Radio Spectral Imaging of an M8.4 Eruptive Solar Flare: Possible Evidence of a Termination Shock

The rising spectrum of the loop-top continuum source (Source II in Figure 3) in 1–2 GHz is consistent with the spectral characteristics of the optically thick portion of gyrosynchrotron radiation at the same frequency range (e.g., Dulk & Marsh 1982). To further confirm the gyrosynchrotron nature of the loop-top continuum source, we utilize concurrent total-power data obtained by the Radio Solar Telescope Network (RSTN) at eight discrete frequencies: 0.245, 0.410, 0.610, 1.415, 2.695, 4.995, 8.800, and 15.40 GHz. The RSTN fluxes for the lowest three frequencies (below 1 GHz) reached over 1000 solar flux units (SFU) at ∼17:57 and have very different temporal behavior from their higher-frequency counterparts. They are likely dominated by coherent emission. Also, as VLA covers the 1.415 GHz band, RSTN fluxes at the lowest four frequencies are excluded from the subsequent analysis.

To enable direct comparison to the spatially resolved VLA observations of the loop-top source, first, we subtract the post-flare background at ∼19:30 from the observed RSTN flux at 17:57 to remove the contribution from the quiescent solar disk and active region. Background subtraction is also performed on VLA data at 17:57 by selecting the same post-flare time as the background in the loop-top region (white box in Figure 4(a)). Second, we take the assumption that the radio emission above 2 GHz is dominated by the loop-top source. This assumption is mostly valid, as VLA imaging reveals that the loop-top source plays a dominant role above ∼1.4 GHz (see Figure 2) during the time of interest. Uncertainties of flux values derived from VLA data are estimated by using the rms variations of a region in the image without the presence of any source. For the uncertainty estimates for RSTN-derived flux values, we take the rms variations of the measured total flux during a nonflaring time.

Zoom In Zoom Out Reset image size

The resulting spectrum of the loop-top source is shown in Figure 4(b). With the addition of RSTN flux at higher frequencies (>2 GHz), the spectrum shows features characteristic of nonthermal gyrosynchrotron radiation, with a positive and negative slope at the low- and high-frequency side (due to optically thick and thin emission, respectively) and a peak flux of ∼400 SFU. Although the combined microwave spectrum does not allow us to accurately determine the source parameters owing to the assumptions taken above and the lack of spatial resolution across the spectrum, for demonstration purposes we perform spectral fitting based on a homogeneous source model by adopting the fast gyrosynchrotron codes in Fleishman & Kuznetsov (2010) to calculate the gyrosynchrotron spectrum. An example fit result and the associated source parameters are shown in Figure 4(b). ⁵ Although the fit parameters are subjected to the limitations noted above and are probably not unique, our analysis demonstrates that the loop-top continuum source is most likely due to the incoherent gyrosynchrotron emission from flare-accelerated nonthermal electrons.

As mentioned earlier, the vector dynamic spectral features of Source III closely resemble the stochastic spike burst event reported in Chen15. The group of spike bursts lasted for around 70 s from 18:06:25 to 18:07:35 UT in the frequency range of 1.0–1.6 GHz. It contains a total of over 10,000 individual bursts within the ∼70 s duration. Similar to the spike bursts reported by Chen15, the bursts are extremely short-lived—most are unresolved by the time resolution of the instrument 50 ms—and have a narrow bandwidth δ ν/ν of only a few percent.

To further study the spectral properties of the spike bursts, we adopt the same technique described in Chen15 to perform a multi-Gaussian fit of the spectral profiles of the spike bursts at each time integration. To reduce the noise in the spectral domain and achieve more robust fit results, we have smoothed the spectral profiles with a 6 MHz wide boxcar window. Further, in order to limit our fitting to sufficiently bright spike bursts, we have also applied a brightness threshold of ${T}_{B}^{\min }=0.7\times {10}^{8}$ K, set as about 4 times of the rms variations of a region in the image without any source. The fitting range of the spike bandwidth (represented by the FWHM of the Gaussian profiles) is limited to 6–100 MHz. Typical examples of the fit results for three selected times are shown in Figure 5(a). From the multi-Gaussian fitting results we obtain a distribution of the spike bandwidth, shown as a histogram in Figure 5(b). Similar to the bandwidth distribution of the spike burst event shown in Chen15 (their Figure S3 in Supplementary Materials), the spikes have an asymmetric distribution that peaks at 22 MHz (or a relative bandwidth δ ν/ν ≈ 2%, density fluctuation δ n_e /n_e ≈ 4%). The brightness temperature distribution is also notably similar to that shown in Chen15. We note, however, that the maximum brightness temperature is two orders of magnitude greater than that reported in Chen15. It can be possibly attributed to the much larger flare (M8.4 versus C1.9) in which our spike bursts are observed (see, e.g., Benz et al. 2005, who reported that coherent radio bursts are generally brighter in larger flares), yet the underlying relationship is highly complex, which involves many factors, including flare timing, shock generation, electron acceleration, and the coherent radiation processes. Nevertheless, the very similar spectrotemporal properties to those reported in Chen15 suggest that the spike bursts are likely associated with the same emission processes.

Zoom In Zoom Out Reset image size

We further derive the centroid location of the radio source at each time and frequency pixel where the spike burst is present by using a 2D polynomial fitting technique following Chen15. The 2D polynomial fitting utilizes the 6 pixels surrounding the pixel where the maximum brightness is located to perform second-order polynomial fitting in two orthogonal directions. The location of each source centroid is found at the peak of the polynomial curves. The uncertainty of the resulting centroid position is estimated by $\sigma \approx {\theta }_{{\rm{FWHM}}}/({\rm{S}}/{\rm{N}}\sqrt{8{\rm{ln}}2})$ (Reid et al. 1988; Condon 1997; Chen et al. 2015, 2018), where the signal-to-noise ratio (S/N) is the ratio of the peak flux to the rms noise of the synthesized image where a source is not present, and θ_FWHM is the FWHM of the synthesized beam. With the θ_FWHM = 199 × 146 at 1.6 GHz and typical S/N values greater than 40, the accuracy of our derived source centroid position is typically better than 1''.

As shown in Figure 3(e), at any given time, the derived centroid locations of the spike bursts at different frequencies form a nearly linear feature with a length of about 10''. This distinctive feature shows some temporal evolution and lasts for about 70 s before it diminishes at 18:07:35 UT (see Figure 3(e) for snapshots at three different times and the associated animation). This feature shows a slight overall movement toward the southwest direction (or a movement toward the lower right corner in Figure 3), which corresponds to a gradual overall frequency drift of the spike burst group toward lower frequencies in the dynamic spectrum (Figure 3(d)). The observed features closely resemble the findings in Chen15, who interpreted the feature as the projection of a presumably 3D termination shock front above the flare arcades, and the overall frequency drift as the movement of the shock front in the loop-top region with a varying plasma density. We note, however, that unlike the event reported in Chen15 and Chen19, this event does not show any sign of sudden disruption of the feature or a split-band feature.

Although VLA radio imaging shows that the spike source is located away from the flare arcades, as expected from the termination shock scenario in which the shock front is situated above the loop tops, it is not immediately clear whether the exact location and orientation of the spike source are consistent with the termination shock interpretation. In the next two subsections, we will take advantage of the concurrent observations obtained by both SDO/AIA and STEREO-A/EUVI from two vantage viewing points and establish the spatial relation between the eruption, the flare arcades, and the SAF and downflow structures.

In Dhakal et al. (2018), by using both SDO/AIA and STEREO-A/EUVI observations, the authors suggested that the event was driven by two preexisting filaments with a "double-decker" configuration. As observed by SDO/AIA, the filaments were formed prior to the flare along the primary polarity inversion line (PIL; red curve in Figure 6) with a northeast–southwest orientation. The double-decker filaments erupted successively ∼12 minutes apart prior to the second GOES SXR derivative peak at ∼17:37 UT. After ∼17:30 UT, the two erupting filaments merged together and became nearly indistinguishable from each other. The erupting filament, seen in SDO/AIA 304 Å, has a writhed shape and directs toward the northwest (Figure 6(b)). The eruption is less evident in SDO/AIA 131 Å images but can be distinguished using the running-difference imaging technique (Figure 6(a)). This passband is sensitive to a much higher temperature (∼10 MK) associated with the Fe xxi line (O'Dwyer et al. 2010), which is presumably emitted by the hot envelope of the magnetic flux rope encompassing (and likely above) the cool filament (e.g., Chen et al. 2014; Cheng et al. 2014). Similar to Dhakal et al. (2018), we track the eruption front seen in SDO/AIA 131 Å, shown as blue dashed lines in Figure 6(a). In STEREO-A/EUVI's limb view, the erupting filament clearly displays a writhed morphology (Figure 6(c)), which strongly suggests that it is a magnetic flux rope in nature (e.g., Ji et al. 2003; Török & Kliem 2005) and is consistent with the morphology of the filament viewed from SDO/AIA.

The conjugate ends of the eruption coincide with two coronal dimming regions in SDO/AIA 211 Å base-difference images (difference of the post- and pre-flare intensity; orange patches in Figure 6) located at the opposite sides of the PIL. These twin coronal dimmings, often observed during the eruption phase of CME-associated events in EUV and SXR, have been interpreted as density depletions at the conjugate ends of the expelled magnetic flux rope (e.g., Sterling & Hudson 1997; Zarro et al. 1999; Miklenic et al. 2011; Cheng & Qiu 2016). Their presence further supports the flux rope nature of the erupting filament.

The appearance of the flare arcades, as viewed by SDO/AIA and STEREO-A/EUVI, is consistent with the geometry of the erupting filament (Figure 7). In SDO/AIA's view, the post-flare arcades are distributed from northeast to southwest, rooted at either side of the pre-flare filament (Figure 7, middle column). In STEREO-A/EUVI's limb view, the same post-flare arcade system is projected to distribute in the north–south direction along the limb, which is consistent with the geometry of the filament that erupted early on (Figure 7, right column). According to the standard picture of eruptive solar flares in three dimensions (Aulanier et al. 2012, 2013; Janvier et al. 2013, 2014, 2015), a large-scale reconnection current sheet is present below the erupting filament and above the post-flare arcade, driving the flare energy release and particle acceleration (see, e.g., a recent study by Chen et al. 2020b).

Zoom In Zoom Out Reset image size

During the flare energy release phase, magnetic reconnection is likely patchy and intermittent (e.g., Aschwanden 2002). At any given time, reconnection occurs within a localized region, forming a newly reconnected flare arcade. Downward-propagating nonthermal electrons propagate along the legs of the flare arcade and produce a pair of compact HXR sources at the conjugate footpoints of the flare arcade as they bombard the dense chromosphere. Chromospheric material heated by the electron beams and/or thermal conduction at different times forms the observed flare ribbons at (E)UV and/or white-light wavelengths, which are usually much more extended than the HXR footpoint source owing to their much slower decay (see, e.g., discussions in Fletcher 2009; Qiu et al. 2010).

In our event, RHESSI 30–80 keV images made during the extended energy release phase (green and blue contours in Figures 7(a), (d), and (g), which correspond to the two intervals we selected for imaging shown in the light curve in Figure 2(a)) reveal multiple pairs of conjugate HXR footpoint sources distributed along the double flare ribbons. The latter is clearly visible in SDO/AIA 1600 Å images (inverse gray-scale background in Figure 7). The location and morphology of the HXR footpoints and UV flare ribbons are consistent with the standard flare scenario discussed above. The flare arcade itself is filled with flare-heated plasma, producing thermal SXR emission (RHESSI 12–15 keV; magenta contours in Figure 7(e)). X-ray spectral analysis using the OSPEX package available in SolarSoft IDL suggests a volume emission measure of 7.8 × 10⁴⁸ cm⁻³ and a temperature of 19 MK (Appendix). Flare-accelerated electrons are often trapped at or above the top of the flare arcade, producing (above) loop-top HXR and/or radio sources (e.g., Gary et al. 2018; Chen et al. 2020a). In this event, as already discussed in Section 2.3, such a loop-top radio source is also present, likely due to gyrosynchrotron radiation from flare-accelerated nonthermal electrons. A loop-top HXR counterpart is not detected by RHESSI. We attribute such a nondetection to its limited dynamic range for imaging the presumably weak coronal source in the presence of strong footpoint HXR sources (e.g., Krucker et al. 2008).

Both the RHESSI 12–15 keV SXR source and VLA gyrosynchrotron radio source display an arcade shape. We adopt a semi-ellipse 3D loop modeling approach to match the morphology of the observed SXR and radio arcade, using the HXR footpoint sources and bright UV flare ribbon kernels as their anchoring points. Free parameters in the 3D loop model include the major and minor axis of the ellipse a and b (with their ratio e = a/b), the inclination angle α of the ellipse plane about the plane perpendicular to the solar surface (a positive angle means a northward inclination), and the rotation angle θ of the ellipse about its center (θ = 0° corresponds to a ellipse with its vertices coinciding with the HXR footpoints or bright ribbon kernels). The relation between the separation of the loop footpoints (2l) in terms of a, b, and θ is

$$\begin{eqnarray}&&{l}^{2}={a}^{2}{b}^{2}/({b}^{2}{\cos }^{2}\theta +{a}^{2}{\sin }^{2}\theta ).\end{eqnarray} \tag{ 1 }$$

With l fixed using the observed footpoint separation, the remaining free parameters that define the 3D semi-ellipse loop are e = a/b, the rotation angle θ, and the inclination angle α. We adjust these parameters until each loop model in projection (from Earth view) matches the morphology of the observed loop-top radio and SXR arcade. The resulting best-fit semi-ellipse loops are shown as the thick orange and magenta curves in Figures 7(b) and (e), respectively. The same loop models are then projected from the viewing perspective of STEREO-A/EUVI (orange and magenta curves in Figures 7(c) and (f)). We will refer to the two model arcades in which the gyrosynchrotron radio source and loop-top SXR are situated, respectively, as the "GS radio arcade" and "SXR arcade" hereafter.

The spike source, as viewed from Earth by the VLA, is located ∼70'' westward in projection from the top of the GS radio arcade (Figure 7(b)). Unlike the loop-top SXR and GS radio sources that have an arcade-like shape, the spike source is unresolved (the synthesized beam is shown in all panels of Figure 7 in the center column as an ellipse). Therefore, the same loop modeling technique described previously cannot be applied to constrain its 3D geometry. Without further constraints, the spike source can, in principle, be located anywhere along the line of sight (LOS) of VLA, shown as a red dashed line in STEREO-A's view in Figures 7 and 8. However, if we adopt the termination shock scenario, it is reasonable to assume that the spike source is located above the top of the flare arcade and makes the same projection angle φ as the loop top of the GS arcade, defined as the angle between the semiminor axis of the semi-ellipse loop model for the GS radio arcade and the plane of the sky (φ ≈ 43°; shown in Figure 8(a)). Therefore, a displacement of d ≈ 98'' from the center of the semi-ellipse loop model for the GS radio arcade (marked as "o" in Figure 8(a)) to the spike source in projection translates into an absolute distance $D=d/\cos \varphi \approx 134^{\prime\prime}$. Knowing the location of the spike source in 3D, we can then derive its (radial) height above the solar surface to be h ≈ 120'' ≈ 86 Mm. Adopting such a height, in STEREO-A/EUVI's view, we mark the inferred spike source location as red contours, located well above the top of the flare arcades. The plane defined by the inferred 3D location of the spike source and the conjugate HXR footpoints is close to the plane where the GS radio arcade is situated, but it is tilted further toward solar south by ∼21°. If we apply the same method on the SXR arcade to estimate the spike's location, it gives a slight difference (∼5'') in the radial height of the spike source. Figure 8 visualizes the 3D spatial relation among the SXR arcade, the GS radio arcade, and the location of the spike source from different viewing perspectives.

Zoom In Zoom Out Reset image size

Our 3D reconstruction results place the best estimate of the spike source location at about ∼120'' above the solar surface, or ∼60 Mm above the apex of the flare arcade. This is generally consistent with the termination shock scenario, in which a shock front is formed at the end of reconnection outflows above newly reconnected, cusp-shaped magnetic loops (see, e.g., MHD simulations in Chen15 and Shen et al. 2018). For this event, as viewed against the disk by SDO/AIA, these newly reconnected loops cannot be clearly distinguished owing to the lack of column depth along the LOS. However, it is expected that they will relax and cool down to background coronal temperatures due to conductive and radiative cooling during the decay phase.

To look for signatures of loops formed around the time of the spike bursts, first, we use the formula given by Cargill et al. (1995) (their Equation 14(E)),

$$\begin{eqnarray}&&{\tau }_{c}=0.0235\displaystyle \frac{{L}^{5/6}}{{\left({Tn}\right)}^{1/6}},\end{eqnarray} \tag{ 2 }$$

where T and n are the initial temperature (in K) and density (in cm⁻³) of a loop with a half-length L (cm), to estimate the loop cooling time. For a loop half-length of 10¹⁰ cm (or 100 Mm; estimated using the distance from the spike source to the center of the semi-ellipse model loop for the GS radio arcade D), plasma temperature of 20 MK, and density of 10⁹–10¹⁰ cm⁻³ typical for flare-heated newly reconnected loops, the loop cooling time τ_c is estimated as ∼2–3 hr. Using this cooling time as a guide, in Figure 7 we show SDO/AIA 193 Å and STEREO-A/EUVI 195 images (differentially rotated back to 18:07 UT; the passbands are sensitive to 1–2 MK coronal plasma; see, e.g., Howard et al. 2008; O'Dwyer et al. 2010). In these images, we find multitudes of well-defined, cool post-flare arcades. One representative semi-ellipse loop model that fits the observed AIA and EUVI arcade features is shown as the thick cyan curve in Figures 7(h) and (i). The apex of the loop is found to be present just below the best-estimate location of the spike source, which is consistent with the scenario of freshly reconnected loops located just beneath a termination shock front. We stress that the semi-elliptical EUV loops shown here may only represent the already-relaxed (and cooled-down) state of the reconnected loops after their shrinkage due to the magnetic tension force (e.g., Reeves et al. 2008). The newly reconnected loops themselves are usually observed to show a cusp shape when viewed from the side (e.g., Tsuneta et al. 1992; Tsuneta 1996), which are not visible in this event owing to the unfavorable viewing perspective.

In the previous subsection, we have established that the spike source is likely located well above the flare arcades visible in radio, EUV, and SXR wavelengths and, possibly, just above freshly reconnected magnetic loops, which is consistent with the flare termination shock interpretation. Here we discuss another important piece of evidence that further supports this scenario: the presence of an SAF and supra-arcade plasma downflows in the close vicinity of the spike source (or shock front). As shown in Figure 9, in SDO/AIA 131 Å (panel (a)) and STEREO-A/EUVI 195 Å (panel (b)) time-series images (both have sensitivity to 10–20 MK hot plasma; Howard et al. 2008; O'Dwyer et al. 2010), a long-lasting SAF structure is seen above the flare arcades from ∼17:50 to ∼19:30 UT. Similar to those previously reported in other eruptive events (Gallagher et al. 2002; Hanneman & Reeves 2014; Innes et al. 2014; Reeves et al. 2017, 2020; Cai et al. 2019), such SAF structures often have a diffuse appearance with many finger-shaped fine structures. Within the SAF structure, multitudes of plasma downflows are identified at about 20 minutes after the time of the spike bursts. Figure 10(b) shows a clear example of a plasma downflow in SDO/AIA 131 Å time-series images that appeared at around 18:25 UT. In the time–distance map of Figure 10(c), the speed of the downflow is found to be ∼166 km s⁻¹ in projection, or ∼227 km s⁻¹ if we adopt the same projection angle of the loop-top GS arcade φ ≈ 43°.

Such an SAF structure is also clearly seen by STEREO-A/EUVI 195 Å with a limb-view perspective (Figure 9(b)). Based on our estimate of the 3D spatial location of the spike source discussed in the previous subsection, in Figure 9(b) we show the inferred location of the same spike source in the STEREO-A/EUVI 195 Å images by applying the same projection angle φ ≈ 43° for each spike centroid obtained at different frequencies. Similar to the spike location in SDO/AIA's view, the spike source is also located close to the top of the SAF structure. Several plasma downflow events are also identified in STEREO-A/EUVI 195 Å running-ratio images (intensity ratio of the current frame to the previous frame 5 minutes earlier) later into the event. Figure 11(b) shows an example of such a plasma downflow event at 19:00 UT. The apparent speed of the downflow is ∼53 km s⁻¹ in projection. Such a speed appears much slower than those measured in SDO/AIA 131 Å images. However, we note that the low speed is most likely due to the selection bias: the low cadence of STEREO-A/EUVI 195 Å images (5 minutes, compared to 12 s of SDO/AIA) only allows downflows with sufficiently slow speeds to be detected in consecutive frames.