Spectroscopic observations of a flare-related coronal jet

Figure 1(a) shows the SXR light curves of the flare. The SXR emissions started to rise at $\sim$08:58 UT and reached peak values at $\sim$09:03 UT before declining gradually until $\sim$09:12 UT. In Fig. 2, the EUV images observed by AIA in 304 Å illustrate the whole evolution of the event (see also the online movie anim304.mov). Before flare, two short minifilaments (F1 and F2) resided in the AR (panel (a)). With the slow rising of F2, the EUV intensities of the flare started to increase at $\sim$08:58 UT and reached peak values at $\sim$09:00 UT (panels (b-c)). Meanwhile, a coronal jet propagates in the southeast direction, which was also observed in 1600 Å (panel (g)). The F1 close to F2, however, was undisturbed and survived the flare (panel (f)). Both of the minifilaments were located along the polarity inversion lines (panel (h)). The morphology and evolution of the C3.4 flare were quite analogous to those of C4.2 flare starting at $\sim$13:36 UT (Zhang et al., 2016a; Dai et al., 2020).

HXR light curves of the flare recorded by RHESSI and Fermi at different energy bands are plotted in Fig. 1(b-c). Note that there was no observation from RHESSI until 09:00:20 UT. Before 08:59:42 UT, there were two small peaks (panel (c)). The HXR emissions at 11$-$26 keV and 26$-$50 keV started to increase sharply at 08:59:42 UT and peaked at 09:00:20 UT before decreasing to $\sim$09:00:40 UT. The HXR peaks indicate that the most drastic release of energy and particle acceleration took place during 08:59:42$-$09:00:40 UT ($\sim$60 s). Afterwards, the HXR emissions between 4 and 26 keV increased gradually and peaked around 09:02:00 UT before decreasing slowly until $\sim$09:04:30 UT, implying their thermal nature from hot plasma ($\sim$10 MK) as a result of ongoing chromospheric evaporation.

Figure 2(h) shows the LOS magnetogram of the flare region observed by HMI at 08:58:15 UT, featuring a central negative polarity surrounded by positive polarities. Such a magnetic pattern is indicative of the fan-spine topology in the corona (e.g., Zhang et al., 2012; Li et al., 2018b; Hou et al., 2019; Yang et al., 2020). In Fig. 3, the left panels demonstrate the top and side views of 3D magnetic configuration of AR 12434. The fan-spine topology is clearly depicted by the blue and yellow lines, and the outer spine is connected to a remote negative polarity to the southeast of fan dome. Below the dome, the green and light violet lines represent the field lines of F1 and F2, respectively. A close-up of the flare region is displayed in Fig. 2(c). The magnetic fields supporting the two minifilaments are sheared arcades instead of twisted flux ropes. The $\mathcal{T}_{w}$ lies in the range of 0.45$-$0.65 for the lower F1 and 0.6$-$0.7 for the upper F2. Figure 3(d) shows the spatial distribution of $\log Q$ within the flare region, highlighting the closed ribbon of high $Q$, which is excellently cospatial with the bright circular ribbon (Fig. 2(c)).

The flare was accompanied by type III radio bursts at 250$-$350 MHz. In Fig. 4, the bottom panel shows the radio dynamic spectra of the flare recorded by e-Callisto/KRIM. The bursts with fast frequency drift rates are noticeable during 08:59:10$-$09:00:40 UT. The radio fluxes at 280, 300, 320, and 340 MHz are extracted and plotted with colored lines in Fig. 1(d). It is revealed that the peaks in radio are roughly correlated with the peaks in HXR, suggesting their common origin. The reconnection-accelerated electrons propagate downward to produce HXR emissions in the chromosphere and propagate upward along open field to produce type III bursts at the same time (Zhang et al., 2016b). Combining with the results of extrapolation in Fig. 3, the real magnetic configuration of the flare region is consistent with previous schematic illustration (Wang & Liu, 2012, see their Fig. 1).

To investigate the radial propagation of the jet, an artificial slice (S1) along the jet spire is selected in Fig. 2(d), which is $\sim$80$\arcsec$ in length. Time-distance diagrams of S1 in 94 Å ($\log T\approx 6.8$), 171 Å ($\log T\approx 5.8$), and 304 Å ($\log T\approx 4.7$) are displayed in Fig. 5. The jet is distinctly observed in all EUV wavelengths, indicating its multithermal nature (Zhang & Ji, 2014b; Joshi et al., 2020a). The kinetic evolution is divided into two phases: a slow rise phase at a plane-of-sky speed of $\sim$131 km s^-1 and a fast rise phase at a speed of $\sim$363 km s^-1, respectively. The transition between the two phases occurred at $\sim$09:00:40 UT, which is denoted by the magenta dashed line. Impulsive heating to reach a temperature of $\geq$6 MK is concurrent with the turning point (panel (a)). The evolution of jet is basically consistent with the breakout model (Wyper et al., 2017, 2018). Magnetic reconnections at the breakout current sheet and flare current sheet lead to intense electron acceleration and heating.

In Fig. 6, the 1330 Å images observed by IRIS/SJI illustrate the evolution of flare and jet in FUV wavelength, which is similar to that in EUV wavelengths. Coherent brightenings of the circular ribbon took place around 09:00:07 UT, indicating null point reconnection (see panel (c) and the online movie anim1330.mov). Unfortunately, the southern part of flare and major part of jet spire were not observed due to the limited FOV of IRIS. The raster observations enable us to carry out spectral analysis of the flare and jet base. In Fig. 7, the left column shows selected FUV images observed by SJI when the jet was covered by the slit. The right column shows the corresponding Si iv spectra of the slit. The spectra of the jet are generally blueshifted, meaning that the jet materials are moving toward the observer.

To precisely quantify the Doppler velocities of the jet, the line profiles of Si iv at the positions marked with cyan lines are extracted and plotted with orange lines in Fig. 8. The entirely blueshifted profiles are satisfactorily fitted with a single-Gaussian function (blue lines in panels (b-e)), and the calculated Doppler velocities ($v_{b}$) are labeled on top of each panel. The profiles with an enhanced blue wing are fitted with a double-Gaussian function (blue and magenta lines in the remaining panels). The sum of two components are drawn with cyan dashed lines, which nicely agree with the observed profiles (orange lines), meaning that the results of double-Gaussian fitting are acceptable. The calculated Doppler velocities ($v_{b}$) of the blueshifted component are also labeled on top of each panel. In Fig. 12, the values of $v_{b}$, ranging from -34 to -120 km s^-1, are marked with blue circles.

Chromospheric condensation at circular flare ribbons has been observed and investigated in the homologous C3.1 and C4.2 flares (Zhang et al., 2016a, b). The redshifted velocities of the downflow reach up to $\sim$60 km s^-1 using the observations of Si iv line. The condensation is primarily driven by reconnection-accelerated nonthermal electrons (Li et al., 2015b, 2017). In Fig. 9, likewise, the left column shows selected FUV images observed by SJI when the circular ribbon was covered by the slit. The right column shows the corresponding Si iv spectra of the slit. The spectra of ribbon are redshifted, indicating plasma downflow or chromospheric condensation.

To quantify the Doppler velocities of condensation, the line profiles of Si iv at the positions marked with cyan lines are extracted and plotted with orange lines in Fig. 10. The profiles are fitted with a double-Gaussian function (red and magenta lines), and the sum of two components are drawn with cyan dashed lines, which gratifyingly agree with the observed profiles. The calculated Doppler velocities ($v_{r}$) of the redshifted component are labeled on top of each panel. In Fig. 12, the values of $v_{r}$, ranging from $\sim$20 to $\sim$80 km s^-1, are marked with red circles. The cause of condensation will be discussed in Sect. 4.2.

As mentioned before, magnetic reconnection occurs not only at the breakout current sheet above the eruptive filament (or flux rope) but also at the flare current sheet below the flux rope (Wyper et al., 2017, 2018). In Fig. 9, dramatic line broadenings of the Si iv line at the jet base are shown in panels (b2), (b3), (b4), (d2), and (d4), implying simultaneous bidirectional reconnection outflows below the jet (e.g., Tian et al., 2014b; Li et al., 2018c; Xue et al., 2018). To work out the Doppler velocities of outflows, the line profiles of Si iv at the positions marked with short green lines are extracted and plotted with orange lines in Fig. 11. The profiles are fitted with a triple-Gaussian function (blue, magenta, and red lines) except in panel (c), which is fitted with a double-Gaussian function. The sum of multiple components are drawn with cyan dashed lines. The calculated Doppler velocities of the redshifted component ($v_{r}$) and blueshifted component ($v_{b}$) are labeled on top of each panel. In Fig. 12, the velocities of reconnection upflow, in the range of -13 and -101 km s^-1, are marked with blue triangles. The velocities of reconnection downflow, in the range of $\sim$17 to $\sim$170 km s^-1, are marked with red triangles. We note that the fast reconnection outflows are observed after 09:00:40 UT, when the jet is rising quickly at a speed of $\sim$363 km s^-1.

It should be emphasized that the chromospheric condensation takes place at the circular ribbon as marked by short cyan lines in Fig. 9. Only redshifted downflow at speeds of 20$-$80 km s^-1 could be identified in the spectra (Figs. 9, 10). The bidirectional outflows are observed inside the circular ribbon and close to the jet base. Simultaneous upflow and downflow could be recognized in the spectra (Figs. 9, 11) and the Doppler velocities of bidirectional outflows are significantly higher than those of condensation. These are the main differences between chromospheric condensation and bidirectional outflows.

Magnetic reconnection is believed to play a key role in the energy release of solar flares (Priest & Forbes, 2002; Priest & Pontin, 2009). Direct evidences of reconnection at current sheets are abundant, including the bidirectional inflows and outflows (e.g., Savage et al., 2012; Ning & Guo, 2014; Wu et al., 2016; Xue et al., 2018; Yan et al., 2018; Chen et al., 2020; Yu et al., 2020b), change of magnetic topology (Su et al., 2013), localized heating to $\geq$10 MK (Seaton et al., 2017; Li et al., 2018c; Warren et al., 2018), and creation of magnetic islands (Li et al., 2016). Using 3D MHD numerical simulations, Wyper et al. (2017) proposed a universal model for solar eruptions, including eruptive flares and coronal jets. Breakout reconnection around an X-type null point in a quadrupolar magnetic configuration is observed and investigated by Chen et al. (2016). Observations of fast reconnection at the breakout current sheet of a fan-spine structure are carried out by Yang et al. (2020).

In our study, impulsive interchange reconnection at the null point was manifested by coherent brightenings of the circular ribbon, HXR peaks, and type III radio bursts around 09:00:00 UT (Fig. 1(c-d) and Fig. 6(c)). Line broadening as a result of bidirectional outflows was absent before the minifilament broke through the fan surface. During the reconnection at the flare current sheet underneath the filament, pronounced upflows and downflows at the jet base were evidenced by significant Doppler line broadenings of Si iv. The jet did not show untwisting motion during its radial propagation, which is probably due to the small $\mathcal{T}_{w}$ of the sheared arcade supporting the minifilament. Taken as a whole, our multiwavelength observations of the flare-related jet support the breakout jet model (Wyper et al., 2018).

Using combined observations of a small prominence eruption on 2014 May 1, Reeves et al. (2015) found evidence for reconnection between the prominence magnetic field and the overlying field. Reconnection outflows at a plane-of-sky speed of $\sim$300 km s^-1 and Doppler velocity of $\sim$200 km s^-1 were detected by SDO/AIA and IRIS, respectively. Moreover, possible reconnection site below the prominence is found (see their Fig. 10). The authors, however, concluded that the reconnection was triggered not by breakout reconnection, but by reconnection occurring along and beneath the prominence.

Using multiwavelength observations from SDO, Hinode/XRT, IRIS, and the DST of Hida Observatory, Sakaue et al. (2018) analyzed a jet-related C5.4 flare on 2014 November 11. The morphology and magnetic configuration of the jet were somewhat similar to the jet in our study. However, the C5.4 flare and jet were caused by magnetic reconnection between the emerging magnetic flux of the satellite spots and the pre-existing ambient fields (Sakaue et al., 2017). Part of the cool H$\alpha$ jet experienced secondary acceleration between the trajactories of the H$\alpha$ jet and the hot SXR jet after it had been ejected from the lower atmosphere, which is explained by magnetic reconnection between the preceding H$\alpha$ jet and the plasmoid in the subsequent SXR jet. In our case, the circular-ribbon flare was caused by eruption of a minifilament underlying the null point (Figs. 2, 3). The fast rise of the jet after $\sim$09:00:40 UT may result from quick ejection of F2 after null-point reconnection (Wyper et al., 2018). The reconnection upflow at the flare current sheet may also contribute to the acceleration of jet, as in the case of coronal mass ejections (CMEs; Zhang et al., 2004).

As mentioned above, chromospheric condensation could be driven by electron beam heating (e.g., Li et al., 2015a, b; Yu et al., 2020a). During the C4.2 flare on 2015 October 16, explosive chromospheric evaporation took place, which was characterized by plasma upflow at speeds of 35$-$120 km s^-1 in the Fe xxi 1354.09 Å line ($\log T\approx 7.05$) and downflow at speeds of 10$-$60 km s^-1 in the Si iv 1393.77 Å line (Zhang et al., 2016a). The estimated nonthermal energy flux above 20 keV exceeds the threshold ($\sim$10¹⁰ erg s^-1 cm^-2) for explosive evaporation (Fisher et al., 1985). Condensation during the C3.1 flare associated with a type III burst is also believed to be driven by electron beams (Zhang et al., 2016b).

To explore the cause of condensation during the C3.4 flare, we focus on nonthermal electrons as usual. In Fig. 2(g), the AIA 1600 Å image at 09:00:39 UT is superposed with intensity contours of HXR emission at 12$-$25 keV during 09:00:20$-$09:00:40 UT (magenta lines). The centroid of the single HXR source is cospatial with the bright inner ribbon, where majority of nonthermal electrons are precipitated. In Fig. 13, the HXR spectrum obtained from RHESSI observation is fitted with a thermal component plus a thick-target, nonthermal component consisting of a broken power law (Rubio da Costa et al., 2015):

where $\delta$ and $E_{c}$ represent the spectral index and cutoff energy of nonthermal electrons. $\mathcal{F}_{c}=\int_{E_{c}}^{\infty}F(E)dE$ denotes the total electron flux above $E_{c}$. The fitted thermal component is plotted with a red dashed line, with the values of thermal temperature ($T$), emission measure (EM) being labeled. The fitted nonthermal component is plotted with a blue dashed line, with the values of $\delta$ and $E_{c}$ being labeled as well. The sum of two components (magenta dashed line) agrees with the observed spectrum.

Before $\sim$09:00:40 UT, the HXR emissions were predominantly produced by nonthermal electrons (Fig. 1(c)). The power of injected electrons above $E_{c}$ is expressed as:

Substituting the parameters obtained from HXR spectral fitting in Fig. 13: $\delta=4.6$, $\mathcal{F}_{c}=5.6\times 10^{35}$ electrons s^-1, $E_{c}=10.3$ keV, then $P_{nth}$ is estimated to be $\sim$1.3$\times$10²⁸ erg s^-1. A lower limit of the total nonthermal energy in electrons is $\sim$2.6$\times$10²⁹ erg, since there was no RHESSI observation before 09:00:20 UT. Considering that the area of HXR source is in the range of (0.25$-$1)$\times$10¹⁸ cm², the total nonthermal energy flux is estimated to be (1.3$-$5.2)$\times$10¹⁰ erg s^-1 cm^-2, which is adequate to drive chromospheric condensation at flare ribbon.

After $\sim$09:00:40 UT, the HXR emission at 25$-$50 keV decreased to the pre-eruption level, while the emission at 12$-$25 keV increased gradually with episodic spikes till $\sim$09:02:00 UT. To investigate the role of heat conduction in driving condensation, we estimate the energy flux of heat conduction using the expression:

where $\kappa_{0}\approx 10^{-6}$ erg s^-1 cm^-1 K^-7/2, $T\approx 14.5$ MK denotes the thermal temperature in the corona, and $L\approx\frac{\pi d}{4}$ denotes the length scale of the temperature gradient ($d\approx 36\arcsec$ represents the equivalent diameter of circular ribbon). $F_{cond}$ is estimated to be $\sim$5.5$\times$10⁹ erg s^-1 cm^-2. Therefore, the condensation after $\sim$09:00:40 UT should be driven by a combination of nonthermal electrons and heat conduction (Sadykov et al., 2015).

As mentioned above, the flare was associated with type III radio bursts, which are generated by electron beams propagating upward along open field (Innes et al., 2011; Chen et al., 2018). The top and middle panels of Fig. 4 show radio dynamic spectra recorded by ZSTS and blen5m during 09:00$-$09:02 UT with the same cadence as KRIM. Enhancement of the microwave emission at 0.98$-$1.43 GHz was obviously demonstrated before 09:00:40 UT. Contrary to the discrete type III bursts owing to the coherent plasma radiation mechanism (Dulk, 1985), the microwave burst seems to be continuous and has no one-to-one correspondence with the type III bursts, implying that the microwave burst was not produced by plasma radiation mechanism. To interpret the relationship between the HXR and radio time profiles of single-loop flares, Kundu et al. (2001) proposed a simple trap model by introducing a critical pitch angle (i.e. loss cone angle). Those injected high-energy electrons with smaller pitch angles are not reflected by the increasing magnetic field as they approach the loop footpoints and will precipitate on their first approach. The remaining electrons with pitch angles outside the loss cone will be trapped in the loop unless pitch angle scattering takes place.

In our case, the accelerated nonthermal electrons before $\sim$09:00:40 UT are composed of three groups. The first group propagates along open field to generate type III radio bursts (Fig. 4(c)). The second group precipitates straightforward into the chromosphere and generates HXR emissions (Fig. 1(b-c)). The third group is trapped in the rising minifilament and generates microwave burst through the gyrosynchrotron emission mechanism (Dulk, 1985; Lee & Gary, 2000; Wu et al., 2016). Of course, the trapped electrons will eventually precipitate once pitch angle scattering switches on. Existence of trapped nonthermal electrons in a kink-unstable filament undergoing a failed eruption has been reported by Guo et al. (2012). After the minifilament breaks through the null point and totally opens up, there are no trapped electrons any more and the microwave emission vanishes. This scenario is qualitative and needs to be validated by in-depth investigations. Additional cases of microwave bursts like in Fig. 4 have been collected, which will be the topic of our next paper.