Extreme-ultraviolet Late Phase Caused by Magnetic Reconnection over Quadrupolar Magnetic Configuration in a Solar Flare

TL;DR

This study investigates the EUV late phase in solar flares, revealing that magnetic reconnection in a quadrupolar configuration causes additional heating and late-phase emissions, supported by observations and modeling.

Contribution

It provides clear evidence linking late-phase EUV emissions to magnetic reconnection overlying the main flare loops in a quadrupolar magnetic setup, clarifying the heating source.

Findings

Late-phase emission originates from longer or higher loops.

Magnetic reconnection in overlying fields causes late-phase heating.

EBTEL model successfully reproduces late-phase EUV emissions.

Abstract

A second emission enhancement in warm coronal extreme-ultraviolet (EUV) lines (about 2-7 MK) during some solar flares is known as the EUV late phase. Imaging observations confirm that the late phase emission originates from a set of longer or higher loops than the main flare loops. Nevertheless, some questions remain controversial: What is the relationship between these two loop systems? What is the heating source of late phase emission, a heating accompany the main phase heating or occuring quite later? In this paper, we present clear evidence for heating source in a late-phase solar flare: magnetic reconnection of overlying field in a quadrupolar magnetic configuration. The event is triggered by an erupted core structure that eventually leads to a coronal mass ejection (CME). Cusp feature and its shrinkage motion high in the late-phase emission region are the manifestation of the later phase reconnection following the main flare reconnection. Using the enthalpy-based thermal evolution of loops (EBTEL) model, we reasonably reproduce the late-phase emissions in some EUV lines. We suggest that a continuous additional heating is responsible for the appearance of the elongated EUV late phase.

Tables

Table 1. Table 1: Properties of the EUV Light Curves of the 2014 April 25 X1.3 Flare †

Line/Passband	Ion	Temperature	Peak Time (UT)			Delay Time (minutes)
(nm)		(MK)	Main Phase	Late Phase		Main Phase	Late Phase
SXR (0.1-0.8)	*	$>$10	00:27:10	*		10	*
MEGSA (6-37)	*	*	00:30:32	03:44:32		13	207
13.3	Fe XX	10	00:30:32	*		13	*
9.4	Fe XVIII	6.5	00:33:32	02:19:52		16	122
33.5	Fe XVI	2.5	00:33:22	03:33:12		16	196
${13.1}^a$	Fe XXI	10	00:35:00	01:14:00		18	57
${9.4}^a$	Fe XVIII	6.4	00:34:00	02:26:02		17	129
${33.5}^a$	Fe XVI	2.5	00:32:00	03:42:00		15	205

Table 2. Table 2: Late Phase Parameters for the EBTEL-based Flare Model

	Parameters	Our model	Hock model	Note
Single loop parameters	$l^{\ast }$	$l_0^{\prime }+i\times \Delta l$	free	Loop half-length (cm)
	$t0$	$t_0^{\prime }+i\times \Delta t$	free	Time of peak impulsive heating (s),$\Delta t=672$ s
	$dt$	672s	300s	Duration of heating (s)
	$Q0$	$Q_0^{\prime }+i\times \Delta h$	free	Amplitude of heating (erg cm-3  s-1)
	$A$	free	free	Loop cross-section area (cm2)
Global parameters	$Nloops$	10	22	Number of EBTEL loops
	$C$	$3.56\times {10}^{-27}$	$3.56\times {10}^{-27}$	Normalization factor (sr  m-2)

Table 3. Table 3: Comparison of Properties from Observations and Modelings

Passband	Ion	Temperature	Observation				modeling
			Peak Intensity	Peak Time	FWHM		Peak Intensity	Peak Time	FWHM
(nm)		(MK)	$(\mu$W)	(UT)	(minutes)		$(\mu$W)	(UT)	(minutes)
9.4	Fe XVIII	6.5	2.000	02:26:02	*		1.985	02:39:02	140
33.5	Fe XVI	2.5	9.071	03:31:42	158		8.071	03:42:32	192

Equations

$$E(t)=K\sum _{{\lambda }_{min}}^{{\lambda }_{max}}\Delta \lambda I_{\lambda }(t),$$

$$\frac{dn}{dt}=-\frac{c_2}{5c_3{k}_{B}T}[\frac{F_c}{L}+c_1{n}^2\Lambda (T)],$$

$$\frac{dP}{dt}=\frac{2}{3}[Q(t)-(1+c_1)n^2\Lambda (T)],$$

$$Q(t)=\{\begin{array}{ll}{Q}_{bkgd}+Q_0+\frac{2Q_0}{dt}(t-t_0)& \text{if }{t}_0-\frac{dt}{2}<t<t_0,\\ Q_{bkgd}+Q_0-\frac{2Q_0}{dt}(t-t_0)& \text{if }{t}_0\le t<t_0+\frac{dt}{2},\end{array}$$

$$t_0=t_0^{\prime }+i\times dt,$$

$$I_{loop}(t)={\int }_{T}DEM(t,T)G(T)dT.$$

$$E_{model}(t)=C\sum _{i=1}^{N_{loops}}{A}_i{I}_{loop,i}(t),$$

$$C=(0.001\frac{W/m^2}{ergs/c{m}^2/s})d\Omega ,$$

$${\tau }_{cool}\doteq 2.35\times 10^{-2}{l}^{5/6}{T}_e^{-1/6}{n}_e^{-1/6}.$$

Full text

Sun: corona — Sun: flares — Sun: UV radiation

\listofchanges

1 Introduction

A solar flare, localised brightening in the solar atmosphere, rapidly releases radiation over a wide range of electromagnetic spectrum. Beside the radiation enhancement, sometimes the flare also accelerates high energy particles and is accompanied with magnetic flux ejected into the interplanetary space, which is manifested as a coronal mass ejection (CME).

Solar flares are generally believed to be a result of magnetic reconnection - the merging of antiparallel magnetic fields and the consequent release of magnetic energy. The free magnetic energy is convert into the kinetic energy of the CME and significant particle acceleration and plasma heating. When the impulsive flare heating is terminated, the plasma will cool down mainly by conduction and radiation. Initially, the energy is transported downward mainly in the form of conductive flux or non-thermal particles and deposited in the transition region (TR) and chromosphere. Due to the Coulomb collisions, heating, and strong ablation, the ambient chromospheric plasma is strongly heated and expands upward, filling the coronal loops, known as the chromospheric evaporation(Antiochos & Sturrock, 1978). As the loop temperature decreases and the density increases, radiation gradually becomes dominant. As the plasma cools, pressure gradients drop to subhydrostatic values, and material drains from the corona (Klimchuk et al., 2008).

Observations show that flares typically experience three stages: (1) a precursor phase, presenting a small emission enhancement at radio, H$\alpha$, UV to EUV wavelengths (e.g., Bumba & Krivský, 1959; Martin, 1980; Van Hoven & Hurford, 1984; Cheng et al., 1985; Warren & Warshall, 2001; Fárník et al., 2003; Contarino et al., 2003); (2) an impulsive phase indicated by rapidly enhancement of a microwave burst and/or a hard X-ray burst that lasts from 100 to 1000 seconds in which protons and electrons are accelerated to energies over 1 MeV , and (3) a decay phase that lasts for several minutes or hours with the gradual increase and decrease of soft X-ray and EUV emissions(Hudson, 2011, and reference therein).

However, recent observations revealed that in some solar flares, warm coronal emission lines (about $2-7$ MK) exhibit a second emission peak (Woods et al., 2011) as seen by the EUV Variability Experiment (EVE; Woods et al., 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al., 2012). This secondary peak, referred to the late phase and not subject to any stages mentioned above, lags behind the GOES X-ray peak for tens of minutes to hours. Woods et al. (2011) proposed four observational criteria to define an EUV late phase: (1) a second peak in the warm emissions (e.g., Fe XV and Fe XVI) after the GOES soft X-ray peak; (2) no significant enhancements in hot emissions (e.g., Fe XX) during the second peak; (3) association with an eruptive event seen in imaging observations; and (4) the existence of a second set of higher and longer loops relative to the main flaring loops. In general, the emission of an EUV late-phase flare is from the synthesis effect of thermal evolution from these two sets of loop systems. The difference in cooling rate between different loops could discriminate the two peaks in warm coronal emission lines (Liu et al., 2013a; Wang et al., 2016). Yet, cooling process of another longer loop alone cannot be sufficient for some long delay (several hours) cases (Hock et al., 2012).

Nevertheless, how is the late phase loop system heated up is still uncovered. Studies have explored the possibility of additional heating (Woods et al., 2011; Hock et al., 2012; Dai et al., 2013; Sun et al., 2013), as well as the long lasting cooling timescale (Liu et al., 2013a; Sun et al., 2013). Using the enthalpy-based thermal evolution of loops (EBTEL) model(Klimchuk et al., 2008; Cargill et al., 2012), Dai & Ding (2018) numerically simulated EUV late-phase flares under two main mechanisms, i.e., long duration plasma cooling and additional heating mechanisms. They found that the late phase peak occurs during the radiative cooling phase of the late-phase loop if it is a long-lasting cooling process, while the additional heating probably makes the late-phase peak take place in the conductive cooling phase. They proposed that the shape of late phase light curves can be used to differentiate the two mechanisms.

Meanwhile, statistical analysis (Woods et al., 2011) showed that the flares with late phase exhibit clustering phenomena in certain active region (AR), implying a specific magnetic configuration of the ARs in which EUV late phase flares are preferentially produced. From direct EUV imaging observation, the basic 2D configuration of the magnetic topology is considered as a quadrupolar configuration - typical symmetric (Hock et al., 2012) or asymmetric (Liu et al., 2013a) quadrupolar configuration. In reality, ARs often show a more complicated configuration. Sun et al. (2013) considered a fan-spine topology with a closed-field configuration, in which the late phase peak comes from the cooling of large post-reconnection loops beside and above the compact fan. This magnetic field configuration has been further verified through observation (Dai et al., 2013; Li et al., 2014; Masson et al., 2017). The key ingredients pertinent to AR magnetic configuration with late phase can be simply summarized as a quadrupolar configuration. This kind of topology distinguishes two sets of loop systems - the external late phase loop system and inner main phase loop system. Sun et al. (2013) suggested that the two systems and their evolutional trends are closely linked by the fan-spine topology in their case. While Hock et al. (2012) considered that these two loop systems have no direct linkage, and it is the CME that stretches the late phase loops to reconnect. In both of cases, during the late-phase stage, cusp-shaped structures are found above main flare region, which is characteristic for ongoing reconnection behind ejecta. Particularly, when considering additional heating, the quantitative results are more consistent with observations (Sun et al., 2013).

Based on the above, the mechanism causing the late phase is still under debate. In this paper, we study a limb flare event with a well-defined EUV late phase. In section  2, we introduce the instruments. In section  3, we present observations and analysis of the event, which are followed by an EBTEL modeling of the late-phase emission in section 3.4. Finally we present summary and conclusion in section 4.

2 Instruments

The data presented in this work primarily come from the Atmospheric Imaging Assembly (AIA; Lemen et al., 2012), which images the coronal plasma through 6 different EUV passbands. Among them, the 13.1 nm (Fe XXI, $\sim$ 10 MK), 9.4 nm (Fe XVIII, $\sim$ 6.4 MK), and 33.5 nm passbands (Fe XVI, $\sim$ 2.5 MK) are sensitive to hot(warm) plasma and can be used for thermal evolution analysis, and the other three passbands, 21.1 nm (Fe XIV, $\sim$ 2.0 MK), 19.3 nm (Fe XII, $\sim$ 1.6 MK), and 17.1 nm (Fe IX, $\sim$ 0.7 MK) are largely sensitive to plasma cooler than 2.0 MK, e.g., bulk coronal plasma. The cadence of these EUV images is 12 s and the pixel size is $0\farcs 6$ . Note that the AIA 13.1 nm passband also includes Fe VIII lines that are expected to be brighten up at relatively low coronal temperatures ($\sim$ 0.4 MK), and the AIA 19.3 nm passband contains a hot spectral line Fe XXIV ($\sim$ 20 MK)(Lemen et al., 2012). The twin spacecraft of the Solar Terrestrial Relationships Observatory (STEREO; Kaiser et al., 2008) provide simultaneous multi-viewpoint from other two places. During the event, STEREO Ahead and Behind are about 157 ∘ west and 165 ∘ east from the Sun-Earth line along the ecliptic orbit around the Sun, while the SDO is situated near the Earth. The Extreme Ultraviolet Imager (EUVI) on the two STEREO spacecraft observe the chromosphere and low corona in four EUV passbands, which enables us to reconstruct the 3D shape of coronal loops using triangulation technique. Here we choose the 19.5 nm (Fe XII, $\sim$ 1.5 MK) passbands from EUVI_A,B and 19.3 nm (Fe XII, $\sim$ 1.6 MK) passband from SDO/AIA to display the evolution of the coronal loop in different angles and reconstruct their geometrical configuration. We use wavelet-enhanced images of STEREO EUVI provided by Johns Hopkins University Applied Physics Laboratory(JHUAPL). This image-processing technique (wavelet-enhanced) gives better visual clarity than the standard EUVI images(Stenborg et al., 2008).

Moreover, we make use of EVE observations, which obtain integrated emission from the Sun over a wide wavelength range (0.1 nm to 105 nm) with unprecedented spectral resolution of 0.1 nm, high temporal cadence (10s), and accuracy of 20% (Woods et al., 2012). EVE provides two set of level 2 data products including the “line” (EVL) product and the “spectra” (EVS) product, which are publicly available at http://lasp.colorado.edu/eve/data_access/evewebdataproducts/level2/.

3 Observations and Results

3.1 Overview of the Event

On 2014 April 25, a solar flare started at 00:17 UT and lasted over eight hours according to the GOES soft X-ray (SXR) flux (Figure 1(a)). The SXR flux( 1 – 8 Å) reached a maximum of $1.3\times 10^{-4}$ Wm*-2*, revealing an X1.3 class flare. At the time of the flare, the associated AR NOAA 12035 was located behind the west limb of the sun. The accompanied CME had an initial speed around 600 km s*-1* at a height of $\sim$ 3Rs. However the velocity decreased to 300 km s*-1* when the CME reached 20 Rs according to the cdaw.gsfc.nasa.gov/CME_list (catalog CME catalog) based on the Large Angle Spectroscopic Coronagraph C2 and C3 observation (LASCO; Brueckner et al., 1995). Despite at that time the magnetic field of the AR can not be measured, the magnetograms recorded three days prior to the eruption revealed a quadrupolar magnetic configuration on the photosphere. The onset of the event was believed to be caused by breakout reconnection(Chen et al., 2016).

3.2 Extremely Large EUV Late Phase

Three emission lines from the EVL data are selected to study the EUV evolution of this event with the wavelength centered at 13.3 nm (Fe XX, $\sim$ 10 MK), 94 nm (Fe XVIII, $\sim$ 6.5 MK), and 33.5 nm (Fe XVI, $\sim$ 2.5 MK). These three EVE lines have complementary imaging observations from AIA. Subtracting the emission several minutes before the eruption, the temporal profiles of irradiance variability (normalized) in these lines during the flare period are plotted as blue, green, and black curves in Figure 1(a), respectively. The intensities of three EVE lines almost simultaneously enhance with the GOES SXR flux. The delay of the first peak (as pointed by the colored arrow) indicates the cooling process of the flare’s main phase. Unlike the only one peak in GOES SXR and 13.3 nm profile, a second peak appears in 9.4 nm and 33.5 nm. The intervals between the two peaks in 9.4 nm and 33.5 nm are 106 and 180 minutes, respectively. These secondary emission peaks in warm EUV lines (about 2-7 MK) are signatures of the EUV late phase. Furthermore, in the warm 33.5 nm line profile, the second peak is much stronger than the first peak, indicative of an extremely large EUV late phase (Liu et al., 2015). The flux ratio of the second peak to the first peak is around 5, much higher than the average value of 0.8 in statistics (Woods et al., 2011).

The EVS spectral data from MEGS-A instrument provide continuous measurement for spectrum irradiance variability of the flare within the wavelength range of 6-37 nm. Here, the routine eve_integrate_line.pro from SolarSoftware (SSW) package is employed to integrate irradiance over this wavelength range using midpoint rule:

[TABLE]

where $\Delta\lambda$ is the wavelength bin, and $K$ is a conversion factor (=$10^{7}\times 2\times\pi\times$ (1AU)2) that transforms the irradiance flux in units of J m*-2* at 1 AU to the radiative loss rate in units of erg s*-1* at the Sun assuming a uniform angular distribution of flare energy release (Woods et al., 2006). The radiative energy-loss rate in this EUV range is calculated according to Equation (1)(Liu et al., 2015) and displayed with shading area in figure 1(b). It is interesting to note that there are also two peaks in the profile of the EUV radiative energy-loss rate. The vertical dashed lines bound the impulsive and the gradual phases from the two enhancements of Fe xvi 33.5 nm line irradiance, the former is from the onset of the impulsive phase at 00:17 UT to its conclusion at 02:00 UT, the latter includes the late-phase EUV enhancement between 02:00 UT and 06:00 UT. We also calculate the total flare EUV output in these two periods by simply integrating the emission with the background emission subtracted. In spite of a higher late-phase peak in the 33.5 nm line, the EUV radiation output releases much less energy ($0.25\times 10^{29}$ erg) during the flare late phase than that ($3.2\times 10^{29}$ erg) during the flare main phase.

We turn to imaging observation such as SDO/AIA and STEREO/EUVI. AIA instrument provides the corresponding imaging observations at 13.1 nm, 9.4 nm and 33.5 nm. After checking the source region, we select out a region restricted to a small region (figure 2(h)) where emission is mainly caused by the main flaring loops and a larger region mainly responsible for the emission of the late phase. The regions are depicted as the boxes in figure 2(h), over which the intensity profiles at different channels are plotted in figure 1(b). Obviously, the light curves from the main phase region (solid lines) behave in a similar way - they rise up, reach the peak, and recovery to the background nearly synchronously. The very close peak times of 13.1 nm (10 MK) to 33.5 nm (2.5 MK) signifies a rapid cooling process of the main phase. In contrast, the brightness of the late phase region (dashed lines in Figure 1(b)) shows a much more gradual evolution. The delay time is 56 minutes for the AIA 13.1 nm, 128 minutes for AIA 9.4 nm, and 204 minutes for AIA 33.5 nm (table  1). There also appears a dimming from 00:17 to 02:00 UT at the 33.5 nm (figure 1(b), blue dashed line) due to depletion of plasma density in areas associated with eruptions. These observations coincide with previous conclusion that two set of loop systems exist in the active region. Different from the compact loop system for the flare main phase, the late phase originates from another set of higher and longer loops.

Chen et al. (2016) analyzed the morphology of this case in detail and argued that the overall configuration of the AR is a quadrupolar magnetic configuration. Figure 2 shows the evolution of the eruption in different view angles during different stages with pseudo 3D schematic at the bottom. Here all the images have been rotated with the eruption direction towards to the top in order to compare with the cartoon. STEREO_A EUVI 19.5 nm provides the disk observation (Figure 2(a)-(c)), STEREO_B 19.5 nm (Figure 2(d)-(f)) and SDO 9.4 nm (Figure 2(g)-(i)) provide limb views. Two sidelobe structures can be easily identified at the AIA 9.4 nm channel, indicating that hot structures similar to the bipolar configuration on both sides in figure 2(j) cartoon. During the flare main phase, a core structure expands outward, pushes the sidelobes aside and finally erupts into the interplanetary space as seen in hot channels (like AIA 9.4 nm in figure 2(g,h), figure 3 and the accompanied movie). The cartoon in figure 2(k) depicts this scenario, but the low temperature coverage of EUVI 19.5 nm channel makes it only see the brightness of the post flare loops (PFLs), with their footpoints marked as P1 and P2. When it comes to the late phase stage, a totally different loop system appears, much longer and higher loops form with remote footpoints labeled as P3,P4 (figure 2(c) and (f)). Figure 2(i) shows the hot part of these loops on the top region. From figure 1(b) we could know that, the emission of the late phase mainly comes from the big box region, namely the late phase loop system. The late phase loop system is often considered as a pre-existing structure somehow connected magnetically with the main phase loop (Liu et al., 2013a; Sun et al., 2013), but our observation seems to be in favor of another scenario - the late phase loop system comes from the newly reconnected large-scale arcades as the overlying field above the quadrupolar configuration is stretched by the erupting CME and then reconnects as shown by Figure 2(i) (Hock et al., 2012).

3.3 Late phase loop evolution

This event presents a novel perspective to the origin of the EUV late phase. Interestingly, unusual large and hot overlying arcades appear above the flare after the CME eruption as seen from the AIA view (figure 3(a)). This structure is invisible in the low temperature wavelengths like AIA 19.3 nm and EUVI_B 19.5 nm. Cusp-shaped loops appeared at the top of the arcades that rapidly retreat sunward, and continuously pile up above the arcade (Figure 3(a) and the accompanying animation). As these overlying arcades cool down, numbers of loops sequentially show up from lower part to higher part (figure 3(d)) at the AIA 19.3 nm passband. Due to a strong cold line (Fe VIII, 0.4 MK) blending, the AIA 13.1 nm passband also shows cold loops during the cooling process (figure 3(c)). Based on the morphology analysis in multiple-temperature, the evolution of the late phase loop system experienced three stages: initial stage, characterised by relatively low temperature high-lying arcades over the flare region (figure 2(j)); eruptive stage, similar to the classical flare magnetic reconnection scenario, in which the erupting CME stretches the overlying field, whose legs seem to curve-in toward the reconnection site; recovery stage, seen as the shrinkage of cusp structure in the high temperature channel (figure 3(a)), which is commonly considered as X-type configuration, as sketched by figure 2(i).

To further investigate the evolution of the late phase loop system, we perform a quantitative analysis. Here we study two evolution: shrinkage motion and cooling process of the late phase loops. We draw three slits: Slit S1 in figure 3(a) is located at the cusp location, while S0 in figure 2(f) and S2 in figure 3(c) indicate the eruption direction are used to trace late phase loops. Figure 4(a),(b) and (c) are the slice-time stacking plots of slit S2 at the AIA 13.1 nm, 9.4 nm and 33.5 nm passbands. A bright core region appears in all these channels with its height above 50 Mm. The time delay of the brightness from 13.1 nm to 33.5 nm indicates the cooling of the overlying arcades. The vertical arrow in each channel gives the timing of the maximum intensity. When the temperature reaches a low level (such as 1 MK ), in the slice-time diagram of slit S2 from AIA 19.3 nm channel and slit S0 from EUVI 19.5 nm channel, a bright feature slowly rises up with a fitting speed of 3.26 km s*-1*. For PFLs, it is generally recognized that this kind of rising motion is an apparent ascending of these overlying loops instead of real mass motion. Here for the late phase loops, we think that the same process could explain this motion. From figure 4 and accompanied movie one can see that the late phase loops behave in the similar manner like PFLs, i.e., the newly reconnected loops continuously accumulate above the flare loops. So this gives us a hint that the duration of the brightness in each channel has direct correlation with the numbers of the shrinkage loops.

In figure 4(d), a series of dark features continuously drop down towards to the flare loop top. These voids known as supra-arcade downflows (SADs) were first observed by Yohkoh SXT and TRACE(e.g., McKenzie & Hudson, 1999; Gallagher et al., 2002) and SADs are closely related to the outflows produced by magnetic reconnection occurring high in the corona. Thus the dark features could be a consequence of newly reconnected loops. We identify the obvious trajectories of three dark features to trace the shrinkage motion. The velocities range from 97 km s*-1* to 143 km s*-1*. The intervals between the neighbouring stripes are 11.2 minutes and 11.3 minutes in the AIA 13.1 nm slice-time stacking plot of Figure 4(d), respectively. These stripes manifest the trajectories of SADs, which could be due to the SADs retract from the reconnection sites high in the corona and continuously cool down, giving rise to consecutive brightness in the different AIA channels.

To quantify the loop length of single late phase loop for the later simulation. We used the IDL routine scc_measure.pro in SSW to trace out the path of the loop in 3D space (Thompson, 2009; Zhou et al., 2017). Because STEREO EUVI_A/B only have cool line, we use the EUVI 19.5 nm ($\sim$ 1.5 MK) and AIA 19.3 nm ($\sim$ 1.6 MK) to reconstruct the loop. Both images in the AIA 19.3 nm and EUVI 19.5 nm at 04:10 UT show multiple clear bright loops. We select out a loop and obtain its loop half length of 138 Mm. Its initial length should be larger because it has retracted before it becomes visible.

3.4 EBTEL modeling of the late phase emissions with additional heating

By far there are two major explanations for the EUV late phase: one is additional heating, and the other is long-lasting cooling. A definite answer perhaps requires modeling of a multitude of loops based on observations (e.g. Qiu et al., 2012; Liu et al., 2013b; Hock et al., 2012). Here, from possible signatures of the reconnection in the high corona, we take a heuristic approach with additional heating to model the late phase. The EBTEL-based flare model(Hock et al., 2012) is employed to simulate radiative output of the late phase loop system. This model uses multiple EBTEL loops (e.g., 22 EBTEL loops) with variable loop lengths and heating rate profiles to synthesize the light curves of several EUV lines as measured by EVE, 13 out of 22 loops are employed to model the late phase emissions. Here we use 10 EBTEL loops to model the late phase radiative output.

3.4.1 the EBTEL model

For a single EBTEL loop, its evolution can be controlled by loop-averaged equation of continuity and energy (Klimchuk et al., 2008; Cargill et al., 2012):

[TABLE]

and

[TABLE]

where $n$, $P$, and $T$ are the mean density, pressure, and temperature of the loop, respectively, which follow from the equation of state, $P=2nk_{B}T$ with $k_{B}$ being the Boltzmann constant, $c_{2}$ (= 0.9) is the typical ratio of average to apex temperature of a coronal loop, $c_{3}$ (= 0.6) is the ratio between coronal base temperature and apex temperature, $Q(t)$ is the volumetric heating rate, $\Lambda(T)$ is the optically thin radiative loss function, $F_{c}=-(2/7)\kappa_{0}(T/c_{2})^{7/2}/l$ ($l$ the half loop length) is the thermal conductive flux, and $c_{1}$ is the ratio of radiative loss rate of the TR to that of the corona.

In addition, we only consider thermal heating $Q(t)$ and ignore non-thermal electron beam heating. The rationality of predigestion mainly relys on following reasons. In the additional heating scenario, the non-thermal heating is unlikely to be the major heating source during the late phase based on previous study that the late-phase arcades do not show obvious HXR emission(e.g. Li et al., 2012, 2014; Sun et al., 2013). In fact, Li et al. (2014) checked the effect of non-thermal beam heating using a flux of which the total energy comparable with that of thermal heating, and found that the non-thermal effect is not significant in the EUV late phase. Thermal heating primarily raises the temperature of the coronal plasma, where non-thermal beam heating primarily raises the density. Liu et al. (2013b) discussed that the increased density caused by the non-thermal beam could somewhat enhance the EUV late-phase emission, but it affects the timing of the EUV late phase much less than a loop length variation. Meanwhile we only calculate the emission from the coronal part, because the footpoints of these loops are located behind the solar limb.

The EBTEL code is publicly accessible at https://github.com/rice-solar-physics/EBTEL. The main program is called ebtel2.pro that computes the evolution of spatially-averaged loop quantities using the above simplified equations. Combined with the CHIANTI atomic database (Dere et al., 1997, 2009), the routine - intensity_ebtel.pro - computes the line intensity as a function of time.

3.4.2 EBTEL-based flare Model

There are three steps to calculate the line emission based on the EBTEL model. First, for each single loop, EBTEL program gives the differential emission measure (DEM) as a function of time and temperature. The inputs of the model are heating function, $Q(t)$ (erg cm*-3* s*-1*) and loop half-length (cm). The heating function has a linear slope, i.e.

[TABLE]

Where $Q_{0}$ is the heating amplitude, $dt$ is the heating duration, which is set to be the interval between two time-adjacent loops, namely 11.2 minutes, and $Q_{bkgd}$ is the background heating at a low level of $10^{-6}$ erg cm*-3* s*-1*. The initial setting is similar to that in Hock et al. (2012) except that here we fix the start time of the heating ($t_{0}$) for each loop based on observations:

[TABLE]

Where $t^{\prime}_{0}$ is the first episode of the late phase heating. As the reconnection continues, higher reconnected loops will shrink backward, and the half-length of these loops, $l$, will increases. Here we simply assume a linear increase in length of consecutive loops and a linear decrease in the heating magnitude.

EBTEL will return $DEM\_COR(t,T)$ (DEM from the corona part) and $DEM\_TR(t,T)$ (DEM from the transition region). Due to occulting effect of the solar limb, here we only need to calculate the emission from the corona. The line radiance is the convolution of the DEM with the contribution function $G(T)$ that contains abundance factor, i.e.

[TABLE]

Note that the contribution function is calculated by the program gofnt.pro in CHIANTI package.

At last, the total emission of the late phase is generated by combining the contribution of all EBTEL loops. To compare with EVL data, a constant normalization factor C is used to convert the radiation at Sun to the irradiance received at Earth (1AU) assuming a uniform (constant) angular distribution of flare energy release, as showed below:

[TABLE]

and

[TABLE]

Where $A_{i}$ is loop cross-section area, which is the same for the modeling loops. $N_{loops}$ is the number of the loops, and $d\Omega$ ($3.56\times 10^{-24}$ sr m*-2*) is the solid angle subtended by 1 m2 at 1 AU. Which yields a normalization factor C of $3.56\times 10^{-27}$(Hock, 2012). All parameters in the EBTEL-based flare model are listed in table  2.

3.4.3 Modeling Result

Using the EBTEL-based flare Model, we reproduce the irradiance in different emission lines for the late phase loop system and compare it with EVE’s observations (figure 5). The late phase emission in hot line (13.3 nm, $>10$ MK) could merely be seen as the late phase emission is largely submerged under main phase emission. This blending effect also affects the 9.4 nm EVE line, resulting in an obvious overlapping of the main phase and late phase emissions during 01:00 UT to 02:00 UT (as shown by the black line in figure 5(b)). So we only use the 9.4 nm data after 02:00 UT to do the fitting. As for 33.5 nm line irradiance, the late -phase bump is clearly identified.

We fit both 9.4 nm and 33.5 nm lines using MPFIT package. The result shows a good agreement between the observations and modeling (figure 5). The observed 13.3 nm emission and modeled one are plotted in the top panel of figure 5. The best-fit gives an initial loop half-length ($l^{\prime}_{0}$) of 179 Mm and heating rate ($Q^{\prime}_{0}$) of $0.022$ erg cm*-3* s*-1*, of which comparable to that in Hock et al. (2012)’s model ( $\sim 0.01$ erg cm*-3* s*-1*), but less than that ($0.2$ erg cm*-3* s*-1*) of case 1 in Li et al. (2012) with one order of magnitude. However, in Li et al. (2012)’s model, only one loop was used to model the late phase loop. the best-fit loop cross-section is $1.3\times 10^{16}$ cm2 corresponding to a loop width of 1.3 Mm.

Using the EBTEL model, we reconstruct the irradiance of the flare late phase and study the role of additional heating in the appearance of an EUV late phase. Our results show that the late phase peak times in observations and modeling for each line are very close with each other (within 15 minutes). Hence the long delay appearing in the warm lines can be well explained. Liu et al. (2013a) estimated the cooling time of the late phase loop arcade by using the formula derived by Cargill et al. (1995) based on a simple cooling model:

[TABLE]

The parameters $l$, $T_{e}$, and $n_{e}$ are, respectively, the loop half-length, electron temperature, and electron density at the beginning of the cooling. Here we use the best-fit loop half-length (179 Mm) as the input. The temperature and density are determined using differential emission measure (DEM) analysis(Schmelz et al., 2011; Cheng et al., 2012). The derived initial temperature of the late phase is 14 MK and density is $\sim 6\times 10^{9}$ cm*-3*. These parameters yield a cooling time around 210 minutes. However, the delay time of the late phase peak (at 05:00 UT) in Fe IX 17.1 nm (0.7 MK) is about 280 minutes. The late appearance of the late phase loop arcade in the EUV band is mainly a cooling-delay effect with the additional consecutive heating.

4 Summary and Discussion

In summary, we examine an extremely large late phase during an eruptive solar flare. The magnetic topology is a quadrupolar magnetic configuration, which facilitates the coexistence of lower core field and high large-scale overlying field. The cusp structure observed in the hot channel evidences the occurrence of magnetic reconnection process(Tsuneta et al., 1992; Aschwanden, 2005), the downward motion of the hot loops represents the shrinkage of newly formed loops(Forbes & Acton, 1996). All these observations suggest the possibility of magnetic reconnection taking place high above. Such a reconnection process is caused by the erupting CME. The overlying arcades are stretched upward by the CME, and the stretched field lines re-close after the reconnection beneath the CME. This process ,similar to the tether-cutting reconnection, happens in the late phase stage. It provides additional heating mechanism for the EUV late phase. The detailed evolution for the late phase loop system is described as follows:

Before the flare, the large-scale overlying arcades connects the outer positive and negative polarities. The quadrupolar magnetic configuration distinguishes the overlying arcades from lower core field. 2. 2.

When the CME erupts, the overlying arcades are stretched outward, the tether-cutting-like reconnection takes place between two legs of the overlying field. The reconnection plays two roles: Magnetic topology is rearranged and magnetic energy is converted to additional heating that is transferred into the late-phase loop system. 3. 3.

As the reconnection continues, the cusp structure retreats backward and show some quasi-periodic characteristics. 4. 4.

As time goes on, these loops cool down and become visible in the low temperature lines, such as the AIA 19.3 nm and EUVI 19.5 nm. Because inner loops form first and then cool down first, like the post-flare loop systems, the loop top shows up a rising motion.

As a summary, we consider the late-phase emission comes from a set of gradually downward moving loops rather than a pre-existing loop system. The observational features also imply the existence of additional heating of the large-scale flare loops, which is shown in the bottom pannel of figure 2.

We also use EBTEL to model the EVE irradiance in several lines. The modeling result shows well agreement with the observations. The peak time in each line is very close to the observations, indicating that additional heating gives rise to the delayed appearance of the late phase.

Liu et al. (2015) and Wang et al. (2016) argued that the extremely large late phase emission as the energy re-deposition from the failed flux rope into the thermal emissions, where Dai et al. (2018) presented a more complicated scenario in their case: The late-phase loops are mainly produced by the first-stage QSL reconnection, while the second-stage reconnection is responsible for the heating of main flaring loops. However, the production of extremely large EUV late phase in this flare is from the late phase reconnection occurring high above the main flare region. The CME originated from main flare is only the trigger.

We acknowledge the use of the data from GOES, from HMI and AIA instruments onboard SDO, and from EUVI instruments onboard STEREO. Z.J.Z. is supported by the grants from the Open Project of CAS Key Laboratory of Geospace Environment. X.C. are supported by NSFC under grants 11722325, 11733003, 11790303, and by Jiangsu NSF under grant BK20170011. D.Y. is supported by National Natural Science Foundation of China under grants 11533005, and 973 Project of China under grant 2014CB744203. Y.M.W. is supported by the grants from NSFC (41574165 and 41774178). J.C. is supported by NSFC through grants 41525015,41774186.