T=1.3-1.6 MKT=3.2-4.0 MKT=8.0-10.0 MK T=1.3-1.6 MKT=3.2-4.0 MKT=8.0-10.0 MK T=1.3-1.6 MKT=3.2-4.0 MKT=8.0-10.0 MK
Fig. 6.—
EM maps of the sigmoidal AR at different temperature intervals and instants. Panels a–c, d–f, and g–i correspond to theintegrated temperature range of 1.3–1.6 MK, 3.2–4.0 MK, and 8.0–10.0 MK, respectively.
In addition to the shearing and converging motions,the rotation of the sunspot also has a significant role inbuilding up the MFR. From Figure 7g and 7h, one can seethat the preceding sunspot, where the right footpoints ofboth conjectured MFRs were anchored, has an obviousrotation motion (indicated in the red circles). The rota-tion angular velocity ( ∼ ◦ h − ) results in a maximal flowvelocity of ∼ − at the edge of the AR where thefootpoints of the MFR are located. The clockwise rota-tion twists the coronal field rooted in this sunspot in theright-handed sense, thus supporting the formation of theMFR. It is however difficult to identify the origin of therotation, which can be due to either a vortex motion inthe photosphere or the emergence of a strongly twistedflux tube, although the probability of the latter is smallfor a mature AR. Non-Linear Force-Free Field Modeling
We use an optimization algorithm proposed by Wheat-land et al. (2000) and implemented by Wiegelmann(2004) to extrapolate the three-dimensional (3D) NLFFFstructure of AR 11520. Due to the plasma pressure be-ing dominated by the magnetic pressure in the corona( β (cid:28)
1; Gary 2001), the coronal magnetic field gener-ally satisfies the force-free criteria, i.e., ∇ × B = α B and ∇ · B =0, where α is a constant along each field line.For the magnetic field above ARs, α varies in space(Wiegelmann & Neukirch 2002). The optimization algo-rithm minimizes the objective function L = (cid:82) V [ B − | ( ∇ × B ) × B | + |∇ · B | ] dV through iteration and thus ap-proaches the solution of the NLFFF equations (Wiegel-mann 2004). Before the extrapolation, we apply a pre-processing procedure to the bottom boundary vector data. This removes most of the net force and torque thatotherwise generally results in an inconsistency betweenthe forced photospheric magnetic field and the force-freeassumption in the NLFFF models (Wiegelmann et al.2006).We compute a time sequence of the 3D NLFFF struc-ture of the AR, covering a period of three days with acadence of 1 hour. The 3D magnetic field structures atfour instants are shown in Figure 8a–8h. One can seethat at 03:00 UT on July 11, the AR included three setsof field lines: two sets of strongly sheared arcades nearthe PIL and the overlying constraining field. The rightand left arcades correspond very well to the observeddouble-J sigmoid if seen from above (Figures 8a and 2a–b). By 07:00 UT on July 12, part of the two groups ofarcade field lines may have reconnected, as manifested bycontinuous sigmoidal field lines (Figure 8b), which forma weakly twisted flux rope. At 15:00 UT on July 12, thetwist in the rope reached a maximum, since more andmore flux was added to the rope by the ongoing recon-nection and the rotation of the sunspot (Figure 8c and8g). At 12:00 UT on July 13, in spite of the significantdecrease of the twist as a consequence of the eruption,the remaining twist still preserved the sigmoidal struc-ture (Figure 8d and 8h). Overall, the time sequence of3D NLFFF structures successfully reproduces the evolu-tion of the sigmoid, including the formation and twistingof an MFR before the eruption, as well as the survival ofa weakly twisted MFR after the eruption.The NLFFF structures provide the significant clues tothe question whether the stable filament resides in a mag-netic arcade or in a low-lying MFR. The HMI vector datashow that the horizontal field in the section of the PIL M agne t i c F l u x ( M x ) a b AIA 94 11-July 03:00UT c AIA 94 12-July 07:00UT d AIA 94 12-July 14:48UT e AIA 94 13-July 12:00UT Vmax=0.6 km/s fghi
Fig. 7.— a: Temporal evolution of the positive (solid line) and negative (dash-dotted line) magnetic flux in the FOV of panel f–i. Thevertical dotted-dash and dash lines show the first appearance of the MFR and the high-lying component of the double-decker MFR. Thevertical solid line donotes the onset time of the flare. b–e: AIA 94 ˚A images overlaid with the contours of the positive (white) and negative(black) polarities of the sunspots. Panel d is an AIA 94 ˚A base-difference image showing the double-decker MFR close to the eruption. Theyellow (red) S-shaped dotted lines indicate the low-lying (the high-lying) MFR. f–i: Line-of-sight magnetograms overlaid by the velocityfield at the photosphere and the field lines of the MFR. The green boxes refer to the region with strong shearing flow along the main PIL;the red circles indicate the region with strong rotation.(An animation this figure is available in the online journal.) under the left half of the sigmoid pointed in the inversedirection (from the negative to the positive side of thePIL). This BP signifies the topology of an MFR thatmust exist at least in this section of the PIL. The mag-netic field modeling suggests that this MFR extendedalong the whole length of the filament. We conjecturethat the sigmoid involved two MFRs, at least in the finaltwo hours before the eruption during which the hot chan-nel was seen. One MFR was high-lying and the other waslow-lying (holding the filament); both existed simultane-ously above the PIL, constituting a stable double-deckerMFR system. From the AIA 94 and 131 ˚A and XRT im-ages, it is obvious that the two branches of the double-decker system had very closely located footpoints at bothends but rather different lengths (Figure 2c).Furthermore, to study the properties of the reconnec- tion during the MFR formation in detail, we plot threerepresentative field lines DF, BC, and AE in Figure 9aand 9b. DF and BC denote the right and left shearedarcades, respectively. AE shows the S-shaped field of theMFR. To further examine the properties of the reconnec-tion at the different locations, we take three north-southoriented cross sections at x = s , s , and s (Figure 9a).The distributions of | J | / | B | (the total current densitynormalized by the total magnetic field) at x = s , s , and s are shown in Figure 9c–9e, respectively. Here, the cur-rent density is given by J = ∇ × B /µ , where µ =4 π × − G m A − . One can see that | J | / | B | at the cross sec-tion x = s is mainly concentrated at the BPs (Figure 9a–9c), where the horizontal photospheric field componentsshow inverse polarity (Figure 9a) and the field lines areconcave up with their bottom points touching the pho- Fig. 8.—
Extrapolated 3D NLFFF configurations corresponding to (a) the sheared arcades, (b–c) the pre-eruption sigmoid, and (d) thepost-eruption sigmoid. a–d: Top view; e–h: Side view. i-l: Distribution of the current density | J | integrated along the line of sight. Thebottom boundary is the vertical component of the vector magnetic field overlain by the horizontal component (arrows). tosphere (Figure 9b). At the cross section x = s , the dis-tribution of | J | / | B | displays an X-shape at the height of ∼ x = s ,the location of high coronal current density ascends toa higher position ( ∼
15 Mm) and is mostly concentratedinside the MFR; thus this current has likely a role inheating the MFR. Based on the above properties, we ar-gue that different types of reconnection, i.e., BP, HFT,and internal reconnection, probably exist simultaneouslyduring the formation of the MFR, either generating thetwist or heating the plasma.We also compare the distribution of the currents withthe emission pattern in the sigmoid. Figure 8i–8l showthe distributions of the current density integrated alongthe line of sight. It can be seen that the concentrationof the currents is mostly along the MFR axis with thelargest magnitude appearing at the regions correspond-ing to the BPs and the HFT. This fact infers that it is thecurrents that heat up the plasma inside and around the sigmoidal MFR, thus making a sigmoidal emission pat-tern. Moreover, one can notice that the current densitynear the main PIL increases before the eruption (Figure8i–j) and decreases afterwards (Figure 8k–l). This canbe qualitatively explained by the partial eruption of theconfiguration which released part of the coronal currents.In addition, we note that the NLFFF model is dif-ficult to reproduce the high-lying MFR in spite of itssignificant success in reproducing the long-term evolu-tion of the sigmoidal AR. Before the eruption, both thetwo sets of sheared arcades and the continuous S-shapedand twisted flux bundle are successfully reproduced bythe NLFFF model (Figure 8a and 8b). Even after theeruption, the NLFFF model is still powerful to recon-struct the MFR with a decreased twist that strongly re-sembles the surviving filament (Figure 8d). However,the NLFFF model does not fully succeed in reconstruct-ing the complex magnetic structure near the eruption.The extrapolated 3D structure at 15:00 UT on July 12only shows a low-lying twisted structure (Figure 8c), butmisses the high-lying MFR that separated from the low-0
S1 S2 S3
A B CD EF Mm X pointBP ab cde
Fig. 9.— a (top view) and b (side view): Representative field lines at 07:00 UT on July 12. The long field line illustrates flux afterreconnection, and the two shorter field lines illustrate flux before reconnection. The bottom boundary is the vertical component of thevector magnetic field overlain by the horizontal component (arrows). The blue (red) contours show the magnetic field strength of –1500 G(1500 G), the green contour display the PIL of AR. c–e: Distributions of | J | / | B | at x =S1, S2, and S3 as shown in panel (a). The locationof the BP and a conjectured HFT (X point) are indicated in panels (c) and (d), respectively. lying twisted field and appeared as the elongated hotchannel structure in the AIA 131 and 94 ˚A passbands.A possible reason for this partial failure can be ascribedto the proximity of the footpoints of the two twisted coro-nal structures (Figure 2c and Figure 7). For a successfulreconstruction of both structures, all four footpoint areasmust be well resolved by the vector magnetogram, whichobviously was not realized. SUMMARY AND DISCUSSION
In this paper, we investigate the origin of an MFR inthe sigmoidal AR that erupted at about 16:10 UT on2012 July 12 and produced an interplanetary magneticcloud that caused the strong geomagnetic storm event onJuly 15. We perform a detailed analysis of the AR’s evo-lution in the three days leading up to the eruption. Thisincludes tracking its morphological evolution, diagnos-ing the DEM properties, characterizing the motions ofmagnetic footpoints in the photosphere, and construct-ing a time sequence of 3D NLFFF models of the coronalstructure.A particularly interesting finding is that two MFRshave been formed above the same PIL of the sigmoidalAR and constituted a stable double-decker MFR systemfor at least two hours prior to the eruption. The con-cept of the double-decker MFR was recently proposedby Liu et al. (2012) to explain two vertically separatedfilaments over the same PIL. These authors payed muchattention to the identification of the double-decker fil-ament and to the discussion of the mechanisms of thepartial eruption of the system. In the present work, wepresent a second case that supports their new conjecturefor the magnetic structure of some CME source regionsand additionally concentrate on the formation process ofthe double-decker MFR. It is found that during a pe-riod of the first 40 hours prior to the eruption, an evolv-ing sigmoid manifested the formation of one MFR, mostlikely the result of reconnection between two groups ofsheared arcades near the main PIL. The driver of the re- connection is attributed to the shearing and convergingphotospheric flows in the vicinity of the PIL, as derivedwith the DAVE technique. The distribution of the cur-rent layers as indicated by the NLFFF extrapolation sug-gests that the reconnection happens simultaneously atthe BPs, i.e., photospheric flux cancellation, and in theHFT in the corona, i.e., tether-cutting. In the presentevent both worked at the same time in the process ofconverting the sheared arcades to the twisted field. Be-sides the shearing and converging flows, the rotation ofthe leading sunspot probably also played a role in formingthe MFR, similar to the vortex motions used for buildingup twist in some simulations (Amari et al. 2003; T¨or¨ok &Kliem 2003; Aulanier et al. 2005). A set of continuous S-shaped hot threads indicates that an MFR structure wasformed about half a day before the eruption. This low-lying MFR also hosted a filament and remained stable inthe eruption.From about two hours before the eruption we find ev-idence for the existence of a second MFR in the form ofa hot channel (Zhang et al. 2012; Cheng et al. 2013a),which was located above the first MFR. Only the sec-ond MFR erupted in the event studied here. The secondMFR could be observed by the AIA high-temperatureand XRT passbands. It is also imaged in the 195 ˚A pass-band, indicating emission in the Fe
XXIV line blend inthis channel ( ≥
15 MK; Milligan & McElroy 2013). Thelocation above the first MFR excludes its formation byemergence from below the photosphere. The high tem-perature suggests an important role for reconnection inthe formation. This and the proximity of the two MFRin the stable phase prior to the eruption suggest that thedouble-decker MFR system may have formed by a split-ting of the initial and low-lying MFR through the inter-nal reconnection. Such a splitting must be consideredas a tentative interpretation, since an MFR is a coher-ent large-scale structure that generally possesses a con-siderable degree of stability against perturbations. Thelow-lying MFR is perhaps most evident from the typi-1cally long-lasting stability of quiescent filaments. How-ever, indications that MFR can split or even completelydisintegrate do exist, both in observations and numericalmodeling. Prominences often show two branches that areclearly separated in height (e.g., Liu et al. 2012; Su et al.2011). The disintegration of a sigmoid by flux disper-sal was described in Tripathi et al. (2009). The verticalsplitting of an MFR in the evolution to an eruption ofonly the upper part was found in the numerical model-ing of the 1997 May 2 eruption (Kliem et al. 2013). Thisevolution was driven by photospheric flows converging atthe PIL and enforcing flux cancellation, and it involvedslow tether-cutting reconnection with the ambient fieldin an HFT formed between the splitting parts of the rope.The flux added between the two parts gradually stabi-lizes (destabilizes) the lower (upper) part of the splittingMFR. Kliem et al. (2013) further demonstrated that adouble-decker MFR system can be in stable equilibriumif the overlying field is sufficiently strong. They alsofound that the configuration admits a partial eruption,with only the upper branch erupting and the bottombranch remaining stable, very similar to the eruption ofthe high-lying hot channel and the stability of the low-lying filament. In the present event, strong perturbationsof the previously formed MFR in the sigmoid were givenby the intrusion of flux along the PIL under the left partof the sigmoid and by the rotation of the sunspot underthe right part of the sigmoid, both of which affected thefootpoint regions of either MFR. The conjectured inter-nal reconnection must have occurred high enough in thecorona (e.g., the second case of Figure 2 in Gilbert et al.2001) so that the remaining MFR could still support thefilament and continuously maintain the sigmoidal pat-tern of the AR.The partial eruption of the double-decker MFR sys-tem possesses some similarities to but also differencesfrom a partial eruption of a single MFR (Gilbert et al.2001; Gibson & Fan 2006, 2008). In that case, the re-connection happens in the interface between the MFRand the surrounding fields, e.g., near the crossing pointof a kinked MFR (Tripathi et al. 2013), which resultsin the escape of the upper part of the MFR with thelower part remaining at the original place. However, oneshould note that the driver of this internal reconnectionis attributed to the helical kink instability, which writhesthe MFR axis and generates a current sheet around theMFR (e.g., Kliem et al. 2010). In contrast, for the case ofthe double-decker MFR, photospheric shearing and con-verging motions drive the reconnection. Therefore, thetimescale of the separation is also different; it is nearlyinstantaneous in the partial eruption model but lasts forhours in the present case.In the early eruption phase, the morphology of thehigh-lying MFR varied from an S-shape to a loop-shape,which is very similar to the linear feature in eruptingsigmoids (e.g., Moore et al. 2001; McKenzie & Canfield2008; Liu et al. 2010; Aulanier et al. 2010; Green et al.2011; Zharkov et al. 2011). The high similarity suggeststhat the linear feature is most likely the MFR itself rather than the current shell above the MFR as suggested byAulanier et al. (2010). The difficulty in identifying thelinear feature with the MFR in previous studies can beattributed to the unavailability of the high temporal andspatial resolution data.As the high-lying MFR slowly ascends to a heightwhere the background field declines rapidly enough, thetorus instability probably triggers and initiates the im-pulsive acceleration of the MFR eruption (Kliem &T¨or¨ok 2006; T¨or¨ok & Kliem 2005; Fan & Gibson 2007;Aulanier et al. 2010; Olmedo & Zhang 2010; Savchevaet al. 2012a; Cheng et al. 2013b, 2014; Dud´ık et al. 2014).The initial brightening at the footpoints of the MFR inall EUV and UV passbands is consistent with an en-hancement of internal reconnection by the commencingeruption. This is followed by a seamless transition to themuch more rapid reconnection in the flare current sheet,in a mutual feedback with the unstable MFR, which notonly formed the flare loops further constraining the fil-ament but also produced the high-energy particles thatstream down along the newly reconnected loops to gen-erate two well-observed flare ribbons.Finally, we find that the NLFFF model of the coronalfield, obtained by extrapolation from a sequence of HMIvector magnetograms, succeeds in simulating importantaspects in the long-term quasi-static evolution of the sig-moidal AR. The model reproduces the formation of atwisted, sigmoidal flux rope from the highly sheared ar-cades in very good agreement with the observed coronalstructures, and it also resembles the weaker sigmoidalstructure after the partial eruption quite well. On theother hand, the double-decker magnetic configurationsuggested by the coronal data could not be found. Weconjecture that this results from insufficient resolutionof the structure in the magnetogram because the foot-points of the two branches were located in close prox-imity. Moreover, such a sequence of static models maycapture complex evolutions only if a much higher timeresolution is realized. These facts suggest that more ad-vanced models or MHD simulations should be developedin the future to deal with complex pre-eruption magneticstructures and their dynamic evolution.We thank Sarah Gibson, Antonia Savcheva, Yingna Su,David McKenzie, Haisheng Ji, and Yang Liu for valu-able discussions, and the referee for constructive com-ments that helped to improve the manuscript. SDO is amission of NASAs Living With a Star Program. X.C.,Y.G., and M.D.D. are supported by NSFC under grants10933003, 11303016, 11373023, 11203014, and NKBRSFunder grants 2011CB811402 and 2014CB744203. X.C.is also supported by Key Laboratory of Solar Activityof National Astronomical Observatories of the ChineseAcademy of Sciences by Grant KLSA201311. J.Z. is sup-ported by NSF grants ATM-0748003, AGS-1156120 andAGS-1249270. B.K. acknowledges support by the DFGand by the Chinese Academy of Sciences under Grant2012T1J0017.
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