# Coronal Densities, Temperatures and Abundances During the 2019 Total Solar
Eclipse:
The Role of Multi-Wavelength Observations in Coronal Plasma Characterization

Giulio Del Zanna DAMTP, CMS, University of Cambridge, Wilberforce Road,
Cambridge CB3 0WA, UK  Jenna Samra Center for Astrophysics $|$ Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA, 02138, USA  Austin Monaghan
HAO, National Center for Atmospheric Research, P.O. Box 3000, Boulder CO
80307-3000, USA  Chad Madsen Center for Astrophysics $|$ Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA, 02138, USA  Paul Bryans HAO,
National Center for Atmospheric Research, P.O. Box 3000, Boulder CO
80307-3000, USA  Edward DeLuca Center for Astrophysics $|$ Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA, 02138, USA  Helen Mason  DAMTP,
CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK  Ben
Berkey  HAO, National Center for Atmospheric Research, P.O. Box 3000, Boulder
CO 80307-3000, USA  Alfred de Wijn HAO, National Center for Atmospheric
Research, P.O. Box 3000, Boulder CO 80307-3000, USA  Yeimy J. Rivera Center
for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA,
02138, USA

###### Abstract

The Airborne Infrared Spectrometer (AIR-Spec) offers an unprecedented
opportunity to explore the Near Infra-Red (NIR) wavelength range. It has been
flown at two total solar eclipses, in 2017 and 2019. The wavelength range of
the much improved instrument on the second flight (July 2, 2019) was shifted
to cover two density sensitive lines from S XI. In this paper we study
detailed diagnostics for temperature, electron density and elemental
abundances by comparing results from AIR-Spec slit positions above the east
and the west limb with those from Hinode/EIS, the PolarCam detector and
SDO/AIA. We find very good agreement in the electron densities obtained from
the EIS EUV line ratios, those from the NIR S XI ratio and those obtained from
the polarized brightness PolarCam measurements. Electron densities ranged from
Log Ne [cm${}^{-3}]$ = 8.4 near the limb, falling to 7.2 at $R_{0}=1.3$. EIS
spectra indicate that the temperature distribution above the west limb is
near-isothermal at around 1.3 MK, while that on the east has an additional
higher-T component. The AIR-Spec radiances in Si X and S XI as well as the AIA
data in the 171, 193, and 211 Å bands are consistent with the EIS results. EIS
and AIR-Spec data indicate that the sulphur abundance (relative to silicon) is
photospheric in both regions, confirming our previous results of the 2017
eclipse. The AIA data also indicate that the absolute iron abundance is
photospheric. Our analysis confirms the importance of the diagnostic potential
of the NIR wavelength range, and that this important wavelength range can be
used reliably and independently to determine coronal plasma parameters.

Solar coronal lines (2038); Solar instruments (1499); Total eclipses (1704);
Spectrometers (1554)

††journal: The Astrophysical Journal

##  1 Introduction

The visible forbidden lines provided the first detailed information about the
plasma conditions in the solar corona, with several spectroscopic observations
carried out in the 1950’s to 1970’s (see the review in Del Zanna & DeLuca,
2018). Since then, most observations have been carried out at shorter
wavelengths in the XUV. However, there is now renewed interest in the
forbidden lines in the visible and especially in the near-infrared (NIR). This
is partly because these lines are significantly enhanced due to photo-
excitation (PE) from the solar disk radiation, hence are easier to measure out
to greater distances from the solar limb, compared to the XUV lines, as shown
e.g. by Habbal et al. (2011) using observations of visible lines.

There have been many studies from the ground based on the visible lines during
total eclipses, as for example Ding & Habbal (2017); Koutchmy et al. (2019).
For a recent review of such observations see Habbal et al. (2021).

In this paper, we focus on the NIR lines, as they offer the possibility for
routine coronal magnetic field measurements via the Zeeman and Hanle effects
(see, e.g. Judge, 1998; Judge et al., 2001), partly thanks to recent
improvements in NIR detectors. Also, measurements of non-thermal widths are
easier to obtain in the NIR than the EUV (for a recent attempt to measure non-
thermal line widths in the EUV see Del Zanna et al. 2019). The NIR lines offer
in principle the same spectral diagnostic applications as the XUV lines, in
terms of measurements of electron densities, temperatures, and elemental
abundances from line ratios (see Del Zanna & DeLuca, 2018). Such measurements
are fundamental constraints to physical models of the middle corona, the
almost unexplored region between 1.5 and 3 solar radii, as reviewed by West et
al. (2022).

Densities and temperatures are obvious key parameters. It has been recognised
in the literature that it is also important to measure elemental abundances.
It is now well established that coronal abundances, depending on the feature
observed, are different to the photospheric ones. Variations are strongly
correlated with the FIP (First Ionization Potential) of an element, with
generally low FIP elements being enhanced, relative to the high-FIP ones (the
so-called FIP effect). The variations are likely related to the plasma heating
processes in the chromosphere (where neutrals are ionized). Also, in principle
they are not significantly modified once established in the corona, so could
be used as a tracer of the origin of the solar wind streams, whenever
elemental abundances are measured in-situ. For details, see the Solar Living
Reviews by Laming (2015) and Del Zanna & Mason (2018).

For the above (and other) reasons, several missions have recently included
diagnostics of NIR lines. Various space-based missions such as ESA’s Proba-3
and the first Indian large solar mission Aditya will observe several forbidden
lines. On the ground, UComp, an improved version of the successful Coronal
Multi-Channel Polarimeter (CoMP) is now operational (Landi et al., 2016;
Tomczyk & Landi, 2019; Tomczyk et al., 2021). A major new facility is the
Daniel K. Inouye Solar Telescope (DKIST, Tritschler et al., 2016; Rimmele et
al., 2020). The main coronal instrument, the Cryogenic Near Infrared
Spectropolarimeter (Cryo-NIRSP, https://atst.nso.edu/inst/cryonirsp) will make
regular observations, but only close to the solar limb and with a small field
of view (FOV). In addition, we note that any ground-based telescope is
strongly limited by atmospheric absorption, except in a few spectral regions.

Cryo-NIRSP is planning to observe a few lines that are known to be observable,
but the NIR is in principle rich in other diagnostics. As the NIR is an almost
unexplored spectral region in solar physics, the Airborne Infrared
Spectrometer (AIR-Spec, Samra et al. 2022) was funded by the NSF and developed
by Smithsonian Astrophysical Observatory (SAO) to explore the NIR.

The instrument has observed the quiescent solar corona during two eclipses, in
2017 and 2019, flying on-board the NSF/NCAR Gulfstream V (GV) at an altitude
of 12 km, where atmospheric absorption is much reduced. The long slit of the
instrument allows measurements of the outer corona, at far greater heights
than Cryo-NIRSP.

The 2.853 µm Fe IX line was detected for the first time during the first
flight (Samra et al., 2018, 2019). Multi-wavelength observations during the
2017 eclipse were presented in Madsen et al. (2019), and used to measure
electron densities, ionization temperatures (i.e. temperatures obtained from
lines of different ions, assuming ionization equilibrium), and elemental
abundances. The results were close to those obtained from an analysis of
earlier SoHO SUMER and UVCS observations of quiescent streamers during solar
minimum (Del Zanna et al., 2018). The electron densities were obtained from
EUV line ratios observed by the Hinode Extreme Ultraviolet Imaging
Spectrometer (EIS, Culhane et al., 2007). Emission measures obtained from both
AIR-Spec and EIS indicated a near-isothermal temperature distribution, and,
perhaps surprisingly, nearly photospheric abundances (Asplund et al., 2009) in
terms of relative abundance between Sulphur and Silicon.

The second flight observed the July 2, 2019 total solar eclipse with a much
improved and modified instrument. The wavelength coverage was shifted so as to
observe the 1.4 µm S XI line, to obtain electron densities directly from the
ratio with the 1.9 µm S XI line. The observations and preliminary results from
this eclipse are described in Samra et al. (2022). The observations were
successful and the 1.4 µm S XI line was recorded for the first time, although
careful atmospheric modeling was required to measure its intensity.

Figure 1: False-color images of the solar corona during the 2019 total eclipse
in three SDO AIA channels. The bottom right image is a composite obtained from
AIA 171 Å (green) and 211 Å (red). The AIR-Spec slits and EIS fields of view
are shown in white. Figure 2: Predicted and measured radiance of the main four
AIR-Spec lines above the east and west limbs. The hotter S XI lines are
stronger above the east limb while the cooler Fe IX line is stronger above the
west limb. Predictions with (full line) and without (dashed line)
photoexcitation were made using the quiescent streamers density model of Del
Zanna et al. (2018) and an isothermal temperature of 1.3 MK. This model fits
the west region best, but does not represent well the east region.  Figure 3:
Narrowband images of the solar corona during the 2019 total eclipse in Fe X
637.4 nm, Fe XI 789.2 nm, Fe XIII 1074.7 nm, and Fe XIV 530.3 nm (private
communication S. Habbal to J. Samra, image credit S. Habbal and M.
Druckmüller). The AIR-Spec slits are overlaid in green.

As we did in 2017, we coordinated multi-wavelength observations for the 2019
eclipse, in particular with the Hinode EIS instrument and the ground-based
PolarCam, a novel micro-polarizer camera. The effectiveness of this camera for
solar observing was demonstrated during the 2017 total solar eclipse, where
polarized brightness (pB) measurements showed good agreement with the pB
observations of the dedicated solar observatory COSMO K-Coronagraph (K-Cor) in
Mauna Loa, Hawaii (Judge et al., 2019). For the 2019 eclipse described here,
the High Altitude Observatory (HAO) in Boulder organised an expedition to the
Cerro Tololo Inter-American Observatory (CTIO) in Chile, taking polarization
measurements in white light with PolarCam.

We note that other studies of the 2019 eclipse, based on observations in the
visible, have been published. Boe et al. (2022) presented narrowband images,
and Hanaoka et al. (2021) used pB continuum images. In this paper, we present
an analysis of the AIR-Spec data, to obtain measurements of electron
densities, ionization temperatures, and elemental abundances. We validate and
compare these results to those obtained from Hinode EIS, PolarCam, and SDO AIA
observations.

##  2 Eclipse observations

###  2.1 AIR-Spec

AIR-Spec observed for about 7 minutes during totality on July 2, 2019
(19:18:16 – 19:26:48 UT) in 9 slit positions. Details of the observation and
data processing are described in Samra et al. (2022). The main lines that were
observed are listed in Table 1, with their typical formation temperatures (the
ranges of temperatures where these lines can be formed are shown in the
Appendix in Figure 12). We discuss here the observations on the east and west
limb, which are co-spatial with the Hinode EIS observations.

Table 1: AIR-Spec target lines.  Ion |  $\lambda$ (nm) | T (MK) | Transition (Upper $\rightarrow$ Lower)
---|---|---|---
S XI | 1393 | 1.9 | 2s22p2 ${\rm{{}^{3}}{P_{2}}}$ $\rightarrow$ 2s22p2 ${\rm{{}^{3}}{P_{1}}}$
Si X | 1431 | 1.3 | 2s22p ${\rm{{}^{2}}{P^{o}_{\nicefrac{{3}}{{2}}}}}$ $\rightarrow$ 2s22p ${\rm{{}^{2}}{P^{o}_{\nicefrac{{1}}{{2}}}}}$
S XI | 1921 | 1.9 | 2s22p2 ${\rm{{}^{3}}{P_{1}}}$ $\rightarrow$ 2s22p2 ${\rm{{}^{3}}{P_{0}}}$
Fe IX | 2853 | 0.8 | 3s23p53d ${\rm{{}^{3}}{F^{o}_{3}}}$ $\rightarrow$ 3s23p53d ${\rm{{}^{3}}{F^{o}_{4}}}$

Figure 1 shows a false-color SDO AIA image obtained from the 171 Å (green) and
211 Å (red) channels, and the locations of the AIR-Spec east and west slits,
as well as the pointings of the EIS slit close to the limb. It is well
established that in the outer corona the 171 Å broad-band is dominated by Fe
IX, formed around 1 MK, while the 211 Å has a significant contribution from Fe
XIV, formed around 2 MK, together with contributions from several other
coronal lines formed at lower temperatures such as those from Fe XIII. It is
therefore already clear from Figure 1 that the corona in the east limb is
hotter than that on the west. We will return to this issue below.

The actual pointing of the AIR-Spec slit varied in time during the eclipse.
The precise pointing of each exposure was obtained using the context images
from the white light slit-jaw camera. As the solar corona was quiescent,
exposures were averaged and data spatially binned to increase the signal to
noise.

We obtained measurements of the radiances of S XI 1.393 and 1.921 µm, as well
as the strong Si X 1.431 µm and the weaker Fe IX 2.853 µm above the east and
west limb, as shown in Figure 2. It is clear that the corona in the west and
east is similar in Si X, which is formed around 1.3 MK, while it is
significantly different as seen in S XI which is normally formed at higher
temperatures. In principle, the differences in the two regions could also be
due to different Si/S relative abundances, although we will show below that
the difference is actually due to higher temperatures being present in the
east.

Figure 2 also shows the values predicted from the quiescent streamers density
model of Del Zanna et al. (2018), photospheric abundances and an isothermal
temperature of 1.3 MK, on the basis of the measurements discussed below. It is
clear that such a model represents quite well the radiances in the west
region. We do not attempt to model the east region as it is multi-thermal.

In Figure 3, we show the AIR-Spec slits overlaid on the narrowband images
described in Boe et al. (2022). The narrowband images are credited to S.
Habbal and M. Druckmüller and were provided to J. Samra in a private
communication from S. Habbal. It is clear from the Fe XIII and Fe XIV overlays
that AIR-Spec sampled hotter material on the east limb than on the west, which
agrees with the electron temperature inferred in Boe et al. (2022). Section
3.3 provides quantitative support for this conclusion.

###  2.2 EIS

Hinode EIS carried out two main ‘rasters’, where the 2″ slit scanned a 60″
off-limb region with 120 s exposure times, resulting in a total duration of
about one hour. The first raster started at 18:36:42 UT above the east limb,
and ended at 19:37:37, just after the end of totality. The second raster
started shortly after the end of totality, at 20:15:41 UT, and scanned a
region above the west limb. The full EIS spectral range, i.e. all of the short
(SW) and long (LW) wavelength channels were telemetered. The maximum number of
detector pixels along the slit, 512, were telemetered.

The EIS data were processed with custom-written software (see, e.g. Del Zanna
et al., 2011) which largely follows the standard SolarSoft eis_prep program.
The hot and warm pixels (i.e. pixels with anomalous counts), and those
affected by particle events are flagged as ‘missing’. We used the SolarSoft
database for the hot and warm pixels. One difference with the standard
software is that the missing pixels are then replaced with values interpolated
along different directions, and the results are visually inspected. Despite
this procedure, the spectra are very noisy. First, this is because of the low
signal. Second, this is because the long exposures resulted in a large number
of cosmic ray hits. Third, this is because the EIS detector has degraded so
much in the past few years that a large area is affected by warm pixels, only
some of which are included in the database. Other differences with the
standard software are that the spectra are rotated, to remove the geometrical
slant, and the fitting of the lines is carried out on the spectra in data
numbers (DN), fitting the bias with a polynomial. To further proceed with the
EIS analysis, we encountered two major problems, concerning the radiometric
calibration and the pointing, as described below.

####  2.2.1 EIS radiometric calibration

An accurate radiometric calibration, at least in relative terms, is necessary
to measure all the key plasma parameters. For example, the best measurements
for the electron density for the present observations are obtained from the
ratio of the Fe XII 186.8 and 192.4 Å lines, as other diagnostic lines e.g.
from Fe XIII were very weak. The relative calibration at 186.8 and 192.4 Å is
not well known and has been changing over time. Del Zanna (2013a) presented a
significant revision of the ground calibration which only applied to data up
to 2012. Indications of time-dependent changes were also found, a problem
later confirmed by Warren et al. (2014). Warren et al. analysed some
observations of the quiet Sun off-limb, and imposing isothermality obtained a
relative calibration for data until 2014\. We have extended this approach and
performed a DEM analysis of a quiet Sun off-limb observations close in time,
on 2019-06-28 at 09:38 UT, with the 2″ slit and 60 s exposures. The relative
calibration was obtained by matching the observed radiances to the predicted
ones, using CHIANTI version 10 (Del Zanna et al., 2021).

The established relative calibration for the short-wavelength (SW) channel was
then used to cross-calibrate the EIS spectra against simultaneous SDO AIA 193
Å observations, taking into account the different spatio-temporal resolutions,
following the methods described in Del Zanna et al. (2011); Del Zanna (2013b).
In turn, the AIA calibration relies on the SDO EVE calibration, although we
note that this could be done only until 2014. The AIA degradation in 2019 was
extrapolated from the cross-calibration EVE sounding rocket flown in 2018,
although that is currently being revised taking into account the latest EVE
sounding rocket flown in Sept 2021.

Details are provided in the Appendix, in Section E. The absolute and relative
calibrations have typical uncertainties of 20%. The above methods have been
extended to provide an EIS calibration for the entire mission, which is the
subject of another paper.

####  2.2.2 EIS Pointing

The precise pointing of the EIS instrument is generally not known. The EIS
pointing is relatively stable, except a 2–3″ jittering on fast time scales,
probably caused by small flexures inside the long (3 mt) structure holding the
optics. Usually, the pointing is established by a cross-correlation with EUV
images. As the off-limb observations considered here do not present any clear
features, the only way we could estimate the pointing was to compare EIS with
the AIA 193 Å data, as described in the Appendix, in Section F.

###  2.3 PolarCam

The PolarCam experiment was sited at CTIO, under the path of totality in
northern Chile, at an altitude of 2200 m. While not high enough to
significantly mitigate telluric absorption, the location has favourable cloud
cover, sitting above the stratus layer, as well as offering the infrastructure
of an existing observatory. The experiment successfully observed totality from
20:38:45 to 20:40:53 UT on 2019 July 2.

The 4D Technologies PolarCam consists of a micropolarising array placed over a
CCD detector. Each superpixel has four subpixels with alternating orientations
of linear polarisation: 0, 45, 90, and 135 degrees. Images of the total linear
polarisation can then be constructed from these four polarisation states. Its
small size and lack of moving parts make such a camera an ideal candidate for
a future CubeSat mission. For the July 2019 eclipse, we mounted the camera on
a Stellarvue 70 mm f/6 refracting telescope behind a bandpass filter centred
at 734 nm with 46 nm FWHM. Acquired images have $1920\times 1200$ pixels, with
2.91 arcsec sampling and 70 ms exposures.

##  3 Plasma characterization

###  3.1 Electron Density

####  3.1.1 Density estimates from polarized brightness measurements

The PolarCam data were calibrated by subtracting a dark image that was taken
with the shutter closed immediately following the eclipse. They were flat
fielded by taking the same exposures but using an opal glass attenuator,
performed 24 hours before the eclipse to mimic conditions as closely as
possible. We also investigated the contribution of sky polarization to the
measurements and found it to be negligible (in contrast to the measurements of
Hanaoka et al., 2021). This is to be expected, given that the sky is several
orders of magnitude darker during eclipse, leading to a negligible
contribution to the polarization from the sky.

The calibrated results of the subpixels with varying polarization state were
combined to produce an estimate of pB for the PolarCam field of view. As in
the 2017 eclipse (Judge et al., 2019), these pB results were compared wuth
those of K-Cor and found to be in good agreement. This comparison also gives a
verification of the PolarCam plate scale and rotation angle, which were
determined independently. The plate scale was determined by measuring the limb
of the Moon and comparaing relative sizes of Sun and Moon for the ephemerides
of CTIO.111https://ssd.jpl.nasa.gov/horizons/ Solar north was determined by
measuring the locations of Bailey’s Beads at second and third contact and
using a Watts Chart (Watts, 1963) to rotate our image. These charts of the
lunar limb show the location of irregularities from a smooth sphere, allowing
us to correlate the position of the bright Bailey’s Beads with lunar (and
hence solar) north. This method of determining the rotation angle of the
PolarCam with respect to solar north was found to be consistent with a cross-
correlation of the data with K-Cor.

A 60 s average of the pB measurements, from 20:39:00 to 20:39:59 UT, was used
to infer the electron density. We followed the standard assumption of
spherical symmetry for the density distribution of the diffuse outer quiescent
corona, and obtained the radial variation of the electron density by inversion
of white-light pB measurements following van de Hulst (1950). The results are
shown in Figure 4.

Figure 4: Electron densities obtained from the HAO PolarCam during the 2019
total eclipse. The AIR-Spec slits and EIS FOV are overlaid.

####  3.1.2 Density estimates from IR and EUV line ratios

Line-of-sight (LOS) averaged electron densities can be obtained directly from
the AIR-Spec S XI ratio, at least out to radial distances where there is
enough signal in the weaker line. However, these density measurements depend
significantly on the distribution of densities along the LOS. In fact, the
intensities of the forbidden lines in the NIR are significantly pumped by PE
from the solar disk radiation, and not just excited by electron collisional
excitation (CE) and cascades. Therefore, the observed intensities are only
partially directly proportional to the square of the local electron density,
as the allowed transitions are. Closer to the Sun, CE dominates over PE, but
further out, depending on the local density, PE becomes dominant. In other
words, it is impossible to obtain accurate electron densities from the
forbidden lines unless a model for the local density distribution is assumed.
More details on this issue are presented in the Appendix, in Section C.

The obvious choice for the diffuse outer corona is spherical symmetry, also to
get consistency with the analysis of the PolarCam observations. We used this
assumption to model the above-mentioned radiances of the SoHO SUMER and UVCS
lines (Del Zanna et al., 2018), and to obtain densities from the Fe XIII 1 µm
NIR forbidden lines observed by CoMP to obtain estimates of the coronal
magnetic field (Yang et al., 2020).

Clearly, if the density distribution is not uniform, the densities obtained
from the forbidden lines would be different to those obtained from the allowed
transitions. In general, the forbidden lines have a significant contribution
from very large (low-density) distances along the LOS, while the intensity of
the allowed transitions mostly originates from the highest density regions. A
comparison of the densities obtained from these two diagnostics therefore
provides useful information on the density distribution. Such a comparison was
carried out by Dudík et al. (2021), using the Fe XIII NIR forbidden lines
observed by CoMP and the Hinode EIS allowed transitions from Fe XIII and Fe
XII. Very good agreement in the LOS-averaged densities from the NIR and EUV
lines was obtained in an active region loop structure, once the
background/foreground emission of the diffuse corona was subtracted.

It is worth noting that densities from allowed transitions are not always
independent of PE effects either. In fact, the populations of the states in
the ground configuration, which are key to obtaining densities also from the
allowed transitions, can be affected by the solar disk radiation. This does
not occur in Fe XII, as most of the transitions in the ground configuration
are around 2000–3000 Å, where there are not many photons from the disk, but it
is not an insignificant effect in Fe XIII, as the pumping of the 1 µm NIR
forbidden lines changes the population of the ground configuration, especially
the ground state. This changes the intensities of all the lines, even those
decaying to the ground state, such as the strong 202 Å line.

On a positive note, as shown by Del Zanna & DeLuca (2018), the PE disk
radiation can easily be included within the CHIANTI programs assuming a black-
body radiation at 6100 K, as it is close to direct 1.4–2.5 µm NIR measurements
from e.g. SORCE.

Figure 5: Electron densities on the east and west limbs during the 2019 total
eclipse. The left-hand plots compare densities obtained from EIS and AIR-Spec
without correcting for LOS effects. The right-hand plots compare radial
density measurements obtained from AIR-Spec and PolarCam with the radial
density model in Del Zanna et al. (2018).

For EIS, we have selected the regions observed by the AIR-Spec slit, obtained
averaged radiances and densities using CHIANTI version 10 from three line
ratios. Figure 5 (left plots) shows a summary of the densities for the east
and west. The densities from the three ratios are in agreement, within the
uncertainties (see the Appendix, Figure 18). The plots also show the densities
from the AIR-Spec line ratio. Again, we see very good agreement, despite the
fact that the observations were not strictly simultaneous. This is to be
expected as little variability was present. The AIR-Spec densities were
obtained including PE.

As mentioned, the actual radial densities would be slightly higher, as the
line-of-sight are averaged values. Figure 5 (right plots) shows the radial
densities obtained from the AIR-Spec measurements assuming spherical symmetry,
as well as those from the PolarCam observations. The results are in agreement,
within uncertainties, and close to the quiescent streamers radial density
model by Del Zanna et al. (2018).

###  3.2 Emission measure and relative elemental abundances from EIS

We have taken averaged EIS spectra in the east and west regions also observed
by Air-Spec, around 0.09  $\rm R_{\odot}$ above the limb. Parts of the EIS
spectra are shown in the Appendix, in Figure 14. The strongest lines are from
Fe X–Fe XIII, Si X and S X. It is clear from the spectra that the east region
had significant emission in the hotter Fe XIII and Fe XIV, and also Fe XV,
which was not visible above the west limb.

Figure 6: The DEMs for the off-limb west and east regions obtained from Hinode
EIS. The points are plotted at the temperature $T_{\rm max}$ of maximum
emissivity, and at the theoretical vs. the observed intensity ratio multiplied
by the DEM value. The wavelength (Å) and ions of a few key lines are shown.

We estimated the differential emission measure (DEM) using a modified version
of the CHIANTI_DEM routine, where the DEM is modelled with a spline. We used
CHIANTI v.10, and to calculate the line emissivities assumed a constant
density of 1.5 108 cm-3 (although the main lines have contribution functions
that are independent of density). We assumed the photospheric abundances of
Asplund et al. (2009). Figure 6 shows the results, while more details on the
lines are given in the Appendix, in Section D. It is clear that the
distribution is nearly isothermal above the west limb, with a peak around 1.3
MK, while the distribution is more multi-thermal and shifted towards higher
temperatures on the east region.

The sulphur abundance is well constrained by the S X 264.2 Å line. Other
weaker lines from S X and S XI are also present and consistent with S/Si and
S/Fe photospheric abundances, as shown in the Appendix in Section D. S X is
formed at the same temperature as Si X and Fe XII, so the relative S/Si or
S/Fe abundance is well constrained. As sulphur, in remote-sensing
observations, behaves like a high-FIP element as do Ne and Ar, as described in
the Appendix A, this is a strong indication that the quiescent streamers had
photospheric abundances, in agreement with previous observations, as reviewed
in the Appendix A. AIR-Spec and AIA observations are consistent with these
results, as discussed below.

###  3.3 Temperatures

The electron temperature is a key parameter seldom measured in the corona. We
refer the reader to Del Zanna & Mason (2018) and to the brief review in
Appendix B. What we measure in this paper is the ionization temperature, i.e.
the electron temperature from emission measure or line ratio analyses,
assuming that the quiet corona is in ionization equilibrium. Such an
assumption is reasonable for the quiescent streamers, and has been validated
with direct measurements of the electron temperature near the limb.

As we describe in the Appendix, there is evidence in the literature that the
temperature distribution also in off-limb QS regions and in quiescent
streamers, up to 3  $\rm R_{\odot}$, is nearly isothermal, with values around
1.3–1.4 MK. We have seen in the previous section that the Hinode EIS
observations do indicate a near-isothermal distribution above the west limb,
at 1.08  $\rm R_{\odot}$. Therefore, the use of line (or imaging) ratios to
measure ‘isothermal temperatures’ is justified. Clearly, if the plasma is
strictly isothermal one would expect to find the same isothermal temperatures
from the various ratios.

As pointed out in the Appendix B, there is also evidence in previous
literature that, except very close to the solar limb, the temperature is
almost constant with distance, at least up to 3  $\rm R_{\odot}$ (still
assuming ionization equilibrium, but without validation).

####  3.3.1 Isothermal Temperatures from AIA, EIS and AIR-Spec line ratios,
and S/Si relative abundance from AIR-Spec

We have calculated the AIA responses as a function of temperature for the main
coronal bands, at 171, 193 and 211 Å, using CHIANTI v10 (Del Zanna et al.,
2021) atomic data and programs and the available AIA effective areas, obtained
from SolarSoft with the evenorm option (in this way the AIA areas are scaled
to agree with EVE), and a constant electron density of 108 cm-3. We used the
photospheric abundances of Asplund et al. (2009), but note that the AIA
coronal bands are all dominated by iron lines (see, e.g. Del Zanna et al.,
2011), so the isothermal temperatures are independent of the choice of
elemental abundances. The AIA 193 vs 171 Å and 211 vs. 171 Å ratios are
strongly dependent on the ionization temperature, while the 211 vs. 193 Å is
not sensitive to temperatures around 1.4 MK, being flat and multi-valued.

We downloaded the AIA data with a cadence of 2 minutes, during the two hours
of the EIS observations. There are only minor changes in the solar corona
during the EIS rasters. However, for each EIS exposure, we took the AIA images
closest in time and obtained averaged AIA DN/s in the two bands for the EIS
regions co-spatial with the locations of the AIR-Spec slits.

Figure 7: Isothermal temperatures in the east and west quiescent streamers
regions covered by the AIR-Spec slits. The top two plots show temperatures
obtained from simultaneous EIS (a) and AIA (b) observations. The bottom two
plots show temperatures obtained from simultaneous AIR-Spec (c) and AIA (d)
observations.

Figure 7 (panel b) shows the isothermal temperatures obtained from the AIA
filter ratios. It is clear, as we have already anticipated, that the eastern
region is hotter than the western one. Figure 7 (panel a) shows a few
isothermal temperatures obtained from EIS iron lines. There is generally good
agreement between the EIS and AIA results, confirming that the eastern region
is hotter and more multi-thermal than the western one, in agreement with the
EIS DEM results. However, we point out that the two AIA filter ratios produce
an effective temperature biased by the thermal distribution and the AIA
responses, as discussed below.

We have also calculated the AIA temperatures by averaging images during the 2
minutes of the total eclipse, for a direct comparison with the AIR-Spec data.
The results are shown in Figure 7, bottom panel, and in Figure 8.

Figure 8: Overlay of temperatures from EIS, AIR-Spec and AIA observations in
the east (top) and west (bottom). For clarity, the data from Figure 7 have
been smoothed before plotting.

Unlike the previous 2017 observation, where a few lines were observed and
enabled us to produce an emission measure loci, in the present case we only
have two AIR-Spec lines to estimate the ionization temperature: Si X 1.431 µm
and S XI 1.921 µm out to 1.3  $\rm R_{\odot}$, as the Fe IX 2.853 µm is too
weak at large distances. The Si X vs. S XI ratio is in principle a good
temperature diagnostic for quiescent streamers, but there are two issues. The
first regards the relative elemental abundances of Si and S. As the relative
S/Si abundances as measured by EIS at 1.08  $\rm R_{\odot}$ are photospheric,
we expect them to be the same at larger distances, so we used the same S/Si
abundances to calculate the isothermal temperature from the NIR ratio.

The second issue relates to the above-mentioned complication that the LOS
radiances not only depend on density and temperature, but also on the relative
importance of the CE and PE processes.

We have adopted the model of spherical symmetry, photospheric abundances and
the densities we obtained from the S XI ratio, to predict the Si X vs. S XI
LOS radiances as a function of temperature (see details in the Appendix,
Section C). By comparison with the observed ratio of the radiances, we then
obtained the isothermal temperatures from the NIR ratio. The values are shown
as diamonds in Figure 7, panel c and as circles in Figure 8.

The gray shaded area in Figures 7,8 indicates the lower and higher
temperatures obtained from the NIR ratio by changing the relative S/Si
abundance by $\pm$20%. As there is close agreement between the AIR-Spec
temperatures and those obtained from the AIA 211/171 Å filter ratio, this
shows that the S/Si relative abundance are constant with distance, as
expected. In fact, the AIA temperatures are independent of the choice of
abundances. If the S/Si relative abundance differed from the photospheric
value by more than 20%, the NIR temperatures would differ from the AIA (and
EIS) ones. The predicted radiances of the NIR lines obtained form the sperical
symmetry model for the west region are also shown in Figure 2. Having
established independently from the S XI the electron density, it is clear that
a constant temperature model reproduces quite well the radial fall off of the
NIR radiances in Si X and S XI quite well. If we used relative Si/S abundances
that were not photospheric, we would find disagreement with the observed
radiances.

###  3.4 AIA forward-model and photospheric abundances

Figure 9: Measured and predicted AIA count rates in the west region. Symbols
indicate the measured count rates. Solid lines show the predicted count rates
using a spherical symmetry model, photospheric abundances, and assuming an
isothermal and constant temperature of 1.3 MK. Dashed lines indicate the
predicted signal increased by a factor of four. Dot-dashed lines show the
values with the 1.2 MK isothermal model.

Having estimated the radial electron density and temperature, it is then
straightforward to calculate the signal in the AIA bands using the spherical
model and compare it to observation. The AIA signal depends not only on the
density and temperature, but also on the absolute AIA radiometric calibration,
and on the absolute iron abundance, as the AIA bands are dominated by Fe
lines. In quiescent streamers, the 171 Å band is dominated by Fe IX, while the
193 band has several Fe XII and Fe XI lines. The 211 Å is mostly dominated by
Fe XIII lines. The absolute AIA calibration has some uncertainty, but the
degradation in these coronal bands has been relatively small (10-30%) over the
years, so we do not expect an uncertainty larger than say 30%, which is the
typical uncertainty in the calibration of the sounding rockets used for the
in-flight calibration of AIA. Therefore, the comparison provides an estimate
of the absolute iron abundance, within 30%.

Considering that a spherically-symmetric isothermal model with T=1.3 MK and
the radial density profile of Del Zanna et al. (2018) represents the AIR-Spec
data in the west region quite well, we have used it to calculate the AIA count
rates up to 1.3  $\rm R_{\odot}$. For simplicity, we have calculated only the
Fe VIII – Fe XIV emissivities and folded them with the expected AIA effective
areas. In fact, these are the main ions contributing to the bands. The results
with photospheric abundance are shown, together with the observed ones, in
Figure 9. It is clear that there is an overall agreement, showing that such
simple model can also represent the AIA observations, and that the absolute
iron abundance on the west streamer must be close to photospheric. If the iron
abundance were coronal, the observed count rates would be a factor of 4
higher.

The small discrepancy between the isothermal temperatures obtained from the
AIA filter ratios and the assumed constant temperature of 1.3 MK is related to
the fact that the ratios we have used, 193 or 211 vs. the 171 Å, provide an
effective temperature weighted by the DEM distribution. If we take the
predicted count rates and estimate the isothermal temperature, we get 1.2 MK
from both 211/171 and 193/171 Å ratios, a value close to the peak of the DEM
(1.26 MK).

Clearly, the isothermal assumption is an approximation to the real
distribution, which we estimated only at 1.08  $\rm R_{\odot}$ with Hinode
EIS. Table 2 shows that the AIA count rates as predicted with a 1.2 and 1.3 MK
isothermal models and with the EIS DEM are close, within 50%. Varying the
isothermal temperature by 0.1 MK does not have a large effect on the predicted
count rates, as shown in Figure 9.

Table 2: AIA observed and predicted DN/s per pixels in the west region at 1.08  $\rm R_{\odot}$ | 171 Å | 193 Å | 211 Å
---|---|---|---
Observed | 103 | 69 | 8.6
Predicted (1.2 MK) | 93 | 77 | 6.4
Predicted (1.3 MK) | 62. | 92 | 8.4
Predicted (DEM) | 55. | 57 | 6.2

##  4 Conclusions

With an improved AIR-Spec instrument, we have shown here the diagnostic
potential of NIR lines to measure reliably and independently electron
temperatures, densities and elemental abundances in the corona, out to large
distances. For the 2019 eclipse, we could only measure lines up to 1.3  $\rm
R_{\odot}$, because of the limited size of the instrument and the slit, in
addition to the short exposures, which were necessary to observe large
sections of the corona during the eclipse. However, NIR lines, being strongly
photo-excited by the disk radiation as the visible lines, have relatively
strong radiances out to large distances, hence are excellent probes to study
the middle corona.

The AIR-Spec results are in agreement with those obtained in the low corona by
the EIS instrument. Consistency with the densities obtained from the PolarCam
pB measurements and with the intensities in the SDO/AIA coronal bands is also
reassuring.

In agreement with the analysis of the first 2017 AIR-Spec flight (Madsen et
al., 2019), we found that the quiescent streamers have Si/S photospheric
abundances, from both the AIR-Spec and the Hinode EIS lines. The spherical
symmetry model which reproduces quite well the AIR-Spec data indicates that
the absolute iron abundance is close to its photospheric value, by comparison
with the AIA count rates. These results are also in agreement with previous
literature (reviewed in the Appendix A) pointing out that the quiescent solar
corona during solar minimum has near photospheric abundances, at least up to
1.3 MK.

Also, in agreement with previous observations and the 2017 AIR-Spec flight, we
found that the quiescent streamer above the west limb is nearly isothermal. On
the other hand, the eastern one had some hotter emission. The results from
EIS, AIA and AIR-Spec are all consistent, and also in agreement with the
eclipse observations in the visible. A simple spherical symmetry model with
constant temperature with radial distance reproduces quite well the AIR-Spec
and AIA observations, up to 1.3  $\rm R_{\odot}$.

We have shown the importance of measuring at least a few key lines formed at
different temperatures to establish the thermal distribution of the plasma, as
we have done at lower heights with Hinode EIS. In fact, single isothermal
ratios have some limitations, as they provide effective temperatures which are
averaged values weighted by the DEM distribution and their temperature
sensitivity.

It is also clear that the analysis of NIR lines is non-trivial as careful
atmospheric modeling is required, as well as a model of the electron density
and temperature distribution, as the radiances cannot be directly used to
measure these parameters. This is because of the variable contribution of the
resonantly scattered component to the line emission, compared to the
collisionally excited one. Once the electron density is established, it is
relatively easy to find a temperature distribution that fits the observations.
Therefore, we recommend that future NIR observations include at least a
density-sensitive line ratio such as the S XI, and at least three lines formed
in the temperature range between 1 and 2 MK for the quiet corona.

As briefly described in Del Zanna & DeLuca (2018), the NIR spectral region is
virtually unexplored but has a great plasma diagnostic potential. The follow-
up to AIR-Spec is the Airborne Coronal Emission Surveyor (ACES), a new imaging
Fourier transform spectrometer that will survey the entire 1–4 µm spectral
range at high (0.5 cm-1) spectral resolution during the April 8, 2024 total
solar eclipse. ACES will fly along the path of totality on the GV, with a 20
cm solar feed stabilized to 6″ RMS over one second. The feed will be provided
by the Airborne Stabilized Platform for InfraRed Experiments (ASPIRE), which
was developed by the AIR-Spec/ACES team for the GV and commissioned in 2021.
ACES will measure many coronal lines, half of which have never been observed
before, and will therefore be a pathfinder for future targeted DKIST and
hopefully space-based observations.

The 2019 AIR-Spec upgrade and re-flight was funded by NSF award # AGS-1822314:
Airborne InfraRed Spectrograph (AIR-Spec) 2019 Eclipse Flight. GDZ and HEM
acknowledge support from STFC (UK) via the consolidated grants to the atomic
astrophysics group (AAG) at DAMTP, University of Cambridge (ST/P000665/1. and
ST/T000481/1). GDZ also acknowledges support from NSF award # AGS-2117582:
MRI: Development of an Airborne Coronal Emission Surveyor (ACES) for his visit
to CfA in 2022. Hinode is a Japanese mission developed and launched by
ISAS/JAXA, with NAOJ as a domestic partner and NASA and STFC (UK) as
international partners. It is operated by these agencies in cooperation with
the ESA and NSC (Norway). SDO data were obtained courtesy of NASA/SDO and the
AIA and HMI science teams. The PolarCam experiment was supported by the
National Center for Atmospheric Research, which is a major facility sponsored
by the National Science Foundation under Cooperative Agreement No. 1852977. We
thank the reviewer for the detailed comments which helped us to improve the
manuscript.

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##  Appendix A Elemental abundances in the quiet Sun

Solar coronal abundances measured with remote-sensing instruments vary with
the structure observed and the temperature of formation of the spectral lines
observed. For a review of measurements of different solar features we refer to
Del Zanna & Mason (2018). Historically, most observations have constrained the
relative abundances between high- (e.g. Ne, O, Ar) and low-FIP (e.g. Si, Fe,
Mg) elements, and take the ratio with the photospheric ones to obtain the FIP
bias. We adopt here the photospheric abundances of Asplund et al. (2009), but
note that the values for several elements (especially C, N, O) are still
debated in the literature, although variations from Asplund et al. are of the
order of 30%. We also note that the Ne, Ar abundances recommended by Asplund
et al. (2009) are not based on actual photospheric measurements.

We focus here on ‘quiet Sun’ (QS) areas during solar minimum, and note that
the presence of active regions has a significant effect on the diffuse QS
emission, as shown e.g. in Del Zanna & Andretta (2011); Andretta & Del Zanna
(2014).

Early QS observations from Skylab in transition-region lines indicated near
photospheric relative abundances, when considering Mg/Ne ratios (see, e.g.
Feldman, 1992; Feldman & Widing, 1993, and references therein). Similar
results were obtained with SoHO CDS, also considering Mg/Ne ratios (see, e.g.
Del Zanna & Bromage, 1999; Young, 2005).

SoHO SUMER was an excellent instrument to measure the relative abundances of
coronal lines in off-limb QS regions. Doschek et al. (1998) used SOHO SUMER
observations to find photospheric Si/Ne abundances in the upper transition
region. Other results involving more elements were unclear, as they depended
on which spectral lines were considered, as discussed by Feldman et al.
(1998). The problem was partly related to the inclusion or not of lines from
the so-called ‘anomalous’ ions of the Li-like and Na-like isoelectronic
sequences (see e.g. Del Zanna et al., 2002, and references therein).

We note that the atomic data for the forbidden lines of Fe ions in the SUMER
spectra were significantly revised by one of us (GDZ), as summarised in Del
Zanna & Mason (2018). The new atomic data were included in CHIANTI version 8
(Del Zanna et al., 2015). A reanalysis of the SUMER observations with these
updated atomic data have indicated relative photospheric abundances,
considering a range of low-FIP elements such as Fe, high-FIP ones such as Ne,
O, and Ar, and the mid-FIP S (Del Zanna & DeLuca, 2018).

The SUMER off-limb spectra were also used by Feldman et al. (1998) to find an
O/H ratio to be close to the photospheric value.

Hinode EIS has been used extensively in the literature to measure the FIP
bias. The instrument observes strong coronal lines from Fe and Si (low-FIP),
but much weaker lines from S and Ar. In most observations, only a weak Ar XIV
can reliably provide the Fe,Si vs. Ar relative abundance in 3 MK plasma, found
in the cores of active regions. The results are that the FIP bias is always
about a factor of 3, as in the example shown in Del Zanna (2013b). This agrees
with an analysis of many quiescent active region cores observed in the X-rays,
where the Fe vs. O, Ne FIP bias is also about 3 (Del Zanna & Mason, 2014),
i.e. lower than 4, the earlier widely adopted value recommended by Feldman et
al. (1992).

The Hinode EIS observations of S XIII, also formed around 3 MK, confirm an Fe,
Si vs. S FIP bias of about 3 (Del Zanna, 2013b) (while the lower charge states
of S often indicate a lower FIP bias of about 2). Therefore, S in remote-
sensing observations shows the same FIP bias as the high-FIP elements O, Ne,
so effectively behaves as a high-FIP element, despite having a FIP of only 10
eV. The behaviour of S as a high-FIP element is also observed in solar
energetic particles (SEP) events measured in-situ, and predicted by Laming’s
theory (see, e.g. Reames, 2018; Laming et al., 2019). It is also interesting
to note that the FIP bias of SEP is about 3, in agreement with the recent
results for active region cores.

On the basis of the above arguments, there is an extended literature on FIP
bias results obtained from Hinode EIS measurements of the strong S X vs. Si X
lines around 264 Å, as they are formed at similar temperatures (which depend
on the feature observed), and are close in wavelength (so the uncertainty in
the radiometric calibration is small). When observing the QS, the S X always
indicates a relative Si, Fe vs. S photospheric abundance, while active regions
show a FIP bias of around 2 (see,e.g. Del Zanna, 2012; Doschek & Warren,
2019).

The AIR-Spec NIR spectra of the 2017 eclipse, when the Sun was very quiet,
have also indicated a photospheric S/Si abundance (Madsen et al., 2019).

It could well be that QS plasma at temperatures higher than 1 MK has a FIP
bias, but past/current instrumentation is not sensitive enough to measure it.
Strong lines from low-FIP elements formed around 2 MK are usually very weak,
and lines formed around 3 MK have no signal in past and current
instrumentation. Spectral lines from high-FIP formed around 2 MK or more have
no signal in the quiet Sun.

Regarding absolute abundances, in earlier literature it was not clear if it
was the low-FIP elements that were more abundant in active regions, or the
high-FIP ones that were less abundant. Line to continuum measurements during
large flares, when the FIP bias is generally 1, indicated photospheric
abundances for all the elements. Regarding quiescent active cores, on the
basis of a filling factor argument, Del Zanna (2013b) suggested that it should
be the low-FIP elements that have increased abundances. Line-to continuum
measurements in the X-rays of the full Sun, when a single active region was
dominating the signal, indicated a Si FIP bias of 2.4 (Del Zanna et al.,
2022), i.e. only about 20% lower than the value suggested by Del Zanna.

Irradiance measurements (i.e. Sun-as-a-star) have been carried out since the
1960’s in the X-rays and EUV. Most measurements were carried out outside of
solar minimum, hence the presence of active regions affected the results in
terms of elemental abundances. One example is the 1969 sounding rocket flight
described by Malinovsky & Heroux (1973). It obtained the best-calibrated EUV
spectrum of the Sun, but active region lines (formed above 2 MK) and even
flare lines were present. Laming et al. (1995) used that spectrum to find
nearly photospheric abundances when considering lines formed in the transition
region and corona, up to 1 MK. The abundances were relative, using mainly
sulphur lines, in combination with lines from low-FIP elements. An FIP bias of
3–4 was instead obtained from higher-temperature lines. A re-analysis of the
same spectrum by Del Zanna (2019) using CHIANTI version 8 found similar
results, showing no FIP bias when considering S X, and an increase to a FIP
bias of about 2 when considering S XI and S XII, formed around 2 MK. As
explained by Del Zanna (2019), this difference is simply due to the fact that
the QS dominates the S X emission (hence the FIP bias is 1), while active
regions dominate the S XI, S XII, hence the increase in the FIP bias. Finally,
we note that X-ray bright points also contribute to the irradiances at 2 MK
with an FIP bias of about 2, as found from line to continuum measurements in
the X-rays (Vadawale et al., 2021).

On the other hand, when analysing irradiances during solar minimum, the
relative abundance between sulphur lines and those of low-FIP elements is
photospheric, as shown by Del Zanna (2019) using the well-calibrated spectra
measured during the solar minimum on 2008 April 14 by the prototype of the
Solar Dynamics Observatory Extreme ultraviolet Variability Experiment (EVE).

##  Appendix B Near-isothermal and constant electron temperature in quiescent
streamers

As reviewed in Del Zanna & Mason (2018), measuring the electron temperature
directly from e.g. line ratios is possible but was rarely applied to
observations, in particular those of the quiet Sun corona above the limb, as
its temperature is about 1 MK and very few diagnostics are available.

The best one is a line ratio from Mg IX. Del Zanna et al. (2008) produced
significantly improved atomic data for this ion, and used off-limb SoHO SUMER
measurements reported by Feldman et al. (1999) to find a temperature of 1.35
MK.

Another possible diagnostic, applied to a quiescent streamer at a large
distance (2.7 $\rm R_{\odot}$), involved measuring the extremely weak
electron-scattered component of the neutral hydrogen Ly $\alpha$ as recorded
by SoHO UVCS (Fineschi et al., 1998). A temperature of 1.1$\pm 0.3$ MK was
found.

Lacking direct diagnostics, the usual assumption to estimate the electron
temperature is to measure the ionization temperature, i.e. the temperature
obtained with line ratios or emission measure analyses, assuming ionization
equilibrium. Early measurements of line ratios from the 1970’s of the inner
corona of the quiet Sun have indicated a temperature distribution around 1.4
MK (cf. Jordan, 1971).

Detailed emission measure analyses obtained with a range of coronal lines
observed by SoHO SUMER clearly indicated an isothermal distribution along the
line of sight for QS off-limb regions (Feldman et al., 1999). A reanalysis of
the same SUMER observations with improved atomic data, shown in Del Zanna &
Mason (2018), confirms this result, with a temperature of 1.35 MK, in exact
agreement with the Mg IX result. This provides a strong indication that for
the QS the ionization temperature is a good measure of the electron
temperature, and that the CHIANTI atomic data, in particular the
ionization/recombination rates for the ions considered, are accurate.

There is also evidence in the literature that the temperature is relatively
constant with radial distance, if one observes quiescent streamers, when no
active regions are present. For example, Skylab ATM observations of EUV
coronal lines out to 1.25 $\rm R_{\odot}$ indicated a nearly constant
ionization temperature (Mariska & Withbroe, 1978). SoHO UVCS observations of
EUV coronal lines in quiescent streamers, between 1.4 and 3  $\rm R_{\odot}$,
also indicated a constant ionization temperature of about 1.4 MK (Del Zanna et
al., 2018). Clearly, close to the solar limb the temperature decreases towards
lower values. Semi-empirical models of the electron temperature in quiescent
streamers also indicated nearly constant values (see, e.g. Withbroe, 1991).
Finally, narrow-band images in iron visible lines during eclipses also
indicate a nearly constant ionization temperature (see, e.g. Boe et al.,
2022).

##  Appendix C Measuring density and temperature using IR line ratios

The mapping from AIR-Spec line ratios to electron density was provided by the
‘DENSITY_RATIOS’ routine in CHIANTI v.10 (Del Zanna et al., 2021). As the IR
lines are significantly photo-excited, the distance from the underlying
photospheric radiation field is a critical parameter in the mapping: as the
radiation becomes diluted with increasing distance, the pumping rate also
decreases. Figure 10 shows the dependence of density on the combination of the
S XI 1.92/1.39 µm line ratio and the distance from Sun center. The AIR-Spec
density estimates were computed by interpolating the density surface in Figure
10 to each line ratio/radial distance pair in the AIR-Spec data. This
procedure produces the density estimates in the left half of Figure 5, which
are not corrected for LOS contributions to the AIR-Spec radiances.

Figure 10: Density as a function of S XI 1.92/1.39 µm line ratio and distance
from Sun center.

In order to estimate the radial (LOS-corrected) density profile, we use the
spherically symmetric model described in Del Zanna et al. (2018) to remove the
AIR-Spec intensity contribution from outside the plane of the sky (POS).
Figure 11 shows the fraction of the total line intensity contributed by each
0.025 R⊙ along the LOS, as predicted by the model. Only 4–5% of the
contribution comes from the 0.025 R⊙ nearest the POS. If we scale the AIR-Spec
S XI intensities by this fraction before taking the line ratio, we obtain the
radial density estimates in the right half of Figure 5.

Figure 11: Fraction of line intensity contributed by each 0.025 R⊙ along the
line of sight. Each curve sums to one along the ‘LOS Distance’ coordinate. The
1.92 µm line has a smaller contribution from the POS than the 1.39 µm line,
resulting in a lower line ratio (and higher density) when only the POS
intensity is taken into account instead of the entire LOS integration.

Figure 12 shows the emissivities (contribution functions, calculated in
ionization equilibrium) of the main AIR-Spec lines, indicating the range of
temperatures where the lines can be formed. We use the emissivity ratio of the
two strongest lines, Si X 1.43 µm and S XI 1.92 µm, to estimate the
temperatures shown in Figures 7c and 8. The contribution functions are
computed using photoexcitation and integrated along the LOS before the ratio
is taken. Because the modeled line ratio includes emission from the entire
LOS, the LOS-averaged AIR-Spec radiances are used to map line ratio to
temperature.

Figure 12: Contribution functions of the main AIR-Spec lines, calculated with
photoexcitation at 1.1 $\rm R_{\odot}$.

As with the density mapping, the distance from the underlying photospheric
radiation field is an important parameter in the mapping from line ratio to
temperature. Figure 13 shows the dependence of temperature on the combination
of the Si X 1.43 µm/S XI 1.92 µm line ratio and the distance from Sun center.
The line ratio is sensitive to temperatures in the 1–2 MK range.

Figure 13: Temperature as a function of Si X/S XI 1.43/1.92 µm line ratio and
distance from Sun center.

##  Appendix D Temperature distribution from EIS

Figure 14: Hinode EIS spectra for the off-limb observation above the east and
west limb (120 s, 2″ slit), around 1.09  $\rm R_{\odot}$. The dashed lines are
the scaled ground-calibration effective area, to show why spectral lines in
the middle of the two SW and LW detectors are stronger.

Figure 14 shows the averaged EIS spectra in the east and west regions, used to
obtain the DEM distribution. The strongest lines are from Fe X–Fe XIII, and Si
X. The west region has significant emission in Fe XIV and Fe XV which is not
present on the east. The S X lines are well observed and provide a strong
constraint on the relative FIP bias between high-FIP and low-FIP elements.

Table 3 shows the results of the DEM analysis on the off-limb observation
above the east limb. Only a few of the lines are shown. $T_{\rm max}$ is the
temperature of the maximum of the contribution function $G(T)$, while the
effective temperature $T_{\rm eff}$ is:

$T_{\rm eff}=\int G{\left({T}\right)}~{}DEM{\left({T}\right)}~{}T~{}dT/{\int
G{\left({T}\right)}~{}DEM{\left({T}\right)}~{}dT}\quad.$ (D1)

For each observed line, the CHIANTI programs search for all the transitions
(that form a blend) within a wavelength range, centred on the observed
wavelength. Only the main lines contributing to the blend are listed, with
their fractional contribution indicated in the last column. Table 4 shows the
results of the DEM analysis on the off-limb observation above the west limb.
Only a few of the lines are shown.

Table 3: Observed and predicted radiances for the off-limb observation above the east limb (120 s, 2″ slit). $\lambda_{\rm obs}$ (Å) are the observed wavelengths, DN is the number of total counts in each line, while $I_{\rm obs}$ is the calibrated radiance (erg cm-2 s-1 sr-1) obtained with our new EIS calibration. $T_{\rm max}$ and $T_{\rm eff}$ are the maximum and effective temperature (log values, in K; see text), $R$ the ratio between the predicted and observed radiances, Ion and $\lambda_{\rm exp}$ (Å) the main contributing ion, and $r$ the fractional contribution to the blend.  $\lambda_{\rm obs}$ | DN | $I_{\rm obs}$ | log $T_{\rm max}$ | log $T_{\rm eff}$ | $R$ | Ion | $\lambda_{\rm exp}$ | $r$
---|---|---|---|---|---|---|---|---
185.20 | 47 | 5.6 | 5.73 | 6.06 | 0.83 | Fe VIII | 185.213 | 0.94
186.61 | 57 | 4.7 | 5.72 | 6.06 | 0.84 | Fe VIII | 186.598 | 0.81
189.93 | 80 | 3.5 | 5.92 | 6.10 | 1.10 | Fe IX | 189.935 | 0.95
188.48 | 142 | 8.9 | 5.93 | 6.10 | 1.06 | Mn IX | 188.480 | 0.11
|  |  |  |  |  | Fe IX | 188.493 | 0.83
197.85 | 128 | 3.8 | 5.93 | 6.10 | 1.15 | Fe IX | 197.854 | 0.93
257.27 | 213 | 41.6 | 6.02 | 6.11 | 0.98 | Fe X | 257.259 | 0.21
|  |  |  |  |  | Fe X | 257.261 | 0.77
184.53 | 403 | 56.4 | 6.03 | 6.12 | 0.80 | Fe X | 184.537 | 0.96
190.03 | 391 | 16.5 | 6.03 | 6.12 | 1.00 | Fe X | 190.037 | 0.86
198.54 | 236 | 7.2 | 5.95 | 6.12 | 1.45 | S VIII | 198.553 | 0.44
|  |  |  |  |  | Fe XI | 198.538 | 0.51
192.81 | 811 | 26.3 | 5.42 | 6.13 | 1.15 | Fe XI | 192.813 | 0.97
188.21 | 1940 | 131.0 | 6.12 | 6.14 | 1.10 | Fe XI | 188.216 | 0.98
188.29 | 1370 | 90.2 | 6.12 | 6.14 | 0.98 | Fe XI | 188.299 | 0.98
180.39 | 475 | 337.0 | 6.12 | 6.14 | 0.90 | Fe XI | 180.401 | 0.98
258.38 | 201 | 37.7 | 6.15 | 6.14 | 1.03 | Si X | 258.374 | 0.97
272.00 | 151 | 20.1 | 6.15 | 6.14 | 1.00 | Si X | 271.992 | 0.98
261.07 | 137 | 21.9 | 6.15 | 6.14 | 1.12 | Si X | 261.056 | 0.98
277.27 | 73 | 14.9 | 6.15 | 6.14 | 1.04 | Si X | 277.264 | 0.98
259.49 | 80 | 14.4 | 6.18 | 6.15 | 1.01 | S X | 259.496 | 0.98
264.24 | 133 | 18.7 | 6.18 | 6.15 | 1.13 | S X | 264.230 | 0.98
193.50 | 3860 | 117.0 | 6.19 | 6.15 | 1.10 | Fe XII | 193.509 | 0.94
195.11 | 6460 | 169.0 | 6.19 | 6.15 | 1.09 | Fe XII | 195.119 | 0.97
192.39 | 1580 | 54.7 | 6.19 | 6.15 | 1.08 | Fe XII | 192.394 | 0.97
200.01 | 113 | 4.1 | 6.24 | 6.17 | 1.14 | Fe XIII | 200.021 | 0.91
191.25 | 124 | 4.8 | 6.28 | 6.17 | 1.03 | S XI | 191.266 | 0.94
251.97 | 67 | 21.3 | 6.24 | 6.17 | 1.05 | Fe XIII | 251.952 | 0.97
202.04 | 1260 | 113.0 | 6.24 | 6.17 | 0.86 | Fe XIII | 202.044 | 0.97
264.79 | 94 | 13.2 | 6.29 | 6.17 | 1.20 | Fe XIV | 264.788 | 0.61
|  |  |  |  |  | Fe XI | 264.772 | 0.36
274.21 | 125 | 17.9 | 6.29 | 6.19 | 0.86 | Fe XIV | 274.203 | 0.95
270.52 | 57 | 8.1 | 6.29 | 6.19 | 0.82 | Fe XIV | 270.520 | 0.97
262.98 | 4 | 0.61 | 6.43 | 6.20 | 1.16 | Fe XVI | 262.976 | 0.26
|  |  |  |  |  | Fe XIII | 262.984 | 0.66
284.16 | 47 | 20.5 | 6.34 | 6.22 | 1.05 | Fe XV | 284.163 | 0.96
Table 4: Observed and predicted radiances for the off-limb observation above the west limb (120 s, 2″ slit). The notation is the same as Table 3.  $\lambda_{\rm obs}$ | DN | $I_{\rm obs}$ | log $T_{\rm max}$ | log $T_{\rm eff}$ | $R$ | Ion | $\lambda_{\rm exp}$ | $r$
---|---|---|---|---|---|---|---|---
185.22 | 48 | 5.8 | 5.73 | 6.07 | 1.08 | Fe VIII | 185.213 | 0.97
189.94 | 109 | 4.7 | 5.92 | 6.08 | 1.08 | Fe IX | 189.935 | 0.98
197.86 | 231 | 6.9 | 5.93 | 6.08 | 0.92 | Fe IX | 197.854 | 0.95
257.25 | 312 | 61.1 | 6.02 | 6.09 | 0.88 | Fe X | 257.259 | 0.20
|  |  |  |  |  | Fe X | 257.261 | 0.78
184.54 | 538 | 75.3 | 6.03 | 6.09 | 0.75 | Fe X | 184.537 | 0.97
190.04 | 575 | 24.3 | 6.03 | 6.09 | 0.83 | Fe X | 190.037 | 0.90
198.56 | 293 | 9.0 | 5.95 | 6.09 | 1.26 | S VIII | 198.553 | 0.54
|  |  |  |  |  | Fe XI | 198.538 | 0.42
256.91 | 117 | 23.2 | 6.10 | 6.09 | 0.96 | Fe XI | 256.919 | 0.98
180.41 | 513 | 364.0 | 6.11 | 6.10 | 0.83 | Fe XI | 180.401 | 0.93
188.22 | 2040 | 137.0 | 6.12 | 6.10 | 0.99 | Fe XI | 188.216 | 0.98
192.82 | 877 | 28.4 | 6.12 | 6.10 | 1.01 | Fe XI | 192.813 | 0.97
256.37 | 223 | 46.1 | 6.16 | 6.10 | 0.81 | Si X | 256.377 | 0.65
|  |  |  |  |  | Fe XII | 256.410 | 0.14
|  |  |  |  |  | Fe X | 256.398 | 0.12
258.36 | 219 | 41.2 | 6.15 | 6.10 | 0.72 | Si X | 258.374 | 0.97
271.98 | 173 | 23.0 | 6.15 | 6.10 | 0.73 | Si X | 271.992 | 0.98
261.05 | 166 | 26.6 | 6.15 | 6.10 | 0.76 | Si X | 261.056 | 0.98
264.22 | 140 | 19.7 | 6.18 | 6.10 | 0.80 | S X | 264.230 | 0.98
193.52 | 2850 | 86.2 | 6.19 | 6.10 | 0.99 | Fe XII | 193.509 | 0.94
192.40 | 1100 | 38.1 | 6.19 | 6.10 | 1.02 | Fe XII | 192.394 | 0.97
195.13 | 4660 | 122.0 | 6.19 | 6.10 | 0.99 | Fe XII | 195.119 | 0.97
264.77 | 63 | 8.8 | 6.29 | 6.11 | 0.88 | Fe XIV | 264.788 | 0.26
|  |  |  |  |  | Fe XI | 264.772 | 0.71
200.00 | 62 | 2.3 | 6.24 | 6.11 | 0.70 | Fe XIII | 200.021 | 0.81
191.26 | 61 | 2.4 | 6.28 | 6.11 | 0.95 | S XI | 191.266 | 0.91
202.05 | 471 | 42.2 | 6.24 | 6.12 | 0.96 | Fe XIII | 202.044 | 0.97
274.17 | 22 | 3.3 | 6.29 | 6.13 | 1.09 | Fe XIV | 274.203 | 0.89
|  |  |  |  | Fe XI | 256.654 | 0.18 |

##  Appendix E EIS calibration

We performed a DEM analysis of a quiet Sun off-limb observations close in time
to the eclipse, on 2019- 06-28 at 09:38 UT, with the 2″ slit and 60 s
exposures. Table 5 gives a list of the main lines. The emissivities were
calculated at a constant density log Ne =8.6. The EIS effective areas were
adjusted to match observation. This calibration was then used for the Eclipse
observations. It is clear that all the main lines are well represented within
$\pm$15%.

Table 5: Observed and predicted radiances for the off-limb observation (60s, 2″ slit) on 2019-Jun-28 used for the EIS radiometric calibration. The notation is the same as Table 3.  $\lambda_{\rm obs}$ | DN | $I_{\rm obs}$ | $T_{\rm max}$ | $T_{\rm eff}$ | $R$ | Ion | $\lambda_{\rm exp}$ | $r$
---|---|---|---|---|---|---|---|---
194.66 | 417 | 22.6 | 5.72 | 6.05 | 1.04 | Fe VIII | 194.661 | 0.95
185.22 | 412 | 97.0 | 5.73 | 6.05 | 1.17 | Fe VIII | 185.213 | 0.96
186.60 | 464 | 75.6 | 5.73 | 6.06 | 1.17 | Fe VIII | 186.598 | 0.85
189.94 | 785 | 67.4 | 5.94 | 6.08 | 1.23 | Fe IX | 189.935 | 0.97
188.49 | 1290 | 162.0 | 5.95 | 6.08 | 1.00 | Fe IX | 188.493 | 0.89
197.85 | 1320 | 78.9 | 5.96 | 6.09 | 1.04 | Fe IX | 197.854 | 0.94
257.26 | 1510 | 589.0 | 6.04 | 6.10 | 0.95 | Fe X | 257.259 | 0.25
|  |  |  |  |  | Fe X | 257.263 | 0.73
177.24 | 346 | 1650.0 | 6.05 | 6.11 | 1.08 | Fe X | 177.240 | 0.98
174.53 | 177 | 2660.0 | 6.05 | 6.11 | 1.19 | Fe X | 174.531 | 0.98
184.54 | 2280 | 637.0 | 6.05 | 6.11 | 1.06 | Fe X | 184.537 | 0.96
190.04 | 3050 | 257.0 | 6.06 | 6.12 | 1.09 | Fe XII | 190.040 | 0.12
|  |  |  |  |  | Fe X | 190.037 | 0.76
184.79 | 164 | 43.3 | 6.12 | 6.13 | 1.20 | Fe XI | 184.793 | 0.93
257.55 | 441 | 170.0 | 6.12 | 6.13 | 1.07 | Fe XI | 257.554 | 0.70
|  |  |  |  |  | Fe XI | 257.547 | 0.25
189.02 | 427 | 47.3 | 6.13 | 6.13 | 0.87 | Fe XI | 188.997 | 0.95
256.92 | 608 | 241.0 | 6.12 | 6.13 | 0.86 | Fe XI | 256.919 | 0.92
181.13 | 150 | 167.0 | 6.13 | 6.13 | 0.89 | Fe XI | 181.130 | 0.97
192.81 | 5040 | 326.0 | 5.42 | 6.13 | 0.91 | Fe XI | 192.813 | 0.96
188.22 | 9190 | 1240.0 | 6.13 | 6.13 | 1.13 | Fe XI | 188.216 | 0.98
188.30 | 6090 | 801.0 | 6.13 | 6.13 | 1.06 | Fe XI | 188.299 | 0.98
180.40 | 1820 | 2570.0 | 6.13 | 6.13 | 1.13 | Fe XI | 180.401 | 0.98
202.71 | 424 | 87.6 | 6.13 | 6.14 | 1.37 | Fe XI | 202.705 | 0.93
258.37 | 1460 | 546.0 | 6.15 | 6.14 | 0.96 | Si X | 258.374 | 0.97
253.79 | 223 | 115.0 | 6.15 | 6.14 | 0.90 | Si X | 253.790 | 0.97
271.99 | 852 | 226.0 | 6.15 | 6.14 | 0.93 | Si X | 271.992 | 0.97
261.06 | 853 | 273.0 | 6.15 | 6.14 | 0.92 | Si X | 261.056 | 0.98
277.27 | 452 | 181.0 | 6.15 | 6.14 | 0.89 | Si X | 277.264 | 0.98
249.39 | 107 | 89.1 | 6.19 | 6.16 | 1.12 | Fe XII | 249.388 | 0.69
|  |  |  |  |  | Fe XII | 249.384 | 0.22
193.51 | 18200 | 1100.0 | 6.19 | 6.17 | 1.13 | Fe XII | 193.509 | 0.94
192.39 | 8090 | 559.0 | 6.19 | 6.17 | 1.02 | Fe XII | 192.394 | 0.96
195.12 | 27800 | 1450.0 | 6.19 | 6.17 | 1.23 | Fe XII | 195.119 | 0.97
200.02 | 1510 | 109.0 | 6.25 | 6.20 | 0.90 | Fe XIII | 200.021 | 0.94
246.21 | 170 | 185.0 | 6.25 | 6.20 | 0.80 | Fe XIII | 246.209 | 0.95
251.95 | 421 | 268.0 | 6.25 | 6.20 | 1.02 | Fe XIII | 251.952 | 0.96
204.94 | 180 | 59.2 | 6.25 | 6.20 | 1.18 | Fe XIII | 204.942 | 0.96
209.92 | 135 | 149.0 | 6.25 | 6.20 | 1.05 | Fe XIII | 209.916 | 0.95
202.04 | 5070 | 906.0 | 6.25 | 6.20 | 0.98 | Fe XIII | 202.044 | 0.96
264.79 | 858 | 239.0 | 6.29 | 6.20 | 0.99 | Fe XIV | 264.789 | 0.72
|  |  |  |  |  | Fe XI | 264.772 | 0.24
274.20 | 835 | 240.0 | 6.29 | 6.22 | 1.05 | Fe XIV | 274.204 | 0.94
252.20 | 58 | 36.3 | 6.29 | 6.22 | 1.20 | Fe XIV | 252.200 | 0.94
211.32 | 370 | 418.0 | 6.29 | 6.22 | 1.06 | Fe XIV | 211.317 | 0.96
257.40 | 180 | 70.1 | 6.29 | 6.22 | 1.14 | Fe XIV | 257.394 | 0.96
270.52 | 398 | 112.0 | 6.29 | 6.22 | 0.99 | Fe XIV | 270.521 | 0.96
284.16 | 445 | 386.0 | 6.34 | 6.24 | 1.23 | Fe XV | 284.163 | 0.96

Figure 15: Emissivity ratios of a selection of EIS lines for the off-limb
quiet Sun observation of 2019-06-28.

Figure 15 shows the emissivity ratios of a selection of lines, from four of
the main ions observed by EIS. The emissivity ratios are essentially the
ratios of the observed intensities vs. the theoretical ones, as a function of
density, calculated for a constant temperature (see Del Zanna et al., 2004).
It is clear that the main density-diagnostic ratios from Fe XII, Fe XIII, and
Si X give consistent densities. Note that the main Fe XII lines, at
192,193,195 Å are somewhat affected by opacity (i.e. their observed
intensities are lower than expected), a typical feature of active region and
off-limb observations, as shown for the first time by Del Zanna et al. (2019).

Figure 16: Results of the analysis to obtain the EIS SW radiometric
calibration relative to AIA 193 Å.

##  Appendix F EIS/AIA Co-alignment

We took the AIA observations during the EIS rasters, and compared them with
the predicted AIA DN/s in the EIS FOV, using the updated EIS calibration. We
reduced the AIA count rates to the EIS spatial resolution, and assumed a slit
step size of 1.9″. The results are shown in Figure 17. The EIS jittering, bias
and point spread function limit the accuracy of the comparison. As the radial
decrease in the signal is very steep, we can accurately estimate the EIS
pointing in the E-W direction (to within 2–4″), while the N-S pointing is more
uncertain (5–10″).

Figure 17: Results of the analysis to obtain the EIS off-limb pointing in the
east and west, by comparing the predicted AIA signal with the observed one.

##  Appendix G EIS densities on Eclipse day

Figure 18:  Electron densities obtained from a selection of EIS line ratios on
the west and east regions. The dashed line indicates the expected radial
density profile for the quiet Sun, from Del Zanna et al. (2018).

Figure 18 shows the Electron densities obtained from a selection of EIS line
ratios on the west and east regions. The uncertainties are obtained by
assuming a $\pm$15 % uncertainty on the observed ratios, projected onto the
theoretical variation of the ratio, to obtain a lower and upper limit, shown
in the plot. The 15 % is a reasonable estimate of the uncertainty due to the
radiometric calibration, which is the main uncertainty. There is generally
good agreement among the three line ratios, especially on the west region.