FORMATION OF A DOUBLE-DECKER MAGNETIC FLUX ROPE IN THE SIGMOIDAL SOLAR ACTIVE REGION 11520

On 2012 July 15, a magnetic cloud reached the Earth at ∼06:00 UT and then gave rise to a strong geomagnetic storm event with the minimal Dst index of −127 nT (∼19:00 UT). Inspecting the AIA data carefully, we find that the magnetic cloud was related to a strong solar eruption that occurred on July 12 and produced an X1.4 class flare and a fast halo CME. The flare was located at the heliographic coordinates S17W08. The corresponding source region is the NOAA AR 11520. The flare SXR flux started to rise gradually at ∼14:50 UT, then rapidly increased from ∼16:10 UT, and peaked at ∼16:49 UT.

In order to investigate the origin of the eruption, we examine the AIA images of the AR in all EUV passbands from July 6 to July 13. The overall evolution of the event is summarized in Table 1. It is found that the AR appeared at the solar limb on July 7 and progressively displayed a sigmoidal structure from July 11 onward. From the XRT Ti-poly and the AIA 94 Å images (Figures 1(a)–(b)), one can see that initially the sigmoid was mainly composed of two groups of J-shaped arcades, whose straight arms were located at the two sides of the PIL with the elbows crossing the PIL at opposite ends. From ∼03:00 UT on 2012 July 12, the two groups of J-shaped arcades gradually transformed to continuous S-shaped field lines (Figures 1(d)–(e)), which is a strong indication that an MFR has formed (e.g., Savcheva et al. 2012a). In the AIA 335 Å images, we only see an overall outer envelope of the sigmoid, in which the detailed evolution of the coronal structure is difficult to detect (Figures 1(c) and (f)). These results show that the formation of the MFR by the reconnection of J-shaped arcades mainly occurs in the core field of the sigmoid, where the plasma has been heated to high temperatures (⩾10 MK); while for the envelope of the sigmoid, the plasma temperature is relatively lower (∼2.5 MK), thus not indicating any strong reconnection. Moreover, in the AIA 304 Å passband, we notice that a J-shaped filament was visible from June 6 onward, located in the right part of the sigmoid. Its presence also indicates high shear or even twist of the sigmoid.

A closer inspection of the data leads us to the conclusion that a high-lying MFR and a low-lying MFR coexisted above the same PIL of the AR for 2 hr prior to the eruption. From ∼14:00 UT on July 12, we can see a diffuse and hot EUV channel structure in the AIA 94 Å passband (elongated S-shaped; outlined by the red dotted line in Figure 2(c)). The temperature of the channel is higher than 6 MK because it can only be seen in the hot temperature passbands (i.e., AIA 94 and 131 Å and XRT Ti-poly) but not in the other lower temperature ones (Figure 2(d)). From ∼16:00 UT, the hot channel showed an accelerating expansion (Figures 2(g)–(i)), with the elbows expanding eastward and westward and the middle moving to the south. Because the channel is diffuse and less bright than the flare signatures, only the animation of the AIA 94 Å images that accompanies Figure 2 permits a full appreciation of the hot channel's shape and dynamics. While the hot channel erupted, the filament (as seen in Figure 2(e)) stayed in place; it did not show any displacement larger than the slight changes in position seen during the preceding days. Such partial sigmoid eruptions are not uncommon (Pevtsov 2002) and have been interpreted as a partial eruption of an MFR, whose top part has become unstable while the bottom part 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 runs into difficulties because the HMI vector field data presented below show a BP section of the PIL only under the shorter left part of the filament (see, e.g., Figure 9(a) below). Moreover, at least some motion of the filament was likely to occur if it was part of the same erupting MFR as the hot channel; however, no motion in the southward direction of the eruption was seen. Next we consider the arcade of loops that dominated the middle and left part of the sigmoid in the AIA 94 Å images prior to the eruption of the hot channel (marked by white arrows in Figure 2(c)). These loops did not show any systematic or significant change in position or shape while the hot channel erupted (see Figures 2(g)–(i) and the accompanying animation). Such a behavior is clearly at variance with the interpretation that a single MFR erupted in part. Finally, we consider the perspective of STEREO-B (Figure 3(a)) and find that the filament was blocked behind the solar limb, indicating that it is low-lying; while the counterpart of the hot channel in the EUV 195 Å passband, probably from the emission of the Fe xxiv line at 192 Å (see, e.g., Milligan & McElroy 2013), is located at a height of ∼90 Mm above the limb in the period of 14:00–16:00 UT, which is far above typical heights of AR filaments (e.g., Tandberg-Hanssen 1995). Thus, we are led to conclude that the hot channel was independent of the magnetic flux of the filament-associated low-lying MFR and constituted a double-decker MFR system already prior to the onset of the impulsive phase of the eruption. Note that the identification of the structure of the filament with a low-lying MFR is further supported by the NLFFF modeling in Section 4.3.

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The explosive eruption of the high-lying MFR commenced at ∼16:10 UT, which resulted in the quick formation and acceleration of a CME and the rapid enhancement of the flare emission at various wavelengths. The CME first appeared as a limb event in the field of view (FOV) of the SECCHI coronagraphs, COR1-A and COR1-B, at ∼16:25 UT and as a halo CME in the FOV of LASCO/C2 at ∼17:00 UT (Figure 4). As for the flare, we note that the most remarkable feature from ∼15:00 UT to 16:10 UT is the brightening of the right arcade of the sigmoid and of the footpoints of the double-decker MFR, which are closely related to the slow rise and accelerating expansion of the high-lying MFR (Figures 2(g)–(i) and attached high cadence movies). After 16:10 UT, the footpoints' brightenings extended along the direction of the PIL. At ∼16:25 UT, the brightenings formed two ribbons in the chromosphere, which separated from each other afterward, as seen in the movies of the AIA 304, 1600, and 1700 Å passbands (see details in attached high cadence movies of Figure 2). From the AIA 94 Å and XRT Ti-poly images, we can see the arcade of flare loops, the ends of which corresponded well with the two separating ribbons (Figures 5(a)–(b)). Underneath the flare loops, the whole filament stayed quietly with the inferred low-lying MFR regardless of the eruption of the high-lying MFR. Moreover, we find that the CME in the COR1 images (Figure 4) mainly consisted of a bright front and a relatively diffuse cavity. We cannot, however, detect a clear appearance of a bright core that is generally thought to be erupted filament material and located at the bottom part of the cavity (Illing & Hundhausen 1983; Vourlidas et al. 2013). This seems to also support that the filament did not erupt, or at least did not fully erupt. Mostly, the whole filament structure was not influenced much by the high-lying MFR eruption.

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With the cooling and disappearance of the flare loops, the signatures of the low-lying MFR again showed up and redisplayed the sigmoidicity of the AR on July 13. In the high temperature passbands (AIA 94 Å and XRT Ti-poly; Figures 5(d) and (e)), one can obviously see that some S-shaped field lines became visible in the AR. The survived filament was located in the middle of the sigmoid as seen in the AIA 304 Å passband (Figure 5(f)).

Due to the multi-passband multi-temperature imaging ability of AIA, differential emission measure (DEM) structures of the plasma in the AR can be constructed. The observed flux F_i for each AIA passband is given by F_i = ∫R_i(T) × DEM(T) dT, where R_i(T) denotes 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 images to the data level 1.5 using the SolarSoft routine "aia_prep.pro" and then degrade the resolution to 24 by the routine "rebin.pro," thus guaranteeing a good coalignment accuracy of 06 between the images in different passbands (Aschwanden et al. 2013). Using the routine "xrt_dem_iterative2.pro" as proposed by Weber et al. (2004) and Golub et al. (2004), we reconstruct the DEM in each pixel. The validation of this inversion method and uncertainties of the DEM results can be found in Cheng et al. (2012).

With the DEM in each pixel, we calculate the emission measure (EM) at the different temperature intervals (ΔT) through the formula EM(T) = $\int _{T-\Delta T}^{T}{\rm DEM}(T^\prime)$dT' to construct the two-dimensional maps of the plasma EM. Figure 6 shows the EM structure of the AR in three temperature ranges. One can see that the emission in the ambient volume of the AR is dominated by cool plasma (1–2 MK; upper row), whereas the emission of the sigmoidal structure is mostly from warm plasma (3–4 MK; middle row). Hot plasma (8–10 MK) contributes the significant emission in the sigmoid center (bottom row).

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The EM maps of the AR provide important clues for understanding the formation of the MFR. From the EM maps in the early phase of the sigmoid, e.g., at 03:00 UT on July 11 (Figure 6(d)), one can only see an indication of the sigmoidal emission pattern at the warm temperature; while at the hot temperature, two groups of clearly sheared sigmoidal arcades have already appeared. Their maximum EM is ∼10²⁸ cm⁻⁵, being comparable to that of the loops in the warm temperature range. With the time elapsing, a clear sigmoidal emission pattern appeared at 07:00 UT on July 12 in the warm and hot temperature ranges, possibly due to the fact that magnetic flux carrying heated plasma was added to the continuous S-shaped field (Figure 6(h)). This demonstrates the gradual pre-eruption evolution of the AR, forming an MFR by reconnection. The low-lying MFR is very well captured in the EM maps, and a trace of the high-lying MFR can be identified as well in Figure 6(i) by the correspondence with the diffuse S-shaped structure marked by the red line in the AIA 94 Å image in Figure 2(c). Finally, we note that the peak EM of the low-lying MFR at 10 MK decreased in Figure 6(i) (to ∼10²⁷ cm⁻⁵); this may correspond to the temporarily reduced rate of flux cancellation (Figure 7(a)).

In this section, we study the photospheric properties during the MFR formation. We first plot the evolution of the line-of-sight magnetic flux of the sigmoidal AR in Figure 7(a). During 40 hr before the eruption, the positive flux increased from ∼3.6 × 10²² Mx to ∼4.0 × 10²² Mx, while the negative flux decreased slightly from ∼1.7 × 10²² Mx to ∼1.5 × 10²² Mx. Overall, there is no significant flux emergence in the period of the MFR formation (Table 1 and Figure 7(a)). After the eruption, the positive flux approximately kept a constant value of ∼4.0 × 10²² Mx, whereas the negative flux quickly decreased to ∼1.0 × 10²² Mx at 00:00 UT on July 14. The decrease is most likely to be attributed to magnetic cancellation along the main PIL as shown in Figures 7(f)–(i).

In order to investigate the driver of the magnetic cancellation, we calculate the transverse velocity of flux elements in the photosphere by applying the differential affine velocity estimator (DAVE) to a temporal sequence of HMI line-of-sight magnetograms. This technique assumes an affine velocity profile within a small window and then executes variational principles to minimize the deviations in the magnitude of the magnetic induction equation (Schuck 2005, 2006). The only free parameter is the window size, which is set to 10 pixels in our calculation. According to the tests by Chae & Sakurai (2008), this window size ensures a relative error less than 20%.

We find that the MFR formation in the sigmoid is associated with three main types of photospheric motions: shearing, converging, and rotational flows (see Figures 7(f)–(i) and the accompanying movie). In the center of the sigmoid there are strong flows toward the PIL, mainly from the positive-polarity side. These consist of the moat flow of the preceding sunspot and of the motion of the sunspot as a whole toward the PIL, both of which persist throughout the time range analyzed. These flows lead to strong magnetic cancellation in the middle of the sigmoid, 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 center of the AR with a velocity of ∼0.3 km s⁻¹; while the adjacent negative flux shows motions in the opposite direction at a velocity of ∼0.2 km s⁻¹ during part of the time. This leads to strong shear flows at a section of the PIL that likely cause significant cancellation, since the polarities are closely butted against each other while possessing a strong relative motion. The shearing motion stretched the loops to form the two sets of J-shaped arcades (Figures 7(b) and (f)). The converging flows initiated the reconnection between their heads and tails, producing the twisted field lines as suggested by Martens & Zwaan (2001). With the continuous photosphere-driven reconnection, more and more J-shaped arcades are converted to the twisted flux and came into being the MFR (Figures 7(c) and (g)).

In addition to the shearing and converging motions, the rotation of the sunspot also has a significant role in building up the MFR. From Figures 7(g) and (h), one can see that the preceding sunspot, where the right footpoints of both conjectured MFRs were anchored, has an obvious rotation motion (indicated in the red circles). The rotation angular velocity (∼3° hr⁻¹) results in a maximal flow velocity of ∼0.6 km s⁻¹ at the edge of the AR where the footpoints of the MFR are located. The clockwise rotation twists the coronal field rooted in this sunspot in the right-handed sense, thus supporting the formation of the MFR. However, it is difficult to identify the origin of the rotation, which can be due to either a vortex motion in the photosphere or the emergence of a strongly twisted flux tube, though the probability of the latter is small for a mature AR.

We use an optimization algorithm proposed by Wheatland et al. (2000) and implemented by Wiegelmann (2004) to extrapolate the three-dimensional (3D) NLFFF structure of AR 11520. Due to the plasma pressure being dominated by the magnetic pressure in the corona (β ≪ 1; Gary 2001), the coronal magnetic field generally satisfies the force-free criteria, i.e., ∇ × B = αB 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 algorithm minimizes the objective function L = ∫_V[B⁻²|(∇ × B) × B|² + |∇ · B|²]dV through iteration and thus approaches the solution of the NLFFF equations (Wiegelmann 2004). Before the extrapolation, we apply a preprocessing procedure to the bottom boundary vector data. This removes most of the net force and torque that otherwise generally results in an inconsistency between the forced photospheric magnetic field and the force-free assumption in the NLFFF models (Wiegelmann et al. 2006).

We compute a time sequence of the 3D NLFFF structure of the AR, covering a period of three days with a cadence of 1 hr. The 3D magnetic field structures at four instants are shown in Figures 8(a)–(h). One can see that at 03:00 UT on July 11, the AR included three sets of field lines: two sets of strongly sheared arcades near the PIL and the overlying constraining field. The right and left arcades correspond very well to the observed double-J sigmoid if seen from above (Figures 8(a) and 2(a)–(b)). By 07:00 UT on July 12, part of the two groups of arcade field lines may have reconnected, as manifested by continuous sigmoidal field lines (Figure 8(b)), which form a weakly twisted flux rope. At 15:00 UT on July 12, the twist in the rope reached a maximum, since more and more flux was added to the rope by the ongoing reconnection and the rotation of the sunspot (Figures 8(c) and (g)). At 12:00 UT on July 13, in spite of the significant decrease of the twist as a consequence of the eruption, the remaining twist still preserved the sigmoidal structure (Figures 8(d) and (h)). Overall, the time sequence of 3D NLFFF structures successfully reproduces the evolution of the sigmoid, including the formation and twisting of an MFR before the eruption, as well as the survival of a weakly twisted MFR after the eruption.

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The NLFFF structures provide the significant clues to the question whether the stable filament resides in a magnetic arcade or in a low-lying MFR. The HMI vector data show that the horizontal field in the section of the PIL under the left half of the sigmoid pointed in the inverse direction (from the negative to the positive side of the PIL). This BP signifies the topology of an MFR that must exist at least in this section of the PIL. The magnetic field modeling suggests that this MFR extended along the whole length of the filament. We conjecture that the sigmoid involved two MFRs, at least in the final 2 hr before the eruption during which the hot channel was seen. One MFR was high-lying and the other was low-lying (holding the filament); both existed simultaneously above the PIL, constituting a stable double-decker MFR system. From the AIA 94 and 131 Å and XRT images, it is obvious that the two branches of the double-decker system had very closely located footpoints at both ends but rather different lengths (Figure 2(c)).

Furthermore, to study the properties of the reconnection during the MFR formation in detail, we plot three representative field lines DF, BC, and AE in Figures 9(a) and (b). DF and BC denote the right and left sheared arcades, respectively. AE shows the S-shaped field of the MFR. To further examine the properties of the reconnection at the different locations, we take three north–south oriented cross-sections at x = s₁, s₂, and s₃ (Figure 9(a)). The distributions of |J|/|B| (the total current density normalized by the total magnetic field) at x = s₁, s₂, and s₃ are shown in Figures 9(c)–(e), respectively. Here, the current density is given by J = ∇ × B/μ₀, where μ₀ = 4π × 10⁻³ G m A⁻¹. One can see that |J|/|B| at the cross-section x = s₁ is mainly concentrated at the BPs (Figures 9(a)–(c)), where the horizontal photospheric field components show inverse polarity (Figure 9(a)) and the field lines are concave up with their bottom points touching the photosphere (Figure 9(b)). At the cross-section x = s₂, the distribution of |J|/|B| displays an X-shape at the height of ∼4 Mm, suggesting an HFT in 3D; this indicates that the reconnection mainly takes place in the corona (Figure 9(d)). At the cross-section x = s₃, the location of high coronal current density ascends to a higher position (∼15 Mm) and is mostly concentrated inside the MFR; thus this current likely has a role in heating the MFR. Based on the above properties, we argue that different types of reconnection, i.e., BP, HFT, and internal reconnection, probably exist simultaneously during the formation of the MFR, either generating the twist or heating the plasma.

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We also compare the distribution of the currents with the emission pattern in the sigmoid. Figures 8(i)–(l) show the distributions of the current density integrated along the line of sight. It can be seen that the concentration of the currents is mostly along the MFR axis with the largest magnitude appearing at the regions corresponding to the BPs and the HFT. This fact infers that it is the currents that heat up the plasma inside and around the sigmoidal MFR, thus making a sigmoidal emission pattern. Moreover, one can notice that the current density near the main PIL increases before the eruption (Figures 8(i)–(j)) and decreases afterward (Figures 8(k)–(l)). This can be qualitatively explained by the partial eruption of the configuration which released part of the coronal currents.

In addition, we note that it is difficult for the NLFFF model to reproduce the high-lying MFR in spite of its significant success in reproducing the long-term evolution of the sigmoidal AR. Before the eruption, both sets of sheared arcades and the continuous S-shaped and twisted flux bundle are successfully reproduced by the NLFFF model (Figures 8(a) and (b)). Even after the eruption, the NLFFF model is still able to reconstruct the MFR with a decreased twist that strongly resembles the surviving filament (Figure 8(d)). However, the NLFFF model does not fully succeed in reconstructing the complex magnetic structure near the eruption. The extrapolated 3D structure at 15:00 UT on July 12 only shows a low-lying twisted structure (Figure 8(c)), but misses the high-lying MFR that separated from the low-lying twisted field and appeared as the elongated hot channel structure in the AIA 131 and 94 Å passbands. A possible reason for this partial failure can be ascribed to the proximity of the footpoints of the two twisted coronal structures (Figures 2(c) and 7). For a successful reconstruction of both structures, all four footpoint areas must be well-resolved by the vector magnetogram, which obviously was not realized.