Pre-eruption Splitting of the Double-Decker Structure in a Solar Filament

The filament eruption under investigation is associated with a GOES-class C3.7 flare and a fast halo CME on 2012 September 27. According to GOES 1–8 Å flux, the flare onsets at 23:36 UT and peaks at 23:57 UT. We investigate the eruption mainly using extreme ultraviolet (EUV) images taken by the Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) onboard the Solar Dynamics Observatory (SDO; Pesnell et al., 2012) and by the Extreme-UltraViolet Imager (EUVI; Wuelser et al., 2004) onboard the ‘Ahead’ satellite (hereafter STA) of the Solar Terrestrial Relations Observatory (STEREO; Kaiser et al., 2008). As of the flare peak, the separation angle between STA and Earth is 125.6 deg. Despite the cloudy weather, the filament splitting was observed in the H$\alpha$ line center and blue wing by the Big Bear Solar Observatory (BBSO).

AIA takes full-disk images with a spatial scale of $0^{\prime\prime}.6$ pixel^-1 and a cadence of 12 s. Among its 7 EUV and 2 UV passbands, we fixated our attention on 131 Å (primarily Fe XXI for flare plasma, with a peak response temperature $\log T=7.05$; Fe VIII for active regions, $\log T=5.6$), 193 Å (Fe XXIV for flare plasma, $\log T=7.25$; Fe XII for active regions, $\log T=6.2$), and 304 Å (He II, $\log T=4.7$). EUVI’s 195 and 304 Å passbands are similar to AIA’s 193 and 304 Å, respectively, but inferior in terms of spatial scale ($1^{\prime\prime}.59$ pixel^-1 ) and temporal cadence ($\sim\,$5 min).

The evolution of photospheric magnetic field in the source region is observed by the Helioseismic and Magnetic Imager (HMI; Scherrer et al., 2012) onboard SDO. In this study we worked with the Space-Weather HMI Active Region Patches (SHARP) vector magnetograms, which are de-projected to the heliographic coordinates with a Lambert (cylindrical equal area) projection method.

The filament of interest is an intermediate filament forming between two active regions. It has a reverse S shape (Fig. 1a) aligned along the PIL that separates the trailing positive polarity of NOAA active region (AR) 11575 on the west from the leading negative polarity of AR 11577 on the east (Fig. 1b). From ground-based H$\alpha$-filtergram observations one can see that the pre-eruption filament in H$\alpha$ (Fig. 1c), especially its northern section, looks much thicker and darker than the post-eruption remnant (Figure 1d), which is typical of partial eruptions. In fact, compared with its appearance during the earlier days, the filament looks darkest and thickest on 2012 September 27, just before its eruption (Figure 2(a–e)).

From over one hour before the flare onset, the filament is observed to gradually split into two branches. Slowly rising upward at a projected speed of $\sim\,$5 km s^-1, the upper branch exhibits swirling motions about its long axis that has a north-south orientation, along with counterstreaming motions along the axis (Figure 3(f & g) and accompanying animation). Similar in 6 different AIA passbands including 131, 171, 193, 211, 304, and 335 Å, the swirling appears clockwise if one looks along the field direction of the axis, i.e., from its southern end associated with positive polarity to northern end with negative polarity (cf. Figure 1b). The swirling also gives an impression that the motion follows a right-handed screw and that the upper branch has a tubular shape whose northern section is broader.

The splitting causes weak brightenings at the splitting interface (see the inset in Figure 3d and the animation accompanying Figure 1), which can be seen in both 304 and 131 Å, suggesting that the filament material, originally dark in 304 Å, is heated to transition-region temperatures. These brightened materials are transported by swirling motions back and forth, apparently along the tubular surface of the upper branch, which is manifested as the alternating black-and-white strips during 22:45– 23:15 UT in a stack plot (Figure 4d and accompanying animation). The stack plot is made by taking a slice along a line segment (marked as ‘S1’ in Figure 3d) from each 304 Å image available during the specified time interval and then arranging the slices in chronological order. S1 has a length of 90 Mm and each slice is averaged over the slit width of 6 pixels. Such slits are hereafter referred to as “virtual slits” to be differentiated from spectrograph slits.

From STA’s viewing angle, one can only see the southern hooked part of the lower branch that is lying low near the surface; the rest of the lower branch is probably behind the limb. The upper branch, on the other hand, has risen high above the limb by 23:06 UT (Figure 3a). Its northern section is bent upward, while its middle section lies flat (Figure 3(a–b)). The northern section of the sigmoidal filament is activated as early as of 22:06 UT on September 27, as captured by an H$\alpha$ blue-wing image (Figure 2f). At 22:51 UT, the splitting of the filament is visible in the H$\alpha$ center, but the upper branch appears to be still adhered to the lower branch (Figure 2g). By the time of 23:26 UT, which is 10 min before the flare onset, the upper branch has completely detached from the lower branch (Figure 2(h & i)).

From about 23:25 UT onward, the swirling motions are replaced by more irregular and drastic motions, while the upper branch accelerates its peeling off from the lower branch and moves quickly westward in projection (see the animation accompanying Figure 3). As seen through the virtual slit S1, this sudden change of dynamics is also demonstrated as the disappearance of alternating black-and-white strips and an increase in speed from about 6 km s^-1 to 24 km s^-1 and a further increase to 68 km s^-1 at the flare onset (Figure 4c). A J-shaped loop bundle is observed to rise synchronously with the upper branch and to disappear at the onset of the eruption (see the animation accompanying Figure 1). The loop bundle outlines the northern section of the sigmoid; its northern footpoint is marked by a diamond in Figure 3d. The loop’s rising speed increases from about 4 km s^-1 to about 18 km s^-1 at 23:25 UT in the stack plot (Figure 4e) made from a virtual slit S2 (Figure 3d), showing a similar evolution profile to the rising filament branch. Hence, it is considered to be part of the upper-branch structure.

Meanwhile, the upper branch of the filament is ‘whipped’ southward from STA’s perspective (Figure 3(b & c)). While its southern leg is still attached to the surface, its northern leg has become too thin to be visible. From SDO’s perspective, the ejection is not associated with any clear rotation of the filament axis (see the animation accompanying Figure 3). We measured the projected height at the horizontal section of the filament along a radial direction (Figure 3c). Despite the coarse cadence of EUVI images, the height-time plot shows a three-phase evolution in terms of the rising speed (Figure 4a), similar to what is observed by SDO. Associated with this southward whipping motion of the filament (see also Liu et al., 2009), an arc-shaped wavefront appears at about 23:30 UT at the periphery of the source region, propagating southwestward, as observed in the difference images of the 193 Å passband (Figure 3h). The wavefront is weak and diffuse, and disappears in a few minutes.

As the flare onsets at 23:35 UT, two flare ribbons appear in the chromosphere, as observed in the AIA 304 Å passband (see the animation accompanying Figure 1). The two ribbons reside at each side of the PIL outlined by the filament (Figure 1b), typical of the classic two-ribbon flares. With the progress of the flare, the two ribbons become thickened and separate from each other (Figure 4f), and the western (eastern) ribbon develops a ‘hook’ at its southern (northern) end, enclosing a pair of coronal dimmings (labeled ‘DN’ and ‘DS’ in Figure 3e and Figure 5a). The two J-shaped ribbons together constitute a reverse S shape, following a similar shape of the pre-eruption filament. The flaring loops that connect the two J-shaped ribbons are highly sheared in the south but potential-like in the north, therefore breaking the central symmetry of the reverse S-shape (Figure 3e). Specifically, in the wake of the eruption, the southern ‘elbow’ of the S shape remains prominent, outlined by disturbed filament material draining towards the surface, which maps the southern footpoint of the remaining filament (labeled ‘LB_sfp’ in Figure 5a); the northern ‘elbow’ of the S shape becomes less recognizable with the presence of potential-like post-flare loops. This is because the eruptive branch mainly resides in the north, which is also evidenced by its footpoints manifested as the conjugated pair of coronal dimming. It is noteworthy that immediately following the draining at LB_sfp at about 23:55 UT, one can see a surge of dark, diffuse material in 304 Å, which subsequently falls back toward the southern elbow (see the animation accompanying Figure 1). Such a back bouncing of falling filament material is well observed in the renowned 2011 June 7 event and reproduced in two-dimensional hydrodynamic simulations by Reale et al. (2013), assuming that magnetic field does not play an important role in such impacts on the surface.

Enclosed by the southern hook, the dimming region DS can be clearly seen in multiple EUV passbands, including 304 Å, 193 Å, 171 Å, 211 Å, and 94 Å (Figure 5), a signature of mass loss associated with the eruption, which has been further corroborated through EUV spectroscopic analysis (Veronig et al., 2019). Enclosed by the northern hook, the dimming region DN is clearly visible in AIA 304 Å, but obscure in other passbands. DS lies in the facular region of AR 11575, associated with relatively strong field, but DN lies mostly in the weak-field region to the north of AR 11577 (see Figure 1b and also Veronig et al., 2019). DS and DN together constitute a pair of conjugated footpoints of the eruptive structure. A similar situation is found not only in the case of a forming flux rope, whose footpoints are identified as a pair of coronal dimmings enclosed by hooked flare ribbons (Wang et al., 2017b), but also for the footpoints of four typical eruptive sigmoids (Cheng & Ding, 2016). It remains to be investigated what causes such an asymmetry in field strength in the footpoints of eruptive structures. It is noteworthy that DS begins to develop at about 23:30 UT, 5 min before the onset of the flare. This is demonstrated by the temporal variation of the average brightness (Figure 4a) sampled in a small box that is moving with the shifting and expanding dimming region (Figure 5c).

Although most of the source region observed in SDO/AIA is behind the solar limb from STA’s viewing angle (Figure 3e), one can see in STA/EUVI 304 Å that where the eruptive prominence’s southern leg is connected to the surface is at the same latitude as DS (Figure 3(b & e)), which provides a direct verification that DS is the southern footpoint of the erupting structure. Recall that the J-shaped loop bundle rises synchronously with the upper branch (§2.3). Its northern footpoint (labeled ‘J-loop_nfp’ in Figure 5a) falls within the northern dimming region DN, which corroborates our conclusion that DN is the northern footpoint of the erupting structure.

At this point we look back at the evolution of the source region leading up to the filament eruption. The filament is formed between AR 11577 and 11575. Both are decayed and categorized as $\beta\gamma$ according to the Mount Wilson classification as of the time of eruption. However, AR 11577 acquires its active-region number starting only from 2012 September 23, as an emerging active region with two major sunspots N1 and P1 moving westward and eastward, respectively (Figure 6b). Meanwhile, the flux concentrations become scattered, and in the field of view specified by Figure 6(b–e) both negative and positive flux decrease in magnitude with time (top of Figure 7). By late September 25 (Figure 6d), N1 has approached P2, the positive-polarity elements from AR 11575.

With the time-series of deprojected, co-registered HMI vector magnetograms (e.g., Figure 6a), we employed the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM; Schuck, 2008) to obtain the flow field (e.g., Figure 6(b–e)) and further calculated the relative helicity flux across the photospheric boundary $S$ as follows (Berger, 1984),

in which $t$ and $n$ indicate the tangential and normal directions, respectively. $\mathbf{A}_{p}$ is the vector potential of the reference potential field that is based on the photospheric $B_{n}$. $\mathbf{V}_{\perp}=\mathbf{V}-(\mathbf{V}\cdot\mathbf{B})\mathbf{B}/B^{2}$ is the photospheric velocity perpendicular to magnetic field lines (Liu & Schuck, 2012). The helicity injection into the active region can be attributed to either flux emergence (the term with $V_{\perp n}$) or photospheric motions that shear and braid field lines (the term with $V_{\perp t}$).

Within a rectangular region that includes N1, P1, and part of P2 (Figure 6b), the shear term with $\mathbf{V}_{\perp t}$ dominates over the emergence term with $V_{\perp n}$ until early September 24 (bottom of Figure 7). An episode of positive helicity injection on September 23 is associated with the emergence of the paired sunspots N1 and P1 in AR 11577, which is followed by an episode of negative helicity injection on September 24, associated with the migration of N1 toward P2 in AR 11575 (Figure 6). After that, contributions to helicity injection from both flux emergence and photospheric motions become negligible. Eventually, although the accumulated helicity is positive by September 27, its magnitude ($\sim 10^{41}$ Mx²) is one order below the typical helicity accumulated in emerging active regions (e,g, Liu et al., 2014, 2016). The filament of interest is already present to the east of AR 11575 before the emergence of AR 11577 (not shown), and maintains an inverse S shape until its eruption on September 27 (Figure 2), indicating that the chirality (helicity) of the filament is not significantly affected by the evolution of AR 11577.

What dominates the evolution of the source region from September 25 onward is the flux cancellation between N1 and P2, the dispersal of P1, and the converging motion of magnetic elements toward the PIL between N1 and P2 at speeds below 0.5 km s^-1 from either side of the PIL (Figure 6(d & e)). It is well known that a flux rope can be formed through tether-cutting-like reconnections in a magnetically sheared arcade. The reconnection can be driven either by dispersal and diffusion of photospheric fluxes or by shearing and converging flows around the PIL (e.g., van Ballegooijen & Martens, 1989; Moore et al., 2001; Green et al., 2011; Aulanier et al., 2010). From September 23 to 26, the flux cancellation rate is roughly $10^{26}$ Mx per day (top panel of Figure 7). But on September 26, both positive and negative magnetic flux become “saturated”, changing little in magnitude with time. Starting from September 27 onward, magnetic flux even increases slightly in magnitude with time. Thus, with the diminishing rate of flux cancellation, we consider it likely that the magnetic structure associated with the sigmoidal filament has taken on a definite form by September 26.

This observation demonstrates that a double-decker filament may form “quiescently” through gradual photospheric evolution, but only split to display two well-separated branches immediately before the eruption. In our case the splitting process begins as early as 1.5 hr before the onset of the flare. The two branches of the double-decker filament must be embedded in two distinct flux bundles before the eruption. This is evidenced by the distinctive separation between the southern footpoint of the remaining filament and that of the eruptive structure (Figure 5a).

The footpoints of the eruptive structure are identified through the conjugated dimming regions DN and DS, the latter of which starts to develop due to the enhancement in rising speed during the precursor stage (Figure 5c). The remaining filament keeps roughly the same sigmoidal shape in H$\alpha$ (Figure 1d), its northern footpoint must be close to the northern end of the filament channel (Figure 1a; labeled ‘FL_ne’ in Figure 5a), just like its sourthern footpoint, as highlighted by draining filament material, is close to the southern end of the filament channel (labeled ‘FL_se’ in Figure 5a). Since this separation in footpoints between the eruptive and remaining branch does not result from magnetic reconnection during the eruption but is rather ‘pre-eruptive’, the double-decker structure must be already present in the apparently single filament long before the eruption. The two flux bundles might be adhered to each other before splitting, similar to the simulation in Kliem et al. (2014). The heating of the splitting interface to transition-region temperatures might be related to the current accumulation and dissipation at the HFT separating the two flux bundles.

The swirling motion and the tubular shape as the motion reveals argue strongly for a flux-rope configuration possessed by the upper branch. However, it is unclear whether the swirling reflects mass motions along twisted field or motions of twisted field itself. On the other hand, reverse S-shaped structures are normally associated with negative helicity (Green et al., 2007; Zhou et al., 2020). Further, footpoints of both the upper and lower branch are clearly left-skewed relative to the PIL, which is also a signature of negative helicity (Chen et al., 2014; Ouyang et al., 2017).

Thus, if the rope is left-handed, the clockwise swirling (see § 2.2) may result from the untwisting of helical field lines, which can be naturally attributed to the decrease in twist density in a flux rope under rise and expansion. It is also possible that part of the twist is transferred to the ambient flux through reconnection between the flux rope and the ambient field, a mechanism proposed for the untwisting motions observed occasionally during the main eruption phase (e.g., Xue et al., 2016). Here due to the absence of obvious reconnection signatures associated with the swirling motions, we surmise that the reconnection rate must be extremely small if this mechanism were indeed at work.

Judging from images taken from two different viewing angles, one can see that the eruptive process does not involve any clear kinking motions (e.g., Gilbert et al., 2007), which excludes the helical kink instability as the trigger of the eruption.

The prominence’s flat part has risen to as high as 80 Mm above the surface at the flare onset (Figure 4a), its arched part is twice as much high at the same time (Figure 3c). Following the procedure in Wang et al. (2017a), we found that the decay index $n=-d\ln B/d\ln h$ at $\sim\,$80 Mm above the photospheric PIL is $3.4\pm 0.6$, and alternatively $n$ at the PIL of the potential field at $\sim\,$80 Mm is $2.3\pm 0.2$; both are significantly above the theoretical threshold value of 1.5 (Kliem & Török, 2006). Hence, the torus instability may be dominant in the eruption of the upper branch.

In conclusion, the double-decker filament under investigation possesses two distinct flux bundles, as demonstrated not only by the two well-separated branches but also by their well-separated footpoints during the precursor and eruption stages. The formation of the double-decker structure is associated with gradual magnetic flux cancellations and converging photospheric flows around the PIL over a few days. The splitting of the two flux bundles before eruption lifts the upper branch to a torus-unstable regime and result in the partial filament eruption. Thus, alternative to the reconnection-driven splitting during eruptions, this scenario provide a new evolutionary path towards partial eruptions of solar filaments. Such filaments may appear single but be actually embedded in a double-decker structure already before eruption (e.g., see also Cheng et al., 2014; Awasthi et al., 2019). The pre-eruption splitting is therefore not only an inherent process in the double-decker structure but also an indicator of the imminent eruption.