# Multi-wavelength observations by XSM, Hinode and SDO of an active region.
Chemical abundances and temperatures

G. Del Zanna DAMTP, Center for Mathematical Sciences, University of Cambridge,
Wilberforce Road, Cambridge, CB3 0WA, UK  B. Mondal Physical Research
Laboratory, Navrangpura, Ahmedabad, Gujarat-380 009, India  Indian Institute
of Technology Gandhinagar, Palaj, Gandhinagar, Gujarat-382 355, India  Yamini
K. Rao DAMTP, Centre for Mathematical Sciences, University of Cambridge,
Wilberforce Road, Cambridge CB3 0WA, UK  N. P. S. Mithun Physical Research
Laboratory, Navrangpura, Ahmedabad, Gujarat-380 009, India  S. V. Vadawale
Physical Research Laboratory, Navrangpura, Ahmedabad, Gujarat-380 009, India
K. K. Reeves Harvard-Smithsonian Center for Astrophysics, 60 Garden St, MS 58,
Cambridge, MA, 20138  H. E. Mason DAMTP, Centre for Mathematical Sciences,
University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK  A. Sarkar
Physical Research Laboratory, Navrangpura, Ahmedabad, Gujarat-380 009, India
P. Janardhan Physical Research Laboratory, Navrangpura, Ahmedabad, Gujarat-380
009, India  Anil Bhardwaj Physical Research Laboratory, Navrangpura,
Ahmedabad, Gujarat-380 009, India

###### Abstract

We have reviewed the first year of observations of the Solar X-ray Monitor
(XSM) onboard Chandrayaan-2, and the available multi-wavelength observations
to complement the XSM data, focusing on Solar Dynamics Observatory AIA and
Hinode XRT, EIS observations. XSM has provided disk-integrated solar spectra
in the 1–15 keV energy range, observing a large number of microflares. We
present an analysis of multi-wavelength observations of AR 12759 during its
disk crossing. We use a new radiometric calibration of EIS to find that the
quiescent AR core emission during its disk crossing has a distribution of
temperatures and chemical abundances that does not change significantly over
time. An analysis of the XSM spectra confirms the EIS results, and shows that
the low First Ionization Potential (FIP) elements are enhanced, compared to
their photospheric values. The frequent microflares produced by the AR did not
affect the abundances of the quiescent AR core. We also present an analysis of
one of the flares it produced, SOL2020-04-09T09:32. The XSM analysis indicates
isothermal temperatures reaching 6 MK. The lack of very high-T emission is
confirmed by AIA. We find excellent agreement between the observed XSM
spectrum and the one predicted using an AIA DEM analysis. In contrast, the XRT
Al-Poly / Be-thin filter ratio gives lower temperatures for the quiescent and
flaring phases. We show that this is due to the sensitivity of this ratio to
low temperatures, as the XRT filter ratios predicted with a DEM analysis based
on EIS and AIA gives values in good agreement with the observed ones.

atomic processes — atomic data — Sun: UV radiation — Sun: X-rays, gamma rays —
Ultraviolet: general – line synthesis

††journal: ApJ

##  1 Introduction

There is ample literature on observations and modelling of relatively large
flares, of GOES X-class C and above, but comparatively little on the weaker
flares in active region (AR) cores, despite the fact that they are much more
frequent. We define here microflares as those events of GOES class A or below,
not to be confused with larger flares, often also called microflares. The
physics of microflares remains elusive, as key spectroscopic observations to
study the evolution of 5–10 MK plasma have been lacking, as discussed in the
review by Del Zanna et al. (2021). The review points out the need for high-
resolution, high-sensitivity spectral imaging in the soft X-rays (100–150 Å)
to study microflares.

An earlier statistical study based on GOES X-ray and Yohkoh Bragg Crystal
Spectrometer (BCS) observations found a relationship between temperatures
($T_{\rm max}$) and X-ray emission measures (EM) at the peak of the X-ray
emission, with lower-class microflares generally having lower temperatures
(Feldman et al., 1996). A-class microflares had temperatures around 5 MK i.e.
close to the ‘basal’ 2–3 MK values of active region cores (cf Del Zanna &
Mason, 2018). One limitation of this and similar studies was the assumption
that the plasma was isothermal.

Yohkoh Soft X-ray Telescope (SXT) broad-band observations of microflares in AR
cores were used to obtain isothermal temperatures ranging between 4–8 MK
(Shimizu, 1995), lasting for 2–7 min.

The sensitivity of the SphinX X-ray irradiance spectrometer, on board the
CORONAS-PHOTON mission was higher than that of the earlier GOES X-ray
monitors, and showed that microflares are indeed very common. Some studies of
the general characteristcs of microflares, produced from the Bremsstrahlung
emission and the isothermal assumption (see, e.g. Kirichenko & Bogachev,
2017), found a relation between $T_{\rm max}$ and EM for the smaller events
that was different to that found by Feldman et al. (1996).

Studies of a few microflares, based on NuSTAR observations of the
Bremsstrahlung emission and again the isothermal assumption (see, e.g. Hannah
et al., 2019; Cooper et al., 2020; Duncan et al., 2021) have been published.
Temperatures were in the range 4–8 MK and little evidence of non-thermal
emission was generally found.

Several questions arise from previous studies of flares. First, is there a
relation between the highest temperatures in the post-flare loops and the
X-ray class ? The above-mentioned Feldman et al. (1996) study clearly
indicates that larger flares have higher temperatures at their peak X-ray
emission, but there are e.g. B-class flares that reach very different maximum
temperatures. In the example discussed below, a B-class flare did not reach 7
MK, while in the textbook case of another B-class flare, observed by Hinode
EIS (Culhane et al., 2007), a peak temperature of 12 MK was reached (Del Zanna
et al., 2011). Perhaps such differences are related to the physical size of
the flaring volume. A study of larger (GOES C8 class) flares by Bowen et al.
(2013) indeed indicated that the peak temperature (in the 10–20 MK range) is
inversely correlated with flare volume.

Second, is the isothermal assumption reasonable for small flares? To address
this question, detailed spectroscopic observations are needed. Some
information was obtained by Mitra-Kraev & Del Zanna (2019) with the analysis
of Hinode EIS observations of a microflare. This event was composed of a
bundle of strands being activated at similar times, with sizes that appeared
resolved at the AIA resolution, 1″. The EIS spectra indicated that these
strands had relatively low peak temperatures (about 4–5 MK) and were nearly
isothermal in their cross-section, although the 5–10 MK temperature range was
not well constrained (see also Winebarger et al., 2012, on the limitations in
this range). The EIS results were consistent with the broad-band observations
by the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA)
(Lemen et al., 2012) and Hinode XRT. Multi-wavelength observations of several
other microflares were studied by Mitra-Kraev & Del Zanna (2019), indicating
that the example provided was a ’typical’ case.

Another science questions about microflares relates to their possible
contribution to the basal heating in AR cores. This basal emission has peak
near-isothermal emission around 3 MK and does not significantly change its
characteristics over time (Del Zanna, 2013a; Del Zanna et al., 2015). Detailed
studies about the frequency of microflares have been lacking. They have
typical lifetimes of about 10 minutes as seen in the EUV (Mitra-Kraev & Del
Zanna, 2019). The older X-ray observations of AR cores from the Solar Maximum
Mission (SMM) X-ray polychromator (Acton et al., 1980) Bent Crystal
Spectrometer (BCS) also showed common weak flaring emission on those
timescales (Del Zanna & Mason, 2014), so it is possible that they were the
same type of events. The Mg xii images from CORONAS-PHOTON also show a peak in
the distribution of AR flaring events around 10 minutes (Reva et al., 2018),
although it is not clear if these are the same features (temperatures are
uncertain as Mg xii can be formed between 5 and 25 MK).

Larger flares such as the B-class textbook case (Del Zanna et al., 2011) show
quick chromospheric evaporation and filling of the flare loops with hot (above
10 MK) plasma, with a slow cooling phase where the plasma radiates at all
temperatures whilst draining back to the chromosphere. In contrast, microflare
loops are observed to cool down to nearly the background 3 MK, but then
drain/disappear very quickly and do not show emission at lower temperatures
(Mitra-Kraev & Del Zanna, 2019). This suggests that microflares do not
contribute to the basal emission in AR cores.

The chemical abundances of the flaring plasma also hold key information
related to the heating and cooling. The chemical abundances of low- FIP
elements such as Fe, Si, relative to those of high-FIP ones such as S,O,Ne
were found to be increased by a factor of about 3.2 (with respect to the
photospheric values) for AR cores, regardless of their size and age (Del
Zanna, 2013a; Del Zanna & Mason, 2014). This is the so-called FIP effect.

The FIP effect has gained a lot of interest in recent literature. It is most
likely caused by ion-neutral separation in the chromosphere, due to the
Ponderomotive force of trapped Alfven waves in magnetically-closed loops (see
references in Laming, 2015). Observationally, there has been a wide range of
different chemical abundances measured in coronal plasma, as reviewed by
Laming (2015); Del Zanna & Mason (2018). Regarding large flares, there is
ample evidence that the flare loops have near-photospheric abundances. We do
not have measurements of abundances in microflares, but if they were available
and were also photospheric, that would also provide an indication that
microflares do not contribute to the basal emission in AR cores.

The Solar X-ray Monitor (XSM) (Vadawale et al., 2014; Shanmugam et al., 2020)
onboard Chandrayaan-2 has been providing disk-integrated spectra in the 1 – 15
keV energy range since September 2019, providing temperatures, emission
measures, and absolute chemical abundances of a few elements, with timescales
of the order of a minute. XSM has a much greater sensitivity than previous
GOES X-ray monitors, and is able to observe microflares down to A 0.01 class.
A discussion of sub-A class flares during the minimum of solar cycle 24, and
which occurred outside of ARs was presented in Vadawale et al. (2021a). The
instrument has also been used to study the X-ray emission of the global quiet
Sun corona, which was found to be dominated by X-ray bright points. A
temperature close to 2 MK and a coronal FIP bias of about two were found
(Vadawale et al., 2021b).

XSM does not have enough sensitivity to measure chemical abundances for
individual microflares, but is able to do so for B-class flares. Mondal et al.
(2021) presented a time-resolved spectroscopic analysis of several B-class
flares occurring in AR cores. During the peak of the X-ray emission,
temperatures reached 6–8 MK, whilst the chemical abundances of Mg, Al, and Si
decreased towards their photospheric values. Similar decreases in the
abundances were found at the peaks of larger flares by the Miniature X-Ray
Solar Spectrometer (MinXSS) CubeSat (Woods et al., 2017; Moore et al., 2018).
During the gradual decay phase, the XSM measurements found that the chemical
abundances returned to their pre-flare coronal values. The MinXSS and XSM
measurements are the first observations of this kind, providing new
observational constraints to models of the atmosphere which include element
fractionation, such as those of Laming (2017).

To complement the XSM observations, in particular to understand the spatial
distribution of the X-ray emission observed by XSM, we have run several multi-
wavelength campaigns, including Hinode HOP 396. For this paper, we have
selected observations during March/April 2020, when a single AR (NOAA 12759)
crossed the solar disk and produced many microflares and several B-class
flares. The main aim of this paper is to present a multi-wavelength analysis
of Hinode XRT and EIS observations, combined with XSM and SDO/AIA during the
AR disk passage, to establish the active region core temperatures and
abundances, and discuss the temperatures of one of the flares, as measurable
by these instruments.

##  2 Observations and Data Analysis

We have analysed a large number of microflares observed by XSM during the
first period of operations and searched for suitable Hinode observations. We
have selected for presentation here observations of AR 12759 during its disk
crossing, as a direct comparison between the XSM irradiances and the signal
measured by the other instruments is straightforward, as this was the only AR
on the disk. Also, we selected one of the flares to study, which occurred on
Apr 9, as it had XRT coverage. EIS observed the AR in several instances during
its quiescent phase, but did not observe any flares.

Figure 1: Top: the XSM 1–15 keV light curve (count rates averaged over 1
minute and scaled by a factor of 5) during the disk crossing of AR 12759. The
red boxes indicate the scaled count rates from the full-disk Be-thin XRT
filter. Bottom: the XSM light curves during three key periods selected for
further analysis (see text).

###  2.1 XSM

XSM observes the Sun from a lunar orbit. It provides disk-integrated solar
spectra at every second in the energy range of 1-15 keV with an unprecedented
energy resolution of 180 eV at 5.9 keV (Mithun et al., 2020). The observed raw
(level-1) spectra at every second are stored in a day-wise data file. Since
the visibility of the Sun varies within the XSM field of view and the Sun also
gets occulted by the moon, the level-1 data contains both solar spectra as
well as non-solar background. We used XSM Data Analysis Software (Mithun et
al., 2021) to generate the level-2 science data product for the Solar
observations by selecting the Good Time Intervals (GTI) based on the observing
geometry and a few other instrumental parameters. To do a spectral analysis of
the XSM spectra we used the “chisoth” model (Mondal et al., 2021). This is a
local model of X-ray spectral fitting package (XSPEC) (Arnaud, 1996), meant
for the spectral fitting of the observed X-ray spectrum. The “chisoth” model
calculates the synthetic photon spectrum from a spectral library, generated by
using CHIANTI v.10. The model takes the logarithm of the temperature,
abundances of the elements with Z$=$2 to Z$=$30, and the volume emission
measure as input parameters.

Fig. 1 shows the XSM 2–15 keV lightcurve during the disk crossing of AR 12759.
By March 28 the outer part of the AR appeared outside the east limb, when the
X-ray ‘background’ increased. During its disk crossing, this AR (the only one
on the visible disc) produced many microflares. A few of the larger, B-class
flares have already been analysed by Mondal et al. (2021). In all those cases,
the behaviour of the chemical abundances was similar, i.e. the abundances were
closer to photospheric values during peak X-ray emission. By April 12 the core
of the AR was behind the west limb. This paper focuses on an analysis of the
quiescent emission from the AR during its disk crossing on the Apr 1, 4, 8 and
the B-class flare that peaked on Apr 9 around 9:12 UT. The XSM lightcurves for
Apr 1, 4, 9 are shown in Fig. 1 (bottom plots, on Apr 8 XSM did not observe).

###  2.2 Hinode XRT

We processed the XRT images using the standard SolarSoft procedures, paying
particular attention in removing saturated images and taking into account the
pointing information stored in the XRT database (SolarSoft dbase). To obtain
the temperatures, we used CHIANTI v.10 (Del Zanna et al., 2021) atomic data
and calculated the responses. The Al poly / Be thin filter ratio is
essentially insensitive to different chemical abundances 111See
http://solar.physics.montana.edu/takeda/xrt_response/xrt_resp_ch1000.html.

We have analysed full-Sun XRT synoptic observations during the AR disk
crossing. The averaged count rates in the Be-thin filter for a selection of
dates are shown in Fig. 1 as boxes, scaled by a normalization factor. There is
generally good agreement in the variability of the XRT signal in this filter
and the XSM count rates, as expected. This is because the XSM sensitivity is
close to that of this XRT filter. The XRT Be-thin full-disk images are also
very useful for checking that AR 12759, even during quiescence, is dominating
the full-disk signal. This means that the XSM signal is also dominated by the
active region, making a direct comparison between XSM and the other
instruments (XRT, EIS, AIA) possible.

There are also many XRT partial-frame observations of the active region during
its disk crossing, with the same filters. We have used one set for a direct
EIS/XRT cross-calibration.

For each XSM flare we searched for available XRT observations. As microflares
last about 10 minutes, it was essential to obtain an XRT cadence of about a
minute, which was obtained with a reduced FOV and the use of two filters. In
many instances, the automatic exposure control (AEC), a safety measure for the
instrument, was too slow to reduce the exposures, and the XRT images during
the peak of the microflares were saturated (the standard AEC works relatively
well for larger flares, as they have a longer duration). One observation which
we could use for analysis was the flare on Apr 9, produced by AR 12759, where
XRT used the Al-poly and Be-thin filters.

Figure 2: Top row: selected regions (boxes) of the AR 12759 core EIS
observations during its disk crossing on 2020 Apr 1, 4, and 8. The images show
the integrated radiances in the Hinode EIS Fe XVI 263 Å line, in calibrated
units. Middle row: SDO AIA 335 Å images during the EIS observations, in DN/s.
Bottom row: XRT Be-thin images (DN/s) at times close to the EIS observations.
All images are negative.

###  2.3 Hinode EIS

For each XSM flare we searched for available EIS observations,but found none.
However, there is an excellent set of observations of AR 12759 during its disk
crossing, allowing us to check the active region evolution.

To process EIS data, we used custom-written software which mostly follows the
standard SolarSoft programs, with the exception that the bias is subtracted
while doing the line fitting, and the particle hits are removed by averaging
procedures along the slit direction.

The main issue we faced in the analysis is related to the EIS radiometric
calibration, and its variations in time and wavelength. Del Zanna (2013b)
presented a significant revision of the ground calibration, with an additional
time-dependent decrease in the sensitivty of the long-wavelength channel,
however this was only valid until 2012, and indicated that further wavelength-
dependent corrections with time would eventually be needed. A long-term
programme was therefore started to analyse data after 2013 and provide a new
radiometric calibration. The preliminary results of this study (Del Zanna and
Warren, 2022, in prep) are used here. More details are provided in the
Appendix.

###  2.4 SDO/AIA

As EIS did not observe the flare on April 9, we used SDO AIA data to study the
thermal structure of the flare. We have used Mark Cheung’s Differential
Emission Measure (DEM) code (Cheung et al., 2015). As input we used averaged
images over 36 s (images at 3 consecutive times) from the six EUV AIA channels
(94, 131, 171, 193, 211, 335 Å) to derive EM maps. We took a minimum log $T$
[K] = 5.7 and 13 temperature bins of width 0.1 dex. The SDO/AIA response
functions were calculated using CHIANTI version 10 considering a constant
pressure of 1015 cm-3 K and chosen abundances. We used the effective areas
with the estimated degradation in the various channels as available within
SolarSoft, noting that such degradation was extrapolated from the last
calibration sounding rocket flight which flew in 2018. Hence, some additional
uncertainty is present.

##  3 Results

Figure 3: DEM for the AR core observed on 2020 Apr 1, obtained from Hinode
EIS. The points are plotted at the temperature $T_{\rm max}$, and at the
theoretical vs. the observed intensity ratio multiplied by the DEM value.
Table 1: List of emission lines from the 2020 Apr 1 active region core.
$\lambda_{\rm obs}$ (Å) is the measured wavelength. DN is the number of total
counts in the line, while $I_{\rm obs}$ is the calibrated radiance (phot cm-2
s-1 arc-second-2) obtained with our new EIS calibration. $T_{\rm max}$ and
$T_{\rm eff}$ are the maximum and effective temperature (log values in K), $R$
the ratio between the predicted and observed radiances, Ion and $\lambda_{\rm
exp}$ (Å) the main contributing line, and $r$ the fractional contribution to
the blend.

$\lambda_{\rm obs}$ | DN | $I_{\rm obs}$ | $T_{\rm max}$ | $T_{\rm eff}$ | $R$ | Ion | $\lambda_{\rm exp}$ | $r$
---|---|---|---|---|---|---|---|---
195.98 | 904 | 13.9 | 5.71 | 5.90 | 1.01 |  Fe viii | 195.972 | 0.85
275.36 | 361 | 52.0 | 5.79 | 5.92 | 0.85 |  Si vii | 275.361 | 0.99
280.73 | 62 | 17.4 | 5.79 | 5.93 | 0.75 |  Mg vii | 280.742 | 0.91
188.49 | 1920 | 61.2 | 5.94 | 6.05 | 0.87 |  Fe ix | 188.493 | 0.90
197.86 | 1580 | 29.1 | 5.96 | 6.07 | 0.86 |  Fe ix | 197.854 | 0.88
184.54 | 2610 | 194.0 | 6.05 | 6.14 | 0.94 |  Fe x | 184.537 | 0.94
192.81 | 6300 | 122.0 | 6.13 | 6.18 | 0.88 |  Fe xi | 192.813 | 0.94
180.40 | 2330 | 856.0 | 6.13 | 6.19 | 1.09 |  Fe xi | 180.401 | 0.97
271.98 | 1040 | 119.0 | 6.15 | 6.21 | 1.02 |  Si x | 271.992 | 0.97
192.40 | 13700 | 283.0 | 6.20 | 6.22 | 1.10 |  Fe xii | 192.394 | 0.96
264.23 | 830 | 97.2 | 6.18 | 6.24 | 0.73 |  S x | 264.231 | 0.98
202.05 | 10300 | 579.0 | 6.25 | 6.27 | 0.81 |  Fe xiii | 202.044 | 0.96
251.95 | 1500 | 379.0 | 6.25 | 6.27 | 1.00 |  Fe xiii | 251.952 | 0.97
188.67 | 1200 | 36.7 | 6.21 | 6.27 | 0.87 |  S xi | 188.675 | 0.58
|  |  |  |  |  |  Fe xii | 188.679 | 0.11
|  |  |  |  |  |  Fe xi | 188.630 | 0.13
281.41 | 102 | 30.4 | 6.26 | 6.30 | 0.90 |  S xi | 281.402 | 0.84
|  |  |  |  |  |  Fe xi | 281.367 | 0.13
285.83 | 83 | 46.0 | 6.27 | 6.31 | 0.73 |  S xi | 285.823 | 0.97
246.89 | 98 | 39.6 | 6.27 | 6.31 | 0.70 |  S xi | 246.895 | 0.98
264.78 | 6230 | 726.0 | 6.29 | 6.33 | 0.98 |  Fe xiv | 264.789 | 0.93
211.32 | 2660 | 913.0 | 6.30 | 6.33 | 1.07 |  Fe xiv | 211.317 | 0.97
278.27 | 31 | 7.1 | 6.32 | 6.36 | 0.69 |  P xii | 278.286 | 0.95
288.40 | 131 | 111.0 | 6.35 | 6.39 | 0.70 |  S xii | 288.434 | 0.98
284.15 | 10700 | 4620.0 | 6.34 | 6.40 | 1.15 |  Fe xv | 284.163 | 0.98
194.42 | 432 | 7.3 | 6.53 | 6.42 | 0.89 |  Ar xiv | 194.401 | 0.75
|  |  |  |  |  |  Fe xi | 194.442 | 0.13
256.68 | 2440 | 398.0 | 6.42 | 6.44 | 0.74 |  S xiii | 256.685 | 0.98
262.98 | 2200 | 263.0 | 6.43 | 6.44 | 1.00 |  Fe xvi | 262.976 | 0.96
249.18 | 680 | 227.0 | 6.48 | 6.47 | 0.65 |  Ni xvii | 249.186 | 0.96
193.88 | 1110 | 19.7 | 6.57 | 6.48 | 1.02 |  Ca xiv | 193.866 | 0.96
201.00 | 200 | 7.3 | 6.64 | 6.48 | 1.07 |  Ca xv | 200.972 | 0.84

###  3.1 EIS results for the quiescent AR core

Hinode EIS observed AR 12759 during its disk crossing with several studies. We
analysed the ATLAS_60 spectra, obtained with 60 s exposures on Apr 1,4, and 8
to obtain the DEM and the FIP effect in the AR core. There was no significant
variability in the AR core during these three observations, as seen in the XSM
light curves (cf Fig. 1, bottom plots) and as observed from XRT. For each
observation, we selected an AR core region using the intensity of the Fe XVI
263 Å line, as shown in Fig. 2. The figure also shows AIA 335 Å images, which
are dominated in the AR core by Fe XVI, and full-Sun XRT Be-thin images, which
show that the AR was dominating the signal from the Sun. The AIA full-disk
images were used to coalign EIS. The AR on Apr 1 was close to the east limb,
on the 4th it was close to meridian and on the 8th it was close to the west
limb.

We adopted the Del Zanna (2013a) chemical abundances, where the FIP bias is
3.2 (low FIP elements increased compared to their photospheric abundances) and
used CHIANTI v.10 to obtain DEMs. To calculate the line emissivities we used a
constant electron density of 2$\times$109 cm-3, a typical average AR value
which fits the main EIS density-sensitive line ratios. The DEM was obtained
using the method described in Del Zanna (1999), where the $DEM$ is assumed to
be a spline function, and considering only low-FIP ions.

The DEM for Apr 1st is shown in Fig. 3. Those for Apr 4, 8 are similar and are
shown in the Appendix. The plasma distribution in temperature has two peaks,
one around 1.5 MK, typical of the diffuse emission in the AR core, and one
around 3 MK, typical of the nearly isothermal hot AR core loops. Both
temperature structures have an FIP bias of about 3, as the main lines are well
reproduced within 20–30% (the uncertainty in the radiometric calibration).

Table 3 lists a small selection of the lines, showing a relatively good
agreement between the low FIP elements (e.g. Fe, Si, Ca) and the high-FIP
element argon. There are several argon lines in the EIS spectra, but they are
all extremely weak in AR core spectra and blended to some degree, some with
unknown transitions. The strongest line is an Ar XIV at 194.4 Å, very close to
a stronger unidentified line at 194.35 Å.

Note that sulphur has a FIP of 10 eV, but can be used as a proxy for the high-
FIP elements. In fact, in remote-sensing observations its variations are in
line with those of the high-FIP elements. The sulphur EIS lines are strong and
cover a wide temperature range, as are the iron lines, so the Fe/S results are
more accurate than Ar/Fe. A few weak lines from other elements (e.g. K, P, Al)
are also present and confirm the chosen abundances.

The Table also gives the total counts (DN) in the lines, as well as the
calibrated intensities. It also indicates $T_{\rm max}$, the temperature where
the line contribution function $G(T)$ has a maximum, and the effective
temperature $T_{\rm eff}$:

$T_{\rm eff}=\int G{\left({T}\right)}~{}DEM{\left({T}\right)}~{}T~{}dT/{\int
G{\left({T}\right)}~{}DEM{\left({T}\right)}~{}dT}\quad,$ (1)

that is an average temperature more indicative of where a line is formed.

The DEM results of the AR core regions selected for Apr 4th and Apr 8th are
similar, as shown in the Appendix, although the AR core on the 8th had a lower
emission in the high temperature peak. We also find, importantly, that the
chemical abundances of the quiescent AR core do not vary, regardless of the
age and the fact that many flares occurred. This result agrees with our
previous studies of several active regions.

###  3.2 XSM results for the quiescent AR core

Figure 4: XSM spectrum during the quiescent phase of AR 12759 (red and blue points with error-bars), together with the best fit model spectrum (red and blue solid lines) and the background signal (grey). The lower panel shows the residuals between observations and best fit model. Table 2: AR parameters obtained from the XSM spectrum. The abundances of Mg,Al, Si are in dex. The EIS abundances are the reference values of Del Zanna (2013a) adopted here. The Feldman are those listed by Feldman (1992), while the photospheric ones are from Asplund et al. (2009).  Date |  log10(T) | EM | Mg | Al | Si
---|---|---|---|---|---
| (K) |  (1046 cm-3) |  |  |
01-04-2020 | $6.47^{+0.01}_{-0.01}$ | $8.67^{+1.9}_{-1.9}$ | $7.78^{+0.07}_{-0.06}$ | $7.05^{+0.11}_{-0.12}$ | $7.89^{+0.05}_{-0.04}$
04-04-2020 | $6.50^{+0.02}_{-0.01}$ | $10.79^{+2.5}_{-1.7}$ | $7.72^{+0.1}_{-0.08}$ | $7.03^{+0.16}_{-0.17}$ | $7.82^{+0.06}_{-0.06}$
EIS |  |  | (8.10) | 6.95 | 8.00
Feldman |  |  | 8.15 | 7.04 | 8.10
Phot. |  |  | 7.6 | 6.45 | 7.51

To measure the absolute FIP effect in the AR core, we have analyzed the XSM
spectra of the quiescent AR on April 1 from 02:29:27 UT to 02:51:03 UT, and
April 4 from 09:30:11 UT to 09:53:49 UT, the timings of the EIS core
observations. Due to the presence of the single AR on the solar disk, the XSM
X-ray emission during this time was dominated by the AR core emission. We have
fitted the XSM spectra with a single temperature model by considering the
temperature, EM, and the abundances of Mg, Al and Si as a free parameters.
Figure 4 shows the XSM best fit model spectra (red and blue solid lined) along
with the observed ones (red and blue points). The best fitted parameters along
with the 1-$\sigma$ error-bars are given in Table 2. The isothermal
temperature of 3 MK agrees with the peak in the DEM as measured by Hinode EIS.
The absolute abundances of Mg, Al and Si are given in dex. The silicon feature
is the most prominent in the XSM spectra. The Si abundance is within 25% the
Del Zanna (2013a) AR core values. The Al abundance is also close, while the Mg
abundance as measured by XSM is lower. We note that the relative Al and Si
abundances were measured by Del Zanna (2013a) using lines formed at lower
temperatures, between 1 and 1.5 MK, while the Mg abundance was estimated by
assuming the same increase over the photospheric value as Si (the Mg lines in
the EIS spectra are formed at much lower temperatures). Del Zanna (2013a)
estimated the absolute abundances assuming a unitary filling factor and
measuring the path length of an AR core loop, so the agreement with the XSM
result is remarkable.

###  3.3 XRT temperatures and EIS / XRT cross-calibration

We have analysed several XRT observations of the AR (at non-flaring times),
and found consistently that the Be-thin/Al-Poly filter ratio has a value
around 0.13 in the AR core. This value is equivalent to a temperature of about
2 MK, significantly lower than the 3 MK measured by XSM. Also, as shown below,
the isothermal temperatures obtained from this XRT filter ratio are
significantly lower than those measured by XSM during the B-class flare.

We initially thought that this discrepancy could be due to an XRT calibration
issue. There have been several reports in the literature about a discrepancy
between the estimated and measured XRT count rates (see, e.g. Mitra-Kraev &
Del Zanna, 2019, and references therein), but not on possible problems in the
relative calibration of the two channels.

We also know that a leakage of visible light in some of the filters can
significantly affect some filter ratios (but not the Be-thin). Currently, it
is possible to correct for this leakage by subtracting specially selected
calibration images from full-frames, but not for partial frames. Also, the
leakage can be more pronounced in partial frames. So, we first checked Al-Poly
full-disk calibration data, which is essentially a flat field, and found that
the variations between the center and the edges of the FOV are within a few
DN/s, hence are negligible. Then we analysed several full-frame XRT synoptic
datasets, and obtained isothermal temperatures for the AR core. The central
part of the AR core is generally saturated in the synoptic observations
(either in the Al-Poly or the Be-thin), except the 1s exposures, where the
signal is often low, so combined images with different exposures need to be
used. The full-disk filter ratios consistently indicate a temperature of 2 MK,
i.e. the same as that obtained from the partial-frame filter ratios. We
therefore conclude that leakage of visible light does not affect the partial
frame Be-thin/Al-Poly observations of this active region.

Figure 5: Top: the EIS raster image in Fe xvi and an XRT Be-thin image of the
AR core. The selected box was used to obtain a DEM from EIS and averaged
signal in the XRT filters. Bottom: isothermal temperature (MK) map in the box
region, obtained from the Be-thin/Al-Poly filter ratio.

To investigate this issue further, we analysed the XRT observations on April 8
and performed a cross-calibration with EIS. A detailed pixel-by-pixel
comparison is difficult, as the two instruments have different spatial and
temporal resolutions, and as the EIS jitter is difficult to quantify. So we
opted for an overall cross-calibration of the whole AR core. We co-aligned the
XRT images against EIS/AIA. Three Be-thin averaged frames around 10 UT are
shown in Fig. 5 (top). We then obtained from the Be-thin/Al-Poly filter ratio
the isothermal temperature map in the AR core region (box), shown in Fig. 5
(bottom). The averaged temperature is 2 MK. The averaged XRT signal in the AR
core in each of the two filters changed by only a few percent during the EIS
observation. The averaged values are 31.6 DN/s in the Be-thin and 233.2 in the
Al-Poly, resulting in a ratio of 0.136. The ratio varied between 0.133 and
0.139 during the EIS scan of the AR core.

As we have a relatively reliable EIS absolute calibration, we can predict the
averaged AR core signal in the two XRT filters. The main issue here is the
chemical abundance of the elements. Having confirmed from the EIS and XSM
analysis that the Ar, S, Si, Fe abundances are consistent with the Del Zanna
(2013a) abundances, indicating an FIP effect of 3.2, we have assumed that the
abundances of the other elements contributing to the XRT bands (mainly O, Ne)
follow the same trend, which is consistent to the X-ray results obtained by
Del Zanna & Mason (2014).

We used the DEM obtained from EIS, which has two peaks, one around 1.8 MK and
one around 2.5 MK, and calculated the XRT signal using the current knowledge
of the XRT effective areas as available in SolarSoft. We obtained the
simulated spectra shown in the Appendix and an averaged value of 25 DN/s in
the Be-thin and 196 in the Al-Poly, resulting in a ratio of 0.128, i.e. only
6% lower than observed, and corresponding to an isothermal temperature of 2
MK. The absolute DN/s are also very close, within 26 and 19%, which is a
remarkable result, considering the uncertainty in the calibration of the
instruments and in the chemical abundances.

In conclusion, the lower isothermal temperatures obtained for the AR core by
the XRT Be-thin/Al-Poly filter ratio are simply due to the fact that the Al-
Poly is sensitive to low temperatures, so the isothermal temperature has a
significant contribution from the peak in the emission measure around 1.8 MK.

Figure 6: XRT negative images (top) and isothermal temperatures (bottom) for a
selection of times during the B-class flare on 2020 Apr 9. Figure 7:
Isothermal temperatures obtained from XSM and XRT during the Apr 9 9:30 UT
flare.

###  3.4 The 9:15 UT flare

The AR produced a B-class flare which started around 9:00 UT and finished by
9:50 UT. Fig. 6 shows a selection of XRT images and corresponding isothermal
temperatures obtained from the Be-thin/Al-Poly filter ratio. The two filters
had exposures within a few seconds, but several images were saturated and were
discarded. The flare started with an activation of a filament and a compact
X-ray emission. Later on, many flare loops became activated and occupied a
significant fraction of the AR core, reaching peak X-ray intensity around 9:15
UT.

From the XRT filter ratio we have also obtained the emission measure for each
pixel. We have then obtained averaged temperatures for the whole AR, weighted
by the EM values, to be compared to the isothermal temperatures obtained from
the spectral fitting of XSM. The XSM spectra were binned in time to increase
the signal to noise. The results are shown in Fig. 7. XSM indicates a peak
temperature of nearly 6 MK, while the peak temperature from XRT is much lower,
although the variations are similar. We have verified that the X-ray signal
from the AR is dominating over that from the whole Sun, looking at the full-
Sun X-ray Be-thin images. Therefore, the XRT temperatures should be directly
comparable to those of XSM.

We note that fitting the XSM spectra with a two temperature component (one for
the quiescent AR core emission and one for the flare emission) would result in
a slightly higher flare component, and the discrepancy would remain.

Figure 8: Top: SDO AIA EUV images at 9:12 UT, during the peak of the
microflare. Bottom: DEM in selected temperature bins obtained from the images.

As the isothermal assumption is clearly an approximation for both the XSM and
XRT datasets, we have explored the effects that a DEM distribution has for
this flare. We selected a time close to the peak, at 9:12 UT, and obtained a
DEM from the six AIA coronal images. We averaged the AIA data over a minute
around 9:12 UT. Fig. 8 (top) shows the AIA EUV images. Hot emission is visible
in the AIA 94 Å band, due to Fe xviii, as described in Del Zanna (2013a). Note
that the filament is still visible in absorption at this wavelengths, but not
in the XRT X-ray images. It is clear from inspection of the other AIA channels
that this flare did not reach temperatures above 10 MK, otherwise the Fe xxi
line would have contributed to the 131 Å band.

Figure 9: Averaged volume EM obtained from the AR core AIA EUV images at 9:12
UT.  Figure 10:  XSM averaged spectrum at 9:12 UT, near the peak, with the
predicted spectrum (red) based on the AIA EM.

To obtain a DEM from the AIA data it is necessary to adopt a set of chemical
abundances. Note that the AIA bands are dominated by Fe lines, while the XRT
filters have contributions from Fe, Ne, O, Mg, and other elements. XSM can
reliably measure the Si abundance, but also provides abundances for other
elements. We performed an analysis of the XSM spectra around 9:12 UT and from
the line to continuum we obtained for Si, Mg, Al, and S, the following
absolute abundances: 7.7, 7.5, 6.5, and 7.1 dex. The Mg, Al, and S are close
to the photospheric values, while the Si abundance is between photospheric
(7.51 dex) and the Del Zanna (2013a) coronal value (8.0 dex). We used these
values for the DEM analysis.

For the other elements we have assumed the hybrid abundances tabulated in the
CHIANTI file "sun_coronal_fludra_1999_ext.abund", as they provide an
intermediate FIP fractionation which is close to the results obtained from the
low-FIP Si and the mid-FIP S, used as a proxy for the high-FIP elements. For
example, the Fe hybrid abundance is 7.83 dex (i.e. between the photospheric
value of 7.50 and the coronal value of 8.0 dex, as Si), and the O, Ne hybrid
abundances are actually close to the photospheric values recommended by
Asplund et al. (2009).

The resulting column EM values for a range of temperatures are shown in Fig. 8
(bottom). We note that the high temperatures are not well constrained, as the
only hot channel with signal was the AIA 94 Å. For this reason, the maximum
temperature for the inversion was set to log $T$[K]=6.9.

From the column EM values we calculated a volume EM by averaging the emission
measures over the core of the microflare, in a region covering 100 * 50 pixels
in the x and y direction, respectively. The resulting volume EM is shown in
Fig. 9. We then used this volume EM to predict the XSM spectrum, which is
shown, together with the observed one, in Fig. 10. There is excellent
agreement between the two, indicating a reliable cross-calibration between AIA
and XSM.

We then preformed forward modelling of the XRT signal, using the same EM and
chemical abundances. We obtained 222 and 1019 DN/s for the Be-thin and Al-Poly
filters, respectively. This results in a ratio of 0.22, equivalent to an
isothermal temperature of 4 MK, nearly the same value obtained from the filter
ratio. We note that adopting a very different set of chemical abundances does
not change the result. In fact, with the photospheric values recommended by
Asplund et al. (2009) or with the Feldman (1992) coronal values we obtain a
ratio of 0.23, i.e. still 4 MK.

##  4 Discussion and conclusions

After a multi-wavelength survey of dozens of microflares and B-class flares
during the first period of operation of the XSM monitor, it became clear how
difficult it is to obtain reliable measurements of these weak, fast evolving
events. XSM X-ray spectra have been great at providing an overview of how
common microflares are in AR cores (even though many small heating events also
occur outside ARs). Given its medium resolution, a multi-temperature analysis
is difficult. However, the instrument has the great capability to measure the
absolute chemical abundances for flares of B-class or above.

Trying to catch a flare with a slit spectrometer such as EIS is notoriously
difficult, especially for microflares, as they only last 10 minutes or so. The
information that can be telemetered is also limited, so are the diagnostics.
On the basis of the present analysis, we developed and tested new EIS
observing sequences for additional diagnostics.

During the multi-wavelength campaign, we also learned how to adjust the AEC to
avoid saturation in the XRT filters as much as possible. On the basis of the
present analysis, we have run new XRT observing sequences with different
filters, as the Be-thin/Al-Poly provides isothermal temperatures which are
much lower than the peak values. With a direct comparison between simultaneous
EIS and XRT observations we were able to explain this result, due to the
sensitivity of the Al-Poly filter to lower temperatures. The improved XRT
observations will be discussed in a following paper.

One important result of our analysis regards the quiescent AR core emission
during its disk crossing, which was found to have a distribution of
temperatures and chemical abundances that did not change significantly over
time. The XRT, EIS and XSM observations were all consistent with each other.

Most of the emission in the AR core was around 1.5 and 3 MK. As the XSM signal
was dominated by the AR core, we were also able to obtain another result: the
XSM spectra during quiescence indicate a FIP bias of about 2.5$\pm$0.2,
adopting the silicon value. This result is important, as previous measurements
did not clearly assess if it was the low-FIP elements that are enhanced in AR
cores or the high-FIP ones to be depleted, relative to their photospheric
values. The EIS observations indicate that the Fe/Si vs. Ar/S abundances are
increased by about a factor of about 3 over the photospheric value. Combining
the XSM and EIS results therefore indicates that the argon and sulphur
abundances are slightly below their photospheric values. Such observations fit
the nanoflare-heated scenario, where high-frequency nanoflares cause this
relatively steady basal heating, and the Alfven waves excited by them cause
the chemical fractionation. In fact, in the physical model discussed by Laming
et al. (2019), a closed magnetic loop behaves as a resonant cavity, where the
waves bounce from footpoint to the other, with a travel time that is an
integral number of the wave half periods. In such case, the ponderomotive
force creates a fractionation of the elements at the top of the chromosphere,
where most of the hydrogen is ionized, and elements with a FIP around 10 eV
such as sulphur are predicted to behave as the high-FIP elements.

In our previous study (Mondal et al., 2021), we used XSM data to show for the
first time that chemical abundances of low-FIP elements quickly decrease
towards photospheric values in B-class flares, with a return towards coronal
values during the gradual phase. AR 12759 produced many such flares during its
disk crossing, but clearly such variations did not affect the abundances of
the AR core. In our previous paper, we have suggested possible reasons for
such abundance variations, pointing out the need for a model to explain the
observations.

It may well be that the same physical processes (e.g. magnetic reconnection in
the corona) heat the basal AR cores and the flare loops, but produce very
different signatures: low-energy and high-frequency nanoflares would slowly
evaporate already fractionated plasma from the top of the chromosphere, while
B-class flares deposit their energy deeper in the chromosphere, causing a
faster evaporation of un-fractionated plasma.

The abundance variations during a flare could be used as a diagnostic to
assess if the low-energy tail of the distribution of microflares is causing
the basal active region heating. Ideally, one would therefore want to see if
also microflares have similar abundance variations as B-class flares. If they
do, this would be an argument in favor of microflares not contributing to the
basal AR core heating.

One of our aims was to provide estimates of the spatial and temperature
distribution of the flare loops producing the XSM signal using multi-
wavelength observations, to complement the analysis of the X-ray full-Sun
spectra. The information on the spatial distribution is provided by the AIA
and XRT, but the temperature distribution turned out to be difficult to
estimate. The AIA analysis was limited, with only one hot band responding to
the flare (the 94 Å). Assuming a continuous multi-thermal emission, we
obtained from AIA a strong peak around 3 MK and a secondary (flare) emission
around 6-7 MK. The 3 MK emission is mostly background/foreground quiescent
emission of the AR core. We are encouraged by the excellent agreement between
the X-ray XSM spectra as predicted from the AIA DEM modelling and the observed
values, especially considering the uncertainty in the AIA calibration.
However, the isothermal approximation fits the XSM spectra equally well to a
multi-thermal distribution. Clearly, the isothermal temperatures from the XSM
analysis are more representative of the ‘true’ peak flare temperatures than
those from the XRT Be-thin/Al-Poly filter ratio, as the latter has a bias
towards the lower temperatures. However, multi-thermal emission is clearly
present and should be taken into account whenever suitable observations are
available.

Better estimates of the temperature distribution can be obtained from
spectroscopic observations or from AIA when temperatures well above 7 MK are
present, as Fe XXI becomes visible in the AIA 131 Å (and also Fe XXIV in the
193 Å band). Also, the XSM spectra of higher-T flares are very different, not
just in terms of slope of the continuum, but also in terms of line emission.

In some respects we were surprised to see a low maximum temperature of about
6-7 MK from this B-class flare, as smaller flares often do produce much higher
temperatures, as in the Del Zanna et al. (2011) example. In this case it is
clear that the higher GOES class is simply due to the presence of an extended
set of flare loops, which fits with the conclusions on the C-class flares by
Bowen et al. (2013) that flares with larger volumes have lower maximum
temperatures.

Further improvements on our understanding of small flares is achievable with
current instrumentation and modelling, but as we mentioned in the
introduction, key new high-resolution spectroscopic observations are needed.

GDZ and HEM acknowledge support from STFC (UK) via the consolidated grants to
the atomic astrophysics group at DAMTP, University of Cambridge (ST/P000665/1.
and ST/T000481/1). KKR acknowledges support from the NASA HSO Connect program,
grant number 80NSSC20K1283. AB was a J.C. Bose National Fellow during the
period of this work. We acknowledge the use of data from the Solar X-ray
Monitor (XSM) on board the Chandrayaan-2 mission of the Indian Space Research
Organisation (ISRO), archived at the Indian Space Science Data Centre
(ISSDC).XSM was developed by Physical Research Laboratory (PRL) with support
from various ISRO centers. Research at PRL is supported by the Department of
Space, Govt. of India. The collaboration between the PRL and Cambridge groups
has been facilitated through the Royal Society Grant No. IES-R2-170199. Hinode
is a Japanese mission developed and launched by ISAS/ JAXA, with NAOJ as
domestic partner and NASA and STFC (UK) as international partners. It is
operated by these agencies in cooperation with ESA and NSC (Norway). AIA data
are courtesy of SDO (NASA) and the AIA consortium. CHIANTI is a collaborative
project involving the University of Cambridge (UK), George Mason University,
and the University of Michigan (USA). We thank the referee for useful comments
on the manuscript.

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##  Appendix A Further details

Fig. 11 shows the two DEMs for the AR core observed on 2020 Apr 4 and 8
obtained from Hinode EIS, while Tables A,A provide the details.

Figure 11: DEM for the AR core observed on 2020 Apr 4 and 8 obtained from
Hinode EIS. The points are plotted at the temperature $T_{\rm max}$, and at
the theoretical vs. the observed intensity ratio multiplied by the DEM value.
Table 3: List of emission lines from the 2020 Apr 4 active region core.
$\lambda_{\rm obs}$ (Å) is the measured wavelength. DN is the number of total
counts in the line, while $I_{\rm obs}$ is the calibrated radiance (phot cm-2
s-1 arc-second-2) obtained with our new EIS calibration. $T_{\rm max}$ and
$T_{\rm eff}$ are the maximum and effective temperature (log values in K), $R$
the ratio between the predicted and observed radiances, Ion and $\lambda_{\rm
exp}$ (Å) the main contributing line, and $r$ the fractional contribution to
the blend. Table 4: List of emission lines from the 2020 Apr 8 active region
core. $\lambda_{\rm obs}$ (Å) is the measured wavelength. DN is the number of
total counts in the line, while $I_{\rm obs}$ is the calibrated radiance (phot
cm-2 s-1 arc-second-2) obtained with our new EIS calibration. $T_{\rm max}$
and $T_{\rm eff}$ are the maximum and effective temperature (log values in K),
$R$ the ratio between the predicted and observed radiances, Ion and
$\lambda_{\rm exp}$ (Å) the main contributing line, and $r$ the fractional
contribution to the blend.

##  Appendix B EIS calibration

A DEM analysis was applied to off-limb quiet Sun observations close in time to
the observations discussed here, to obtain the relative EIS calibration using
the strongest coronal lines. The advantage is that the plasma is nearly
isothermal and isodensity, and removes from the coronal lines blending with
cool lines. This is an extension of the method used by Warren et al. (2014),
where strict isothermality was assumed. The line ratio method adopted in Del
Zanna (2013b) was also extended, using both quiet Sun and Active region
observations. The calibration relative to AIA was also assessed, as was AIA
against SDO EVE. Further details are given in Del Zanna and Warren (2022).

##  Appendix C XRT forward modelling

Fig. 12 shows the simulated XRT signal for the quiescent AR core on Apr 8.

Figure 12: Simulated XRT signal for the quiescent AR core on Apr 8.