# Diagnostics of non-Maxwellian electron distributions in solar active regions
from Fe XII lines observed by Hinode/EIS and IRIS

G. Del Zanna DAMTP, Center for Mathematical Sciences, University of Cambridge,
Wilberforce Road, Cambridge, CB3 0WA, UK  V. Polito Bay Area Environmental
Research Institute, NASA Research Park, Moffett Field, CA 94035, USA  Lockheed
Martin Solar and Astrophysics Laboratory, Building 252, 3251 Hanover Street,
Palo Alto, CA 94304, USA  J. Dudík Astronomical Institute, Academy of Sciences
of the Czech Republic, 25165 Ondřejov, Czech Republic  P. Testa Harvard-
Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02193, USA
H.E. Mason DAMTP, Center for Mathematical Sciences, University of Cambridge,
Wilberforce Road, Cambridge, CB3 0WA, UK  E. Dzifčáková Astronomical
Institute, Academy of Sciences of the Czech Republic, 25165 Ondřejov, Czech
Republic

###### Abstract

We present joint Hinode/EIS and IRIS observations of Fe XII lines in active
regions, both on-disk and off-limb. We use an improved calibration for the EIS
data, and find that the 192.4 Å / 1349 Å observed ratio is consistent with the
values predicted by CHIANTI and the coronal approximation in quiescent areas,
but not in all active region observations, where the ratio is often lower than
expected by up to a factor of about two. We investigate a number of physical
mechanisms that could affect this ratio, such as opacity and absorption from
cooler material. We find significant opacity in the EIS Fe XII 193 and 195 Å
lines, but not in the 192.4 Å line, in agreement with previous findings. As we
cannot rule out possible EUV absorption by H, He and He II in the on-disk
observations, we focus on an off-limb observation where such absorption is
minimal. After considering these, as well as possible non-equilibrium effects,
we suggest that the most likely explanation for the observed low Fe XII 192.4
Å / 1349 Å ratio is the presence of non-Maxwellian electron distributions in
the active regions. This is in agreement with previous findings based on EIS
and IRIS observations independently.

atomic processes — atomic data — Sun: UV radiation — Ultraviolet: general

††journal: ApJ

##  1 Introduction

Spectral lines from Fe XII provide a wide range of plasma diagnostics for the
solar corona, as this ion produces strong lines and is highly abundant. The
strongest transitions are in the extreme ultraviolet (EUV), and have been
routinely observed by the Hinode Extreme Ultraviolet Imaging Spectrometer
(EIS) (Culhane et al., 2007). Among them, the most intense lines are three
decays to the ground state, from 4P states of Fe XII , at 192.4, 193.5, and
195.1 Å. These Fe XII EIS lines have been widely used for a range of
diagnostic applications, especially in active regions.

Fe XII also produces several weaker forbidden lines in the UV from transitions
within its ground configuration. These include the 1242 Å line which has been
observed by e.g., SoHO SUMER (Wilhelm et al., 1997), and the 1349 Å line,
observed by the Interface Region Imaging Spectrograph (IRIS) (De Pontieu et
al., 2014). Because of the difference in the excitation energies between the
ground configuration states and the upper levels emitting the EUV lines, the
ratios of the UV forbidden lines to any of the 192.4, 193.5 and 195.1 Å lines
observed by EIS provide a direct and important diagnostic of the electron
temperature, largely independent of any assumption of ionisation equilibrium,
although the ratios also have a density dependence as shown in Fig. 1. For the
same reason, these ratios are also excellent, unexplored diagnostics for the
presence of non-Maxwellian electron distributions (NMED), see e.g., Dudík et
al. (2014). In this case, independent measurements of the electron temperature
are necessary.

We have recently obtained strong evidence that NMED effects are present in
active regions (Lörinčík et al., 2020; Dudík et al., 2017), especially in the
active region coronal loops and also the so-called moss, a thin layer at the
footpoints of the 3 MK loops (Fletcher & De Pontieu, 1999; Testa et al.,
2013), where Fe XII emission is brightest (see, e.g., Tripathi et al., 2008;
Testa et al., 2016).

The ratios of the Fe XII UV forbidden lines vs. the EUV lines is also
sensitive to any EUV absorption due to the presence of cool material such as
filaments and spicular material, which could significantly affect many
diagnostic applications of EUV lines. Most of the EUV absorption is due to
photoionisation of the ground state of neutral hydrogen, with a threshold at
912 Å, but significant absorption can also be due to photoionisation of the
ground states of neutral helium (threshold at 504 Å) and ionised helium
(threshold at 228 Å). Such absorption is widespread in the solar corona, and
is easily visible in active regions filaments. However, any absorption due to
low-lying emission such as spicules is more difficult to measure, as it is
inter-mingled with the moss emission. De Pontieu et al. (2009) carried out a
comparison between the Fe XII forbidden line observed by SoHO SUMER at 1242 Å
and the 195.1 Å line observed by Hinode/EIS in an active region. They found
that the 195.1 Å / 1242 Å ratio in moss regions was a factor of about 1.5
lower than expected and concluded that a likely explanation for the
discrepancy was absorption in the EUV due to cool plasma. They used an early
version of CHIANTI, the one which was available at that time. Since then, a
large-scale scattering calculation for Fe XII (Del Zanna et al., 2012)
significantly changed (by 30–50%) the populations of the ground configuration
states. The new calculations consequently increased significantly the
intensities of the forbidden lines. The improved Fe XII atomic data were made
available in version 8 of CHIANTI, and are also those in the current CHIANTI
v.10 (Del Zanna et al., 2021). With the improved atomic data, the 195.1/1242 Å
ratio decreases by about a factor of 1.5, bringing them in better agreement
with the ratios observed by De Pontieu et al. (2009) in the moss regions,
although not with the loop regions.

Figure 1: Theoretical intensity ratio (ergs) between the EUV 192.4 Å EIS line
and the UV 1349.4 Å IRIS forbidden line, calculated with CHIANTI v.10 and a
range of electron densities and temperatures.

As IRIS is capable of measuring the Fe XII 1349 Å line with a faster cadence
than that of SUMER for the 1242 Å line (about one hour), we devised a Hinode
campaign (HOP 246) of simultaneous EIS/IRIS active region observations. The
campaign started on 2014 February 14 and was mostly run in March 2014 on a few
active regions, in particular following the disk passage of AR 12014 during
the second half of the month. In spite of relatively long IRIS exposures
(30s), the signal for the Fe XII 1349 Å line, a weak forbidden transition, was
consistently low, except for a few observations when the active region was
near the limb. An analysis of two of those observations was presented by Testa
et al. (2016). Their results focused on Doppler flows and widths, but also
indicated a significant discrepancy (up to nearly a factor of two) between the
observed and predicted 195.1 Å / 1349.4 Å ratios, with the observed ones being
systematically higher. The discrepancy increased with the new atomic data in
CHIANTI version 8 (Del Zanna et al., 2015), relative to version 7 and seemed
to indicate a problem with the atomic data. This was surprising since the
benchmarking of Fe XII with observations generally showed good agreement (see
a summary in Del Zanna & Mason, 2018). After further investigation, this
discrepancy was found, for the most part, to be explained by the errant
inclusion of an obsolete keyword in eis_prep, and the adopted EIS calibration,
which is different from the updated version used here.

To test the Fe XII 192.4 Å / 1349.4 Å diagnostics, we analysed the HOP 246
observations, but also searched the entire IRIS and EIS databases for any
other suitable observations where the Fe XII lines were observed by both
instruments. We analysed several of these datasets and in the process
identified a series of problems associated with the EIS Fe XII observations,
as discussed below.

Section 2 outlines the data analysis and describes some of the main issues we
encountered which affected the selection of the observations. Section 3
describes the observations analysed here, while Section 4 summarizes our
conclusions. An Appendix provides supplementary information.

##  2 Data analysis and selection

###  2.1 EIS

The EIS data were processed with custom-written software (see, e.g., Del Zanna
et al., 2011). EIS saturation is at 16000 DN, however we found indications of
some non-linear effects for lower values approaching this threshold (Del Zanna
et al., 2019). The strongest EIS 195.1 Å line was sometimes saturated (or
close to saturation) in the AR moss regions. For this reason (and for other
reasons discussed below) observations of the weaker 192.4 Å line were used
instead.

An analysis of a large number of EIS observations of different features, on-
disk, off-limb, with different exposures, slit combinations, summarised in Del
Zanna et al. (2019), revealed several anomalies in the 192.4, 193.5, and 195.1
Å lines. The main ones affect the instrumental widths of the 193.5, and 195.1
Å lines and their reduced intensities (compared to the weaker 192.4 Å line),
in all active region and many off-limb observations. The only explanation
found for the anomalous ratios and widths of these lines was the ubiquitous
presence of opacity effects. In fact, these three lines are decays to the
ground state, so the ratios of these lines are insensitive to density and
temperature variations. Their theoretical ratios show agreement with well-
calibrated observations of the quiet Sun within 1% (Storey et al., 2005; Del
Zanna & Mason, 2005). Opacity effects were found to decrease the intensity of
the stronger 195.1 Å line by about 40%. Note that in active region
observations the relative intensity of the 195.1 Å line should actually
increase (compared to the quiet Sun) due to the presence of a weak Fe XII
density-sensitive transition (Del Zanna & Mason, 2005).

To diagnose the presence of NMED, the temperature needs to be estimated
independently. The Fe XI lines, identified by Del Zanna (2010) and used in
Lörinčík et al. (2020) offer such a diagnostic, but are generally not
telemetered, and in one of the observations discussed here are very weak, so
we had to resort to standard emission measure analyses.

To measure electron densities and for a meaningful comparison with IRIS, we
need to convert the EIS DN values to physical units using a radiometric
calibration. Del Zanna (2013a) presented a significant revision of the ground
calibration, with an additional time-dependent decrease in the sensitivity of
the long-wavelength channel. That calibration substantially affected the
ratios of the 192.4, 193.5, and 195.1 Å lines, which in quiet Sun on-disk
observations were forced to agree with theory and previous observations. As
further wavelength-dependent corrections as a function of time were clearly
needed, and the calibration only considered data until 2012, a long-term
program was started by GDZ and H.P.Warren, both of the EIS team, to provide an
improved radiometric calibration. Here we adopt these new calibration results,
as discussed in the Appendix.

###  2.2 IRIS

The IRIS and EIS observations are generally carried out simultaneously, but
are not necessarily co-spatial. In fact, the EIS slit is moved from west to
east to ‘raster’ a solar region, while the IRIS slit is moved in the opposite
direction (see e.g., Testa et al., 2016). Several IRIS observations were
carried out with a roll angle of 90 degrees, so that some co-spatial and co-
temporal EIS/IRIS observations were guaranteed. In some instances, several
EIS/IRIS rasters were repeated, so it was possible to check the solar
variability.

In addition to the available IRIS and EIS datasets, we also analysed context
images using images from the Atmospheric Imaging Assembly (AIA; Lemen et al.,
2012) telescope on board the Solar Dynamic Observatory (SDO; Pesnell et al.,
2012) in the 193 Å broad band filter, to select observations with small solar
variability (we note that the AIA 193 Å band is typically dominated by the
three Fe XII 192.4, 193.5, and 195.1 Å lines in the moss regions; e.g.,
Martínez-Sykora et al. 2011).

IRIS level 2 data were used. The data were spatially binned as described
below, to improve the signal. The Fe XII line was fitted with a Gaussian in
each pixel and the conversion to physical units was performed afterwards. The
radiometric calibration of the IRIS instrument is discussed in Wülser et al.
(2018). The uncertainty in the IRIS calibration for the data analysed here is
of the order of 20–30%

We also note that Testa et al. (2016) showed that in cases with low signal-to-
noise (especially when the peak DN in the line is less than 10), the intensity
of the line is likely to be under-estimated by up to $\sim 15$ percent. For
the comparisons with EIS, we typically only consider the regions where the
IRIS line has averaged peak DN above 20. Hence, we have not applied any such
corrections to the IRIS intensities.

During the analysis of the on-disk observations, we noticed the presence of an
unidentified photospheric (very narrow) line at exactly the rest wavelength of
the 1349.4 Å Fe XII line (see the Appendix). We have estimated that the
contribution of this line to on-disk moss regions is however minimal, of the
order of 5% in some locations, by using the C I 1354.28 Å line as a reference.

In addition, we estimate that the theoretical emissivity of the 1349.4 Å Fe
XII line is accurate to within 10%. As mentioned, the new atomic model
(CHIANTI, v8) increased the intensities of the forbidden lines by 50 percent
or more. A benchmark of the v.8 atomic data against quiet Sun off-limb SoHO
SUMER observations indicated excellent agreement (Del Zanna & DeLuca, 2018).
The population of the upper state of the 1349.4 Å line is mainly driven by
cascading effects. Improvements with future atomic calculations cannot be
ruled out. However, it is unlikely that larger calculations would affect the
line by more than a few percent. In the main scattering calculations, all
states up to $n=4$ were included by Del Zanna et al. (2012). Cascading effects
from higher states up to the main $n=6$ were included with an approximate
(distorted wave) calculation, showing an increase in the forbidden lines by
about 3%. These cascading effects were not included in CHIANTI v8 as the size
of the model ion would have been very large, and as a 3% increase was deemed
negligible.

###  2.3 On-disk observation - 2014 March 29

Following the above-mentioned data selection constraints, we analysed several
observations. A large scatter in the 192.4 Å / 1349.4 Å ratios was found,
although consistent results among the various measurements were also found. We
provide results for one of the on-disk observations, that obtained on 2014
March 29 by IRIS at 23:27-02:14 UT, i.e., the same observing sequence analyzed
by Testa et al. (2016).

The EIS raster we focus on here was obtained during 23:24 and 23:50 UT. Note
that in Testa et al. (2016) a later raster obtained a couple of hours later
(2014 March 30 01:36-02:02) was analyzed. In the brightest moss regions, the
EIS 195.1 Å line reached 15,000 DN, i.e., was very close to saturation. Fig. 2
(top) shows an image of the integrated intensity of the Fe XII 192.4 Å line
and its ratio (ergs) with the 195.1 Å line. The expected ratio is 0.31, which
is generally observed on-disk, but not in the brightest moss regions, where
the ratio increases to values around 0.4, an indication of some opacity
effects. We have assumed that the opacity effects in the 192.4 Å line are
negligible (see discussion below), and used this line for the comparison with
IRIS.

Figure 2: Top: intensity image in the Fe XII 192.4 Å line and ratio with the
195.1 Å line (ergs) for the 2014-03-29 observation. Note that the ratio should
have a value of 0.31. Bottom: intensity image of the IRIS 1349.4 Å line and
the 192.4 Å / 1349 Å ratio (ergs).

The IRIS raster was obtained with a -90o roll angle, 30s exposures and
stepping the 0.33′′ slit by 1′′, with 64 steps. The IRIS data were rotated and
rebinned by a factor of 12 along the slit, to obtain a spatial resolution in
the EW direction comparable to the EIS one, as EIS rastered with about 2′′
steps using the 2′′ slit. In the other direction, the IRIS data were first
interpolated linearly over a 0.33′′ grid, and then rebinned by a factor of 3,
to achieve a spatial resolution of 1′′, equivalent to the EIS pixel size along
the slit.

The contribution of the unidentified cool line blending the IRIS Fe XII line
was estimated by removing 4% of the C I line at 1357.13 Å. This resulted in a
small correction, of the order of 5 percent in a few places, i.e., not
affecting the main results.

As the effective spatial resolution of EIS is about 3–4′′(partly due to the
jitter during the long exposures), for a direct pixel-to-pixel comparison, the
IRIS data were convolved to obtain an effective spatial resolution close to
the EIS one. Such smoothing was not carried out in the analysis by Testa et
al. (2016), which may explain why a broader scatter in the ratios was found in
their analysis, compared to what is shown here. Finally, the EIS and IRIS
images were co-aligned by cross-correlation. The resulting IRIS image is shown
in Fig. 2 (bottom), together with the calibrated ratio of the 192.4 Å / 1349.4
Å lines (in ergs). It is clear that a pixel-to-pixel comparison has some
limitations, as in some places the morphology in the EIS and IRIS lines is not
quite the same. That is partly due to the non-simultaneity, partly due to the
EIS effective resolution which is very difficult to model. However, overall
the comparison is satisfactory. Figure 2 shows that the 192.4 Å / 1349.4 Å
ratio varies significantly, between values close to 30 in some regions to
around 15 in the brightest regions.

The 192.4 Å / 195.1 Å ratio (shown in Fig. 2) is indicative of some opacity
effects, which would be significant in the 195.1 Å line, but relatively small
(about 10%) in the weaker 192.4 Å line (see a discussion below on opacity
issues).

Figure 3: The 192.4 Å / 1349.4 Å ratio for the observation on 2014-03-29, as a
function of the calibrated intensity in the IRIS line.

A scatter plot of the 192.4 Å / 1349.4 Å ratio as a function of the calibrated
intensity in the IRIS line is shown in Fig. 3. It shows a large variation of
about a factor of two, with lower values where Fe XII is brightest, in the
moss regions. We selected three moss regions, indicated as B1, B2, and B3 in
Fig. 2 and measured the averaged density. The averaged intensities (obtained
from the pixel-by-pixel measurements) in the lines, their ratios and the
averaged densities are shown in Table 1. The averaged density is about 3
$\times 10^{9}$ cm-3 using the Fe XIII lines. The densities from Fe XII are
higher, partly because of opacity effects. We then measured the temperature
distribution with both an EM loci and a DEM method, using coronal abundances.
For the DEM analysis we used a modified version of the CHIANTI v.10 programs,
where the DEM is modelled as a spline function and the routine MPFIT is used.
The DEM results for the region B1 are shown in Fig. 4 as an example. The
temperature distribution is multi-thermal, but the Fe XII and Fe XIII lines
can also be reasonably modelled with an isothermal plasma around 2 MK. In the
moss region B1, the averaged ratio is about 19, lower than 25.1, the expected
value calculated with the measured density and the DEM.

Note that this is the same AR observed in Testa et al. (2016) (although not
observed at the same time; see sec. 2.3), where we recall the 195.1 Å / 1349.4
Å ratios were found higher than predicted (up to nearly a factor of two). We
tracked down the reason for this large difference, which was mostly due to an
obsolete keyword (correct_sensitivity) in the EIS standard eis_prep software,
and the different EIS calibration used.

The large variations in the ratio and the very low values (about 15) need to
be explained. They could be due to strong EUV absorption by neutral hydrogen
and helium emission or other non-equilibrium effects discussed below. Cool
filamentary material is always present in active regions, but its absorption
is difficult to quantify, unless it is higher up in the corona and the
underlying emission can reliably be estimated. In this observation, and the
other ones we have analysed, we did not find obvious evidence that the lower
ratios were due to cool filaments. However, we cannot rule out the possibility
that neutral hydrogen and helium is intermixed with the moss emission.

Figure 4: Top: DEM for the B1 region, indicated in Fig. 2. The points are plotted at the effective temperature, and at the theoretical vs. the observed intensity ratio multiplied by the DEM value. The wavelengths (Å) and main ion are indicated. Bottom: emissivity ratio of the main Fe XIII lines in the B1 region. Table 1: Intensities I (ergs) and ratios R (ergs) in the moss regions observed on 2014-03-29. Values in parentheses are DN. The last column shows the densities from the Fe XIII 204 Å / 202 Å ratio. Region | I (192 Å) | I (195 Å) | I (1349 Å) | R (192/195 Å) | R (192/1349 Å) | Log Ne
---|---|---|---|---|---|---
B1 | 1480 (11905) | 3970 (45533) | 78 (1100) | 0.37 | 19.0 | 9.5
B2 | 1850 (14881) | 4630 (53015) | 94 (1330) | 0.40 | 19.7 | 9.45
B3 | 1280 (10274) | 3180 (36400) | 41 (581) | 0.40 | 31.2 | 9.5

We have analysed other on-disk observations of active regions, and found
similar results to those shown above. Aside from other observations of the
same AR at the end of March 2014, we have analysed in detail an observation on
2013 Oct 7 and one on 2013 Nov 30.

###  2.4 Off-limb observation of 2013-10-22

To reduce the possible effects of absorption by cool material, we have
searched for off-limb observations with minimal filament material.
Unfortunately, only one suitable observation was found. This was obtained on
2013-10-22. The EIS study designed by us (cam_ar_limb_lite_v2) was rich in
diagnostic lines and had a good signal, as the exposure was 45 s. One problem
with this observation was the presence of a storm of high-energy particles so
each exposure had to be inspected to remove those particle hits, as standard
cosmic ray removal procedures did not work. In spite of this, some anomalous
intensities are still present due to residual particle hits/warm pixels in
some weaker lines. EIS rastered during 06:45–8:51 with the 2′′ slit an off-
limb region where a small active region was present. Most of the AR was
located well behind the east limb, as we could judge from AIA observations of
the following days.

We checked for the presence of cool filaments or spicular material using AIA
observations in 304 Å, but also 193 Å and 211 Å, together with H$\alpha$
observations by the Kanzelhöhe Observatory. The co-alignment of AIA with EIS
was achieved using a slicing method for the AIA 193 Å data to produce a
pseudo-raster corresponding to EIS Fe XII 192.4 Å. We find that best co-
alignment is found if the AIA is rotated with respect to EIS by about 0.5∘, as
well as shifted by a few arc seconds in both axes. The Kanzelhöhe H$\alpha$
data traditionally have excellent pointing, which we verified by comparison
with AIA 193 Å, focusing on filaments off-limb. Thus, the Kanzelhöhe H$\alpha$
data were coaligned with EIS analogously to AIA data.

The context AIA and H$\alpha$ data are shown in Figure 5 alongside the EIS
raster. We have selected two regions for further analysis, which are labelled
as ’AR’ and ’QR’.

The H$\alpha$ data and the AIA coronal images do not show any indications of
absorption by cool material off-limb in these regions. The main absorption
would be due to neutral hydrogen and neutral helium, with a minor contribution
from ionized helium.

The AIA 304 Å images show some emission above the limb in the ‘AR’ region, but
the amount of ionized helium is difficult to quantify, for multiple reasons,
including uncertainties in the chemical abundances, instrument calibration,
and coronal contribution to the band. We estimate that in the ‘AR’ region the
Si XI 303.33 Å line alone accounts for about a quarter of the AIA count rates
(which are about 40 DN s-1). In fact, with the DEM distribution we obtained,
the intensity of the Si XI line results 5280 (erg s-1 cm-2 sr-1). Using the
estimated effective area of the AIA channel (for this observation and
normalised to EVE), that is equivalent to an average of 11 DN s-1 per AIA
pixel due to Si XI. We note that the resonance He II lines at 303.8 Å are
formed at higher temperatures and have much larger optical thickness than
H$\alpha$, which in turn has similar optical thickness to the H and He
continua around 195 Å (e.g. Wang et al., 1998; Anzer & Heinzel, 2005). Thus,
the presence of weak-signal structures in He II, but not in H$\alpha$ along
the LOS is still consistent with negligible absorption of EUV radiation by
chromospheric or transition-region material.

IRIS scanned the same region from east to west with the 0.33′′ slit, 30s
exposure times and ‘sparse rastering’, i.e., the slit location was stepped by
1′′. The interesting area above the limb, where some IRIS signal from Fe XII
was present, was observed almost simultaneously by IRIS and EIS. We performed
the IRIS and EIS data reduction and calibration in a similar way to that
described in the previous section.

Figure 5: Context observations of the 2013-10-22 off-limb active region. The
EIS Fe XII 192.4 Å line is shown in the panel (a), while the AIA 193 Å pseudo-
raster is shown in panel (b). Panels (c)–(f) show snapshots from AIA and
Kanzelhohe H$\alpha$ observations, all coaligned to match the EIS and IRIS
observations.

Figure 6: Summary of the EIS/IRIS comparison on the off-limb AR observation on
2013-10-22.

Figure 6 shows a summary of the EIS/IRIS comparison. As for the on-disk cases,
the 192.4/195.1 Å is higher in the brightest regions, indicating some opacity
effects. The width of the 195.1 Å line is also larger in the same regions. As
in the previous cases, the 192.4Å / 1349.4 Å ratio varies significantly from
values around 30, north of the AR, to values around 15 closest to the core of
the AR. Figure 7 shows the scatter plot of this ratio. Averaged intensities
and ratios in those regions are shown in Table 2.

Figure 7: Scatter plot for the off-limb AR observation on 2013-10-22. Table 2: Intensities I (ergs) and ratios R (ergs) in the two the off-limb regions observed on 2013-10-22. Values in parentheses are intensities in DN (the exposure times for EIS and IRIS were 45 and 30 seconds, respectively).  Region | I (192 Å) | I (195 Å) | I (1349 Å) | R (192/195 Å) | R (192/1349 Å) |
---|---|---|---|---|---|---
AR | 1545 (19412) | 2920 (51907) | 73 (3343) | 0.53 | 21 |
QR | 880 (11049) | 1770 (31521) | 28.1 (1288) | 0.50 | 31 |

Figure 8 shows the emissivity ratios of the EIS Fe XII and Fe XIII lines, in
the quiet off-limb region (above) and active region (below). It is clear that
both regions are affected by opacity, which reduces the intensities of the Fe
XII 193.5 and 195.1 Å lines, compared to the 192.4 Å one. The densities
obtained from the Fe XII lines are close to those obtained from the Fe XIII
lines, considering the Fe XII 192.4 Å line, and the fact that this line is
likely underestimated because of opacity effects (see discussion below). We
adopt the Fe XIII densities as they are more reliable. The QR and AR regions
have densities around 4 and 10 $\times$ 108 cm-3.

Note that the Fe XIII lines include the photoexcitation effects, which affect
the population of the ground state and the density diagnostics by up to 10%,
as discussed in Dudík et al. (2021). They are caused by the large flux of
photons emitted by the disk around 1 $\mu$m, and resonantly absorbed by the
two near-infrared Fe XIII lines within the ground configuration. We have also
explored the effects due to photoexcitation in the Fe XII model ion,
considering that several transitions within the ground configuration fall in
the visible and far UV, but we did not find significant changes. We used
observations of the solar irradiance in the far UV and visible.

We have looked at the spatial distribution of various line ratios sensitive to
temperature and found that the temperature so obtained is relatively constant
in the off-limb regions. We produced EM loci plots for the quiet Sun and AR
regions, finding that observations are consistent with an almost isothermal
plasma around log $T$ [K]=6.2–6.25, which is the typical formation temperature
of Fe XII. We have then performed a DEM analysis using a set of strong lines
from Iron, not density-sensitive. The results are shown in Fig. 9 and confirm
the near isothermality of the plasma emission, with a marked higher
temperature component in the AR. The DEM analysis also indicated that the S/Fe
relative abundance is close to photospheric around 1.2 MK (using a S X line).

Figure 8: Emissivity ratios of the EIS Fe XII and Fe XIII lines, in the quiet
off-limb region (above) and active region (below).

Figure 9: DEMs for the quiet off-limb region (above) and active region (below)
for the 22-Oct-2013 observation. The points are plotted at the temperature
$T_{\rm max}$ of the maximum in the emissivity, and at the theoretical vs. the
observed intensity ratio multiplied by the DEM value. The wavelengths (Å) and
main ion are indicated.

We regard the spatial variation in the 192.4 Å / 1349.4 Å ratio as important,
since this is independent of any calibration issues, and largely independent
of the small variation in the density and temperature in the off-limb regions.
The averaged ratio in the QR region (31) is close to the expected value, 34.1,
obtained by folding the emissivities with the DEM distribution. On the other
hand, the AR value (21) is significantly lower than the expected value (30.9,
with the DEM shown above). The lowest values near the limb (around 15) are
even more difficult to explain.

As there is no clear indication for absorption by filament material, and as
opacity effects would decrease the 192.4 Å line by only a small amount (see
Sect. 3.1), we speculate that the main effect that could be responsible for
changing the ratio is NMED. The fact that the ratio has values close to the
expected ones in the northern part of the off-limb region, suggests that the
EIS vs. IRIS radiometric calibration is reasonably accurate.

##  3 Possible effects on the Fe XII line ratio and the temperatures

###  3.1 Opacity effects

Following Del Zanna et al. (2019), the optical thickness at line centre can be
written as

$\tau_{0}=8.3\,10^{-21}\,f_{lu}\frac{\lambda^{2}}{\Delta\lambda_{\mathrm{FWHM}}}\;N_{l}\,\Delta
S$ (1)

where $f_{lu}$ is the absorption oscillator strength, $N_{l}$ is the number
density of the lower level, $\Delta S$ the path length,
$\Delta\lambda_{\mathrm{FWHM}}$ is the FWHM of the line profile in Å, and
$\lambda$ is the wavelength in Å. For the 195 Å line, $f_{lu}=2.97/4$,
neglecting the weaker line.

The population of the lower level can be written as

$N_{l}={N_{l}\over N({\rm Fe\,XII})}\,{N({\rm Fe\,XII})\over N({\rm
Fe})}\,Ab({\rm Fe})\,\frac{N_{\mathrm{H}}}{N_{\mathrm{e}}}\,N_{\mathrm{e}}\;,$
(2)

where $N_{l}/N({\rm Fe\,XII})$ is the relative population of the ground state,
${N({\rm Fe\,XII})/N({\rm Fe})}$ is the peak relative population of the ion,
$Ab({\rm Fe})$ is the Fe abundance, $N_{\mathrm{H}}/N_{\mathrm{e}}=0.83$, and
$N_{\mathrm{e}}$ is the averaged electron number density.

Considering the box above the active region, as we have assumed for
photospheric abundances, we have $Ab({\rm Fe})=3.16\,\times 10^{-5}$. From the
EM loci / DEM analysis, we have $EM=10^{28.3}$ [cm-5] and log $T$[K]= 6.25,
approximately. With this temperature, ${N({\rm Fe\,XII})/N({\rm Fe})}=0.21$
using the CHIANTI ionisation equilibrium. Assuming the density from the Fe
XIII line ratio ($1\times 10^{9}$ cm-3, we have $N_{l}/N({\rm Fe\,XII})=0.75$
for these values of $T$, $N_{\mathrm{e}}$. From the $EM$ and $N_{\mathrm{e}}$
values, assuming a filling factor of 1, we obtain a path length of
2$\times$1010 cm, from which we obtain $\tau_{0}=0.96$ for the 195.1 Å line,
and $\tau_{0}=0.32$ for the 192.4 Å line, as this transition has an oscillator
strength a third of the 195.1 Å line.

Assuming that the source function $S_{\nu}(\tau_{\nu})$ does not vary along
the line of sight, the peak intensity of each line is

$I_{\nu}=S_{\nu}\,\left(1-e^{-\tau_{0}}\right)\;.$ (3)

Recalling that the line source function $S_{\nu}$ is:

$S_{\nu}={2\,h\,\nu^{3}\over c^{2}}\;\left({g_{u}N_{l}\over
g_{l}N_{u}}-1\right)^{-1}\;,$ (4)

with standard notation, we find that $S_{195}/S_{192}=1.04$ using the
statistical weights $g$ and the level populations calculated with the model
ion.

For $\tau_{0}(195)=0.96$, the ratio of the intensities is then
$I_{192}/I_{195}=0.43$, which is higher than the optically thin value of 0.31
and closer to the observed value of 0.53 for the region.

To estimate how much the weaker 192.4 Å line is suppressed for an optical
depth of 0.32, as our simple assumption is equivalent to the average escape
factor formalism, we consider the homogeneous case discussed by Kastner &
Kastner (1990), and obtain an escape factor of about 0.89, i.e., the 192.4 Å
line is suppressed by about 10%. Indeed if we increase the 192.4 Å line
intensity by this amount, the emissivity ratio curves would result in a
slightly lower electron density, in better agreement with the values obtained
from the Fe XIII ratio.

Finally, for the quiet off-limb ‘QR’ region, if we repeat the above estimates,
considering the lower $EM$ and lower density, we obtain
$\tau_{0}(192.4)=0.33$, i.e., a similar optical depth, in agreement with the
fact that the observed ratio is very similar.

Figure 10: Non-Maxwellian $\kappa$-distributions (top row) and their influence
on the Fe XII 192.4 Å and 1349.4 Å lines, whose contribution functions are
shown in the middle panels. The energy excitation thresholds for these two
lines are denoted by dashed lines in the top panel. Bottom panel shows the
behaviour of the 192.4 Å / 1349 Å ratio with $\kappa$, assuming peak formation
temperatures.

Figure 11: Diagnostics of the NMED represented by $\kappa$-distributions using
the ratio-ratio technique. Individual colors represent the value of $\kappa$,
while the cross of different sizes represent the observed line ratios in the
QR and AR boxes. The photon noise uncertainty $\sigma_{\mathrm{phot}}$ (light
blue), as well as added 20% to 30% calibration uncertainties $\sigma_{20,30}$
(violet and black, respectively) are shown. Colored asterisks in the right
panel denote the DEMκ-predicted line intensity ratios (see Section 3.3 for
details). Note that both axes are scaled logarithmically.

Figure 12: Observed ratios in each individual pixel corresponding to Figure 7
are overplotted on the theoretical diagnostic curves. Two sets of curves are
shown, for log($N_{\mathrm{e}}$ [cm-3]) = 8.6 and 9.4, representing the lowest
and highest densities detected. The points are color-coded either according to
the electron density (left panel) or according to the Fe XII 1349 Å intensity
(right panel).

###  3.2 Non-Maxwellian electron distributions (NMED)

####  3.2.1 NMED effects on the Fe XII ratio

To evaluate the effects of NMED, we considered the $\kappa$-distributions, a
well known class of non-Maxwellian distributions characterized by a near-
Maxwellian core and a power-law high-energy electron tail (see, e.g.,
Livadiotis, 2017; Lazar & Fichtner, in press). We use the standard expression
for $\kappa$-distributions of the second kind (see the discussion in
Dzifčáková et al., 2021), namely

$f_{\kappa}(E)dE=A_{\kappa}\frac{2}{\sqrt{\pi}\left(k_{\mathrm{B}}T\right)^{3/2}}\frac{E^{1/2}dE}{\left(1+\frac{E}{(\kappa-3/2)k_{\mathrm{B}}T}\right)^{\kappa+1}}\,,$
(5)

where $E$ is the electron kinetic energy, $T$ is the temperature,
$k_{\mathrm{B}}$ is the Boltzmann constant, and $A_{\kappa}$ is a constant for
normalization to unity. From the expression above it follows that the slope of
the high-energy power-law slope of the high-energy tail of a
$\kappa$-distribution is $\kappa+1/2$. The shape of the $\kappa$-distributions
as a function of $E$ is depicted in the top row of Figure 10.

The synthetic spectra for Fe XII and Fe XIII were obtained using the KAPPA
database (Dzifčáková et al., 2015, 2021), which allows for calculation of
spectra for $\kappa$-distributions using the same atomic data as CHIANTI
version 10 (Dere et al., 1997; Del Zanna et al., 2021). We calculated the Fe
XII and Fe XIII line intensities for a range of temperatures $T$ and $\kappa$
values and found that the EIS/IRIS ratio of Fe XII 192.4 Å / 1349 Å line
intensities offer unprecedented sensitivity to NMED, with the difference
between Maxwellian and $\kappa$ = 2 being of about a factor of two, depending
on temperature. This sensitivity to NMED comes from the widely different
wavelengths, and thus excitation energy thresholds of the two lines - 192.4
and 1349 Å (cf., Dudík et al., 2014).

The line contribution functions $G(T,\kappa)$ of the two lines, equivalent to
intensities normalized to unity emission measure, are shown in Figure 10. For
low $\kappa$ = 2, the peak formation of the Fe XII 192.4 Å line occurs at
higher $T$, and its intensity decreases. The shift in the temperature of the
peak, as well as about half of the decrease of the peak, are due to the
behaviour of the ionization equilibrium with $\kappa$ (Dzifčáková & Dudík,
2013; Dzifčáková et al., 2021). The decrease in excitation due to relatively-
lower amount of electrons in the $\kappa$ = 2 distribution at few hundred eV
(top panel of Figure 10) also contributes to the decrease of the peak of the
Fe XII 192.4 Å line. Compared to that, the forbidden 1349.4 Å line intensity
increases for low $\kappa$ (bottom row of Figure 10) despite the decrease of
the relative ion abundance. The reason is chiefly that the forbidden line,
whose excitation cross-section decreases with $E$, and which is excited by
electrons at energies of $E$ $\geq$ 9.2 eV, experiences excess excitation by
the relatively-higher peak of the $\kappa$ = 2 distribution (top row of Figure
10). The overall result is that for decreasing $\kappa$, the Fe XII 192.4 Å /
1349 Å line intensity ratio decreases (bottom panel of Figure 10).

However, one line ratio sensitive to $\kappa$ is not enough to determine the
$\kappa$ from observations. This is because the distribution function has two
independent parameters, namely $T$ and $\kappa$ (Equation 5), which thus need
to be determined simultaneously. (e.g., Dzifčáková & Kulinová, 2010; Mackovjak
et al., 2013; Dudík et al., 2014, 2015; Lörinčík et al., 2020; Dzifčáková et
al., 2021). Therefore, it is advantageous to combine this ratio with a
primarily temperature-sensitive Fe XII / Fe XIII ratio, which allows for de-
coupling of the sensitivities to $\kappa$ and to $T$ (see Figure 11) provided
the plasma is in ionization equilibrium. For the latter ratio, we chose the Fe
XII 192.4 Å line together with the unblended and well-observed Fe XIII 202.0 Å
line, thus minimizing the photon noise uncertainties. The ”ratio-ratio”
diagnostic diagram for $T$ and $\kappa$ is then constructed by plotting the
dependence on one line ratio upon the other one, see Figure 11. There, the
colored curves denote individual values of $\kappa$, with black being
Maxwellian and red corresponding to $\kappa$ = 2. Individual values of log($T$
[K]) are denoted by gray isotherms intersecting the curves for different
$\kappa$.

####  3.2.2 NMED measurements

The line intensity ratios of Fe XII 192.4 Å / 1349 Å together with the Fe XII
192.4 Å / Fe XIII 202.0 Å observed in the AR and QR boxes are shown in Figure
11 together with their uncertainties, consisting of photon noise uncertainty
$\sigma_{\mathrm{phot}}$ (light blue) as well as the added 20–30% calibration
uncertainty, denoted as $\sigma_{20}$–$\sigma_{30}$ (violet and black crosses,
respectively). This uncertainty is conservative, but is shown nevertheless
because the instruments were not cross-calibrated independently. We note
however that the differences in the observed Fe XII 192.4 Å / 1349 Å ratio are
systematic between the quiet Sun and active region (see Figure 6. That means
the differences between AR and QR shown in the diagnostic diagram in Figure 11
are not a result of purely calibration uncertainty, since the calibration is
the same for both the QR and AR. Note also that we have corrected the Fe XII
192.4 Å line intensity for the optical depth effects, as discussed in Section
3.1.

In the QR box, where the observed ratio is higher and about 30, the plasma is
consistent with the Maxwellian or weakly NME distribution within the
uncertainties (left panel of Figure 11). However, in the AR box, the observed
ratio (of about 20) corresponds to NMED with the value of $\kappa$ $<$ 5–10
even considering the calibration uncertainties. The value of $\kappa$ is
possibly even lower, $\kappa$ = 2–3, as indicated by the photon noise
uncertainty (Figure 11).

We note that the theoretical diagnostic diagram consisting of the Fe XII 192.4
Å / 1349 Å together with the Fe XII 192.4 / Fe XIII 202.0 Å line intensity
ratios also show some dependence on electron density. However, this dependence
on density is much weaker than those of the Fe XI line ratios previously
employed for diagnostics of $\kappa$ by Lörinčík et al. (2020). Given that
electron density can be determined nearly independently of $\kappa$ (see,
e.g., Dudík et al., 2014, and references therein), we are confident that the
current determination of NMED effects is not influenced by uncertainties in
the determination of $N_{\mathrm{e}}$.

The estimate of the uncertainty in electron density of $\approx$0.1 dex in
log($N_{\mathrm{e}}$ [cm-3]) (see Figure 8) leads only to small changes in the
theoretical diagnostic curves in Figure 11 (see Appendix C); meaning that the
result of $\kappa$ $\lesssim$ 5–10 in the AR box holds even when this
uncertainty in the electron density is taken into account.

To illustrate the spatial variations in the NMED, we overplotted the ratios in
all the pixels in the off-limb observation of 2013 October 22, corresponding
to Figure 7, on the NMED ratio-ratio diagrams (see Figure 12). We color-coded
the individual points either by the electron density $N_{\mathrm{e}}$ (left
panel) or the observed Fe XII 1349 Å intensity (right panel). The electron
densities were measured using the Fe XII 186.9 / 192.4 Å density-sensitive
ratio, and were found to range between log($N_{\mathrm{e}}$ [cm-3]) = 8.6 to
9.4. We note that the highest values are found in the active region where the
Fe XII 1349 Å line is brightest.

Figure 12 shows that the spread in the location of the observed Fe XII 192.4 Å
/ 1349 Å ratio is well matched by the theoretical curves. In agreement with
Figure 7, the larger Fe XII 1349 Å intensities correspond to locations that
are more non-Maxwellian. Finally, the Fe XII 192.4 Å / Fe XIII 202.0 Å ratio,
plotted on the horizontal axis, which is dominantly sensitive to $T$,
indicates that the plasma is nearly isothermal, with all the points being
clustered close to the log($T$ [K]) = 6.25 isotherm.

We therefore conclude that the NMED effects provide a possible explanation for
the observed anomalously low Fe XII 192.4 Å/1349 Å line intensity ratios.

###  3.3 Plasma multithermality

The diagnostics of $\kappa$ in the previous section assumed that the plasma
can be described by two parameters, $\kappa$ and $T$. However, as we have seen
earlier in Section 3.1, if interpreted as Maxwellian, the observations
indicate presence of some degree of multi-thermality (see Figure 9).

Generally, if the plasma is multi-thermal, the differential emission measure
(DEMs) can be a function of $\kappa$ (Mackovjak et al., 2014; Dudík et al.,
2015; Lörinčík et al., 2020). This has consequences for the diagnostics of
$\kappa$, as these DEM${}_{\kappa}(T)$ could affect the predicted line
intensities and their ratios that need to be compared with the observed ones.
In fact, once the synthetic line intensities and their ratios are obtained for
the respective DEM${}_{\kappa}(T)$, each of the ratio-ratio diagnostic curves
in Figure 11 collapses to a single point representing the two synthetic line
intensity ratios predicted by the respective DEMκ.

In order to take the possible plasma multithermality into account, we
performed the DEM${}_{\kappa}(T)$ inversions in the AR box for each $\kappa$
using the same method as in Section 3.1. In doing so, we used the respective
line contribution functions $G(T,\kappa)$ as inputs. We note that this DEM
analysis for variable $\kappa$ was done only for the AR box, as the quiet-Sun
region (QR) intensities are already consistent with Maxwellian.

The DEMκ-predicted points for each $\kappa$ are shown in the right panel of
Figure 11 as series of colored asterisks, where the color represents the value
of $\kappa$. It is seen that each point is close to the respective curve for
the same $\kappa$, as expected. This analysis confirms that the Fe XII
intensities in the active region can be explained by non-Maxwellian
$\kappa$-distributions, as the points for $\kappa$ = 2–5 are a relatively
close match to the observed intensities, while the Maxwellian point is still
outside of the error-bars even if the calibration uncertainty is
conservatively assumed to be 30%.

###  3.4 Time-dependent ionization (TDI)

In the presence of heating and cooling events occurring on short timescales,
the possible effects of time-dependent ionization (TDI) on our diagnostics
should also be considered. A full treatment of TDI requires detailed modelling
of dynamic heating events in ARs, including its effect on both ion charge
state distribution and the relative level population. As such, it is outside
the scope of this work. Nevertheless we refer the reader to existing
literature on this subject as well as theoretical arguments which indicate (to
demonstrate) that TDI effects are likely not significant enough to explain the
observed discrepancies in the intensity ratio of the two Fe XII lines. For
instance, a relevant recent work is that of Olluri et al. (2015), who
presented simulations of a quiet solar region from the three-dimensional
magnetohydrodynamic code (MHD) code Bifrost (Gudiksen et al., 2011) including
non-equilibrium ionization, showing that the Fe XII ion was found to be close
to its ionization equilibrium. Although a quiet Sun case might not be entirely
applicable to our observations (the Fe xii emission in a quiet region will be
primarily emitted in the corona whereas in a bright AR it will mostly be
confined to the TR), we note that in the same simulation the TR ions were
significantly out of equilibrium (see Figure 15 in Olluri et al., 2015).
Another example comes from the simulations of nanoflare-heated coronal loops
by Bradshaw & Klimchuk (2011), where the “warm” emission, which includes Fe
XII and Fe XIII, was mostly close to equilibrium, even if the hotter emission
was significantly out of equilibrium.

In the following paragraphs we also discuss possible effects of TDI on both on
the (1) Fe XII relative emission as well as the (2) ion charge state
distribution.

(1) TDI effects could lead to changes in the relative level population of Fe
XII, and thus changes in the 192.4 Å / 1349 Å line intensity ratio. The EIS
192.4 Å line is an allowed transition with a very short decay time, of the
order of picoseconds. On the other hand, the IRIS 1349 Å forbidden line is a
decay from the 2P1/2 state, one of the metastable levels in the ground
configuration, which have typical decay times that are much longer. The
lifetime of the 2P1/2 level is only 4 milliseconds, so timescales this short
would be needed to alter significantly the intensity of the IRIS line,
compared to the equilibrium calculations. However, unlike the upper state of
the EIS 192.4 Å line, which is solely populated from the ground state, the
population of the 2P1/2 is more complex. To assess it, we have looked at the
dominant processes, calculated in equilibrium at the temperatures and
densities of the active regions we have observed. We find that about half of
the population of the 2P1/2 is due to cascading from higher states, most of
which are connected to the ground state, 4S3/2. Nearly 30% of its population
comes from the ground state, and nearly 20% from the 2D5/2 state, which has a
longer lifetime of 0.4 s. In turn, about 90% of the 2D5/2 population comes
from cascading from high-lying states, which again are mostly connected to the
ground state.

Therefore, non-equilibrium effects with timescales shorter than 0.4 s would
affect the population of the 2D5/2 state but in turn change only by a small
amount the intensity of the IRIS line. Overall, the ratio of the IRIS and EIS
lines would be affected by at most 20% if the timescales are shorter than 0.4
s.

(2) TDI effects could affect our observed ratios through the ion charge
distributions. The timescales for ion charge distributions to reach
equilibrium are considerably longer in the solar corona. For example, at
coronal densities, the Fe XII has an ionization equilibration timescale of the
order of 102 s (Smith & Hughes, 2010), which is apt to be prolonged if there
are flows in the plasma that lead to mixing of plasma from regions of
different temperatures. Therefore, the TDI effects could affect the ionisation
temperatures we have estimated. We recall that we estimated the temperature
(via DEM analysis or line ratios) using lines from successive ionization
stages of Iron. In particular, we used the Fe XII / Fe XIII line intensity
ratio for simultaneous diagnostics of $T$ and $\kappa$ (see Sect. 3.2). For
the measured Fe XII 192.4 Å / 1349 Å ratio in the AR box to be consistent with
Maxwellian, the complementary Fe XII 192.4 Å / Fe XIII 202.0 Å ratio would
need to be different by about a factor of 10 (see the right panel of Figure
11). This means that for the plasma to be Maxwellian, the Fe XII / Fe XIII
ratio should be at least 5 instead of the measured value of 0.5. Therefore, to
explain the observations, the TDI effects would have to lead to departures
from the Fe XII / Fe XIII ratios by about at least an order of magnitude (cf.
Figure 11), which we deem unlikely, as the two ions are typically formed at
similar temperatures and regions even in cases where the heating is transient
and strong (see, e.g., Figures 2–3 of Reale & Orlando, 2008).

Based on the considerations above, we suggest that TDI alone cannot easily
explain the observed Fe XII ratios in our AR observations, although future
numerical investigation will be necessary to rule it out completely.

##  4 Discussion

As described in Section 3, assuming that NMED are present offers by itself a
satisfactory explanation for the departures in the Fe XII 192.4 Å / 1349 Å
line intensity ratio in the observed active regions. We now discuss the
implications this finding entails, with emphasis on the timescales involved.
These include:

  * •

timescale for equilibration of free electrons to a Maxwellian fluid,

  * •

timescales for spontaneous emission,

  * •

timescales for TDI effects,

  * •

typical timescales for evolution of the AR emission,

  * •

spectrometer exposure times,

  * •

possible coronal heating frequency.

With the timescales for spontaneous emission and TDI effects were already
discussed in Section 3.4, we now examine the remaining ones, as well as their
possible interplay.

###  4.1 Timescales for maintaining NMED

Our analysis of the NMED effects was based on the $\kappa$-distributions
(Section 3.2), which have only one extra parameter, $\kappa$, and are assumed
to be time-independent. However, once accelerated and non-Maxwellian, the bulk
of the free electrons tends to thermalize due to collisions. Meanwhile, the
same free electrons drive ionization, recombination, and excitation processes
necessary for creation of the observed spectra. The timescale
$\tau_{\mathrm{e}}$ for equilibration of the free electrons to a Maxwellian
electron fluid due to both electron–electron and electron–ion collisions is
given by Equation (3.50) of Goedbloed & Poedts (2004), which in cgs units is:

$\tau_{\mathrm{e}}=\frac{1.09\times
10^{10}}{\mathrm{ln}\Lambda}\frac{\tilde{T}^{3/2}}{ZN_{\mathrm{e}}}\,,$ (6)

where ln$\Lambda$ is the Coulomb logarithm, $\tilde{T}$ is electron
temperature in keV units, and $Z$ is the proton number. Taking $Z$ = 1
(considering that most of the ions in the solar corona are Hydrogen ions),
ln$\Lambda$ $\approx$ 10, and using the measured values of
log($N_{\mathrm{e}}$ [cm-3]) = 9.1 and log($T$ [K]) = 6.25 (corresponding to
$\tilde{T}$ of about 0.22 keV), we obtain $\tau_{\mathrm{e}}$ $\approx$ 0.1 s.

We note that the above classical formula holds for the bulk of the electron
distribution function, as the electrons in the high-energy tail are
progressively less collisional, with the collision frequency decreasing with
with kinetic energy $E$ as $E^{-3/2}$. In addition, the acceleration of
progressively higher-$E$ electrons can also take longer (see Bian et al.,
2014), although the details will depend on the acceleration mechanism itself;
which, if indeed operating in the solar corona, is as of yet unknown. If the
acceleration occurs due to turbulence, as derived by Bian et al. (2014), then
the parameter $\kappa^{*}$ = $\kappa+1$ describes the competing timescales of
electron acceleration and collisional timescales, $\kappa^{*}$ =
$\tau_{\mathrm{acc}}/2\tau_{\mathrm{coll}}$ (see Equation (14) of Bian et al.,
2014). It follows that if the measured $\kappa$ values as low as 2–3 in active
regions are correct, the electrons must be continuously accelerated.
Otherwise, we would not be able to see changes in the measured Fe XII 192.4 Å
/ 1349 Å ratio due to NMED effects, as the electrons would return to
equilibrium Maxwellian distribution within a fraction of the exposure times
required for our remote-sensing spectroscopic measurements.

In addition, it should be noted that the timescales for spontaneous emission
in Fe XII (discussed in Section 3.4) are much shorter, by orders of magnitude,
than the electron equilibration timescale $\tau_{\mathrm{e}}$ derived above.
Therefore, the level population of Fe XII reflects the changes in the electron
distribution much faster, and is likely in equilibrium even in the case if the
electron distribution undergoes evolution.

###  4.2 Implications for coronal heating

It is interesting to consider the implication of continuous re-acceleration of
non-Maxwellian electrons (Section 4.1) in terms of coronal heating. We
speculate that if continuous re-acceleration is connected to the frequency of
the ”nanoflare” heating of the solar corona, our observations may suggest
novel constraints on the nanoflare heating models. We note that the current
leading nanoflare or nanoflare train models (see, for example, Cargill, 2014;
Barnes et al., 2016; Viall & Klimchuk, 2017; Reva et al., 2018; Warren et al.,
2020, and references therein) typically consider heating durations of the
order of tens of seconds with separation between individual heating events as
large as of the order of 102–103 s. In addition, recent observations of moss
variability in ARs with IRIS suggest that heating durations of the order of
tens of seconds are common (Testa et al., 2013, 2014, 2020).

Our implication that the re-acceleration occurs continously can be reconciled
with these works if the heating occurs due to short individual bursts (so that
electrons are re-accelerated), while the duration of the envelope of the
heating can be as long as 101–102 s. One mechanism that behaves this way is
slipping reconnection, which is the general mode of reconnection in three
dimensions (see, e.g. Janvier et al., 2013; Dudík et al., 2014). During
slipping reconnection, individual field lines reconnect many times, indeed
sequentially, with different field lines, while their footpoints slip across
the solar surface. The slipping reconnection in many small-scale quasi-
separatrix layers has been shown to be a viable coronal heating mechanism
(Yang et al., 2018) and is indeed sometimes observed to occur in moss regions
(Testa et al., 2013). However, other mechanisms can also lead to many
individual heating events occurring due to a longer-duration conditions of
energy release in a coronal loop. One can imagine that, for example, wave-
particle resonance interactions would behave much the same way as long as the
larger-scale wave lasts. Such speculations are however out of the scope of the
present work, and we do not engage in them further. Nevertheless, we do note
that if the scenario of frequent re-acceleration events occurring within a
longer-duration heating envelope is correct, the behavior of emission within
individual emitting strands (as well as their collective emission) should be
modeled in detail, as there are many timescales involved, as mentioned at the
beginning of this section, including the timescale for equilibration of the
relative level population, TDI effects, and the NMED effects.

##  5 Summary

We have investigated coordinated Hinode/EIS and IRIS observations of Fe XII
lines. While the EIS observes the allowed lines in the EUV part of the
spectrum, the IRIS observes the forbidden line at 1349 Å. We find that the
ratio of these two lines decreases strongly with the increase in intensity of
the forbidden 1349 Å line in active regions. In the quiet Sun, the Fe XII
192.4 Å / 1349 Å ratio is about 30–40, while in active regions, the ratio
decreases down to values of below 20, even reaching values as low as 10 in
some cases. These measurements were accompanied by determination of the
temperature and emission measure using lines of Fe IX–Fe XVI, as well as
electron densities using density-sensitive Fe XII and Fe XIII lines from EIS.

Using synthetic spectra obtained from CHIANTI version 10, we investigated
whether the behaviour of the Fe XII 192.4 Å / 1349 Å ratio could be due to its
dependence on electron temperature and density. Especially in active regions,
we found significant and systematic discrepancies in the observed 192.4 / 1349
Å ratio with respect to the predictions based on the synthetic spectra
obtained by CHIANTI. In the AR box that we selected for detailed analysis, we
measured values of log($T$ [K]) = 6.25 and log($N_{\mathrm{e}}$ [cm-3]) = 9.1,
resulting in a predicted Fe XII 192.4 / 1349 Å ratio of about 30, while the
observed value is about 20.

We reviewed the potential causes of this discrepancy, including:

  1. 1.

Opacity effects on the Fe XII EUV lines,

  2. 2.

presence of cool plasma along the line of sight,

  3. 3.

plasma multithermality,

  4. 4.

dependence of the observed ratio on non-Maxwellian electron distributions
(NMED).

  5. 5.

effects due to time-dependent ionization (TDI)

Opacity in the Fe XII lines was detected as an increase in width of the EUV
lines, especially the 193.5 and 195.1 Å lines (see Del Zanna et al., 2019).
Being the weakest of the three transition, the 192.4 Å line is least affected.
Based upon the measured temperatures and emission measures, we estimated that
the optical depth in the 192.4 Å line is about 0.32 (and 0.96 for the 195.1 Å
line), leading to suppression of the Fe XII 192.4 Å line by about 10%. This
effect was therefore deemed insufficient to explain the discrepancies in the
192.4 Å / 1349 Å ratio. We subsequently corrected the observed 192.4 Å line
intensity accordingly to account for self-absorption.

The relative absence of cool material along the line of sight was checked
based on the AIA 193 Å and H$\alpha$ observations by the Kanzelhöhe Solar
Observatory. We note that the two wavelengths have similar optical thickness
(Anzer & Heinzel, 2005) and that the absorption near 195 Å occurs due to the H
I, He I, and He II continua. Our selected QR and AR for the quiet and active
region were also chosen to be above the H$\alpha$ spicules, and in regions
devoid of prominence material, so that the absorption by the H and He continua
was deemed negligible.

We used the the $\kappa$-distributions to study the influence of the NMED on
the line ratio. Using the updated KAPPA database (Dzifčáková et al., 2021)
corresponding to CHIANTI version 10, it was found that the Fe XII 192.4 Å /
1349 Å ratio decreases with increasing number of high-energy electrons (i.e.,
lower $\kappa$). The observed Fe XII ratio of about 20 in the AR can be
explained by NMED with $\kappa$ as low as 2–3, although calibration
uncertainties are significant. In addition, the spatial distribution of the
ratio matches well the theoretical diagnostic curves for NMED, where the
lowest observed ratios correspond to strongly NMED plasmas. These theoretical
curves for NMED are only weakly dependent on electron density and show strong
sensitivity to $\kappa$, making the Fe XII ratio one of the best diagnostic
options for the NMED. In addition, the plasma multithermality was ruled out as
the cause of the departure of the Fe XII ratio in active regions, since any
DEM effects would only exacerbate the the discrepancy.

Finally, based on theoretical arguments as well as existing literature, we
concluded that TDI effects alone are likely insufficient to explain the
observed discrepancies in the Fe XII ratio, although they cannot be ruled out.

Our measurements employed a new EIS calibration, which will be described in
detail in a separate publication. The uncertainty inherent in the calibration
limits the determination of $\kappa$ from our measurements. Nevertheless, the
off-limb quiet Sun and active region are observed simultaneously, and the new
calibration shows that the ratio in the quiet Sun is consistent with
Maxwellian electrons, in accordance with independent previous measurements
from EIS (Lörinčík et al., 2020), but also X-ray instruments (Kuhar et al.,
2018), which do not show presence of accelerated particles in quiet Sun
regions. This indicates that the relative EIS/IRIS calibration is likely
correct.

For the reasons listed above, we are left with NMED as the most likely,
simplest cause of the anomalously low Fe XII 192.4 Å / 1349.4 Å ratio in the
observed active regions.

Using Equation (3.50) of Goedbloed & Poedts (2004) we calculated that the
timescale $\tau_{\mathrm{e}}$ for equilibration of the free electrons to a
Maxwellian electron fluid is given by $\tau_{\mathrm{e}}$ $\approx$ 0.1 s, for
the core of the distribution, using the values of temperature and density
measured. Given that the Fe XII lines were observed with exposure times of
tens of seconds, this suggest that the electrons must be continuously
accelerated or re-accelerated over these timescales, otherwise they would
return to equilibrium Maxwellian distribution within a fraction of second. Our
observations could thus provide interesting new constraints on the nanoflare-
based coronal heating models.

Observations with well-calibrated instruments in the future could use these or
similar allowed-to-forbidden coronal line ratios to diagnose the presence of
NMED. One attractive option is EUVST, as it will observe the same lines as the
EIS SW channel, and UV lines with a high sensitivity, hopefully measuring the
diagnostic ratios with a cadence of a fraction of a second.

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). VP was supported by NASA under contract
NNG09FA40C (IRIS). PT was supported by contract 8100002705 from Lockheed-
Martin to SAO, NASA contract NNM07AB07C to the Smithsonian Astrophysical
Observatory, and NASA grant 80NSSC20K1272. J.D. and E.Dz. acknowledge support
from Grants No. 20-07908S and 22-07155S of the Grant Agency of the Czech
Republic, as well as institutional support RVO:67985815 from the Czech Academy
of Sciences. GDZ, JD, and HEM also acknowledge support from the Royal Society
via the Newton International Alumni programme. We thank the anonymous referee
for careful reading and useful comments. IRIS is a NASA small explorer mission
developed and operated by LMSAL with mission operations executed at NASA Ames
Research center and major contributions to downlink communications funded by
ESA and the Norwegian Space Centre. 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. H$\alpha$ data were provided by the Kanzelhöhe
Observatory, University of Graz, Austria.

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##  Appendix A  Blending of the IRIS Fe XII line

As the IRIS spectral range is rich in unidentified narrow lines due to
photospheric/chromospheric lines, as well as molecular lines, we have analysed
one full spectral IRIS atlas during a flare, and measured the intensities of
all the known and unknown cool lines in the spectra. The observation was
obtained on 2013-10-11 with a long dense IRIS raster that started at 23:55 UT.

Fig. 13 shows superimposed two spectra, one obtained on a moss region (pixel
values 240:260 in solar X and 130:160 along the slit), and the other one at
pixel coordinates 73 (solar X) and 192 (solar Y) on a flare ribbon, reduced by
a factor of 20. It is clear that in the moss region the 1349.4 Å line is due
to Fe XII, as it has the expected width. The spectrum in the ribbon is instead
solely due to an unidentified narrow cool line, with a wavelength coincident
with that of the Fe XII line. The spatial distribution of this unidentified
line is quite different than that of most known lines such as the Cl I 1351.66
Å. It is similar to that of the strong C I lines at 1357.13, 1354.28 Å, but is
actually closest in morphology to another unidentified line at 1350.69 Å. The
ratios of the known C I lines are relatively constant, so a possible way to
estimate the contribution of the unidentified line at 1349.4 Å is to consider
the observed ratios in the ribbons with the C I lines. For example the ratio
(in data number) with the C I 1354.28 Å ranges between 0.02 and 0.07.

Figure 13: IRIS FUV1 spectra around the Fe XII 1349.4 Å line.

##  Appendix B EIS radiometric calibration

Briefly, 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 with an isodensity in these cases and possible
issues related to the presence of NMED are avoided. Also, this removes
blending with cool lines from a few coronal lines. This is an extension of the
method used by Warren et al. (2014), where strict isothermality was assumed.
The established relative calibration for the short-wavelength (SW) channel was
then used to calibrate the EIS spectra, for a direct cross-calibration with
simultaneous SDO AIA 193 Å data, taking into account the different spatio-
temporal resolutions, basically following the methods described in Del Zanna
et al. (2011); Del Zanna (2013b). Good agreement (to within a few percent)
between the AIA DN/s predicted from EIS, and those observed by AIA (re-scaled
to the lower spatio-temporal resolution of EIS) is imposed, noting that a
typical spatial scatter around 10% is normally found. We used the modelled AIA
degradation as available in SolarSoft, with the option of the normalisation
with SDO EVE. We also checked this AIA calibration against simultaneous SDO
EVE observations, using the latest EVE calibration, which in itself relies on
a comparison with a few sounding rocket flights and adjustments using line
ratios, following the methods adopted for EIS (Del Zanna, 2013a). In turn, the
prototype EVE flown on the sounding rocket flights is regularly calibrated on
the ground. The absolute calibration of the EVE prototype is deemed accurate
to within 20%, although detailed comparisons carried out on the first flight
showed larger discrepancies (40%) for some of the strongest lines (Del Zanna &
Andretta, 2015; Del Zanna, 2019). The overall accuracy of the EIS absolute
calibration adopted here, considering all the comparisons, could be estimated
to be in the range 20–30%. Such a reliable calibration in the EUV (a
notoriously difficult problem) could only be established for EIS data in 2013
and 2014, as in 2014 the failure of EVE MEGS-A meant that no direct AIA/EVE
cross-calibrations could be carried out. After 2014, the only useful cross-
calibration EVE sounding rocket was flown in 2018. The results of the EIS
improved calibration will be published in Del Zanna and Warren (2022, in
preparation).

Figure 14: Dependence of the NMED diagnostic diagrams on log($N_{\mathrm{e}}$
[cm-3]). The diagnostic curves shown by full lines and the observed ratios
correspond to Figure 11 right. Dashed a dot-dashed lines denote changes in
electron density equal to 0.1 dex.

##  Appendix C Electron density uncertainties and the diagnostics of $\kappa$

The measurements of $\kappa$ done in Section 3.2.2 required prior
determination of electron density. However, the electron densities is also
subject to uncertainties of the measured line intensities, especially the
photon noise. Note we do not consider the calibration uncertainty, since all
lines used for measurements of $N_{\mathrm{e}}$ are observed by the same
channel of EIS.

The photon noise uncertainties are shown by gray stripes in the emissivity
ratio plots on Figure 8. It is seen that the photon noise introduces
uncertainty into the measurements of log($N_{\mathrm{e}}$ [cm-3]) of about 0.1
dex for Fe XIII, and slightly larger, $\approx$0.15 dex, for the Fe XII 186.9
Å and 192.4 Å pair of lines.

In Figure 14, we show the changes in the diagnostic diagram for the box AR
(see also right panel Figure 11) that occur due to the 0.1 dex uncertainty in
the measurements of log($N_{\mathrm{e}}$ [cm-3]). This uncertainty in electron
density is shown by different linestyles. It is seen that for the smallest
considered value of $\kappa$ = 2, the difference is negligible, while
uncertainty in $\kappa$ slightly increases with increasing $\kappa$ (i.e.,
approaching Maxwellian). However, even then, the curves for $\kappa$ = 10 and
Maxwellian still do not overlap. Therefore, our determination that the NMED
represent a viable explanation of the Fe XII 192.4 Å / 1349 Å ratio observed
in the AR is not influenced in the uncertainties in the measurements of
electron density.