11institutetext: Université Paris–Saclay, CNRS, Institut d’astrophysique
spatiale, 91405, Orsay, France
11email<EMAIL_ADDRESS>
# Spectroscopic evidence of cool plasma in quiet Sun HRIEUV small scale
brightenings

A. Dolliou Spectroscopic evidence of cool plasma in quiet Sun HRIEUV small
scale brighteningsSpectroscopic evidence of cool plasma in quiet Sun HRIEUV
small scale brightenings S. Parenti Spectroscopic evidence of cool plasma in
quiet Sun HRIEUV small scale brighteningsSpectroscopic evidence of cool plasma
in quiet Sun HRIEUV small scale brightenings K. Bocchialini Spectroscopic
evidence of cool plasma in quiet Sun HRIEUV small scale
brighteningsSpectroscopic evidence of cool plasma in quiet Sun HRIEUV small
scale brightenings

(Received 19 April 2024; accepted 17 May 2024)

###### Abstract

Context.  A large number of the small and the short-lived EUV brightenings
have been detected in the quiet Sun (QS) over the past three years, by the
High Resolution Imager of the Extreme Ultraviolet Imager (HRIEUV) on board
Solar Orbiter. It is still uncertain whether these events reach coronal
temperatures, and thus if they directly participate to coronal heating.

Aims. In this work, we evaluate the maximum temperature of 11 EUV brightenings
in the QS, through plasma diagnostics involving UV/EUV spectroscopy and
imaging.

Methods. We use three QS observations coordinated between HRIEUV, the Spectral
Imaging of the Coronal Environment (SPICE/Solar Orbiter), the EUV Imaging
Spectrometer (EIS/Hinode), and the Atmospheric Imaging Assembly (AIA/SDO). We
detected events in HRIEUV, ranging from $0.8\text{\,}$ to
$6.2\text{\,}\mathrm{Mm}$ in length. We then identified nine of them in SPICE
and AIA, as well as three in EIS. We investigated their temporal evolution
using their light curves, and applied temperature diagnostics, such as the
LOCI Emission Measure (EM) and the differential EM (DEM). We also estimated
the electron density of one event identified in EIS.

Results. These events are dominated by emission of plasma at chromospheric and
TR temperatures, and they barely reach temperatures above
$1\text{\,}\mathrm{MK}$. As such, we concluded that their contribution to
coronal heating is not dominant. The estimated density of one of the event is
$n_{\mathrm{e}}=$ $(1.8\pm
1.3)\text{\times}{10}^{10}\text{\,}{\mathrm{cm}}^{-3}$.

###### Key Words.:

Sun: corona – Sun: transition region – Sun: UV radiation – Instrumentation:
high angular resolution – Instrumentation: spectrographs

##  1 Introduction

The corona is the outer layer of the solar atmosphere. It is maintained at
temperatures above $1\text{\,}\mathrm{MK}$ through processes only partially
understood. For this, wave heating and magnetic reconnexions are predicted to
play a major role. See, for instance, Reale (2014), Van Doorsselaere et al.
(2020) and Viall et al. (2021) for reviews on these arguments.

Observations in active regions (AR) indicate that the heating is impulsive in
nature (Lundquist et al., 2008; Ugarte-Urra et al., 2019) and that most of it
happens at unresolved spatial scales (Hudson, 1991). One of the main theories
(Parker, 1988) suggests that the corona is formed through a large number of
small-scale ($\sim 10^{24}$ erg) and impulsive heating events called
”nanoflares”. They are the consequence of reconnexion of magnetic fields. The
definition of a nanoflare has evolved since then (Klimchuk, 2015). They can
now refer to any impulsive and small-scale energy dissipation, regardless of
the physical mechanism responsible for it, such as magnetic reconnexion or
wave. Because of the unresolved size of the nanoflares, this heating has been
investigated in active regions for decades through the comparison of
observational signatures (i.e Cargill & Klimchuk, 1997; Parenti et al., 2017)
and modellings (i.e. Parenti et al., 2006; Parenti & Young, 2008; Bingert &
Peter, 2011; Bradshaw et al., 2012; Cargill, 2014). While most of the studies
focused on AR, evidence of waves (i.e. McIntosh et al., 2011; Hahn & Savin,
2014) and magnetic reconnexion (i.e. Tripathi et al., 2021; Upendran &
Tripathi, 2021; Kahil et al., 2022) have also been found in the quiet Sun
(QS).

Observations showed that the energy distribution of X-ray microflares to
flares (Crosby et al., 1993; Hannah et al., 2008) and EUV brightenings
(Berghmans et al., 1998; Aschwanden et al., 2000; Joulin et al., 2016) follows
a power law, with the lowest-energy events being the more frequent. As of now,
all of the detected events can not, by themselves, explain coronal heating
(Hudson, 1991; Aschwanden & Parnell, 2002). It has been speculated that
impulsive events at even shorter and unresolved scales might provide the
necessary power to heat the corona. The new generation of instruments,
observing at high spatial and temporal resolutions, confirms what was
predicted by the impulsive heating models: more and more short-scale events
are detected in the EUV. Example of them include small
($7.5\text{\,}\mathrm{Mm}$) and cool
($2.5\text{\times}{10}^{5}\text{\,}\mathrm{K}$) loops (Winebarger et al.,
2013) detected with the High-Resolution Coronal Imager (Hi-C) sounding rocket
flights (Kobayashi et al., 2014). Likewise in Hi-C, Régnier et al. (2014)
detected $680\text{\,}\mathrm{km}$ length and 25-second duration ”EUV bright
dots” at the edge of active regions. Antolin et al. (2021) identified small
($1\text{\,}$ to $2\text{\,}\mathrm{Mm}$) and very short lived (up to
$15\text{\,}\mathrm{s}$) ”nanojets” in large coronal loops, with the Interface
Region Imaging Spectrograph (IRIS; De Pontieu et al., 2014), and the
Atmospheric Imaging Assembly (AIA; Lemen et al., 2012), on board the Solar
Dynamics Observatory (SDO; Pesnell et al., 2012). Young et al. (2018) reviewed
the properties of UV bursts observed by AIA and IRIS. In addition to EUV,
X-ray bursts associated with smaller flares have been extensively studied
(Hannah et al., 2010, 2019; Buitrago-Casas et al., 2022), as such emission
could provide enough energy to heat the corona (for a review, see Hannah et
al., 2011).

The Solar Orbiter mission (Müller et al., 2020; Zouganelis et al., 2020),
launched in February 2020, carries, among others, the Extreme Ultraviolet
Imager (EUI; Rochus et al., 2020) and the UV Spectral Imaging of the Coronal
Environment (SPICE; Anderson et al., 2020). EUI includes the Extreme
Ultraviolet High Resolution Imager (HRIEUV), with a response function centred
around the Fe X $174.5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ line
($1\text{\,}\mathrm{MK}$). One of the novelties of this mission is to approach
the Sun at 0.28 AU. At this distance, the spatial resolution of HRIEUV reaches
about $200\text{\,}\mathrm{km}$. Such resolution was confirmed in-flight by
Berghmans et al. (2023), who measured the full width at half maximum (FWHM) of
dot-like features in the corona. The average FWHM over all the features was
equal to 1.5 pixels, which showed that the spatial resolution of HRIEUV is
limited by the two-pixels Nyquist limit. The combination of the temperature
sensitivity and the high spatial cadence makes HRIEUV and SPICE suitable
instruments to study coronal heating.

On 2020 May 30, HRIEUV made its first high cadence $5\text{\,}\mathrm{s}$
observation of the QS, while Solar Orbiter was at 0.558 AU from the Sun.
During the $4\text{\,}\mathrm{min}$ sequence, Berghmans et al. (2021)
automatically detected 1468 small ($400\text{\,}$ to
$4000\text{\,}\mathrm{km}$) and short-lived ($10\text{\,}$ to
$200\text{\,}\mathrm{s}$) EUV brightenings (here called events). They are low
in the atmosphere, between $1000\text{\,}$ and $5000\text{\,}\mathrm{km}$
above the photosphere (Zhukov et al., 2021), and they are concentrated around
the chromospheric network.

In this paper, we aim at verifying if, indeed, these events contribute to the
heating of the corona. If that is the case, they should, at least, reach
coronal temperatures. However, temperature diagnostics were challenging on
2020 May 30, as no spectroscopic data were available at that time. Instead,
the HRIEUV field of view was within that of AIA, which had its coronal
channels running at a $12\text{\,}\mathrm{s}$ cadence. Dolliou et al. (2023)
used the AIA channels to perform temperature diagnostics on the same dataset.
They looked for delays between the AIA light curves, that could be signatures
of plasma cooling from temperatures above $1\text{\,}\mathrm{MK}$ (see also
Viall & Klimchuk, 2016). They concluded that the event dataset might be
dominated by brightenings not reaching temperatures above
$1\text{\,}\mathrm{MK}$. Another possibility raised by the authors, was that
AIA did not temporally resolve the fast plasma cooling from coronal
temperatures. In the present study, we demonstrate that these events are
dominated by plasma below $1\text{\,}\mathrm{MK}$.

Only a few studies, up to now, have investigated these events using
spectroscopy. Huang et al. (2023) identified three EUV brightenings in HRIEUV
and in SPICE on QS observations. The events had emission in the chromospheric
(C III, $\log{T}=4.8$) and the transition region (O VI, $\log{T}=5.5$) lines,
and two of them were detected in the Ne VIII line ($\log{T}=5.8$). Nelson et
al. (2023) also identified EUV brightenings in the QS with HRIEUV and IRIS.
The events showed strong and diverse responses in the chromospheric lines. The
authors concluded that these EUV brightenings could include a large variety of
events with multiple physical origins. These two studies provided results
consistent with events barely reaching coronal temperatures.

In this work, we apply spectroscopic diagnostics to multiple EUV brightenings
detected by HRIEUV. To cover the required wide temperature range, we analyse
data from SPICE and, for the first time, with brightenings detected by HRIEUV,
the EUV Imaging Spectrometer (EIS, Culhane et al., 2007), on board the Hinode
spacecraft (Kosugi et al., 2007). Section 2 presents the QS observations with
HRIEUV, SPICE, AIA, and EIS. Section 3 details the events detection with
HRIEUV, their identification in the other instruments, and the different
diagnostics applied. We show that the events are dominated by plasma at
chromospheric and TR temperatures in Sect. 4. We discuss the implication of
these results in Sect. 5.

##  2 Observations and data reduction

Table 1:  Detailed information on the datasets used in this work.
$D_{\mathrm{Sun}}$ is the distance between Solar Orbiter and the centre of the
Sun. $\theta$ is the separation angle between the Solar Orbiter view and the
Earth perspective. The number of events refers to the events listed in Table
3. $\Delta t$ is the observation cadence. When no time is indicated in the
”Time” column, this means that the observation is available during the whole
HRIEUV sequence. Figure 1: Quiet Sun datasets on 2022 March 8 (first column),
17 (second column) and on 2023 April 4 (third column). Upper row: field of
view of HRIEUV (green) within the FSI 174 image. Middle row: field of view of
HRIEUV as seen by AIA 171. The AIA images are cropped in $\mathrm{S_{1}}$ (b)
and $\mathrm{S_{2}}$ (e), to save reading time of the detectors during the
high cadence mode. Lower row: HRIEUV image with the field of view of the SPICE
(red), the EIS context (white) and the EIS 25-step (cyan) rasters. SPICE is in
a three -step raster mode on 2022 March 8, 17, and in sit and stare mode on
2023 April 4.

We use datasets from the Solar Orbiter Observing Plan (SOOP) called
’R_BOTH_HRES_HCAD_Nanoflares’. The objective of this SOOP is to capture the
fast temporal variations of small and short-lived EUV brightenings, and to
compare their properties among the quiet Sun (QS), active regions (AR) and
coronal holes (CH). The SOOP is made of coordinated observations between Solar
Orbiter instruments (Auchère et al., 2020; Zouganelis et al., 2020). Here, we
use datasets from HRIEUV and SPICE. The observations were also made in
collaboration with instruments from other Earth-perspective observatories,
including AIA and EIS.

We selected three QS observations, which we call $\mathrm{S_{1}}$,
$\mathrm{S_{2}}$, and $\mathrm{S_{3}}$. Table 1 provides the information for
the three observational sequences. Detailed descriptions of the instruments
and the data are given in the following section for HRIEUV (Sect. 2.1), SPICE
(Sect. 2.2), AIA (Sect. 2.3) and EIS (Sect. 2.4).

To identify and follow the evolution of small and short-lived events in all of
the instruments, we need a careful co-registration. We developed tools for the
co-registering of the HRIEUV and the SPICE sequences. They are regrouped
within the euispice_coreg Python
package111https://github.com/adolliou/euispice_coreg, consulted on 2024 April
16, and the details of the method are given in Appendix A.

###  2.1 EUI

EUI is the UV imager on board Solar Orbiter. It includes a Full Sun Imager
(FSI) at two passbands and two high-resolution imagers (HRI). The two filters
of FSI are centred around the Fe X
$174.53\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (FSI 174) and the He II
$303.78\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (FSI 304) lines. HRI consists
of two telescopes, namely HRILy$\alpha$ and HRIEUV.

The HRIEUV response function peaks at $1\text{\,}\mathrm{MK}$, but includes a
contribution from transition-region (TR) emission. The CCD detector contains
2048$\times$2048 pixels, with a pixel size of 0.492′′, resulting in field of
view of $1007.6^{\prime\prime}\times 1007.6^{\prime\prime}$. The pixel size on
the corona can be derived from the Solar Orbiter–Sun distance (Table 1). At
1.004 $\textup{R}_{\odot}$ from the centre of the Sun, it is equal to
$172\text{\,}\mathrm{km}$, $134\text{\,}\mathrm{km}$, and
$115\text{\,}\mathrm{km}$ during $\mathrm{S_{1}}$, $\mathrm{S_{2}}$, and
$\mathrm{S_{3}}$ respectively. In addition to HRIEUV, we also use both FSI
imagers to co-register HRIEUV and SPICE. FSI 174 and FSI 304 have a pixel size
of $4.44^{\prime\prime}$, and a field of view of $224.96^{\prime}\times
227.34^{\prime}$.

We use Level 2 (L2) FITS files from the EUI Data Release 6.0 (Kraaikamp et
al., 2023). The data processing of the EUI FITS files from level 1 (L1) to L2
includes a dark-frame correction, a flat-field correction, and a normalisation
by the integration time. The pointing information in the FSI files metadata is
also corrected with a limb-fitting method. As this method cannot be applied to
imagers that do not observe the full Sun, there are uncertainties in the
pointing information of HRIEUV. Therefore, we co-register the HRIEUV sequence
with FSI using a cross-correlation technique. Further details are given in the
Appendix A.

Figure 1 shows the field of view of HRIEUV on the Sun as imaged by FSI 174
(top row) and AIA 171 (middle row). An HRIEUV image (bottom row) is also
displayed for each observation sequence. The fields of view cover QS areas.

###  2.2 SPICE

Table 2: SPICE lines in the three-step raster sequences and the context
rasters in $\mathrm{S_{1}}$ and $\mathrm{S_{2}}$. $\lambda$ is the theoretical
position of the line, and $T$ is the temperature of the maximum emission.

SPICE is a UV spectro-imager that images the solar spectrum over two CCDs,
called the short wavelength ($704\text{\,}$ to
$790\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) and the long wavelength
($972\text{\,}$ to $1049\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) detectors.
When imaging $\mathrm{S_{1}}$ and $\mathrm{S_{2}}$, SPICE was running a three-
step raster with a 25-second cadence. In addition to this, each dataset also
includes a 96-step context raster. The pixel size is $4^{\prime\prime}\times
1^{\prime\prime}$. The slit chosen was $4^{\prime\prime}$ wide, and the
resulting field of view for the three-step raster is $12^{\prime\prime}\times
832^{\prime\prime}$. The spatial resolution of SPICE was measured in-flight
during the commissioning phase, as the FWHM of the point spread function
(PSF). It was estimated to be between 6′′ and 7′′ (Fludra et al., 2021), which
is about six to seven times higher than the spatial resolution of HRIEUV (see
also Plowman et al., 2023). The spatial resolution of SPICE must therefore be
taken into consideration when identifying HRIEUV events with SPICE. Multiple
small brightenings captured by HRIEUV, close to one another, may be unresolved
in the SPICE images.

Spectrally, each series contains selected line profiles listed in Table
LABEL:table:spice_lines. They cover a temperature range from $\log{T}=4.0$ to
$6.0$. The three-step rasters share the same spectral windows as the context
raster.

We use L2 data for SPICE, taken from the Data Release 4.0 (SPICE Consortium et
al., 2023). The processing from the L1 to the L2 FITS files includes a initial
pointing correction, a dark subtraction, a flat-fielding, a burn-in
correction, a distortion correction and a radiometric calibration. We also
apply a sigma-clipping algorithm to remove possible spikes, that can be caused
by cosmic rays. Similarly to HRIEUV, there are uncertainties in the pointing
information of the SPICE FITS files, which must be corrected. For each
dataset, we co-align the SPICE context raster with either FSI 304 or HRIEUV,
depending on the data availability. The details about the procedure are given
in Appendix A. As a second step, the three-step rasters are then co-
registered, as they have a fixed and known position with respect to the
context raster.

The uncertainties in the intensity of the SPICE pixels include the
contributions from the dark current, the read noise and the shot noise (see
also Huang et al., 2023). They are computed with the SPICE data-analysis
Python package sospice222https://github.com/solo-spice/sospice, consulted on
2024 April 16. The spectral lines are fitted with Gaussian functions using the
SolarSoft SPICE data analysis software333https://github.com/ITA-Solar/solo-
spice-ql, consulted on 2024 April 16. The software returns the values and the
uncertainties of the fitting parameters. The fitted parameters are then used
to calculate the radiance of the line.

To constrain our results for the plasma-temperature analysis, we used the
information that some lines are not detectable in the spectra. This will be
used to set an upper limit to the radiance of the regions where the spectrum
is averaged. When no line is detected, we assume a radiance equivalent to that
of a line with an amplitude of 2$\sigma$ and a width given by the median of
the line widths in the whole context raster. Here, $\sigma$ is the combination
of the dark and the read noise (see also Parenti et al., 2017). In this work,
the radiance is calculated over an extended area including several pixels (see
section 3.1). In this case, the noise is defined as the root sum square of the
noise in the pixels of that region, divided by the number of pixels.

The SPICE data include a sit-and-stare sequence on $\mathrm{S_{3}}$. The field
of view is displayed in Fig. 1 (c). No clear signature of events was seen in
the data. We therefore consider that no events were detected by SPICE.

###  2.3 AIA

AIA is a EUV–UV imager that includes six EUV channels distributed within four
telescopes. For $\mathrm{S_{1}}$ and $\mathrm{S_{2}}$, AIA was available in a
special six-second cadence mode, to follow the HRIEUV high cadence as close as
possible. The objective was to capture the full thermal evolution of the EUV
brightenings detected by HRIEUV. Only four channels (171, 131, 193, 304) are
available during this mode. Figures 1 (b), (e) shows an AIA 171 image taken
from the $6\text{\,}\mathrm{s}$ cadence mode, respectively for
$\mathrm{S_{1}}$ and $\mathrm{S_{2}}$. The bottom of the AIA images has been
cropped during the special mode to allow the fast reading of the detector and
to keep the high cadence. Full-Sun images were also obtained every
$96\text{\,}\mathrm{s}$. Figures 1 (h) shows an AIA 171 image taken during
$\mathrm{S_{3}}$, when AIA was not running the high-cadence mode.

The level 1 AIA datasets are prepared with the aiapy open project (Barnes et
al., 2020)444https://gitlab.com/LMSAL_HUB/aia_hub/aiapy, consulted on 2024
April 16. First, the pointing information is updated. Then, the images are
deconvolved with the PSF estimated by the Richardson–Lucy deconvolution
algorithm. Finally, the roll angle of the images is removed and the
degradation in time of the CCD is corrected.

We project the AIA images on the HRIEUV pixel grid using sunpy (The SunPy
Community et al., 2020) and the reproject library from Astropy (Astropy
Collaboration et al., 2013, 2018, 2022). The AIA 171 images are then co-
aligned with the HRIEUV images. This step removes the average shift caused by
the separation angle between Solar Orbiter and SDO. The resulting shift
correction is applied to the AIA 193, 131, and 304 channels.

###  2.4 EIS

EIS is an EUV spectrometer imaging the solar spectrum on a short-wavelength
($170\text{\,}$ to $210\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) and a long-
wavelength detector ($250\text{\,}$ to
$290\text{\,}\mathrm{\SIUnitSymbolAngstrom}$). The $\mathrm{S_{3}}$ dataset is
made of a context raster and a faster 25-step raster sequence. The slit is 2′′
wide, with a 1′′ pixel size along the slit. At 1.004 $\textup{R}_{\odot}$ from
the centre of the Sun, the pixel size corresponds to about
$1441\text{\,}\mathrm{km}$ and $721\text{\,}\mathrm{km}$ in the Solar corona.
The spatial resolution of EIS is estimated to be around
$3^{\prime\prime}$555https://sohoftp.nascom.nasa.gov/solarsoft/hinode/eis/doc/eis_notes/08_COMA/eis_swnote_08.pdf,
consulted on 2024 April 16. The context raster acquired the full spectrum,
while the smaller ones only covered selected lines (see Table 4). In this
study, we use lines emitted from chromospheric (He II
$256.32\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) to coronal (Fe XVI
$262.98\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) temperatures.

The EIS data reduction and analysis are performed with the eispac Python
package666https://github.com/USNavalResearchLaboratory/eispac, consulted on
2024 April 16. The data have been previously prepared with the ”eis_prep”
routine available via solarsoft in Interactive Data Language (IDL) . During
the preparation, the CCD bias and the dark-current background are subtracted.
The cosmic rays, along with the hot and the cold pixels are flagged. The
wavelengths are corrected for the orbital motion, the temperature effect, and
the tilt of the slit relative to the CCD. We also correct the pointing
information with the co-registration algorithm developed by Pelouze et al.
(2019). We also use the recent radiometric calibration of Del Zanna et al.
(2023, submitted to ApJ), which corrects for the temporal degradation of the
CCD. Using eispac, we perform line fitting with one or multiple Gaussian
functions, to compute the line radiance.

Figures 1 (c), (f), and (i) display the field of view of EIS on an HRIEUV
image for $\mathrm{S_{1}}$, $\mathrm{S_{2}}$, and $\mathrm{S_{3}}$
respectively. We can see that the uncertainties between the instruments or
spacecraft pointings resulted in no overlap between the fields of view of EIS
and SPICE. For this reason, no event could be observed by SPICE and EIS
simultaneously. We then did a separate analysis.

While EIS datasets were available for all three observation sequences, we only
use the one for $\mathrm{S_{3}}$, because no HRIEUV events could be seen in
EIS. One possible reason is that both datasets had lower exposure time (10 and
$30\text{\,}\mathrm{s}$) compared with that of $\mathrm{S_{3}}$ (15 and
$60\text{\,}\mathrm{s}$), for the 25-step and the context rasters
respectively.

##  3 Method

Figure 2: Event detected on 2022 March 17 ($\mathrm{S_{1}}$), so-called
$\mathrm{E_{9}}$. The HRIEUV (left panel) and the SPICE images are centred
around $\mathrm{E_{9}}$. The HRIEUV image is taken at the acquisition time of
the left-hand SPICE slit. The position of the slit is displayed as a dashed
line on the HRIEUV and the SPICE images. The two white lines in HRIEUV delimit
the field of view of the SPICE slit. The red rectangle is the event region,
defined in Sect. 3.1.1. The temperature ($\log{T}$) of the maximum emissivity
of each SPICE line is indicated within parentheses above each image. The
latitude on the $y$-axis of the SPICE images refers to the position of the
slit marked with a white dashed line.  Figure 3: Images of four AIA channels
centred around the location of $\mathrm{E_{9}}$. The images are the closest in
time to the HRIEUV image in Fig. 2, taking into account the delay caused by
the light travel time. The red rectangle is the event region. Figure 4:
HRIEUV (top-left panel) and EIS images centred around the event
$\mathrm{E_{10}}$, on 2023 April 4 ($\mathrm{S_{3}}$). The HRIEUV image is
taken at the time closest to that of the EIS slit position indicated by dashed
white lines. The event region (red), along with the background regions 1
(orange) and 2 (purple) are displayed as rectangles. These regions are defined
in Sect. 3.1.2. The temperature $\log{T}$ of the maximum emissivity of each
line is indicated inside parenthesis on top of the image. The white arrow in
the Fe XI image indicates the large coronal loop standing above
$\mathrm{E_{10}}$.

The events were detected in HRIEUV data using the automated wavelet detection
code described by Berghmans et al. (2021). We then selected a sub-population
of the events in the overlapping region observed by the different instruments.
We did not include events that were located only partially within the field of
view, or events that were not clearly detected in either EIS or SPICE. Many of
the smaller events detected in HRIEUV could not be identified in EIS, while
most of them were identified in SPICE. As a matter of fact, we could only
report two events that showed no signature in SPICE. These two events are
displayed in Figs. 17 and 18. They are discussed in Sect. 5, and they are not
included in our dataset. Table 3 lists the final dataset which consists of
eight events in $\mathrm{S_{1}}$, one in $\mathrm{S_{2}}$, and two in
$\mathrm{S_{3}}$.

Table 3 presents their given name, an estimation of their lifetime and of
their apparent length. The lifetime is set by the period when the event is
visible above the background emission. We measure the apparent length $l$ in
the HRIEUV image at the time of the intensity peak. $\mathrm{E_{11}}$ was a
special case, as it had a resolved loop-like shape. In that case, we measured
the length along the loop $L\approx\frac{1}{2}\pi l$. Both $L$ and $l$ are
lower limits, as the loop may be tilted with respect to the line of sight, and
it might only be partially visible in the HRIEUV passband.

During their lifetime, some of the observed events show multiple peaks in
HRIEUV intensity. These multiple peaks may share the same physical origin, or
they can be unrelated. As the apparent shape of the events can change between
the peaks, we analyze the peaks separately unless specifically mentioned.

The event detection with HRIEUV and their identification in SPICE and EIS are
discussed in Sect. 3.1. The diagnostics including the light curves, the
emission measure (EM) LOCI, the differential EM, and the line ratios are
described in Sect. 3.2.

###  3.1 Event detection

Table 3: Events identified in HRIEUV and in either SPICE ($\mathrm{E_{1}}$ to
$\mathrm{E_{9}}$) or EIS ($\mathrm{E_{10}}$ and $\mathrm{E_{11}}$) data. From
left to right, the columns present the central time in UTC, the name, the
lifetime $\tau$, the apparent length $l$, and a short description of their
apparent shape. The ”on a structure” description indicates that the event is
located on a larger structure.

####  3.1.1 Identification of the events within SPICE and AIA

In $\mathrm{S_{1}}$ and $\mathrm{S_{2}}$ images, we identified nine HRIEUV
events both in SPICE and AIA. In this section, we provide the information on
how we identified these events, and how we build the light curves that will be
used for analysis. The event called $\mathrm{E_{9}}$, detected in
$\mathrm{S_{2}}$, will be used to illustrate the analysis steps. Section 4.1
discusses the results for three events including $\mathrm{E_{9}}$, while
Appendix B presents the results for the rest of the events. Examples of events
seen by HRIEUV, SPICE and AIA are also available as movies in the multimedia
materials.

Figure 2 shows the HRIEUV and the SPICE images centred around
$\mathrm{E_{9}}$, at the time of an HRIEUV intensity peak (00:36:19 UTC). At
that time, $\mathrm{E_{9}}$ appears in HRIEUV as a single bright dot, as part
of a larger structure. Another peak in HRIEUV is observed at 00:33:19 UTC. At
this time, $\mathrm{E_{9}}$ appears as two distinct bright dots within the
same structure. These two dots are unresolved by SPICE (see Fig. 19).

In Fig. 2, the event shows strong emission in C III, O IV, and O VI, but none
in Ne VIII nor in Mg IX. In these wavebands, the spectrum is often dominated
by noise, and no line can be detected. This is particularly true for Mg IX, as
it is a weak line in the QS. This property is not restricted to
$\mathrm{E_{9}}$; no emission in Mg IX could be associated with any of events
identified in SPICE. As a result, we only use this line in Sect. 4.1.2 to
provide an upper limit on the event EM around $\log{T}=6.0$. The full movie of
Fig. 2 is available in the multimedia materials.

We used SPICE to select the area that includes the entire event (see Fig. 2).
Because of the different resolution of the two instruments, the area must be
small enough not to include the nearby brightenings or structures seen in
HRIEUV. However, the region must also be large enough to include the event
during its whole lifetime. For some events ($\mathrm{E_{1}}$,
$\mathrm{E_{2}}$, $\mathrm{E_{5}}$, and $\mathrm{E_{8}}$), the HRIEUV and the
SPICE intensity peaks in O VI are spatially shifted, despite them being co-
temporal. The shifts are less than the SPICE pixel size of
$4\text{\,}\arcsec$$\times$$1\text{\,}\arcsec$, which is within the
uncertainties of the co-alignment method. We apply a spatial correction to the
event’s mask in HRIEUV up to the the SPICE pixel size.

In addition to HRIEUV and SPICE, we observe the event in four AIA channels
(171, 131, 193 and 304). Figure 3 shows the $\mathrm{E_{9}}$ event region on
the AIA images reprojected onto the HRIEUV pixel grid. The AIA images are
those closest in time to the HRIEUV image of Fig. 2 (left). The difference in
time between HRIEUV and AIA corresponds to the difference in light time travel
between Solar Orbiter and SDO. In $\mathrm{S_{2}}$, the large separation angle
between Solar Orbiter and the Earth perspective (Table 1) produces a spatial
shift on the location of $\mathrm{E_{9}}$. To correct this shift, we assume
that HRIEUV and AIA 171 are sensitive to similar plasma temperatures. A
spatial correction is applied to the event regions in AIA. The same values are
used for all of the AIA channels. The brightenings show a different morphology
and position in AIA 304 compared with the other channels. This was to be
expected, as the plasma emitting at chromospheric and TR temperatures might
not be at the same height. As a result, they can appear at different positions
on an imager (Fig. 3). The full movie of Fig. 3 is available in the multimedia
materials.

####  3.1.2 Identification of the events with EIS

In $\mathrm{S_{3}}$, we detected two events within HRIEUV images and
identified them in EIS data. Figure 4 shows the HRIEUV and the EIS images
centred around $\mathrm{E_{10}}$. This event was captured by the context
raster with a 60-second exposure time. Multiple EUV brightenings observed in
HRIEUV were located on $\mathrm{E_{10}}$. Two of them were detected less than
$60\text{\,}\mathrm{s}$ prior the time the EIS slit passes through the
structure. $\mathrm{E_{10}}$ is clearly detected in O V, and in the Fe lines
with temperature sensitivity up to that of Fe XI ($\log{T}=6.15$). In addition
to $\mathrm{E_{10}}$, a large coronal loop is also visible in the HRIEUV image
and in the EIS raster in the lines emitting at $\log{T}=6.15$ and above (see
Fe XI in Fig. 4). As the event is mostly visible in the cooler lines, and the
coronal loop in the hotter lines, we infer that the loop lies above
$\mathrm{E_{10}}$. Because of this, we need to isolate the emission of the
event from that of the background and the foreground along the line of sight,
including the loop. For this reason, we define two ”background” regions (1 and
2) shown in Fig. 4. Their location is designed to be representative of the
background and the foreground emission near $\mathrm{E_{10}}$, including that
of the large coronal loop.

We also identified another event, $\mathrm{E_{11}}$, within the 25-step raster
sequence. $\mathrm{E_{11}}$ (Fig. 20) appears as a loop-like structure. It is
clearly detected in the EIS He II line, but not in any of the Fe lines. We
conclude that $\mathrm{E_{11}}$ does not have enough plasma emission at
$\log{T}\geq 5.7$ to be detected in the ${Fe\textsc{}}$ lines above the noise
level, in a 15-second exposure.

###  3.2 Plasma diagnostic

For all the events and their background regions, we average the intensity
within the selected boxes. The lines are fitted over the averaged spectrum, to
obtain the radiance. When no line is detected within the box, the radiance is
being replaced by an upper limit defined in Sect. 2.2. As an example, Fig. 21
displays the fitting with Gaussian functions of the SPICE spectra spatially
averaged over the $\mathrm{E_{9}}$ event region (Fig. 2).

####  3.2.1 Temperature diagnostics

We aim to measure the temperature of the events, taking into account their
possible multi-thermal nature. In the following, we assume an optically thin
solar atmosphere, an electron density $n_{\mathrm{e}}$ and an hydrogen density
$n_{\mathrm{H}}$. The intensity of a spectral line $I$ is given by

$I=\int_{L}G(n_{\mathrm{e}},T)\leavevmode\nobreak\
n_{\mathrm{e}}(s)n_{\mathrm{H}}(s)\leavevmode\nobreak\ \mathrm{d}s$ (1)

The emission is integrated over the line of sight $L$. The contribution
function $G(n_{\mathrm{e}},T)$ contains the relevant atomic physics for the
line formation. When needed, we use the CHIANTI atomic database (Dere et al.,
1997), version 10.1 (Del Zanna et al., 2021; Dere et al., 2023), to compute
$G(n_{\mathrm{e}},T)$. Under the ionization equilibrium provided by CHIANTI,
we assume the coronal abundance given by Asplund et al. (2021), and a typical
coronal electron density of $10^{9}$ cm-3. The contribution functions of the
SPICE and the EIS lines used in this work are displayed in Fig. 22. We see
that they cover a wide range of temperature. This is extremely useful to
constrain the temperature diagnostics and reach the goal of this work:
establishing whether the HRIEUV are coronal features. As will be further
discussed, SPICE is mostly sensitive to chromospheric and transition region
lines, while the EIS spectrum contains mostly transition region and coronal
lines.

One can rewrite Eq. 1 using the ideal gas approximation. Given that in the TR
and the corona the pressure gradient is much lower than the temperature and
density gradients, we can assume that the density depends only on the
temperature. In that case, the DEM can be defined with a change of variable in
Eq. 1. The DEM represents the distribution, along the line of sight, of the
plasma with temperature.

$\mathrm{DEM}(T)=n_{\mathrm{e}}(T)n_{\mathrm{H}}(T)\frac{\mathrm{d}s}{\mathrm{d}T}$
(2)

Equation 1 can be rewritten into the following.

$I=\int_{T}G(T)\leavevmode\nobreak\ \mathrm{DEM}(T)\leavevmode\nobreak\
\mathrm{d}T$ (3)

The DEM can be estimated by inverting the set of Eqs. 3 from measured lines
radiance. In our work, $\mathrm{E_{10}}$ is detected in EIS lines over a wide
range of plasma temperatures (Fig. 4), which is a suitable condition for the
DEM inversion. We then estimate the DEM with the inversion method developed by
Hannah & Kontar (2012).

Table 4 reports the intensity values of the lines measured in the event and
the background regions. We used all of the line to estimate the DEM for the
three regions, except for the density-sensitive Fe XIII lines. The reasons
behind this removal are further discussed in Sect. 4.2.1. The DEM is computed
from $\log{T}=5.0$ to $6.6$. For each line, we compute the ratio of the
synthetic radiance obtained with the DEM, over the measured radiance. They are
displayed in Table 4, and provide an estimation of the inversion uncertainty.
They are all within the 30% uncertainties of the atomic physics (Guennou et
al., 2013), meaning that the DEM is consistent with observations. The results
of this analysis are given in Sect. 4.2.1.

The events detected within $\mathrm{S_{1}}$ and $\mathrm{S_{2}}$
($\mathrm{E_{1}}$ to $\mathrm{E_{9}}$), are identified in SPICE. Contrary to
EIS, the low number of SPICE lines prevents us from estimating the DEM.
Instead, we use the Emission Measure (EM) LOCI method (Del Zanna & Mason,
2018a, for further details), which provides an upper limit on the DEM. The EM
is defined as the integration of the DEM over the whole temperature range.

$\mathrm{EM}=\int_{T}\mathrm{DEM}(T)\leavevmode\nobreak\ \mathrm{d}T$ (4)

The EM LOCI method provides the EM necessary to produce a given line
intensity, assuming an isothermal plasma. For a given spectral-line intensity,
the LOCI curve ($\mathrm{EM_{L}}$) is defined as the following:

$\mathrm{EM_{L}}(T)=\frac{I}{G(T)}$ (5)

We compute the LOCI curves using the C III, O IV, O VI, and Ne VIII lines. Mg
IX is not included, as the line is never detected above noise levels. The
event’s EM must be isolated from the contribution of the foreground and the
background emission along the line of sight. Differently from the EIS data,
SPICE data contain the temporal information on the lines intensity. We use
them to estimate this background emission by averaging the light curves over
two time intervals of two minutes. The intervals are called B1 and B2, and
they are set before and after the event, respectively (Fig. 6). The results of
the EM LOCI method are given in Sect. 4.1.2, and in Appendix B.

####  3.2.2 Electron density diagnostics

In addition to the temperature, we estimate the density of $\mathrm{E_{10}}$
using the ratio of line intensities. In the EIS dataset, the ratio of Fe IX
188.49/197.04 (Young, 2009, b) and Fe XIII (203.80 + 203.83)/202.04 (Young et
al., 2009) are density-sensitive. The dependence on density of the Fe XIII
lines between $\log{n_{\mathrm{e}}}=8$ to $10$ can be explained by the
existence of a metastable level (3s23p2 3P2) above the ground level (3s23p2
1P2) (for more details, see Del Zanna & Mason, 2018b). In the Fe IX line
ratio, only the $197.86\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ is density
sensitive. We could not perform similar diagnostics with the SPICE lines, as
they did not provide density sensitive line ratio. The analysis is performed
with the CHIANTI database and software available via SolarSoft. The results of
this analysis are given in Sect. 4.2.2.

##  4 Results

Figure 5: HRIEUV images centred around $\mathrm{E_{2}}$ (a) at the time of the
second HRIEUV peak, and $\mathrm{E_{4}}$ (b) at the time of the single HRIEUV
peak. The red rectangles are the event regions (see Sect. 3.1.1).  Figure 6:
HRIEUV, SPICE, and AIA light curves for $\mathrm{E_{9}}$ (a), $\mathrm{E_{4}}$
(b), and $\mathrm{E_{2}}$ (c). The vertical black lines indicate the SPICE
times closest to the HRIEUV peaks, when the EMs are estimated in Fig. 7. The
two background time intervals of two minutes, defined in Sect. 3.2.1, are
represented by two vertical blue lines in each panel. The left blue line
indicates the end of B1 (before the event), and the right blue line indicates
the start of B2 (after the event). The upper limits of the SPICE radiance are
shown as horizontal dotted lines. When the line is not detected above noise
levels, the radiance is being replaced by its upper limit, and the point is
marked by a downward pointing arrow.  Figure 7: EM estimated with the LOCI
method of $\mathrm{E_{9}}$ (a), $\mathrm{E_{2}}$ (b) and $\mathrm{E_{4}}$ (c)
at the time of their HRIEUV peaks, using four SPICE lines. The EMs of the
event are shown for each SPICE line with colored curves. Dotted curves
indicate that the radiance is an upper limit. The black full curves display
the EM for the event. The dotted and the dashed black lines are the EMs for
the B1 and B2 background time intervals. B1 also includes upper limits in O IV
for $\mathrm{E_{2}}$ and in Ne VIII for $\mathrm{E_{4}}$. The black (event)
and grey (B1 and B2) regions delimit the 2$\sigma$ uncertainty of the EMs.
Figure 8: (a) Light curves of HRIEUV and five EUV channels of AIA with
intensities averaged over the $\mathrm{E_{10}}$ event region. The time
interval when the EIS slit passes over the event is delimited by two blue
vertical lines. (b) DEM of the event $\mathrm{E_{10}}$, along with the
background regions 1 and 2. The ratios of the reconstructed radiance over the
observed one is plotted on the effective temperature of each line.  Figure 9:
Line ratio Fe IX 188.49/197.04 at $\log{T}=6.0$, computed with the radiance
and the uncertainty in the $\mathrm{E_{10}}$ event region. The ratio provides
an estimation of the electron density equal to $\log{n_{\mathrm{e}}}=10.09\pm
0.41$. This figure has been obtained with dens_plotter in the CHIANTI
software.

###  4.1 Transition region events detected in SPICE and AIA data

In the following, we analyze the temporal evolution (Sect. 4.1.1) and obtain
temperature diagnostics (Sect. 4.1.2) of the $\mathrm{S_{1}}$ and
$\mathrm{S_{2}}$ events. We present the results for the events
$\mathrm{E_{2}}$, $\mathrm{E_{4}}$, and $\mathrm{E_{9}}$, as they are
representative of the different light curve behaviours that we encountered.
$\mathrm{E_{9}}$ was already introduced in Sect. 3.1.1, while $\mathrm{E_{2}}$
and $\mathrm{E_{4}}$ are displayed in Fig. 5 with HRIEUV, at the time of their
intensity peak. The results for the rest of the events are displayed in
Appendix B.

####  4.1.1 Light curves

Figure 6 shows the HRIEUV, the SPICE, and the AIA light curves averaged over
the $\mathrm{E_{2}}$, $\mathrm{E_{4}}$, and $\mathrm{E_{9}}$ regions. The
events $\mathrm{E_{9}}$ and $\mathrm{E_{4}}$ (Fig. 6 (a) and (b)) are visible
in all light curves, apart from that of Ne VIII. Both events are also poorly
detected in H I Ly-$\beta$. All the intensity peaks in SPICE are co-temporal
to the peaks in HRIEUV, except for a 25-second negative delay for the H I
Ly-$\beta$ peak in $\mathrm{E_{4}}$. Likewise, no significant delay is
observed between the HRIEUV and the AIA light curves. We notice that the the O
IV and the O VI light curves behave very similarly to the HRIEUV one.

In the event $\mathrm{E_{4}}$ (Fig. 6 (b)), the background intensity in HRIEUV
and AIA 171 increases after the event. We also observe an increase in the
background intensity of the chromospheric (C III, AIA 304) and TR lines (O IV
and O VI). The increase in the C III light curve is the most significant, as
its value almost doubles compared with the value before the event. Due to the
different temperatures of formation of these lines (Fig. 22), we suggest that
the common background increase is due to an increase in density at these
temperatures.

For the event $\mathrm{E_{2}}$ (Fig. 6 (c)), the HRIEUV light curve has two
peaks. The first HRIEUV peak (00:38:08 UTC) is co-temporal with the peak in
the Ne VIII light curve. At that time, no emission in O VI is detected. The
second HRIEUV peak (00:40:13 UTC) is co-temporal with the peak in O VI, and it
is $25\text{\,}\mathrm{s}$ earlier than the peak in the C III light curve.
These are indications that emission at coronal temperatures dominates at the
first peak, while TR emission dominates for the second one. At 00:40:13 UTC,
the cooling plasma passes through the emissivity peaks of O VI followed by
that of C III. This example shows that the interpretation in terms of
temperature of HRIEUV is not straightforward, as it images both warm and cool
plasma. The interpretation of the peak in O IV is uncertain, but it may be the
signature of cooling plasma from the coronal temperature imaged by the first
peak of HRIEUV.

The results are confirmed by the AIA light curves of $\mathrm{E_{2}}$ (bottom
rows of Fig. 6 (c)). The two peaks have a similar amplitude in HRIEUV and in
AIA 171. The amplitudes of the other AIA channels are lower at the first
HRIEUV peak (00:38:08 UTC) compared with second one (00:40:13 UTC). At the
first peak, the plasma probably reaches a temperature close to the sensitivity
peaks of HRIEUV and AIA 171 (0.9 – $1\text{\,}\mathrm{MK}$), but below that of
AIA 193 ($1.5\text{\,}\mathrm{MK}$). At the second HRIEUV peak, the light-
curve behavior of the AIA channels is probably caused by the TR (AIA 171, 193,
131) and chromospheric (AIA 304) contributions to the response function of the
channels.

The light curves of $\mathrm{E_{2}}$ (Fig. 6 (c)) show that, when the HRIEUV
peak is caused by a plasma at coronal temperatures, we would expect the Ne
VIII emission to be detected in SPICE. In fact, under corona temperature
assumption, higher HRIEUV intensity would mean higher density of the plasma at
this temperature. The events $\mathrm{E_{1}}$, $\mathrm{E_{3}}$, and
$\mathrm{E_{4}}$ all have peaks higher than $\mathrm{E_{2}}$. If they were
caused by a coronal contribution (same temperature than $\mathrm{E_{2}}$) they
would be visible in the Ne viii, and even possibly in the Mg ix lines, as the
EM is probably higher. We anticipate that this is not the case, as shown in
Fig. 7. This is an important result, as part of the ambiguity of the EUV
brightening temperature originates from the broad response of the HRIEUV and
the AIA imagers. In $\mathrm{E_{2}}$, we have determined whether the coronal
or the TR part of the response function contributed the most to the HRIEUV
intensity peak. This is the evidence that the HRIEUV and AIA intensity peaks
in $\mathrm{E_{9}}$ and $\mathrm{E_{4}}$ mostly originate from a plasma
emitting at TR temperatures (Fig. 6 (a) and (b)).

####  4.1.2 EM results

Figure 7 shows the results of the EM LOCI method applied to the SPICE data at
the time of the HRIEUV peaks. For $\mathrm{E_{9}}$ and $\mathrm{E_{4}}$, in
the temperature range up to $\log{T}=5.6$, the EM of the event is higher than
that of the backgrounds (panels a, b). In particular, for the first HRIEUV
peak of $\mathrm{E_{9}}$, the EM of the event is higher in the whole
temperature range (panel a, top).

The EM of $\mathrm{E_{2}}$ displays different behaviors (Figure 7 (c)). In the
first peak (top panel), the EM of the event is similar to the one of the
background. Only at temperatures above $\log{T}>5.7$ does the EM increase a
small amount. We suggest that the HRIEUV intensity peak might be caused by the
coronal lines within the band. The absence of Mg IX emission above the noise
level in the SPICE data can be due to an insufficient increase in the EM. We
recall that this line is generally weak or absent in the QS. At the second
peak (bottom panel) of the HRIEUV light curve, the event’s LOCI stands above
the background EM up to $\log{T}=5.6$. Other examples are given in Figs. 13
and 15 in Appendix B.

We conclude that, in most cases, the event EM is dominated by plasma at
chromopheric and TR temperatures during the HRIEUV intensity peaks. At the
emissivity peak of O VI ($\log{T}=5.5$), the background-subtracted EM reaches
values between $(3.3\pm 1.3)\text{\times}{10}^{25}\text{\,}{\mathrm{cm}}^{-5}$
($\mathrm{E_{4}}$) and $(8.8\pm
2.1)\text{\times}{10}^{25}\text{\,}{\mathrm{cm}}^{-5}$ (second peak of
$\mathrm{E_{9}}$). In one case (Fig. 7 (c), top panel), we suspect the event
to be dominated by coronal temperatures. Above $\log{T}=5.6$, the event and
the background EMs are close within $2\sigma$ uncertainty range, with one
exception (Fig. 7 (a), top panel). The SPICE spectrum does not include strong
coronal lines. We then further investigate the temperature behavior of these
brightening by analyzing EIS data, which are rich in coronal lines. This is
presented in the next section.

The absence of detectable Mg IX emission in the spectra of the events places
constraints on the amount of EM (and thus density) at these temperatures. We
can provide an upper limit by using the upper limit of the radiance defined in
Sect. 2.2 and using Eq. 5. Taking $\mathrm{E_{9}}$ as an example (Fig. 6 (a)),
we estimate the EM to be below
$1.0\text{\times}{10}^{26}\text{\,}{\mathrm{cm}}^{-5}$ at $\log{T}=6.0$. Using
this value, we estimate the density as $n=\sqrt{\frac{\mathrm{EM}}{hf}}$,
where $h$ is the event thickness along the line of sight, and $f$ the filling
factor of $\mathrm{E_{9}}$ over the event region (Joulin et al., 2016). To
estimate $h$, the event is assumed to be located on a loop with a circular
cross-section. $h$ is then equal to the width of the apparent loop. This width
is measured by fitting a Gaussian function to the HRIEUV intensity on a
perpendicular cut to the loop axis, at the position of the HRIEUV intensity
peak. The width is defined as the Full Width at Half Maximum of the Gaussian
function. For $\mathrm{E_{9}}$, we measure $h=$ $0.56\text{\,}\mathrm{Mm}$. We
also estimated the filling factor $f$ using HRIEUV. To do so, we compute the
ratio of the so-called ”event” pixels (pixels where the event is detected)
over the ”QS” pixels (where the event is not detected within the selected
event region). The event pixels are selected using a $3\sigma$ threshold above
the average intensity $\mu$ of the QS . Both the spatial average $\mu$ and
standard deviation $\sigma$ of the QS are measured within the event region, at
a time prior to the event (00:30:49 UTC). At the time of the second HRIEUV
intensity peak (00:36:14 UTC), we obtain a filling factor equal to $f=0.35$.
Using the above expression, we derive an upper limit of the density of
$n_{\mathrm{e}}=$ $2.3\text{\times}{10}^{9}\text{\,}{\mathrm{cm}}^{-3}$

###  4.2 Event detected with EIS

In the following, we apply temperature and density diagnostics to
$\mathrm{E_{10}}$, which is observed with EIS. The event was captured at a
single time by the 60-step context raster, preventing us from constructing
light curves. Nevertheless, we could perform a density diagnostics and the
differential emission measure analysis, providing more precise information on
the temperature distribution of the plasma. The event and the background
regions of $\mathrm{E_{10}}$ are displayed in Fig. 4.

Figure 8 (a) shows the light curves of HRIEUV and five EUV channels of AIA,
obtained by averaging the intensity over the event region of
$\mathrm{E_{10}}$. The vertical lines mark the interval of acquisition of EIS.
As for the previous events ($\mathrm{E_{2}}$, $\mathrm{E_{4}}$, and
$\mathrm{E_{9}}$), there is no apparent delay between the peaks in the HRIEUV
and the AIA light curves. We also see that EIS starts observing the event
$1\text{\,}\min$ after the HRIEUV peak, meaning that the following temperature
and density diagnostics are obtained close to the event peak. This event was
long ($19\text{\,}\min$) in HRIEUV, with multiple brightenings. Here we only
concentrate on the period recorded in coordination with EIS.

####  4.2.1 DEM results

We compute the DEM in the event and the background regions to infer the
temperature distribution of the event. We recall that this event is located
below a large scale loop, visible in the hot lines of EIS (see Fig. 4). We
will take this into consideration when interpreting our results. To compute
the DEM, we included all the lines listed in Table 4, except for the density-
sensitive Fe XIII lines. As $\mathrm{E_{10}}$ is undetected in the Fe XIII
lines (Fig. 4), removing them does not impact our results.

Figure 8 (b) shows the DEM of the $\mathrm{E_{10}}$ event (blue line) and of
the two background regions (magenta and yellow lines). For these inversions,
we mostly use lines from Fe ions to reduce the uncertainty related to the
assumption of the elemental composition. The only exception is the O V
$192.91\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ line, because it could
constrain temperatures below $\log{T}=5.5$. The event’s DEM is higher than
that of the background regions at $\log{T}\leq 6.0$, while they are similar
for $\log{T}\geq 6.0$. For all three DEMs, we observe a common peak around
$2\text{\,}\mathrm{MK}$, which is probably caused by the line-of-sight
integration of the corona, including the large coronal loop standing above
$\mathrm{E_{10}}$. The DEM of the event also shows a second peak around
$\log{T}$ = 5.9, due to the abundance of Fe VIII and Fe IX. Below
$\log{T}=5.2$ and above $\log{T}=6.45$, the DEMs are poorly constrained due to
the lack of observed lines. We conclude that $\mathrm{E_{10}}$ barely reaches
coronal temperatures, and it is dominated by plasma at TR temperatures.

####  4.2.2 Density diagnostics

We derived the electron density of $\mathrm{E_{10}}$ using the density-
sensitive Fe IX 188.49/197.04 line ratio (see Sect. 3.2.2). The ratio is
computed with the line intensities of the event, at the effective temperature
$\log{T}=6.0$ of the Fe IX lines (Table 4). This high density confirms that we
are probably observing a compact, small-scale event, occurring low in the
solar atmosphere.

Figure 9 displays the theoretical ratio as a function of the density, as
predicted by CHIANTI, with a superposition of the measured one. We obtain a
ratio of $0.33\pm 0.04$, which corresponds to a density equal to
$n_{\mathrm{e}}=$ $(1.8\pm
1.3)\text{\times}{10}^{10}\text{\,}{\mathrm{cm}}^{-3}$.

For comparison, we inferred the density of the coronal loop in the foreground
of the event at the position occupied by the event. We use the Fe XIII (203.80
+ 203.83)/202.04 line ratio (see Sec. 3.2.2) and assumed a temperature
$\log{T}=6.25$. We obtained a loop density of $(4.3\pm
0.3)\text{\times}{10}^{8}\text{\,}{\mathrm{cm}}^{-3}$. This value is typical
of coronal loops (Reale, 2014) and supports our idea that this loop is higher
above $\mathrm{E_{10}}$.

##  5 Discussion

In this work, we have produced evidence that small EUV brightenings detected
by HRIEUV in the QS are, for the most part, dominated by plasma at
chromospheric and TR temperatures. This is, at least, true for our observed
features. As such, their direct contribution to coronal heating is
insignificant. To obtain these results, we analyzed three QS observation
sequences coordinated between multiple instruments. We identified nine events
with HRIEUV, AIA and SPICE, and three events with HRIEUV and EIS. We resume
our main findings in the following.

Most of the smaller EUV brightenings visible in SPICE (up to
$2.5\text{\,}\mathrm{Mm}$), for temperatures below $\log{T}=5.6$, have a
higher EM than their background/foreground. The larger event
($\mathrm{E_{10}}$, $6.2\text{\,}\mathrm{Mm}$) identified in EIS, barely
reaches coronal temperatures, and it is also dominated by plasma at TR
temperatures. We estimated the electron density to be equal to
$n_{\mathrm{e}}=$ $(1.8\pm
1.3)\text{\times}{10}^{10}\text{\,}{\mathrm{cm}}^{-3}$. This value is an order
of magnitude above the typical electron densities in the QS near the effective
temperatures of the Fe IX ($n_{\mathrm{e}}\approx 10^{9}$
$\text{\,}{\mathrm{cm}}^{-3}$ at $T=$
$1.12\text{\times}{10}^{6}\text{\,}\mathrm{K}\mathrm{,}$ Dere, 2020).

We investigated the light curves from lines at different temperatures (HRIEUV,
SPICE, and AIA), and obtained two main results: (1) For most events, and
especially for the smaller ones, all of the intensity peaks are co-temporal.
This is consistent with the results of Dolliou et al. (2023) using AIA data
only. (2), For most events, the HRIEUV light curve follows the behavior of O
VI, including the co-temporality of the peak in intensity (for instance, see
Fig. 6). Thus, these events are probably dominated by TR temperatures over
their lifetime. To conclude, we present evidence that the thermal behavior of
these events reflects that of cool features.

The events observed with SPICE showed strong emission in the TR lines, but
rarely in the Ne VIII and never in the Mg IX lines. These conclusions were
also found in the three events analyzed by Huang et al. (2023), which barely
produced emission in Ne VIII. While most of the events detected by HRIEUV were
clearly identified in SPICE, we can report two exceptions in $\mathrm{S_{1}}$.
One of them is a small ($0.3\text{\,}\mathrm{Mm}$) and short-lived one-minute,
dot-like event (Fig. 17). It is only detected in HRIEUV and possibly in the C
iii line. The other event is a larger ($1.9\text{\,}\mathrm{Mm}$) loop-like
event of five-minute lifetime (Fig. 18). It is detected in HRIEUV and barely
in AIA 171. It is unclear whether the lack of signal can be explained by a low
EM, or because the event is dominated by plasma at coronal temperature not
covered by the SPICE lines. Although being a minority, these events detected
only in HRIEUV should be further investigated, as they may be good candidates
for reaching coronal temperatures and possibly participate, even a small
amount, to sustaining the corona.

Nelson et al. (2023) analyzed 15 EUV brightenings on $\mathrm{S_{1}}$ between
00:04:12 UT and 00:33:33 UT. They used datasets from HRIEUV, AIA, and the
IRIS. Our event’s dataset in $\mathrm{S_{1}}$ (Table 3) does not overlap with
theirs. IRIS covered chromospheric lines, from $\log{T}=$ 4.0 to 4.9. The
authors compared the HRIEUV light curves with those of the Mg II
($\log{T}=4.3$) and Si IV lines ($\log{T}=4.9$). They found no typical
behavior, the light-curve peaks having either positive, negative, or no time
delays. Our results showed that the intensity peaks in the SPICE TR light
curves were mostly co-temporal with the HRIEUV ones (Fig. 6 (a) and (c) for
instance). The C iii lines in SPICE ($\log{T}=4.8$) are close to the
temperature emissivity of Si IV, while H I Lyman-$\beta$ is close to that of
Mg II. The delays between the HRIEUV and the C III intensity peaks are within
$25\text{\,}\mathrm{s}$ of one another for the majority of events, although we
did detect delays up to $300\text{\,}\mathrm{s}$ for $\mathrm{E_{8}}$ (see
Fig. 14). We also observed delays below $1\text{\,}\min$ between the intensity
peaks in H I Lyman-$\beta$, C III, and O VI for $\mathrm{E_{1}}$ (Fig. 12).
Positive and negative delays are also observed between the peaks in the Ne
VIII and the O VI light curve on $\mathrm{E_{2}}$, $\mathrm{E_{3}}$, and
$\mathrm{E_{7}}$ (Fig. 6 (b), 12 (b), 14 (b)). They might be signatures of
plasma cooling or heating passing through the temperature sensitivity of the
lines. As for Nelson et al. (2023) and Dolliou et al. (2023), we conclude that
the population of the events are not uniform and can reach different
temperatures. The short delays between the peaks of the TR and the HRIEUV
light curves suggest that the lines observed in SPICE can explain what is seen
in HRIEUV.

Our results are in line with the finding that the interpretation of what is
observed in EUV imagers is not straightforward. It is known that, under
certain plasma conditions, the cool emission can dominate the measured signal,
even though the peak of the response function of the band is centred at a
coronal line. This has been investigated for HRIEUV (Tiwari et al., 2022) and
for other imagers such as AIA (Schonfeld & Klimchuk, 2020) or TRACE
(Winebarger et al., 2002).

The density of $\mathrm{E_{10}}$ was estimated to $(1.8\pm
1.3)\text{\times}{10}^{10}\text{\,}{\mathrm{cm}}^{-3}$ at $\log{T}=6.0$, (see
Sect. 4.2.2). We can compare this value with the upper limits on the density
of $\mathrm{E_{9}}$, equal to
$2.3\text{\times}{10}^{9}\text{\,}{\mathrm{cm}}^{-3}$ at $\log{T}=6.0$ (Sect.
4.1.2). We conclude that the smaller events detected with SPICE have less
plasma at coronal temperature compared with $\mathrm{E_{10}}$.

The properties of the brightenings are similar to the loops previously
observed with Hi-C in the intermoss of an active region (Winebarger et al.,
2013), even though much smaller in length. Their electron temperature
($\log{T}\approx 5.4$) and density ($\log{n}\sim 10$) closely match our
results. The authors also observed close to no delay between the peaks of the
AIA and the Hi-C light curves. Furthermore, modellings showed that the heating
events are low-lying in the atmosphere, up to $2\text{\,}$ to
$3\text{\,}\mathrm{Mm}$ above the photosphere. These heights are also
consistent with EUV brightenings detected with HRIEUV (Zhukov et al., 2021).
In addition to active regions, cool (less than $0.5\text{\,}\mathrm{MK}$) and
low-lying (up to $5\text{\,}\mathrm{Mm}$) loops have also been observed in the
QS with IRIS (Hansteen et al., 2014). Magnetic reconnexions involving these
types of loops are good candidates to explain the physical origin of the
events analysed in our work. They concentrated around the chromospheric
network (Feldman et al., 1999; Sánchez Almeida et al., 2007), which is
consistent with HRILy$\alpha$ observations by Berghmans et al. (2021).
Signatures of magnetic flux cancellations associated with EUV brightenings
(Kahil et al., 2022) already suggested that magnetic reconnexion triggered by
the footpoints may play an important role. With this work, we argue that the
electron temperature (below $1\text{\,}\mathrm{MK}$) and density (above
$5\text{\times}{10}^{9}\text{\,}{\mathrm{cm}}^{-3}$) of the EUV brightenings
observed with HRIEUV is also consistent with cool loops subjected to impulsive
heating.

We showed that the brightenings analyzed in our work barely reach coronal
temperatures. While some of them can reach temperatures up
$1\text{\,}\mathrm{MK}$ (for instance $\mathrm{E_{2}}$ and $\mathrm{E_{10}}$),
they are, for the most part, dominated by TR plasma. As this study was limited
to 12 events, more statistical work is necessary, to verify if these
observations can be generalized. If this is the case, this would mean that
these events do not directly contribute to the coronal heating, as they do not
reach coronal temperatures. Additional modelling work us necessary to
reproduce the properties of the EUV brightenings (Winebarger et al., 2013;
Hansteen et al., 2014). Such modelling will have to take into account the new
spectroscopic constraints for these events, set by the latest results from the
Solar Orbiter observations.

###### Acknowledgements.

The authors thank the anonymous referee for the useful comments that helped to
improve the manuscript. The authors gratefully thank the AIA, the EIS, the
EUI, and the SPICE teams for the planning of the observations. The authors
thank F. Auchère for his help in the preparation of SPICE data. A.D.
acknowledges funding from CNES and the Ecole Doctorale Ondes et Matière
(EDOM). Solar Orbiter is a space mission of international collaboration
between ESA and NASA, operated by ESA. The EUI instrument was built by CSL,
IAS, MPS, MSSL/UCL, PMOD/WRC, ROB, LCF/IO with funding from the Belgian
Federal Science Policy Office (BELSPO/PRODEX PEA C4000134088); the Centre
National d’Etudes Spatiales (CNES); the UK Space Agency (UKSA); the
Bundesministerium für Wirtschaft und Energie (BMWi) through the Deutsches
Zentrum für Luft- und Raumfahrt (DLR); and the Swiss Space Office (SSO). The
development of SPICE has been funded by ESA member states and ESA. It was
built and is operated by a multi‑national consortium of research institutes
supported by their respective funding agencies: STFC RAL (UKSA, hardware
lead), IAS (CNES, operations lead), GSFC (NASA), MPS (DLR), PMOD/WRC (Swiss
Space Office), SwRI (NASA), UiO (Norwegian Space Agency).This work used data
provided by the MEDOC data and operations centre (CNES / CNRS / Univ. Paris-
Saclay. Hinode is a Japanese mission developed and launched by ISAS/JAXA,
collaborating with NAOJ as a domestic partner, NASA and UKSA as international
partners. Scientific operation of the Hinode mission is conducted by the
Hinode science team organized at ISAS/JAXA. This team mainly consists of
scientists from institutes in the partner countries. Support for the post-
launch operation is provided by JAXA and NAOJ (Japan), UKSA (U.K.), NASA, ESA,
and NSC (Norway). This research was supported by the International Space
Science Institute (ISSI) in Bern, through ISSI International Team project
#23-586 (Novel Insights Into Bursts, Bombs, and Brightenings in the Solar
Atmosphere from Solar Orbiter). This research used version 0.7.4 (Barnes et
al., 2021) of the aiapy open source software package (Barnes et al., 2020).
This research used version 5.0.1 ((Mumford et al., 2023) of the SunPy open
source software package (The SunPy Community et al., 2020). This research used
the open source sospice Python package. This research used CHIANTI version
10.1. CHIANTI is a collaborative project involving George Mason University,
the University of Michigan (USA), University of Cambridge (UK) and NASA
Goddard Space Flight Center (USA).

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##  Appendix A Alignment algorithm

Figure 10: Example of the result of the alignment between SPICE and FSI for
$\mathrm{S_{2}}$. (a) the FSI 304 synthetic raster is displayed in the
background along with the 80 and 90 % percentile as contours of the not
aligned C III SPICE map. (b) The same composite image after the alignment. (c)
SPICE C III map corrected after the alignment.

We developed tools to co-register the SPICE and the HRIEUV sequences. For
$\mathrm{S_{1}}$, the SPICE Ne VIII image of the context raster is co-aligned
with an HRIEUV synthetic raster. The latter is built by selecting the HRIEUV
image closest in time to each of the raster steps. We build SPICE images by
summing the intensity over the spectral window. The same technique is applied
to $\mathrm{S_{2}}$ with the C III line and the FSI 304 sequence.

Figure 10, as an example, illustrates the result for the $\mathrm{S_{2}}$
data. We co-align the SPICE context raster with the FSI 304 synthetic raster,
using a cross-correlation method. The offset found with this correlation is
then applied to the values of the pointing information in the FITS headers.

The HRIEUV temporal sequences are co-registered with FSI images. For
$\mathrm{S_{1}}$ and $\mathrm{S_{3}}$, we co-align the HRIEUV images closest
in time to each of the FSI 174 images in the dataset. The cross-correlation
technique is the same as the one discussed for SPICE. We then apply a
correction to the spacecraft jitter, inspired by Chitta et al. (2022). The
HRIEUV dataset is divided into sub lists, with the first images being those
already co-aligned with FSI 174 images. Every HRIEUV image is then co-aligned
with the first image of its sub-list. As a last step, we corrected remains of
the jitter by again cross-correlating the HRIEUV sequence within sub-lists,
this time with overlapping images between the sub-lists.

For $\mathrm{S_{2}}$ (2022 March 17, 00:18 – 00:48 UTC), only FSI 304 images
at one-minute cadence were available before 00:16 UT, and we had to adapt the
co-registration procedure. We first co-align an HRIEUV and an FSI 174 image at
09:50:04 UTC, to locate the position of the HRIEUV field of view on that of
FSI. As FSI 174 and FSI 304 share the same field of view, we can co-align the
HRIEUV images with the FSI 304 image closest in time.

These methods are available through the
euispice_coreg777https://github.com/adolliou/euispice_coreg Python package.

##  Appendix B Additional events in $\mathrm{S_{1}}$

In this Appendix, we present the results for the events in $\mathrm{S_{1}}$
(Table 3) that were not discussed in Sect. 4.1. Figure 11 shows HRIEUV images
centred around the events at the time of one of their HRIEUV peak. The results
of their light curves and the EM LOCI method are displayed for
$\mathrm{E_{1}}$, $\mathrm{E_{3}}$, $\mathrm{E_{5}}$ (Fig. 12 and 13), and for
$\mathrm{E_{6}}$, $\mathrm{E_{7}}$, $\mathrm{E_{8}}$ (Fig. 14 and 15). As an
example, $\mathrm{E_{5}}$ seen with HRIEUV and SPICE is displayed in Figure
16, and as a movie in the multimedia materials.

For most events, the O vi intensity peaks are co-temporal with the those of
HRIEUV. Exceptions include $\mathrm{E_{7}}$ (Fig. 14 (b)), that has two HRIEUV
peaks co-temporal with either O vi or Ne viii. Similar results were found for
$\mathrm{E_{2}}$ in Figure 6 (c), and discussed in section 4.1.1. We suggest
that these two peaks in HRIEUV are caused by either the TR or the coronal
contribution to the response function of the channel. Delays between peaks in
HRIEUV and in C iii are also observed. They can reach up to
$300\text{\,}\mathrm{s}$ for $\mathrm{E_{8}}$, which is the largest event
detected in $\mathrm{S_{1}}$ (Fig. 14 (c)). In that case, the C iii intensity
peak is after those of HRIEUV, suggesting a plasma cooling to chromospheric
temperature.

The EMs of all of the events (Fig. 13 and 15) shows that they are dominated by
plasma below $\log{T}=5.6$. Only the EM of $\mathrm{E_{7}}$ is clearly
enhanced for $\log{T}>5.6$ (Fig. 15 (b), bottom panel). We conclude the events
are dominated by plasma at chromospheric and TR temperatures, with some of
them barely reaching coronal temperatures.

Figure 11: HRIEUV images centred around the events detected in
$\mathrm{S_{1}}$ and $\mathrm{S_{2}}$ (see Table 3), that are not discussed in
Sect. 4. The red rectangles are the event regions, that are defined in section
3.1.

Figure 12: HRIEUV, SPICE, and AIA light curves for $\mathrm{E_{1}}$ (a),
$\mathrm{E_{3}}$ (b) et $\mathrm{E_{5}}$ (c). The vertical black lines
indicate the SPICE times closest to the HRIEUV peaks, when the EMs are
estimated in Fig. 13. The two background time intervals of two minutes,
defined in Sect. 3.2.1, are represented by two vertical blue lines in each
panel. The left blue line indicates the end of B1 (before the event), and the
right blue line indicates the start of B2 (after the event). $\mathrm{E_{5}}$
only includes $B_{1}$, as it is before another larger event. The upper limits
of the SPICE radiance are shown as horizontal dotted lines. When the line is
not detected above noise levels, the radiance is being replaced by its upper
limit, and the point is marked by a downward pointing arrow. This figure is
similar to Fig. 6 Figure 13:  EM estimated with the LOCI method of
$\mathrm{E_{1}}$ (a), $\mathrm{E_{3}}$ (b), and $\mathrm{E_{4}}$ (d) at the
time of their HRIEUV peaks, using four SPICE lines. The EMs of the event are
shown for each SPICE line with colored curves. Dotted curves indicate that the
radiance is an upper limit. The black full curves display the EM for the
event. The dotted and the dashed black lines are the EMs for the B1 and B2
background time intervals. B1 also includes upper limits in O IV for
$\mathrm{E_{2}}$ and in Ne VIII for $\mathrm{E_{4}}$. The black (event) and
grey (B1 and B2) regions delimit the 2$\sigma$ uncertainty of the EMs. This
Figure is similar to Fig. 7.

Figure 14: Same as Fig. 12, for $\mathrm{E_{6}}$, $\mathrm{E_{7}}$, and
$\mathrm{E_{8}}$. Figure 15:  Same as Fig. 13, for $\mathrm{E_{6}}$,
$\mathrm{E_{7}}$, and $\mathrm{E_{8}}$. Figure 16:  The HRIEUV (left panel)
and the SPICE images are centred around $\mathrm{E_{5}}$, at the time of its
peak in HRIEUV intensity on $\mathrm{S_{2}}$. The position of the slit is
displayed as a dashed line on the HRIEUV and the SPICE images. The two white
lines in HRIEUV delimit the field of view of the SPICE slit. The red rectangle
is the event region selected, and it is defined in Sect. 3.1.1. The
temperature ($\log{T}$) of the maximum emissivity of each SPICE line is
indicated within parentheses above each image. The latitude on the $y$-axis of
the SPICE images refers to the position of the slit marked with a white dashed
line. This Figure is similar to Fig. 2. Figure 17: Similar to Fig. 16, for a
small ($0.3\text{\,}\mathrm{Mm}$) dot-like event not clearly identified in
SPICE.  Figure 18: Similar to Fig. 16, for a loop-like event
($1.9\text{\,}\mathrm{Mm}$) not clearly identified in SPICE.

##  Appendix C Supplementary Material

Line | Event region | Region 1 | Region 2
---|---|---|---
| $I_{\mathrm{ev}}$ | $I_{\mathrm{th}}/I_{\mathrm{ev}}$ | $T_{\mathrm{eff}}$ | $I_{\mathrm{b1}}$ | $I_{\mathrm{th}}/I_{\mathrm{b1}}$ | $T_{\mathrm{eff}}$ | $I_{\mathrm{b2}}$ | $I_{\mathrm{th}}/I_{\mathrm{b2}}$ | $T_{\mathrm{eff}}$
O V⋆ 192.91 | $29.75\pm 1.97$ | $0.95$ | $5.40$ | $14.41\pm 2.98$ | $0.90$ | $5.40$ | $16.86\pm 1.93$ | $0.71$ | $5.40$
Fe VII 195.39 | $12.62\pm 1.15$ | $0.74$ | $5.52$ | $6.60\pm 1.08$ | $0.69$ | $5.52$ | $6.44\pm 0.93$ | $0.65$ | $5.52$
Fe VIII⋆ 194.66 | $14.41\pm 1.03$ | $1.08$ | $5.81$ | $6.56\pm 0.80$ | $1.09$ | $5.781$ | $8.41\pm 0.86$ | $0.86$ | $5.82$
Fe VIII 186.60 | $51.97\pm 3.80$ | $0.91$ | $5.82$ | $26.41\pm 2.36$ | $0.83$ | $5.79$ | $20.58\pm 2.72$ | $1.08$ | $5.83$
Fe VIII 185.21 | $66.17\pm 4.17$ | $1.04$ | $5.83$ | $28.66\pm 2.54$ | $1.10$ | $5.80$ | $31.21\pm 3.00$ | $1.03$ | $5.83$
Fe IX⋆ 188.49 | $32.47\pm 1.53$ | $0.88$ | $6.00$ | $11.44\pm 1.07$ | $1.00$ | $6.02$ | $17.00\pm 1.19$ | $0.93$ | $6.06$
Fe IX 197.86 | $10.73\pm 1.04$ | $1.25$ | $6.01$ | $5.83\pm 0.82$ | $0.94$ | $6.03$ | $5.60\pm 0.79$ | $1.39$ | $6.07$
Fe X 184.54 | $78.96\pm 4.54$ | $1.00$ | $6.09$ | $37.33\pm 3.57$ | $1.08$ | $6.14$ | $71.11\pm 4.49$ | $0.93$ | $6.13$
Fe X⋆ 190.04 | $27.75\pm 1.47$ | $0.93$ | $6.09$ | $15.22\pm 1.17$ | $0.87$ | $6.14$ | $30.78\pm 1.90$ | $0.70$ | $6.13$
Fe XI⋆ 188.21 | $248.20\pm 6.65$ | $1.04$ | $6.17$ | $183.67\pm 5.99$ | $1.04$ | $6.21$ | $255.50\pm 6.49$ | $1.05$ | $6.18$
Fe XII⋆ 195.12 | $493.54\pm 5.71$ | $0.99$ | $6.22$ | $456.49\pm 5.70$ | $0.99$ | $6.24$ | $527.55\pm 6.22$ | $0.98$ | $6.22$
Fe XIII⋆ 202.12 | $474.31\pm 8.87$ | N/A | $6.25$ | $502.77\pm 8.93$ | N/A | $6.26$ | $520.98\pm 9.35$ | N/A | $6.25$
Fe XIII⋆ 203.83 | $229.28\pm 10.39$ | N/A | $6.25$ | $207.45\pm 9.29$ | N/A | $6.26$ | $254.79\pm 10.74$ | N/A | $6.25$
Fe XIV 264.79 | $209.35\pm 8.24$ | $0.98$ | $6.29$ | $223.93\pm 8.20$ | $0.93$ | $6.29$ | $256.47\pm 8.99$ | $0.82$ | $6.29$
Fe XV 284.16 | $1053.09\pm 24.83$ | $1.01$ | $6.35$ | $980.05\pm 20.96$ | $1.02$ | $6.33$ | $1018.45\pm 25.12$ | $1.05$ | $6.34$
Fe XVI 262.98 | $40.01\pm 3.31$ | $0.90$ | $6.41$ | $35.35\pm 3.00$ | $0.87$ | $6.41$ | $52.83\pm 3.80$ | $0.67$ | $6.41$
Table 4: EIS line radiances and uncertainties (in
$\text{\,}\mathrm{mW}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{m}}^{-1}\text{\,}{\mathrm{sr}}^{-1}$),
fitted from the spectra averaged over the event $\mathrm{E_{10}}$ regions
(ev), and the background 1 (b1) and two (b2) regions. These values are used
for the calculation of the DEM shown in Fig. 8 (b). For each region, the ratio
of the reconstructed over the observed radiance is given for each line, along
with the logarithm of their effective temperature in Kelvin. The wavelengths
are in $\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, and the lines marked with a
star are blended. The Fe XIII lines are not used for the DEM inversion, so
their reconstructed to observed ratio is marked ”N/A”.  Figure 19: Same as Fig
3, for the HRIEUV intensity peak of $\mathrm{E_{9}}$ at 00:33:19 UTC. Figure
20: Images of HRIEUV and EIS centred around $\mathrm{E_{11}}$, visible in the
He II $256\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ line. The white dotted
lines show the position of the slit at 06:34:41 UTC, and the red rectangle is
an area centred around $\mathrm{E_{11}}$. The temperatures ($\log{T}$) of the
peak emissivity are indicated within parentheses for each line. Figure 21:
Averaged spectra over the event mask of $\mathrm{E_{9}}$ at 00:36:09 UTC (Fig.
2), along with the fitting of Gaussian functions. No Mg ix line is detected.
The temperature ($\log{T}$) of the peak emissivity is indicated within
parentheses for each line.

Figure 22: Contribution function of the SPICE (left) and EIS (right) lines
computed with CHIANTI V10.1, assuming a coronal abundance (Asplund et al.
2021), the recommended ionisation fraction by CHIANTI, and an electron density
equal to $n_{\mathrm{e}}=$
$1\text{\times}{10}^{9}\text{\,}{\mathrm{cm}}^{-3}$.