# Observations of the Current Sheet Heating in X-ray during a Solar Flare

A.A Reva Space Research Institute,
Profsoyuznaya 84/32,
117997, Moscow, Russia  S.A. Bogachev Space Research Institute,
Profsoyuznaya 84/32,
117997, Moscow, Russia  I.P. Loboda Space Research Institute,
Profsoyuznaya 84/32,
117997, Moscow, Russia  A.S. Ulyanov  Space Research Institute,
Profsoyuznaya 84/32,
117997, Moscow, Russia  A.S. Kirichenko Space Research Institute,
Profsoyuznaya 84/32,
117997, Moscow, Russia

###### Abstract

In the solar corona, magnetic reconnection occurs due to the finite
resistivity of the plasma. At the same time, resistivity leads to ohmic
heating. Therefore, the reconnecting current sheet should heat the surrounding
plasma. This paper presents experimental evidence of such plasma heating
caused by magnetic reconnection. We observed the effect during a C1.4 solar
flare on 16 February 2003 at the active region NOAA 10278, near the solar
limb. Thanks to such a location, we successfully identified all the principal
elements of the flare: the flare arcade, the fluxrope, and, most importantly,
the presumed position of the current sheet. By analyzing the monochromatic
X-ray images of the Sun obtained by the CORONAS-F/SPIRIT instrument in the Mg
XII 8.42 Å spectral line, we detected a high-temperature ($T\geq$ 4 MK)
emission at the predicted location of the current sheet. The high-temperature
emission appeared during the CME impulsive acceleration phase. We believe that
this additionally confirms that the plasma heating around the current sheet
and magnetic reconnection inside the current sheet are strongly connected.

Solar corona (1483); Solar x-ray emission (1536); Solar coronal mass ejection
(310); Solar flares (1496)

††journal: ApJ

##  1 Introduction

Plasma in the solar corona has such a low resistivity that its motion can be
treated in the approximation of the ideal magneto-hydrodynamic (MHD). In this
approximation, the connectivity of the magnetic field is conserved: two points
that belonged to the same field line will continue to belong to the same field
line during plasma motion (see chapter 2 in Priest, 2014).

Nonetheless, plasma in the solar corona has non-zero resistivity, and,
therefore, the connectivity of the magnetic field lines can change. The most
important manifestation of this process is magnetic reconnection: a mutual
annihilation of two magnetic lines of opposite polarities at the ‘magnetic
separator.’

Changes of the coronal magnetic field induce the electric current inside the
separator. This current prevents reconnection of the magnetic field lines. If
the magnetic field continues to change, the separator will bifurcate into a
current sheet: a thin layer of electric current. Eventually, due to the finite
resistivity of plasma, the induced current will slowly dissipate, and the
magnetic structure will slowly relax to a potential configuration. This
process is called ‘steady reconnection’ (see chapter 1 in Somov, 2006).

If the magnetic energy is accumulated faster than it is dissipated by ohmic
heating, the current sheet size will increase. Eventually, the current sheet
can reach such a size that it becomes unstable, and the whole amount of
accumulated energy will be released catastrophically through the ‘impulsive
reconnection.’

Impulsive reconnection is a central element of the standard model of a solar
flare (Carmichael, 1964; Sturrock, 1966; Hirayama, 1974; Kopp & Pneuman,
1976). In this model, before the flare begins, the active region has the
following configuration: a loop arcade, a fluxrope (cylindrical twisted
magnetic structure) above the arcade, and a current sheet between the arcade
and the fluxrope (see Figure 1). The flare starts when the current sheet
becomes unstable, and impulsive reconnection begins inside it. The
reconnection process produces two plasma flows, one of which pushes the
fluxrope up and may lead to a coronal mass ejection (CME). At the same time,
inside the reconnection region, the electrons are accelerated by the induced
electric field. The accelerated electrons move along the magnetic field lines
towards the chromosphere, where they slow down, heat plasma, and produce a
bremsstrahlung hard X-ray (HXR) emission. The heated plasma fills the magnetic
loops above the chromosphere, making them visible in soft X-ray and EUV
spectral ranges.

Figure 1: Standard flare/CME model. 1) the fluxrope; 2) the current sheet; 3)
the flare arcade.

The current sheet is a vital element of the standard flare model. At the same
time, it is one of the hardest objects on the Sun to observe. One of the main
reasons is that there are no effective ways to directly measure magnetic
fields or electric currents in the solar corona. Another reason is that the
current sheet is a very thin structure. It has a huge size in the $Y$ and $Z$
directions in Figure 1, but negligible size along the $X$ axis (several
meters, or even several cm). So the plasma emission inside the current sheet
is expected to be negligible compared to the emission of the surrounding
coronal plasma.

Despite this, several authors reported signatures of the current sheet
observed during solar flares. In the imaging observations, a long thin linear
structure above the flaring active region is usually interpreted as a current
sheet signature (Lin et al., 2005; Savage et al., 2010; Reeves & Golub, 2011;
Zhu et al., 2016; Seaton et al., 2017). Besides that, an elongated double
Y-shaped dark structure can appear below the CME core in the Fe 171 Å images
(Reva et al., 2016a). In the spectroscopic observations, researchers consider
a high-temperature emission from the presumed location of the current
sheet—below the CME core and above the flaring active region—as a signature of
the current sheet (Ciaravella et al., 2002; Ko et al., 2003; Ciaravella &
Raymond, 2008). Recently, Warren et al. (2018) presented multi-wavelength
observations of the current sheet using both imaging (AIA; Lemen et al., 2012)
and spectroscopic (EIS; Culhane et al., 2007) instruments.

In all the examples listed above, the authors reported, not the direct
observations of the current sheet, but rather its indirect observational
signatures. Among such indirect evidence, one of the most important is the
plasma heating in the vicinity of the current sheet caused by the ohmic
heating due to the finite resistivity of the coronal plasma.

Mechanisms of such heating are actively studied with the theoretical models
and the numerical MHD simulations. These studies showed that ohmic heating
(Reeves et al., 2010, 2019), adiabatic compression (Birn et al., 2009; Reeves
et al., 2019), and turbulence (Ye et al., 2020) can effectively heat plasma
inside the current sheet. Some of the thermal energy accumulated inside the
current sheet may leak away due to thermal conduction, which will heat the
surrounding plasma and widen the visible size of the current sheet (‘thermal
halo’; Yokoyama & Shibata, 1998; Seaton & Forbes, 2009; Reeves et al., 2010).
Using MHD simulations, Reeves et al. (2010) showed that thermal conduction
could leak up to 50 % of the energy released during the reconnection.

Figure 2: Comparison of the images obtained by the EIT 195 Å (left), SXI
(middle), and the Mg XII spectroheliograph (right). The images were taken on
16 February 2003.

For many reasons, it is hard to experimentally study the relationship between
the current sheet heating and magnetic reconnection rate. First of all, as
mentioned above, the observations of current sheets (even indirect) are rare.
Secondly, most solar telescopes—such as AIA/SDO or XRT/Hinode (Golub et al.,
2007)—cannot detect high-temperature plasma in a monochromatic mode. The hot
plasma emission in their images is mixed with a low-temperature background,
which complicates the analysis of the heating.

In this work, we report reliable signatures of the plasma heating up to
temperatures higher than 4 MK detected in the vicinity of the coronal current
sheet in a monochromatic mode. We also experimentally confirmed the
relationship between the plasma heating and the reconnection rate, which we
derived from the observation of CME acceleration. In section 2, we describe
the experimental data used in the research. In section 3, we present the
obtained results; then, in section 4, we discuss them and make the
conclusions.

Figure 3: Active region NOAA 10278 on the disc. Left: H$\alpha$ image obtained
with the PICS telescope. Right: magnetogram obtained with MDI. Images were
taken on February 11, 2003. The yellow dashed line indicates the position of
the limb at 23:00 UT on February 16, 2003.

##  2 Experimental Data

Table 1: List of instruments. | Instrument | Reference
---|---|---
Location and dynamics of high-temperature plasma | Mg XII spectroheliograph | Zhitnik et al. (2003)
| SXI | Hill et al. (2005); Pizzo et al. (2005)
Location of the HXR sources | RHESSI | Lin et al. (2002)
CME structure and dynamics | EIT | Delaboudinière et al. (1995)
| TRACE | Handy et al. (1999)
| Mk4 | Elmore et al. (2003)
| LASCO | Brueckner et al. (1995)
Magnetic field configuration | MDI | Scherrer et al. (1995)
Prominences and filaments in H$\alpha$ | PICS | DOI: 10.5065/D65719TR

The event (flare and CME) that we have studied in this paper occurred on 16
February 2003 near the western edge of the Sun. To study it, we used several
instruments to get most of the information about plasma heating, details of
the reconnection process, and CME structure. The full list of data used in the
study is presented in Table 1.

The most important instrument for our study was the Mg XII spectroheliograph
that operated on board the CORONAS-F/SPIRIT satellite from 2001 till 2003
(Oraevsky & Sobelman, 2002; Zhitnik et al., 2002). Considering that the
instrument may not be well known to some readers, we will briefly describe
some of its important features.

The instrument is an imaging spectroheliograph based on Bragg-crystal optics.
It obtained monochromatic X-ray images of the solar corona in the Mg XII 8.42
Å spectral line. During the selected period of observations, the
spectroheliograph worked with a 2 min cadence and a binned resolution of 8′′.

The main feature that distinguishes the Mg XII spectroheliograph from other
imaging instruments is its temperature selectivity. The Mg XII 8.42 Å line
produces a noticeable signal only at temperatures higher than 4 MK. So, the
corresponding images clearly outline the high-temperature plasma on the Sun
without any contribution from the low-temperature background (see Figure 2).
This gives an effective way to study the plasma heating processes in many
objects: large-scale flares (Grechnev et al., 2006; Urnov et al., 2007; Reva
et al., 2015), CMEs (Kirichenko & Bogachev, 2013; Reva et al., 2017), and even
microflares (Reva et al., 2012; Kirichenko & Bogachev, 2017a, b; Reva et al.,
2018).

It is important to note that the instrument is equipped with a crystal mirror
and, therefore, had dispersion. In the Mg XII images, each point of the Sun
looks like a short profile of the Mg XII 8.42 Å spectral line. To lessen this
effect, we numerically deconvolved the Mg XII images. For more details, see
Appendix A.

Figure 4: Evolution of the CME. Green: EIT telescope; blue: Mk4 coronagraph;
red: LASCO C2 coronagraph.

The pointing system of the CORONAS-F spacecraft had a significant residual
jitter. To correct it, we used data from the Solar X-ray Imager (SXI; Hill et
al., 2005; Pizzo et al., 2005) that worked on board the GOES-12 satellite. The
telescope provided full-disk soft X-ray solar images in the 6-60 Å wavelength
range with a spatial resolution of $\approx$ 10′′ and a 5′′ pixel size. The
‘Be-thin’ channel of SXI is sensitive to the same temperatures as the Mg XII
spectroheliograph, but with a noticeable contribution of low-temperature
background. The orientation of the Sun in the SXI images is known. Using
cross-correlation, we determined the shift between the Mg XII images and the
‘Be-thin’ SXI images. Then we shifted the Mg XII images by the corresponding
value to correct the jitter.

During the selected period of observations, all of the SPIRIT telemetry was
allocated to the Mg XII data. This improved the cadence of the observations,
but, as a result, the data of other instruments of the SPIRIT complex were not
available.

Below we briefly describe other instruments used in this research.

The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI; Lin et al.,
2002) observes HXR spectra from 3 keV to 17 MeV. Using Fourier-based methods,
RHESSI can synthesize HXR images in the same spectral range.

The Extreme ultraviolet Imaging Telescope (EIT; Delaboudinière et al., 1995)
on the Solar and Heliospheric Observatory (SoHO; Domingo et al., 1995) takes
solar images at the wavelengths centered at 171, 195, 285, and 304 Å. The
instrument has a pixel size of $2.6^{\prime\prime}$ and a spatial resolution
of $5^{\prime\prime}$. The EIT had two observational modes: synoptic and ’CME
watch.’ In a synoptic mode, it takes images in all four channels every 6
hours. In the ‘CME watch’ mode, the telescope takes images in the 195 Å
channel every 12 min.

The Transition Region And Coronal Explorer (TRACE; Handy et al., 1999) is a
space-based telescope that observes the Sun in EUV and white-light. It had a
limited field of view ($8.5^{\prime}\times 8.5^{\prime}$) but a high spatial
resolution (1′′).

Mk4 coronameter is a ground-based instrument located at Mauna Loa Solar
Observatory (DOI: 10.5065/D66972C9; Elmore et al., 2003). It builds images of
the solar corona from 1.14 to 2.86 $R_{\odot}$ in the white light (700–900 nm)
with a spatial resolution of 5.95′′ and a cadence of 3 min.

Large Angle Spectroscopic Coronagraph (LASCO; Brueckner et al., 1995) is a set
of white-light coronagraphs that observe solar corona from 1.1 $R_{\odot}$ up
to 30 $R_{\odot}$ (C1, 1.1–3 $R_{\odot}$; C2, 2–6 $R_{\odot}$; C3, 4–30
$R_{\odot}$). In 1998, LASCO C1 stopped working, and for this research, only
C2 and C3 data are available. Coronagraph C2 has a resolution of
$11^{\prime\prime}$, and C3 has a resolution of $56^{\prime\prime}$.

The Michelson Doppler Imager (MDI; Scherrer et al., 1995) on the SOHO
satellite maps the line of sight component of the photospheric magnetic field
with a $4^{\prime\prime}$ resolution and 90-min cadence.

Polarimeter for Inner Coronal Studies (PICS, DOI: 10.5065/D65719TR) is a
ground-based instrument located at Mauna Loa Solar Observatory. It takes
H$\alpha$ images (6563 Å) with a field of view of 2.3 $R_{\odot}$, a spatial
resolution of 2.9′′, and a cadence of 3 minutes.

Figure 5: Kinematics of the CME core. Top: the distance between the CME core
and Sun’s center; middle: the CME core’s velocity; bottom: the CME core’s
acceleration. Green: data of the EIT telescope; purple: data of the Mk4
coronagraph; red: data of the LASCO/C2 coronagraph; blue: data of the LASCO/C3
coronagraph. Figure 6: CME topology. Copper inner circle: TRACE image; copper
outer circle: EIT image; blue: Mk4 image. The dotted line marks the presumed
location of the current sheet. The images were taken on 16 February 2003.

##  3 Results

###  3.1 Flare Topology and Dynamics

The studied event was a typical solar flare associated with a CME, which
developed in full agreement with the standard views on how a solar flare
should evolve. This is very important for our study because it is thanks to
the standard configuration of the flare we are sure about where the current
sheet was located.

Taking this into account, let us describe the flare topology and dynamics. The
pre-flare configuration (5 days before the flare) is shown in Figure 3, where
the left panel is the H$\alpha$ image, and the right panel is the
corresponding MDI magnetogram. The flare occurred in the active region NOAA
10278. On 11 February 2003, this active region was approximately in the center
of the solar disk. The most prominent feature of the active region seen in
H$\alpha$ images (left panel) was a filament that was slightly tilted to the
East-West direction and was located between two areas of opposite polarities.
We match this filament to the fluxrope of the further CME.

This filament was seen in H$\alpha$ images all five days from February 11
until February 16, when the active region reached the solar limb. At this
moment, the region took the same position as in our sketch for the standard
flare/CME model (see Figure 1). So, this was the best projection to observe
the current sheet.

Approximately at this time, the CME started to erupt. To study this process,
we used synthetic images combined from EIT data obtained in EUV and two white
light images: one from the Mk4 coronameter and the second one from the LASCO
C2 coronagraph (see Figure 4). The CME had a classic 3-part structure in
white-light images: bright core, dark cavity, and bright frontal loop (Illing
& Hundhausen, 1985; Webb & Hundhausen, 1987). As we said above, we identify
the CME core with the filament (fluxrope) that was seen in the H$\alpha$
images before the CME (Illing & Athay, 1986). In this case, the fluxrope
should be aligned along the $Y$ axis in Figure 1.

Observation of the CME motion gives an indirect way to measure the
reconnection rate during a solar flare. Generally, we can expect a simple
relationship: the faster is the reconnection rate, the faster is the CME
acceleration.

Taking this into account, we measured the CME coordinates during its motion
(for details of the measurement method, see Appendix B). The result—the CME
height, velocity, and acceleration as a function of time—is shown in Figure 5.
From these plots, we see that CME evolution consists of three main phases:

  1. 1.

before $\approx$ 22:35, the CME structure was stable;

  2. 2.

from $\approx$ 22:35 to $\approx$ 23:10, the CME impulsively accelerated from
0 to 250 km s-1; the acceleration peaked at $\approx$ 200 m s-2;

  3. 3.

after $\approx$ 23:10, the CME gradually accelerated to $\approx$ 500 km s-1
during 9 hours with an acceleration of $\approx$ 10–20 m s-2.

Figure 7: Hot plasma dynamics observed with the Mg XII spectroheliograph. Blue
corresponds to low intensities, red and yellow correspond to high intensities.
Contours mark the location of the RHESSI 6–12 keV emission. Figure 8: X-ray
flux dynamics. Top: the Mg XII lightcurves of region-1 (thin black line) and
region-2 (thick black line). Middle: the RHESSI count rates. Black line: 3–6
keV channel; red line: 6–12 keV channel; blue line: 12–25 keV channel. Purple
lines mark the RHESSI nights. Bottom: GOES flux. Red line: 1–8 Å channel; blue
line: 0.5–4 Å channel.

The observed flare topology is consistent with the standard flare model. We
can clearly see a flare arcade, a fluxrope, and a cavity that surrounds the
fluxrope (see Figure 6). The CME evolution is also consistent with the
standard model. It has a stable phase, an impulsive acceleration phase
(probably caused by the impulsive reconnection), and a steady acceleration
phase (probably caused by the solar wind; Yashiro et al., 2004). Since the
studied flare looks and behaves exactly as the standard model predicts, it is
natural to assume that a current sheet should exist between the flare arcade
and the CME core.

###  3.2 Observation of the Plasma Heating

As we said above, the main goal of this paper was to find clear evidence of
plasma heating in the vicinity of the reconnecting current sheet. For this
purpose, we carefully checked all the Mg XII images obtained during the
studied event. Thanks to the specific temperature sensitivity of the Mg XII
spectroheliograph (starting from $T\geq 4$ MK), we consider the corresponding
images as a good marker of plasma heating. As soon as the signal appears in a
Mg XII image, we can conclude that the plasma temperature increases to 4 MK or
higher.

The observed dynamics of hot plasma is shown in Figure 7. We found two high-
temperature regions during the flare. The first one (the brightest one)
appeared at 21:53 UT and existed for $\approx$ 5 hours. The region was
compact, and its location approximately coincides with the top of the flare
loop seen in the TRACE 195 Å image. Plasma heating near the looptop region is
a typical feature of a solar flare, and for this reason, we do not consider it
in detail. The looptop plasma heating takes place under the current sheet in
the so-called ‘cusp’ region of the magnetic configuration. Such a source is
often associated with a looptop hard X-ray emission: another typical detail of
a solar flare. The HXR emission appears at the same place (see Figure 7) and
at the same time (see Figure 8) as region-1.

Figure 9: Comparison of the Mg XII, TRACE, EIT, and Mk4 images. Inside yellow
contour: signal of the Mg XII spectroheliograph (blue corresponds to low
intensities, red and yellow correspond to high intensities). Copper inner
circle: TRACE image; copper outer circle: EIT image; blue: Mk4 image. The
images were taken on 16 February 2003.

The most interesting for us was the second high-temperature region. At 22:28
UT, a faint linear structure appeared above the flare arcade. It gradually
increased its length but decreased its intensity. Eventually, the linear
structure faded away, reaching the maximal length of 250 Mm. In other parts of
the CME, there was no hot plasma.

Figure 10: Relative timings of the CME’s acceleration (black line at the top),
the derivative of the GOES 1–8 Å flux (red line at the top), and the linear
structure (region-2) intensity in the Mg XII images (green line at the
bottom).

The hot linear structure was located between the flare arcade and the CME core
(observed in the Mk4 images) and inside the dark cavity observed in the EIT
images (see Figure 9). Such a location coincides with the presumed position of
the current sheet that should exist during CME.

Two important features distinguish this second plasma region from the first
one. The first feature is the location. Region-2 is clearly not associated
with the top of the flare loop and with a ‘cusp’ region. Another feature is a
significant difference in brightness and size. Region-2 is much larger than
the compact region-1, but, despite this, it is much fainter. The peak flux of
the linear structure was $\approx$ 4 % of the peak flux from the compact,
bright source (see Figure 8), while the brightness ratio (pixel intensity
ratio) was $\approx$ 0.5–1 %. This seriously justifies that region-1 and
region-2 were heated by two different mechanisms. We want to emphasize that
region-2 is observed simultaneously with region-1. So, we cannot explain them
as two consecutive stages of the same heating mechanism.

The timing of the plasma heating is in good agreement with the CME motion. The
flare begins at $\approx$ 21:53 UT when the plasma heating starts near the
looptop region of the arcade, and the HXR emission starts to rise (see Figure
8). We did not find any signatures of plasma heating in the current sheet
(region-2) during this stage. Approximately 30 minutes later, the second stage
associated with the CME motion started. At $\approx$ 22:30 UT, the CME
impulsively accelerated from zero up to $v\approx 300$ km s-1 with an
acceleration of $a\approx$ 100–200 m s-2. Due to the fast CME motion, the
current sheet should be elongating rapidly in the $Z$-direction (see Figure
1), and just at this time, we observed an additional plasma heating around the
presumable location of the current sheet. The CME acceleration lasted about 30
minutes, which is in excellent agreement with the observed duration of plasma
heating in region-2 (see Figure 10).

Sadly, the RHESSI data were not available during the CME impulsive
acceleration (see Figure 8). For this reason, we do not have information about
the dynamics of the HXR emission.

##  4 Discussion and Conclusion

The appearance of high-temperature plasma in the solar corona is typical for
solar flares and usually relates to the magnetic reconnection process. Bright
sources of thermal X-ray emission usually appear above the top of magnetic
loops during the impulsive phase of solar flares. They may be heated by
energized electrons or by super-sonic plasma flows.

In a typical magnetic configuration of a flare region, the bright loop-top
source is not the only high-temperature region that may appear above the loop
during a flare. A much fainter but much larger source may appear higher in the
corona due to a diffusion of thermal energy from the region of magnetic
reconnection.

Usually, this second source (named region-2 in our study) cannot be observed
due to its low brightness, which does not allow it to be distinguished from
the low-temperature background. We succeeded in this study due to two main
factors. The first one is the region’s location and orientation: the CME
occurred at the solar limb, and the current sheet was aligned along the line
of sight. Such a location and orientation are favorable to detect faint
emission of the current sheet. The second one is the temperature sensitivity
of the Mg XII spectroheliograph. The instrument detects a high-temperature
emission without the contribution of low-temperature background.

The low brightness ratio of faint and bright components ($\sim$ 1 %) also
contributes to the difficulties of the registration. We think that this ratio
is typical for flares, but, of course, we have no confirmation of this since
only one such event was detected.

The appearance of the faint component we associate with the heating caused by
the reconnection inside the current sheet. Comparison of the emission and CME
dynamics confirms this idea. The faint high-temperature component appears
approximately at the same time as the CME impulsively accelerates. According
to the standard CME model, the CME impulsively accelerates during impulsive
reconnection inside the current sheet. We think that this clearly indicates
that the energy for plasma heating in region-2 comes from magnetic
reconnection, which is in good agreement with standard views on solar flares.

Another indirect evidence of the connection between heating and reconnection
is the relative timing of region-1 and region-2 emissions. Region-2 appears
during the rising phase of the Mg XII and GOES fluxes of region-1 (see Figure
8). According to the Neupert effect (Neupert, 1968), the HXR emission of a
flare correlates with the derivative of the SXR emission. The GOES 1–8 Å flux
derivative—our estimate of the HXR emission—peaks when we observe region-2
(see Figure 10). Since HXR emission is a signature of the reconnection, we
think that such a correlation further strengthens our interpretation.

The hot plasma was detected in the previous observations of the current
sheets. Ciaravella et al. (2002); Ko et al. (2003); Ciaravella & Raymond
(2008) studied current sheets observed with Ultraviolet Coronagraph
Spectrometer (UVCS; Kohl et al., 1995) and reported temperatures around 6 MK.
The current sheets analyzed by Zhu et al. (2016) and Seaton et al. (2017) had
temperatures around 8–10 MK, while the ones analyzed by Hannah & Kontar (2013)
and Warren et al. (2018) had temperatures around 10–20 MK. Finally, Landi et
al. (2012) presented observations, in which current sheet temperature never
exceeded 3 MK. Most likely, the difference in the current sheet temperatures
is caused by the difference in the reconnection rate.

Our conclusion that the current sheet heating is caused by the reconnection
inside it is consistent with the MHD theory and simulations (Yokoyama &
Shibata, 1998; Seaton & Forbes, 2009; Reeves et al., 2010). However, it is
difficult to compare this conclusion with other experimental works. Current
sheet observations are rare, and only a couple of them allow studying the
dynamics of the current sheet heating relative to the dynamics of the
reconnection.

The first such example is a current sheet observed during an X8.3 flare on
2017 September 10 (Warren et al., 2018). At the time of writing, this is the
most detailed observation of the current sheet (see references in Chen et al.,
2020). In this event, some reconnection signatures—the CME impulsive
acceleration (Gopalswamy et al., 2018; Veronig et al., 2018), the hard X-ray
emission, the derivative of the soft X-ray emission, and the microwave
emission (Gary et al., 2018)—correlated with each other and occurred during a
small period of time ($\approx$ 15:50–16:00 UT). On the other hand, other
reconnection signatures—downflows (Longcope et al., 2018) and turbulence
(Cheng et al., 2018; Warren et al., 2018) inside the current sheet—were
observed for $\approx$ 1 hour after the first reconnection signatures appeared
($\approx$ 16:00–17:00 UT). The current sheet itself appeared after the first
reconnection signatures ($\approx$ 16:00 UT) and hot plasma inside it was
observed for $\approx$ 1 hour in the 94 Å channel of Solar Ultraviolet Imager
(SUVI; Seaton & Darnel, 2018).

Another example is the current sheet observed during the CME on 2009 April 17
(Reva et al., 2016a). The event was observed with the TESIS EUV telescope that
build images of the solar corona in the Fe 171 Å line up to distances of 2
$R_{\odot}$ from the Sun center (Kuzin et al., 2011; Reva et al., 2014). The
current sheet looked like a double Y-shaped darkening in the Fe 171 Å images.
Such darkening indicates that the current sheet is heated (although, it is not
clear up to what temperature). The heating (darkening) occurred simultaneously
with the CME impulsive acceleration (signature of the reconnection). At the
start of the CME impulsive acceleration phase, GOES and SphinX (Gburek et al.,
2011) registered a short duration flux increase.

All of these three examples—this work, Reva et al. (2016a), and Warren et al.
(2018)—exhibit a similar pattern. During the CME eruption, a short-duration
reconnection signatures appear, which are followed by the long-duration
reconnection signatures. The heating inside the current sheet starts
approximately when the short-duration reconnection signature appears. The hot
plasma inside the current sheet is observed during the lifetime of the long-
duration reconnection signatures. These similarities support our conclusion
that heating inside the current sheet is caused by the reconnection.

However, there are differences between these events. In this work and Reva et
al. (2016a), the heating starts slightly before the short-duration
reconnection signatures; in Warren et al. (2018), it starts after. In this
work and Reva et al. (2016a), the impulsive CME acceleration is a long-
duration signature; in Warren et al. (2018), it is a short-duration signature.
These differences and the fact that some reconnection signatures have short
duration and some long duration show that the reconnection dynamics has a
complex structure, which may vary from one event to another.

We are sure that the energy for the current sheet heating comes from the
magnetic reconnection. However, the exact mechanism of the heating is unclear.
As we said in the Introduction, ohmic heating (Reeves et al., 2010, 2019),
adiabatic compression (Birn et al., 2009; Reeves et al., 2019), and turbulence
(Ye et al., 2020) can heat current sheet. Sadly, our data don’t allow us to
determine the heating mechanism.

Figure 11: Deconvolution of the Mg XII images. Left: image before
deconvolution; right: image after deconvolution.

Another issue that we would like to discuss is the relative weakness of the
studied flare. Usually, current sheets are observed during strong flares (X
and M classes), while the flare in this work is only C1.4. Figure 3 shows that
most of the flaring active region was visible. Even if we take into account
partial occultation by the disk, the flare would still be of a C class.

We believe that the studied event is an example of reconnection heating
occurring as a universal process in flares from C to X class. Most likely,
reconnection heating is less intense in weak flares than in strong ones, and,
therefore, plasma is heated to lower temperatures and has lower emission
measure. As a result, such heating is rarely observed in weak flares because
it is difficult to detect faint hot emission.

We think that monochromatic imagers similar to the Mg XII
spectroheliograph—for example, see Kuznetsov et al. (2016); Kirichenko et al.
(2021); Reva et al. (2021)—can help us study reconnection heating. We hope
that such instruments will be created in future and that they will improve our
understanding of the processes occurring inside the current sheets during
solar flares.

This is the Accepted Manuscript version of an article accepted for publication
in the Astrophysical Journal. IOP Publishing Ltd is not responsible for any
errors or omissions in this version of the manuscript or any version derived
from it. The Version of Record is available online at
doi:10.3847/1538-4357/ac6b3d. This research was funded by a grant from the
Russian Science Foundation (grant No 21-72-10157,
https://rscf.ru/project/21-72-10157/). Mk4 coronameter (DOI: 10.5065/D66972C9)
and PICS (DOI: 10.5065/D65719TR) data are provided courtesy of the Mauna Loa
Solar Observatory, operated by the High Altitude Observatory, as part of the
National Center for Atmospheric Research (NCAR). NCAR is supported by the
National Science Foundation. The RHESSI satellite is a NASA Small Explorer
(SMEX) mission. SXI full-disk X-ray images are supplied courtesy of the Solar
X-ray Imager (SXI) team. The SOHO/LASCO data are produced by a consortium of
the Naval Research Laboratory (USA), Max-Planck-Institut fur Aeronomie
(Germany), Laboratoire d’Astronomie (France), and the University of Birmingham
(UK). MDI and EIT data are supplied courtesy of the SOHO/MDI and SOHO/EIT
consortia. SOHO is a project of international cooperation between ESA and
NASA.

##  Appendix A Mg XII Deconvolution

The Mg XII spectroheliograph used Bragg crystal optics. As a result, the
instrument has dispersion: its images are a convolution of the spatial
component with the profile of the Mg XII 8.42 Å line. More details about this
effect could be read in Kuzin et al. (1994) or Reva et al. (2021).

The Mg XII $\lambda=8.42$ Å line is a Ly-$\alpha$ doublet of a hydrogen-like
Mg ion: $\lambda_{1}=8.4192$ Å ($1s\ {}^{2}S_{1/2}$ – $2p\ {}^{2}P_{3/2}$) and
$\lambda_{2}=8.4246$ Å ($1s\ {}^{2}S_{1/2}$ – $2p\ {}^{2}P_{1/2}$). The ratio
of the line intensity should be 2:1.

The Mg XII images consist of two slightly shifted images overlayed one onto
another (see Figure 11a). The majority of the pixels in the Mg XII images do
not have a signal: they consist of several isolated hot objects. In the
direction of the dispersion, the boundaries of those objects contain only a
signal from one of the doublet components. The profile of the doublet
components overlaps only inside those objects.

To deconvolve the Mg XII images, we use the following algorithm.

  1. 1.

We start at the boundary of the image that corresponds to the short
wavelengths.

  2. 2.

For each pixel, we calculate the intensity of the weaker component (divided by
two).

  3. 3.

We subtract this value from the pixel that corresponds to the location of the
weaker component of the doublet.

  4. 4.

We move in the direction of the dispersion to the next pixel that corresponds
to a longer wavelength.

  5. 5.

We repeat steps 2–4 until we reach the boundary of the image.

The result is shown in Figure 11b. The algorithm successfully eliminates the
second component of the doublet. The images become less elongated and easier
to interpret.

There are several issues that this algorithm does not address. Firstly, it
does not deconvolve the line width. It cannot be deconvolved in a
straightforward way because the line width is determined by the Doppler
broadening, which varies from pixel to pixel. Secondly, the line ratio of the
Ly$\alpha$ doublet could deviate from the theoretical value (Sylwester et al.,
1986; Laming, 1990). If this effect is present, it can distort the deconvolved
images. Finally, if significant plasma motions along the line of sight are
present, the Doppler shifts will distort the images.

##  Appendix B CME Kinematics Measurements

For the measurements of the CME coordinates, we used the data of the EIT
telescope, Mk4 coronameter, and LASCO coronagraphs. We used a simple point-
and-click method. To estimate the errors of the measurements, we repeated the
procedure nine times for each image.

In the Mk4 and LASCO images, we aimed at the CME core’s center. Since the core
was not seen in the EIT images, we aimed for the lowest part of the dark
cavity in the EIT images.

The coordinates measured in the EIT images (lowest part of the dark cavity)
and the white-light images (CME’s core) are different parts of the CME. We
cannot simply combine these coordinates and compute derivatives (velocity and
acceleration). Furthermore, the point-and-click method is subjective, and
different instruments image corona differently. The center of the core in
images obtained by different instruments corresponds to slightly different
parts of the CME. In order to compute derivatives, we need to recalculate
coordinates measured in the EIT images to the CME’s core coordinates and
adjust the core coordinates measured by different white-light instruments.

To solve the problem, we adopted the method from Reva et al. (2016b). We
assumed that the CME expands proportionally and that the temporal dependence
of the heights of different parts of the CME could be linearly scaled. Then we
picked scaling coefficients so that temporal dependence of the CME core height
seamlessly transitions from one instrument to another.

After scaling the data, we numerically differentiated the radial distance and
obtained radial velocity. Then we numerically differentiated velocity and
obtained acceleration. For the differentiation, we used the local least-square
approximation method (Wood, 1982; Reva et al., 2017). The result of the
measurements is presented in Figure 5.

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