A Solar Magnetic-fan Flaring Arch Heated by Non-thermal Particles and Hot Plasma from an X-ray Jet Eruption

We have investigated an M1.3 flare that occurred on 2014 January 13 near the solar limb. Figure 1 shows the GOES SXR (0.5$-$4 Å and 1$-$8 Å) light curves, the flux derivative, and the RHESSI hard (30$-$100 keV) and soft (12$-$25 keV) X-ray light curves of the flare event. The M-class flare started around 21:48 UT and peaked at 21:51 UT. The flare emission rapidly decayed to half its peak flux by about 21:53 UT, which shows that the flare heating was impulsive.

Figure 2 (and its associated animation) shows context images of the flare obtained by $\it{SDO}$/AIA at 21:53 UT. The AIA intensity images in different channels (i.e., 1600, 304, 211, 94, 131, and 193 Å) exhibit variable temperature-dependent plasma behavior. Their peak temperature responses are given in Table 2 (Lemen et al., 2012; O’Dwyer et al., 2010). The AIA 193 Å channel has temperature response peaks in both 1.5$-$2 MK and 17$-$20 MK ranges. Due to the bright background emission from 1.5$-$2 MK plasma, it is difficult to distinguish the enhancement of hot temperature (17$-$20 MK) emission in the 193 Å intensity images. Therefore, for the AIA 193 Å channel, we display the running difference image (panel (f)) in order to expose the increased emission at the cusp.

For comparison, the running difference image of the AIA 211 Å channel (response peak of $\sim$2 MK) is shown in panel (c). The hot cusp is not observed in the 211 Å difference image, which confirms that the enhancement of the emission at the flaring arch/cusp region in 193 Å does not come from 1$-$2 MK plasma. The AIA multi-channel images and the corresponding movie depict (1) an apparent flare brightening at the lower eastern footpoint region at the flare start time (21:48 UT), and (2) a cool jet ejected in the AIA 1600 and 304 Å channels near the flare peak time ($\sim$21:51 UT). After the jet ejection, hot plasma along the loop expands upward and develops a flaring arch/cusp in the 94, 131, and 193 Å channels as the brief flare begins to decay ($\sim$21:53 UT).

Figure 3 shows the aligned intensity images of $\it{SDO}$/AIA and $\it{Hinode}$/EIS. The top panels (a$-$e) are the AIA intensity images in different channels (i.e., 193, 304, 171, 94, and 131 Å) with same FOV of the Hinode/EIS raster at the flare peak time (21:51 UT). The middle row displays the pseudo raster image using the AIA 131 Å channel images observed at the nearest time of the Hinode/EIS raster scan for comparison (panels f$-$j). The bottom panels (k$-$o) show the Hinode/EIS total intensity image for the Ca XVII 192.85 Å wavelength window, which includes Fe XI,  XII,  XIV,  XXIV, O V, and Ca XVII emission. The marked timings indicate the start time of the raster scan. The intensity contour of the EIS Ca XVII 192.85 Å emission is overlaid onto the AIA 131 Å image in the middle row (panel g).

Figure 4 shows the Hinode/XRT Be_thin images before ($\sim$19:33 UT) and after ($\sim$22:09 UT) the flare peak at higher temperatures. Panels (d) and (e) show the XRT intensity images with the cleaned RHESSI HXR and SXR intensity contours (50, 60, 70, 80, and 90%) overlaid. The colored contours indicate HXR (20-50 keV: orange and purple) and SXR (12-20 keV: green and blue) emission observed by RHESSI at the closest time to the XRT images, respectively.

The XRT images reveal that the hot plasma fan loop/arch already exists before the flare onset (Figure 4, a$-$c). At the GOES flare start time ($\sim$21:48 UT), a strong footpoint brightening was also detected in the XRT images, and the cusp shape loop structure intensity enhanced with time. The temporal behavior in the HXR (20$-$50 keV) and SXR (12$-$20 keV) emission is supplied by the RHESSI observations (the contours in the (d) and (e) panels). The HXR emission only appears early in the event between 21:45 and 21:54 UT near the footpoint brightening, and the SXR emission moves from the footpoint to the loop top region from 21:50 to 21:59 UT.

Using the multi-wavelength imaging observations from EUV to X-ray, we have investigated the temporal behavior of the plasma in the flaring fan loop at different temperatures. Figure 5 shows 7 EUV and 3 SXR light curves from the footpoint region (F) and along the flaring loop (B$-$E). The light curve from the region A shows the active region emission near the flare as a reference point. From top to bottom, we plotted the light curves in descending temperature order. As previously discussed, the response of the AIA 193 Å channel is double-peaked at $\log T\sim$1.5$-$2 MK and $\sim$17$-$20 MK (Lemen et al., 2012). Since the EIS measurements conclude that the loop-top is dominated by hot Fe XXIV emission, we assume that the prevailing AIA 193 Å channel peak response temperature is $\sim$18 MK in the cusp region.

The relatively cooler coronal emission (304, 171, 211, and 335 Å) is only observed at the flaring footpoint (region F) with a sharp peak at the start time of the flare. Meanwhile, the flaring temperature plasma of XRT and AIA 193, 131, and 94 Å emission, along the flaring loop/arch (region B$-$E) persists for a longer duration. The peaks in the AIA 304 Å light curve from the region C$-$E are due to the saturation pattern of the flaring footpoint brightening. Considering the temperature responses of AIA and XRT, the light curves show that the intensity peak of the loop top region has a time shift from the higher to lower temperature channels (i.e., XRT Be_thick to AIA 94 Å) in descending temperature order. The time shift of the intensity peak is interpreted as the cooling of the plasma with height in the loop (Viall & Klimchuk, 2012; Ryan et al., 2013; Thiemann et al., 2017).

Flows are also detected as intensity peaks traveling along the arch system. Figure 6 depicts the time-distance diagrams illustrating these flows in the AIA 304, 94, and 131 Å passbands. In the AIA 304 Å channel, a cool jet structure is ejected at 21:48 UT (the flare start time), and its projected velocity on the plane of the sky is $\sim$250 km s^-1. Then, the plasma descends with a velocity of $\sim$65$-$75 km s^-1. Panesar et al. (2016a) reported active region jet ejections with flares using AIA 304 and found that their speeds ranged 110$-$400 km s^-1, which is consistent with this jet speed. The 131 Å diagram displays that expansion of coronal plasma outwards after the jet ejection with a velocity of $\sim$700 km s^-1, and then the emission is sustained about an hour locally. The 94 Å intensity also shows an enhancement at different loop locations, but this emission does not appear to increase at the ejection site. These observations suggest that the cooling time varies spatially along the fan loop.

If the flaring loop is located along the plane of the sky, the line of sight velocity of the moving plasma would be not significant. However, if the loop is tilted from the plane of the sky, the velocity component of the line of sight would increase with the tilt angle. The observed strongly red-shifted emission in this flaring loop could be interpreted as strong upflows or downflows along the loop depending on the angle between the loop and the plane of the sky. If the loop leg tilts away from the observer, the red-shifted emission would be interpreted as an upflow along the loop. Conversely, if the loop leg tilts toward the observer, the red-shift would be considered emanating from a downflow. We do not know the loop orientation because it is projected at the limb, and the tilt angle of the loop will determine the direction of flows (i.e., upflow or downflow). Therefore, the loop tilt angle and 3-D direction are critical for removing this degeneracy in the Doppler velocities in order to understand where the reconnection occurs and how the flows originate.

Taking advantage of the multiple vantage points between the $\it{STEREO}$/EUVI and $\it{SDO}$/AIA observations, we reconstructed the 3-D path of the flaring loop. Figure 15 shows nearly co-temporal 195 and 304 Å images from both EUVI and AIA. The EUVI and AIA images are processed via Multi-Scale Gaussian Normalization to clearly show the loop path (Morgan & Druckmüller, 2014). To trace the loop, we employ the stereoscopic reconstruction technique, scc_measure.pro (Thompson, 2009) to determine the 3-D coordinates of these points in the heliographic system. Using an equipotential line between two different angle images, points are selected along the jet in the 304 Å channel (black diamond) as well as along the flaring loops in the 193 and 195 Å channels (blue and green crosses). The detailed analysis is available in the Appendix. Using the points along the loop, we determined an average tilt angle of 51^∘ for the plane of the coronal loop with respect to the plane of the solar equator. The calculated 3-D coordinates are displayed in Figure 16. The panels (a) and (b) display the constructed loop as seen from Earth and from STEREO-A, respectively. The reconstruction matches well with the observations. Panel (c) is the view from solar north. We find that the direction of the hot loop from its eastern foot to the cusp region (green crosses with line) is tilted away from us. Thus, from the 3-D construction using STEREO data, we conclude that the observed fast velocity hot plasma component is due to upflowing material along the loop.

We extrapolated the coronal magnetic fields using SDO/HMI vector magnetograms and the NFFF extrapolation code described in Hu et al. (2010). Since we have used the HMI magnetogram from three days before the limb flare (from when the active region was in view), the magnetic field configuration is typically expected to differ from that at the time of the flare. We note from the observed EUV images, though, that the active region loop configuration does not change much for the next three days. Thus, we assume that the magnetic configuration also remains mostly unchanged. Then, by comparing the HMI magnetogram with SDO/AIA 1600 Å images carefully, we identified the location of the jet ejection related to the flare, which is a localized region of positive polarity isolated within the active region’s globally dominant negative polarity (the red box in Figure 17 (a)).

The vector field shown in the black rectangle of Figure 17 outlines the cutout used for the extrapolation, with dimensions of $1024\times 512$ pixels centered at (766.55, -128.63) arcseconds. To reduce the computational cost, we rescaled the original field and used a $512\times 256\times 256$ pixel grid volume in the $x$, $y$, and $z$ directions (panel (c)). The $x$, $y$, and $z$ vectors refer to the local Cartesian coordinate system, which is obtained after the active region has been de-projected and de-rotated to the disk center. The $z$-direction is the line of sight, and the transverse field is in the $x-y$ plane.

The average deviation between the observed ($\mathbf{B}_{t}$) and the extrapolated ($\mathbf{b}_{t}$) transverse field on the photospheric boundary is indicated by the following metric:

where $M=N^{2}$, represents the total number of grids points on the transverse plane. In order to minimize the contribution from the weaker fields, the grid points are weighted with respect to the strength of the observed transverse field. Since $E_{n}$ represents the normalized vector error between $\mathbf{b}_{t}$ and the measured $\mathbf{B}_{t}$, a perfect correlation will give $E_{n}=0$. In the present case, the error in the weighted transverse field corresponds to $E_{n}=0.21$, which is acceptable for the current analysis.

For further investigation of the magnetic field topology, we look at the regions of strong variation in the field line connectivity (Demoulin et al., 1996). Such regions, having a high value of the squashing factor Q, are thought to be the plausible places for magnetic reconnection to occur (Priest & Démoulin, 1995). Here, the squashing factor is calculated by following Liu et al. (2016).

The extrapolated magnetic field and the Q map also show that there is an inner loop structure (yellow color in Figure 17 (c)), and its field line connectivity changes sharply at the location between the inner loop and surrounding field lines (having high Q values). This configuration implies that the jet ejection originates from magnetic reconnection in the null region above the isolated region of positive polarity with the fan-spine magnetic topology. In addition, we observe a remote brightening at the surface in the AIA 1600 Å images concurrent with the jet and flare brightening (Figure 2). The location of the other loop footpoint from the extrapolated magnetic field corresponds to this remote brightening location, which confirms that the extrapolated field is consistent with the EUV observation.

Figure 18 shows zoomed-in images of the extrapolated field lines and Q map for the jet reconnection region (panel (a): top view; panel (b): side view). The field lines and the circular bottom boundary of contours of high log Q value in the jet base suggest that this region has a fan-spine structure. Panel (c) is an extracted view of the jet-base on the $x-z$ plane showing where the highest Q value is observed. The small, narrow (purple) region having the highest Q value is the most plausible reconnecting null point between the erupting field and the magnetic fan arch.

To understand the connectivity with the trans-equatorial loop that appears to be connected to the loop-top region, we take a magnetogram cutout from January 11 at 23:00 UT with dimensions of $1000\times 1200$ pixels centered at (774.8, 23.25) arcseconds (Figure 19 (a)). This extraction was rescaled to a $256\times 300\times 300$ pixel grid volume in the $x$, $y$, and $z$ directions. In this case, we get $E_{n}=0.3$.

Figure 19 shows the extrapolated magnetic field (lower resolution) and the Q map for the flaring active region and the active region at the north end of the trans-equatorial loop. From the AIA 94 Å image, we can see the cusp shape of the flaring loop top region and the trans-equatorial loop, which appears to be connected with the two loop systems. Our extrapolated magnetic field shows that those two loop bundles are close to each other, and that the top of the fan loop could be seen as the observed cusp shape at the limb. Furthermore, the cusp-shape region also has high Q value, implying that this location is also a plausible place for magnetic reconnection.

Using multi-wavelength observations of the limb flare from two unique vantage points, we find a hot cusp-shaped structure at the fan loop/arch apex exhibiting strong upflows during the impulsive phase. Strong plasma flow during flares is typical and is often interpreted as a response of the plasma to energy release and heating. One possible flow source is reconnection outflow (i.e., bidirectional flows originating from the reconnection point traveling near the Alfvén speed) (Wang et al., 2007; Tian et al., 2014). Another possibility is evaporation flow, which is heated plasma ejected from the chromosphere due to energy injection from accelerated particles (Milligan & Dennis, 2009; Polito et al., 2016b; Lee et al., 2017).

To understand whether the flow to the loop-top region is reconnection outflow or evaporation flow, we must consider the temperature dependence of the flow velocity. If the flows were due to evaporation, which is the result of a pressure difference due to heating, their speeds would be dependent on temperature and would be comparable to the sound speed. The measured temperature in Figure 12 suggests that evaporation flows would be $\sim 370-550$ km s^-1 for temperatures of 10$-$22 MK, and the velocity would increase with temperature. The speeds calculated from the Hinode/EIS Doppler velocity measurements combined with the derived loop tilt angle from STEREO-A observations show that the de-projected observed velocities are consistent with the the evaporation flow scenario.

For the upflows to be reconnection outflows, the reconnection region needs to be located below the cusp region. The temperature measurements along the loop indicate that the hottest region is the curved loop structure (region C in Figure 2), just below the upflowing plasma. The spectral line profile at the curved loop shows that this hot plasma has blue- and red-shifted bidirectional flows. Assuming a coronal magnetic field strength of 30 G (Nakariakov & Ofman, 2001; Van Doorsselaere et al., 2008; Jess et al., 2016), the Alfvén speed would be about $\sim 1000-3000$ km s^-1 for the measured density of $\sim 10^{9}-10^{10}$ cm^-3. The observed velocity is slower than the expected Alfvén speed.

Our targeted flare for this study is impulsive with a duration of only $\sim$5 minutes in the GOES SXR light curve. This impulsive heating is in contrast to long duration events in which the decay phase has continued heating for many hours (Reeves & Warren, 2002; Warren, 2006; Savage et al., 2012) or a second phase of robust heating (Qiu & Longcope, 2016; Zhu et al., 2018). For this impulsive flare case, we expect for the theoretical models of loop cooling timescales to be consistent with the observed cooling times. We test this hypothesis by comparing the theoretical cooling times with the observed temporal evolution.

We calculated the conductive ($\tau_{C}$) and radiative ($\tau_{R}$) cooling timescales for the flaring loop (Cargill et al., 1995; Bradshaw & Cargill, 2010), using:

where $k_{b}$ is Boltzmann constant, $\kappa_{0}$ is the coefficient of thermal conduction, and $\gamma=\frac{5}{3}$. The optically thin radiative loss function of $R=n^{2}\chi T^{\alpha}$ is referred from equation (3) in Klimchuk et al. (2008). Using the half-length of the loop from the magnetic field extrapolation ($L=0.9\times 10^{5}$ km) plus the measured density ($n=2\times 10^{9}$ cm^-3) and temperature ($T\sim 22$ MK at the loop top) from the EIS observations, the calculated conductive and radiative cooling timescales for the flare plasma at the loop-top are approximately 38 s and 180000 s, respectively. The conductive cooling is dominant in this flare loop due to its high temperature and low density. Then, we fitted the temporal evolution of the temperature using the conductive cooling model for static and evaporative cooling (equations (3a) and (3b) from Cargill et al. (1995)). These fits are provided in Figure 20.

The observed temporal evolution of temperature in the flare plasma is measured from the GOES, XRT, and AIA light curves (Figures 1 and 5). These emission profiles reveal that the intensity peak has a delay from hotter temperature channels to cooler ones. Table 2 gives the peak times of the intensity for the near loop-top regions (C and D in Figure 5) per channel. The time delays relative to the GOES SXR emission and the peak response temperature of the high temperature channels are also provided in the table. We overlaid the observed evolution of cooling plasma (triangle and diamond symbols) in Figure 20. The peak temperature of each channel is determined from its dominant spectral lines (O’Dwyer et al., 2010, 2014). We also plotted the temperature range using the half width of the peak temperature response function as an error bar since the channels are composed of more than one line and the response function is broad.

Overall, taking into account the broad temperature response function, the observed temperature evolution is consistent with the conductive cooling curve for the evaporation (solid line) rather than the static (dashed line) case. The observed evolution of the temperature in the flaring loop arcade (region C) agrees well with the model. This result implies that there was insignificant additional heating of the flaring fan loop after the impulsive energy input from the jet. Moreover, it indicates that this flaring loop cooled down by conduction with evaporation.

However, the cusp (region D) experiences a time delay in the cooling curve of $\sim$15 min for the emission from the AIA 94 and 131 Å channels (7$-$11 MK). There could be several reasons for the observed longer cooling time for the flare cusp. First, continued reconnection of substrands of the fan loop could extend the cooling time (Reeves & Warren, 2002; Warren, 2006). But in this scenario, we also expect a longer cooling time in region C since it is also part of the flaring fan loop. Second, there might be a prolonged heating from secondary reconnection at the cusp region after the initial impulsive phase (Qiu & Longcope, 2016; Zhu et al., 2018). Hernandez-Perez et al. (2019) studied the same flare and proposed that there would be slow local reconnection near the kinked loop apex due to the increase of the thermal pressure by continuous plasma upflows. The grey area in Figure 20 shows the GOES flare duration when the jet ejection appeared. The impulsive heating from the jet contributes to the GOES SXR spike and the creation of the hot plasma ($>10$ MK). The additional heating process would be responsible for the declining phase of the flare SXR flux seen by GOES and the delayed intensity peaks of the AIA 131 and 94 Å light curves from the cusp region.

The extrapolated magnetic fields and their connectivity show that there are two possible places where magnetic reconnection might take place. One is near the cool jet ejection site where footpoint brightening is observed (Figure 17). The other is the cusp region above the loop-top where the two loop systems are in contact (Figure 19). Reconnection at either of these locations could plausibly convert sufficient amounts of magnetic energy into thermal and kinetic energies to produce this flare.

If we consider that the higher coronal magnetic reconnection at the cusp region produces the flare, as prescribed by the standard eruptive flare model, the observed non-thermal velocity and temperature measurements are consistent with the model expectation (Doschek et al., 2014). Also, the hot and upflowing plasma in the cusp region can be interpreted as the newly formed current sheet or evaporation flows by injection of energy from the reconnection. However, if there is such continuous reconnection above the loop-top, we expect HXR emission at the loop-top region. No HXR emission was observed at the loop-top when the flare starts, and the observed cooling time implies that the flaring loop was impulsively heated with no evidence for continued heating. We note that the loop cusp experiences a longer cooling time for 7$-$11 MK plasma in the decay phase of the flare, but this process requires an additional heating mechanism separate from that of the impulsive phase, perhaps by secondary reconnection at the cusp.

Another possibility supported by all of these observations is that the external reconnection of the blowout jet (i.e., external (interchange) reconnection taking place at the jet eruption region) energized this flare. The cool jet ejection in the AIA 304 and 1600 Å images and the enhanced RHESSI HXR emission at the flaring loop footpoint at the base of the jet support this scenario. If we consider that the external reconnection produced the jet spire and heated the flare plasma, the HXR emission should only be observed at the footpoint, not the loop-top region, which is consistent with our observation. Following from this hypothesis, the observed temperature and velocity structure above the loop-top region would be interpreted as the evaporation flow and outflows driven by the lower atmospheric reconnection. The SXR emission enhancement at the flare loop-top can also be explained as the increased density from the evaporated plasma that results from the accelerated particles driven from the chromosphere by the jet reconnection.

A comprehensive set of observed features consists of the following: 1) primary footpoint brightening with HXR emission, 2) lack of HXR emission at the loop-top, 3) upflowing hot plasma along the loop-top, 4) enhancement of the loop-top SXR emission after the footpoint brightening, 5) short duration of the event in the GOES SXR light curve, and 6) the magnetic topology characterized by an overlying magnetic-fan loop system. We infer from this feature set that this flare is an example of a flaring arch (Martin & Svestka, 1988; Svestka et al., 1989; Fontenla et al., 1991; Hanaoka, 1997; Moore et al., 1999; Moore & Sterling, 2007) that is energized by external reconnection associated with an underlying blowout jet eruption. Flaring arches have been reported as a particular component of some flares Martin & Svestka (1988); Svestka et al. (1989); Fontenla et al. (1991). This class of events has chromospheric elements at one foot of a coronal flare loop with traversing X-ray and H$\alpha$ emission. The hot plasma in flare arches is confined in the body of the magnetic-fan arch structure, and the accelerated electrons and hot X-ray emission propagate through the arch from its explosive foot.

Figure 21 provides a schematic cartoon of the blowout jet and the magnetic-fan arch model for this flare. Panel (a) depicts the onset of the external reconnection between the erupting jet-base and extended magnetic-fan arch. The strong brightening at the fan-spine loop footpoint (see Figure 2 (a$-$f) and its animation, and Figure 18), results from that external reconnection. The blowout jet is observed as a cool plasma ejection in the AIA 304 Å images. Even though we do not see the sites of the internal and external reconnection directly due to image saturation, we propose that the jet-productive field eruption is a mini-filament eruption. Sterling et al. (2015, 2016, 2017) have proposed mini-filaments as the typical instigating component of blowout jet eruptions. The cool jet plasma (0.05 MK) and the chromospheric brightening at the base of the erupting field in the AIA 1600 Å images (refer to Figure 2 (b$-$d) of Hernandez-Perez et al. (2019) and its animation) just before the jet eruption are manifestations similar to those of jet-productive mini-filament eruptions in active regions (Sterling et al., 2017). Panel (b) depicts the magnetic fields after the external reconnection (observed as the low-lying flare arcade and extended flaring arch). The arrow represents the heated plasma upflows and accelerated electrons that fill the magnetic arch. The cusp is filled with hot plasma observed at Fe XXIV.

This scenario explains the impulsive behavior of this flare and lack of HXR emission at the loop top region. Previously, Moore & Sterling (2007) suggested a related magnetic-arch-blowout scenario for a narrow streamer puff CME. Our observation would be the specific case in which the magnetic arch field lines are strong enough that the eruption remains confined.

We note that there is a remote brightening at the other foot of the flaring loop in the AIA 1600 Å channel, seen as a remote flare ribbon (Figure 2’s animation and Figure 17 (b)). One of the observational characteristics of the flaring arch is a secondary remote brightening due to the propagation of the accelerated electrons and hot plasma along the arch. We estimated the propagation speed of the energy injection from the jet footpoint brightening to the remote brightening. The time difference between the two brightenings is measured from the AIA 1600 and 304 Å  intensity images with cadences of 24 s and 12 s, respectively. Loop distance between the reconnection brightening and remote brightening is calculated using the extrapolated magnetic field and the distance between the two footpoints from the AIA 1600 Å image. The measured time difference is 12 seconds, which is the AIA temporal resolution limit. The distance along the extrapolated magnetic loop structure is $\sim 1.8\times 10^{5}$ km. The resulting estimated propagation speed is $\sim 1.5\times 10^{4}$ km s^-1, which is $\sim$15 times the Alfvén velocity. Similar observational features were reported by Tang & Moore (1982). They showed large flares that had remote H$\alpha$ bright patches with type III reverse slope bursts. They interpreted the H$\alpha$ patches as chromospheric heating signatures caused by the accelerated non-thermal electrons propagating from the flare-reconnection end of the closed loop. Their estimated traveling velocity was $\sim 10^{5}$ km s^-1, much faster than the Alfvén speed. The observed speed in our flaring arch also implies that accelerated electrons from the jet reconnection region impacted and heated the other footpoint of the magnetic fan.