Manifestations of Three-dimensional Magnetic Reconnection in an Eruption of a Quiescent Filament: Filament Strands Turning to Flare Loops

Prior to its eruption on 2012 August 31, the filament was quiescent for more than one Carrington rotation (Figure 1(a)). In Figure 1(b), two legs of the eruptive filament can be distinguished. The eastern leg was composed of strands anchored in footpoints located in a close spatial proximity. Some of the filament strands observed in this leg were bright in all of the EUV filter channels of AIA, and best seen in the 131 and 171 Å (see Figures 1(b), (e), and the animation accompanying Figure 1). The brightness of the filament strands might be due to enhanced TR or coronal emission during the eruption (see, e.g., Parenti et al. 2012; Williams et al. 2014, respectively). The western leg was not as spatially concentrated as the eastern leg, as it spread through more than 400'' in the neighborhood of several active regions. Here we also observed several bright strands composing the filament; however, the majority of them were obscured by the rest of the erupting filament at some point during the event.

Rising of the filament can first be distinguished in the EUV filter channels data at around 19:30 UT (see the animation accompanying Figure 1). At the same time, the GOES X-ray emission started to increase (Figure 1(i)). During the eruption of the filament, the GOES emission kept rising until it reached its broad maximum at ≈20:15–20:30 UT. Hinode/XRT data reveal hot flare loops after the onset of the eruption (panel (g)), with a bulk of emission present underneath the erupting filament. At the maximum of the impulsive phase, the arcade of flare loops was fully formed (panel (h)). Later, during the gradual phase of the flare (after ≈20:30 UT) this arcade progressively cooled, as it was observed in filter channels of AIA with lower typical temperatures, such as 304 Å (panel (d), also see Section 4.2). Filament apex left the field of view of the instrument at around 20:00 UT (panels (b)–(c)), but its legs remained observable until ≈21:30 UT, when they completely disappeared.

A pair of flare ribbons formed at the onset of the eruption. During the course of the eruption, both ribbons underwent complicated elongation and developed hooks. For their description we use acronyms "N" (resp. "P") for negative (resp. positive) polarity, "R" for ribbon, and "RH" for ribbon hook (Figure 1(c)).

Panels (a)–(d) of Figure 1 indicate that during the eruption the ribbon hook NRH, encircling the filament's eastern leg, both propagated westward and shrunk. Its morphology and evolution throughout the course of the eruption is detailed in the following section.

The evolution of the flare ribbons was studied using data of the 1600 and 1700 Å filter channels. Dudík et al. (2016) introduced a method of using ratios of these filter channels in order to enhance the TR emission of C iv in flare kernels with respect to the photospheric contributions. NRH in the observed ratios is shown in Figure 2. In each individual frame, NRH was manually traced by identifying multiple nodes along it (red squares) which were then interpolated using the spline function (red dashed lines). Here we mainly focus on the interaction of the ribbon NR with footpoints of the filament encircled by what later became NRH. Therefore, we were selecting edges of the ribbon NR in the direction of its propagation (ribbon front), while we primarily focused on the morphology of NRH.

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Kernels which composed NR first appeared at ≈19:32:20 UT (panel (a)). The ribbon then elongated to a J-shaped structure, creating the hook NRH. Afterwards, NRH started to propagate toward the west and contract. Panels (d)–(e) show that the ribbon joined with the kernels located in the internetwork to the west, while the tip of the hook elongated in a V-shaped trajectory (arrow "a1" in panel (d)). Later, the tip of the hook further elongated toward NW in a circular shape (arrow "a2" in panel (f)), while the straight part of the ribbon "jumped" over a supergranule located at around [−680'', −360''] (panels f–j). After ≈21:00 UT (panels (k)–(l)), propagation of the ribbon decelerated and the ribbon started to gradually fade away.

Panel (l) shows the evolution of the ribbon throughout the course of the eruption at a 2 minute cadence. Lines indicating the positions of the ribbon were color-coded in order to distinguish between the times in which the ribbon was observed, ≈19:30 UT to ≈22:00 UT, coded from blue to red, respectively. Deceleration of the ribbon propagation can be seen by comparing mutual distances between the blue curves at the beginning of the eruption and the red curves at its end. Note the brief acceleration of NRH through a small region at [−690'', −320''] and of the straight portion of NR through the supergranule located at [−680'', −360''].

In this section we focus on the evolution of the filament leg located inside the evolving NRH as well as overlying corona. Figure 3 shows NRH and its surroundings as observed in the 171 and 94 Å filter channels of AIA.

We first analyze the 171 Å observations processed using MGN (panels (a)–(l), see the animated version). There, blue dashed lines mark the derived positions of NRH. At the beginning of the eruption (Figures 3(a)–(b)), footpoints of the filament were distributed along a narrow region approximately ≈40'' long.

Bright strands composing the filament (hereinafter strands) were found to have footpoints located inside the hook (black and white circles named F1–F4). This finding is in agreement with results of 3D simulations of flux rope eruption of Zuccarello et al. (2015) and analysis of reconnection geometries occurring at ribbon hooks of Aulanier & Dudík (2019). According to the HMI observations of the photospheric magnetic field strength, these footpoints were located in regions of varying B_LOS at the boundary of strong-field regions dominated by the negative polarity (Figure 3(m)).

The appearance of NRH seen in panels (a) and (b) of Figure 3 was followed by several changes in the configuration of the filament strands. As NRH started to propagate and contract, the curved part of the hook ("elbow") crossed the footpoint F1 (panel (c)). This means that the intensity enhancements corresponding to the chromospheric or transition region flare ribbons changed position, apparently moving through the location of F1 in the plane of sky. (In the following, we will further refer to the locally perpendicular motion of the ribbon as "sweeping," similarly as in Aulanier & Dudík 2019). After the ribbon swept F1, the strands anchored there disappeared (panels (c)–(d)). We note that this description is of morphological evolution only, while the physical interpretation is left to Section 5.2.

At the same time, the footpoint F4 and strands anchored therein started to fade away and drift toward NE. There, they got obscured by new bright strands, which appeared in position F5 located inside NRH in a strong-field region (B_LOS ≈ −120 G) close to F3 and F4. Later on, the elbow of the hook propagated toward SW and swept footpoints of strands located between F1 and F2 (panels (d)–(f)) and then the footpoints F2 (≈20:10 UT, panel f) and F3 (≈20:36 UT, panel (i)). In the meantime, more and more strands anchored in F5 appeared. This trend of footpoint sweeping remained throughout the whole propagation of the hook elbow toward SW, until ≈21:00 UT, when all the footpoints were concentrated in F5. Finally, F5 was swept away after ≈21:30 UT and all the strands rooted therein disappeared (see panels (k)–(l) and the accompanying animation).

Strands rooted in footpoints F2, F3, and F5, as well as in between them are also detailed in Figure 4 (also see the accompanying animation). Panels (a)–(j) show a detailed view of NRH at a higher cadence of two minutes. Panels (k) and (l) show time–distance diagrams containing the emission of filament strands anchored in studied footpoints, constructed along the arrow shown in panel (a). The arrow was directed perpendicularly to the filament strands and drawn in a location where contribution from the coronal moss emitting in the background was low. In panel (l), the emission of loops anchored in the footpoints F2, F3, and F5 is denoted by blue captions. Times at which the emission of strands anchored in F2 and F3 disappeared are marked with blue "X" symbols. These were found to correspond to the moments at which NRH swept the footpoints of the respective strands, i.e., ≈20:14 UT for F2 and ≈20:38 UT for F3. In the same panel, a motion of strands lasting between ≈20:18 UT–20:36 UT can also be seen between the two "X" symbols. It corresponds to sequential disappearing of filament strands rooted between F2 and F3 due to the sweeping of their footpoints and its velocity was found to be about 8 km s⁻¹. We note that fitting this motion with a single linear regression was difficult due to bright material downfalling along the strands. This phenomenon occurs along the majority of the observed strands and is most evident after the onset of the eruption at ≈19:30 UT and later between ≈20:20 UT and 20:40 UT, i.e., when the footpoints between F2 and F3 were swept (see the animation accompanying Figure 3).

Broadening of the patch of filament strands anchored in F5 can also be traced in these time–distance diagrams. At ≈20:00 UT, the patch of strands anchored in the newly formed footpoint F5 was about ≈6'' wide (t1 in panel (l)). At about 20:12 UT, after NRH swept F2 and started to sweep the footpoints between F2 and F3, the patch of strands started to broaden in both directions along the cut at uneven velocities of 8 and 3 km s⁻¹. This apparent drifting lasted for about 30 minutes and in the end, the patch was ≈23'' wide (t2 in panel (l)).

We note that the broadening of F5 might be caused by the dynamics of the filament plasma itself. Motions of plasma within a stationary filament model were found by Luna et al. (2012). There, authors performed spectral synthesis of condensations moving along filament field lines. The synthetic Hα, 171, and 211 Å emission showed that vertical filament strands can become illuminated by falling filament plasma (see animation (b)) accompanying Figure 11 in Luna et al. 2012), which is similar to our observations. Nevertheless, even the footpoint F5 was eventually swept by the ribbon.

Finally, we note that the period during which the strands rooted in the footpoints F1–F3 seemingly drifted to F5 corresponds well to the impulsive and peak phases of the flare (shaded area in Figure 1(i)).

Figure 3 shows a bundle of coronal loops anchored in a neighborhood of NRH ("CL," white arrow in Figure 3(a)). Figures 3(d)–(e) show that after the tip of NRH elongated in a V-shaped trajectory (Section 3.2), it started to converge toward CL. Later on (panel (f)), CL became encircled by the tip of NRH and consequently started to fade away as it was swept by NRH (panels (f)–(h)). After ≈20:36 UT (panel (i)), CL was not visible anymore. Finally, the tip of NRH straightened over the region where CL was located. This can, however, only be seen in the shape of NRH in 171 Å (panels (k)–(l)), as it was not sufficiently bright in the ratios of the 1600 and 1700 Å filter channels.

The fading of CL was further investigated using a time–distance diagram constructed along the cut shown in Figure 3(b) (Figure 5). Here, the background emission was excluded by setting the minimal intensities plotted higher than the intensity of the background (100 DN s⁻¹ px⁻¹) found by averaging in regions close to CL. Figure 5 thus only contains the emission of CL and bright filament blobs and strands passing through the field of view (FOV) during the eruption. According to this time–distance diagram, CL was fading since ≈20:04 UT, until it disappeared at ≈20:30 UT. The emission present later at position ≈10'' of the cut originates in the tip of NRH which appeared under the cut.

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Note that the fading of CL is not sequential as is observed in Figure 4 for the disappearance of bright filament strands, mainly because of its brief apparent broadening after ≈20:16 UT. This effect is caused by the passage of strands of the erupting filament throughout the FOV. Analysis of fading of CL is also complicated by oscillations of CL throughout the course of the eruption (see the animation accompanying Figure 3). Despite these complications, Figure 5 indicates that the period during which CL faded and disappeared roughly corresponds to the period of sweeping of the filament strands anchored in F2, F3, and between them.

To investigate the appearance of flare loops in a vicinity of NRH, we reviewed the 94 Å filter channel observations (Figures 3(n)–(x), see also the accompanying animation). These filtergrams were averaged in three consecutive exposures to minimize the noise in the 94 Å. NRH was indicated using orange dashed lines.

The first flare loops were observed around 19:48 UT and were sheared (Figures 3(o), 1(g)). Afterwards, arcade of less-sheared flare loops with footpoints in the elbow of NRH appeared (panels (p)–(q)). It was generally difficult to distinguish individual flare loops within this arcade. Some of the conspicuous ones are denoted by "fl1" and "fl2" (see panels (r) and (t), respectively); however, their footpoints cannot be easily distinguished due to overlapping structures. Later on, as the arcade cooled, flare loops were seen in 171 and 211 Å filter channels showing cooler emission (Figures 3(j)–(l) and 6(a), respectively).

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As is apparent in panels (p)–(r) of Figure 3, most of the arcade formed suddenly without showing any sequence in appearance of flare loops. Therefore, it was not possible to study the evolution of particular flare loops at the same time as the hook swept footpoints of the filament strands. On the other hand, panels (q)–(x) show that the footpoints of the arcade correspond to the propagating NRH, which means that flare loops emerge in locations which were originally located inside NRH and then swept by it. Therefore, we emphasize that this arcade is not a result of the standard aa–rf reconnection between two coronal loops, as described in the standard CSHKP model, but occurs in a purely three-dimensional magnetic reconnection geometry.

We note that we also observed emission projected to the interior of NRH, such as flare loops anchored in NRH slipping toward the tip of the hook (orange arrow "i1" in panel (n), see also Lörinčík et al. 2019), projected flare loops with conjugate footpoints located to the east (arrow "i2" in panel (q)), and multithermal emission of filament strands during the broadening of the patch of strands rooted in F5 (arrow "i3" in panel (t)).

Because of the nature of the flare loop emission observed in the 94 Å filter channel, we could not directly identify flare loops formed as a product of reconnection of the filament's bright strands. Therefore, we attempted to find such a flare loop using filter channels typically sensitive to cooler emission such as the 171, 193, and 211 Å. In these filter channels, due to high count rates in active regions, MGN can be utilized in order to enhance individual flare loops within the flare loop arcade.

Figure 6(a) shows the 211 Å observations of the flare arcade during the gradual phase of the flare. The temperature response of this filter channel peaks at ≈2 MK and the emission typically observed in active regions is dominated by Fe xiv (Del Zanna 2013). The arcade observed within this channel formed at around 21:00 UT by cooling of the arcade observed in the 94 Å. Within this arcade, numerous individual flare loops connecting PR with NR and NRH can be seen. In 211 Å, these loops are bright and their structure further enhances by the MGN technique. Some of the loops that stand out are anchored in F1, F2, and in F4, i.e., in the previous footpoints of bright strands of the erupted filament (see Figures 3(a)–(b)).

To study the evolution of the flare emission, we selected a distinct loop anchored in F2 ("X"-symbols in Figure 6(a)) and averaged intensities along it for each EUV filter channel of AIA. Note that for averaging, we only used the positions marked with thick symbols, since the thin ones also include emission of the ribbon PR. Smoothed light curves normalized to the maximum of the loop emission are shown in Figure 6(b). The emission at the selected locations is first visible in the 94 Å filter channel. As more and more flare loops appeared, the light curve gradually rose to its peak between ≈20:45–21:00 UT. After that the arcade started to cool, as the emission increased in the 335 Å which peak temperature response is at 3 MK and then in the 171, 193 Å, and 211 Å filter channels (1–2 MK). Light curves of these filter channels peaked between ≈21:50–22:00 UT.

Note that the 131 Å emission in these locations is weak, reaching only about 10 DN s⁻¹ px⁻¹; therefore, it is likely that the flare loops here do not reach the 11 MK temperatures required for emission of Fe xxi (O'Dwyer et al. 2010; Petkaki et al. 2012).

In order to verify whether the flare loop selected using the 211 Å data can be associated with the hot emission observed at earlier times, we estimated its cooling time. To do that, we use the combined radiative-conductive cooling time (Equation (14E) in Cargill 2014):

$$\begin{eqnarray}&&{\tau }_{\mathrm{cool}}=\displaystyle \frac{2-\alpha }{1-\alpha }3{k}_{{\rm{B}}}{\left(\displaystyle \frac{1}{{\kappa }_{0}^{4-2\alpha }{\chi }^{7}}\displaystyle \frac{{L}^{8-4\alpha }}{{({n}_{0}{T}_{0})}^{3+2\alpha }}\right)}^{1/(11-2\alpha )}.\end{eqnarray} \tag{ 1 }$$

There, L is the loop length, n₀ and T₀ are electron density and temperature, κ₀ is the Spitzer coefficient of thermal conduction, and k_B is the Boltzmann constant. α = −1/2 and χ = −31.5 Wm⁻¹ K^−7/2 are parameters of fits of the radiative-loss function (see, e.g., Dudík et al. 2011).

Loop length was calculated using elliptical approximation of the loop arc. Major and minor axes of the adopted ellipse are indicated with yellow dashed lines in Figure 6(a). Both axes of this ellipse were spherically deprojected, assuming that the loop arc is normal to the solar surface. Length of the loop was then found to be ≈130 Mm. As we do not posses any spectroscopic observations and loop cooling times are much more dependent on the loop lengths than on n₀ and T₀, for purposes of rough estimate of τ_cool, we assumed typical electron density in flare loops of n₀ = 10¹¹ cm ⁻³ (see, e.g., Polito et al. 2017). Using the aforementioned equation we calculated the time needed for cooling of a loop with an initial temperature of T = 7.10⁶ K (94 Å) down to ≈2.5 × 10⁶ K (211 Å) as around 85 minutes. Results of calculations of the loop cooling times are also dependent on adopted values of parameters of fits of the radiative-loss function. For example, using α = −1/2 and χ = −31.81 Wm⁻¹ K^−7/2 (Kuin & Martens 1982) would result in prolonging of the loop cooling times by about 15%. However, even this result would still correspond, within tens of percent, to the cooling of plasma indicated by the temporal shifts between the maxima of light curves in Figure 6(b). Therefore, the selected loop could have been among the hot flare arcade observed in the 94 Å data after the onset of the eruption. We note that such long cooling timescales are typical for long active region loops (see, e.g., Froment et al. 2015; Li et al. 2015; Lionello et al. 2016).

In this work we analyzed evolution of a hook of one of the ribbons observed during the eruption of a quiescent filament observed on 2012 August 31. Before the eruption, bright strands composing the filament were anchored in footpoints F1–F4 located inside the ribbon hook. After the onset of the eruption, the propagating hook started to sweep these footpoints, which resulted in the disappearance of strands anchored therein and was followed by formation of flare arcade rooted in regions swept by the ribbon hook. This lasted for about 150 minutes, until all the filament strands were swept. Since the apparent boundary between the newly formed flare loops and the filament strands well corresponded to the propagating hook, this was likely be caused by magnetic reconnection.

In the following, we provide a brief summary of the evolution of each footpoint and filament strands rooted therein.

• At the onset of the eruption, the ribbon hook appeared close to the northern footpoint F1. The hook then started to elongate as well as propagate in a perpendicular direction and swept F1. As a consequence, the strand anchored in this footpoint disappeared. A few minutes later, a flare loop with a footpoint located in a neighborhood appeared in the 94 Å channel.
• Subsequently, the propagating hook swept the footpoints F2 and F3, which then became footpoints of flare loops. At the same time, we observed fading of a bundle of long and straight coronal loops CL located at the tip of the hook.
• Strands anchored in the footpoint F4 started to drift and fade away at the onset of the eruption. Their motion was traced only for a brief period of time, as they eventually became obscured by strands anchored in the position F5. Nevertheless, F4 also became the footpoint of flare loops, as it was eventually swept by the hook.
• Footpoint F5 and strands anchored therein appeared roughly at the same time as the hook swept F1. In the animation accompanying Figure 3 it can be seen that the first strands which appeared in F5 could have been formed by downfalling material from larger altitudes. Therefore, field lines composing the erupting flux rope might have been present at this position even before the eruption of the filament, but only became visible after being illuminated with emitting material. Later on, during the sweeping of the footpoints F2–F3, the patch of strands rooted in F5 widened. F5 was, however, eventually swept by the hook too and strands rooted therein turned into flare loops.

The arcade of hot flare loops was observed in the 94 Å filter channel in regions swept by the hook. Due to fuzziness of the arcade in this filter channel, we could not distinguish individual flare loops within the arcade. However, well-defined flare loops were observed later on in the coronal channels of AIA. Some of them were found to originate in the swept footpoints F1–F5. By estimating the cooling time in one particular case, we verified that these loops correspond to the hot 94 Å arcade observed after the onset of the eruption.

In all five cases listed above, filament strands were observed to turn into flare loops once swept by the propagating ribbon hook. Propagation of ribbons is, according to the standard CSHKP model of solar flares, a consequence of ongoing magnetic reconnection. However, reconnection of filament field lines into flare loops, occurring at evolving ribbon hooks, cannot be described by this model, since it does not include ribbon hooks in which footpoints of erupting flux ropes are located. Therefore, a three-dimensional approach is required to address this observed conversion of filament strands into flare loops.

Our observations are, however, consistent with the recent predictions of the 3D extensions of the standard solar flare model of Aulanier & Dudík (2019). These authors identified new three-dimensional reconnection geometries that involve the flux rope field line, located within the hooks of the QSL footprints, reconnecting to become a flare loop. In one of these reconnection geometries, the ar–rf reconnection, flux rope field lines composing a modeled flux rope (r) reconnect with coronal arcades (a) into new field lines composing the flux rope (r) and flare loops (f ).

These predictions are in our case consistent with observations of the disappearance of filament threads and formation of flare loops (i.e., "r" → "f"). Moreover, sweeping of footpoints F2–F3 was found to be contemporal with gradual fading of coronal loops CL which could be the "a" component of the ar–rf reconnection. If so, the previous location of the CL footpoint should become a part of the post-reconnection flux rope "r." This is the case here. Even though no particular flux rope field line is seen to originate from this location after it is swept by the hook, it is now a part of the coronal dimming area, which is interpreted as a consequence of the evacuation of flux rope plasma by the eruption (e.g., Dissauer et al. 2018).

However, note that unlike the model, where individual field lines can be traced in their entirety, the observations only show lower parts of filament strands and lower parts of coronal loops rooted nearby. This is due to the erupting filament being large, with length comparable to the solar radius (Figures 1(a)–(b)). We were not able to identify the conjugate footpoints of CL near the positive-polarity ribbon hook and thus verify if they composed an arcade overlying the filament (a), as predicted by the model. Nevertheless, the observed dynamics of lower portions of the filament strands being swept by the ribbon together with the coronal loops, conforms well with the predictions of the model.

Despite the fact that the MHD model used in Aulanier & Dudík (2019) is in the zero-β approximation and thus does not predict the emission of the constituents of individual reconnection geometries, we have for the first time shown that the filament strands reconnect to become flare loops. This indicates a 3D reconnection process irrespective of the fact that some constituents of the ar–rf reconnection geometry were not identifiable in the present filament eruption. In the future, more events, especially eruptions of filaments with bright and distinguished footpoints, need to be studied for identification of all four constituents partaking in the ar–rf and other reconnection geometries predicted by Aulanier & Dudík (2019).

In summary, we observed sweeping of many filament footpoints by the propagating hook, which was always followed by the appearance of flare loops rooted in the original filament footpoints. This reconnection of field lines composing the filament into flare loops is not described by the standard CSHKP model of solar flares, since this model does not include the hooked ribbons. It, however, conforms the predictions of the 3D extensions to the standard model as described in Aulanier & Dudík (2019), where flux rope field lines at the hook can reconnect to become flare loops. In our observations, this phenomenon was observed for all of the visible filament footpoints located within the hook.

In addition, the sweeping of some of the filament strands and footpoints was found to be cotemporal with the disappearance of a nearby coronal arcade. These observations are consistent with the three-dimensional ar–rf reconnection geometry predicted by Aulanier & Dudík (2019), in which field lines of the modeled flux rope reconnect with a coronal arcade at the ribbon hook into new field lines composing the flux rope and a flare loop. Since only three constituents of the ar–rf reconnection geometry were clearly identifiable in the present filament eruption, more events, especially eruptions of filaments with bright and distinguished footpoints, should be studied for identification of all four constituents partaking in this reconnection geometry.