The quiescent 3 MK emission in non-flaring ARs could be due to a range of processes, involving for example magnetic reconnection, turbulence, nanoflare storms (see e.g., Cargill, 2014, and references therein), or Alfven waves (see e.g., van Ballegooijen et al., 2011). Most theoretical models predict the presence of some hot plasma above 3 MK (the “smoking gun”), see e.g., Cargill (1994) and Cargill and Klimchuk (2004). The presence of such hot plasma has been a matter of much debate in the literature, as its emission is very weak and difficult to observe. For a recent list of relevant references, see e.g., section 6.2.5 in Hinode Review Team et al. (2019).

The EUV has excellent diagnostics for lower-temperature plasma, up to about 4 MK, but only a few “hot” lines. For example, the Hinode EIS instrument (Culhane et al., 2007) provided excellent EUV observations of 1–4 MK plasma with e.g., Fe xvii, Ca xvii lines, but is “blind” in the 5–10 MK range. Only the very hot (about 15 MK) flare lines from Fe xxiii and Fe xxiv are observed (see e.g., Winebarger et al., 2012).

There are some studies of the hot emission based on full-disk spectra (see e.g., Sylwester et al., 2010; Miceli et al., 2012) or imaging (in e.g., Mg XII Reva et al., 2018), but few spatially-resolved spectroscopic observations of the 5–10 MK plasma in AR cores exist. They were at the limits of the instruments and provided an unclear picture. For example, EUNIS-13 observed significant signal in the Fe xix 592.2 Å line (Brosius et al., 2014), in the core of AR11726. However, unpublished analysis of EUNIS-13 observations of AR11724 and AR11723 (by A.Daw) indicated a much weaker or no signal in the same Fe xix line.

The Solar Maximum Mission (SMM) X-ray polychromator (Acton et al., 1980) Flat Crystal Spectrometers (FCS), had a collimator of about 15′′ × 14′′ and provided some observations of quiescent ARs, which were analyzed by Del Zanna and Mason (2014). It was only possible to put an upper limit to the emission measure at 7–10 MK of about three orders of magnitude lower than the peak value at 3 MK.

Parenti et al. (2017) found a few places where faint Fe xix emission was observed by SoHO SUMER, but it was necessary to integrate for 2 h and average spatially to achieve enough signal. The Fe xix intensity implied in some places an emission measure around 2.5–3 orders of magnitude below the peak. As SUMER only observed one hot line from Fe xix, it was not possible to establish the temperature (or the distribution of temperatures) producing the weak signal in the line, which in principle is formed between 6 and 12 MK in ionization equilibrium.

Observations of Bremsstrahlung emission in quiescent ARs with FOXSI and NuSTAR have confirmed the FCS and SUMER results, indicating little emission at high temperatures, although also in these cases the actual temperature distribution of the hot plasma could not be established. For example, Ishikawa et al. (2014) used FOXSI to place an upper limit in the 4–15 MK range, while the peak emission around 3 MK was constrained by Hinode XRT and EIS observations. Hannah et al. (2016) used NuSTAR observations to also find upper limits to the temperature distribution between 3 and 12 MK. The upper limit of the emission measure at 10 MK is about three orders of magnitude lower than the peak at 3 MK.

Reva et al. (2018) used CORONAS-F/SPIRIT Mg xii images to estimate an upper limit of the emission measure around 10 MK about four orders of magnitude lower than the peak value around 3 MK, which was constrained by SoHO EIT imaging. However, the information from Mg xii is somewhat limited as this ion in equilibrium is formed over a very broad temperature range, from 4 to well over 15 MK.

On the other hand, some evidence of hot emission was found by Marsh et al. (2018), also using FOXSI and NuSTAR observations. The lower temperatures were constrained using SDO AIA and Hinode XRT images. Nanoflare modeling was able to reproduce in some cases the FOXSI and NuSTAR observations.

To make progress, we need new observations to be combined with the predictions of nanoflare modeling (see e.g., López Fuentes and Klimchuk, 2015; Barnes et al., 2016a,b; Athiray et al., 2019). Regarding such nanoflare models, it is important to point out that they often tend to over-estimate the strength of the hot emission, although they can also predict no emission, depending on what assumptions are made (Barnes et al., 2016a). Given these uncertainties (observational and theoretical) on the strength of the hot emission, we provide below two simulations, one based on the FCS and SUMER observations, one on the López Fuentes and Klimchuk (2015) simulations, just to show what signal we might expect to observe.

In summary, to constrain the cadence and energy release in the heating events, we require measurements of strong unblended hot lines with a high sensitivity (to measure the weak emission) and high spectral resolution (a few km s⁻¹). Measurements of the electron density in the hot lines in the 10⁸–10¹¹ cm⁻³ regime would also be needed. High spatial resolution (1′′ or higher) is not required to characterize the hot emission, as we expect it to be well below such resolutions, and as there would always be several individual loop structures (strands) along the line of sight.

There is ample literature on observations and models of flares of GOES C class and above (see e.g., the reviews by Fletcher et al., 2011; Shibata and Magara, 2011; Benz, 2017). Most observations, however, have been of the flare loops formed as a by-product of chromospheric evaporation. It is generally thought that magnetic reconnection occurs in the corona, but the mechanisms by which energy is transferred and deposited into the chromosphere are not clear. Thermal conduction by electrons and non-thermal electrons have been considered for a long time, but other processes could be at play, as e.g., large-scale Alfvén waves (Fletcher and Hudson, 2008) or high-energy protons. A significant amount of particles need to be accelerated in the corona, but how is not clear. The most interesting but poorly observed aspects are those related to the reconnection region. Significant progress has been made on chromospheric evaporation.

Very few spectral observations showing strong Doppler flows in hot lines possibly associated with the magnetic reconnection region exist (see e.g., Imada et al., 2013; Tian et al., 2014; Polito et al., 2018; Warren et al., 2018). The likely reason is that the emission is weak, because reconnection is occurring in low-density plasma and on spatial scales well below current resolutions. Also, as we have mentioned, if the plasma is out of ionization equilibrium, very different line intensities can be expected. This was shown, e.g., by Imada et al. (2011). The effects can easily be of one order of magnitude, and depend critically on the local electron density and the timescale of the heating.

Early X-ray observations (e.g., from Skylab, SMM/UVSP, SMM/BCS) indicated strong upflows and non-thermal broadenings during the impulsive phase, but did not provide stigmatic images. The upflows were usually a weak component, compared to a strong stationary component, contrary to the predictions from hydrodynamic modeling. Only few spatially-resolved observations from SoHO SUMER in hot lines (mostly Fe xix and Fe xxi) exist, showing interesting behavior in the line profiles (see e.g., Kliem et al., 2002) during the peak phase.

Spatially-resolved observations in Fe xix from SoHO CDS during the impulsive phase of two M-class flares showed that line profiles were symmetric and blue-shifted by about 150 km s⁻¹, decreasing with time (Brosius, 2003; Del Zanna et al., 2006). CDS also observed some lines formed around 1-3 MK, which showed weaker upflows. Non-thermal broadenings in Fe xix of about 50 km s⁻¹ were also decreasing with time, following the upflows. The pattern of upflows appeared to follow the predictions from hydrodynamic modeling (Del Zanna et al., 2006). A few other CDS observations followed. Such features are hard to observe as they are short-lived (of the order of minutes) and the Fe xix intensities are weak, typically a few times up to one order of magnitude weaker than the intensities in the post-flare loops.

Several Hinode EIS observations of chromospheric evaporation have been published (see e.g., Milligan and Dennis, 2009; Del Zanna et al., 2011; Brosius, 2013; Young et al., 2013). We also have many IRIS (De Pontieu et al., 2014) observations of chromospheric evaporation, but they only included Fe xxi for large (C-class) flares, and low-temperature lines. EIS observed 1–3 MK lines and hot lines from only Fe xxiii and Fe xxiv, formed above 10 MK. Asymmetric profiles were often observed, which was puzzling. On the other hand, IRIS observations of Fe xxi (see e.g., Brosius and Daw, 2015; Polito et al., 2015; Young et al., 2015) have normally shown symmetric profiles, with temporal evolutions following the CDS results of Del Zanna et al. (2006), i.e., decreasing upflows and non-thermal widths with time. Simultaneous observations from EIS (≃3–4′′) and IRIS (≃0.33′′) clarified that some of these asymmetries could be due to a superposition of different components along the line of sight (Polito et al., 2016). The kernels of chromospheric evaporation appear in fact to be small in size, about 1–2′′ as seen with IRIS and AIA (see e.g., Young et al., 2015). A superposition of different flows during long exposure times could also explain asymmetric line profiles (see e.g., Mandage and Bradshaw, 2020). For larger flares, high-cadence IRIS observations provide an indication that a cadence of tens of seconds would be sufficient to observe the fastest flows at the start of the evaporation (see e.g., Graham and Cauzzi, 2015).

M-class and X-class flares often show upflows of a few hundreds of km s⁻¹ in hot lines. Smaller flares, however, have shown weaker upflows. For example, upflows in Fe xxiii of only 50 km s⁻¹ were observed during the impulsive phase of a B-class flare (Del Zanna et al., 2011). Interestingly, stronger upflows of about 170 km s⁻¹ were seen in Fe xvi (formed around 3 MK), before any signal could be seen in Fe xxiii. It could well be that stronger upflows were present in the hot lines but the sensitivity was not sufficient to observe them.

Generally, plasma diagnostics of flares, from the smallest to the bigger events have been limited by the lack of observations of lines formed in the 5–10 MK range and of measurements of electron densities at such temperatures. Measurements of time-dependent ionization have also been lacking, although some evidence that non-equilibrium ionization is present durgin flares has been found (see e.g., Kawate et al., 2016).

Measurements of hot line profiles in the kernels of chromospheric evaporation are needed, as well as their temporal evolution during the formation of the flare loops. We have hydrodynamic models, such as HYDRAD (see e.g., Bradshaw and Mason, 2003, and following updates) where we can predict flows with time-dependent ionization, following energy deposition in the chromosphere by thermal and non-thermal particles, but are missing the key observations to constrain the models.

A statistical study of flares within AR cores using RHESSI Bremsstrahlung emission in the 6–12 keV energy range showed peak temperatures of 10–15 MK and total estimated energies of 10²⁸–10³⁰ erg (Hannah et al., 2008). They were called microflares but were actually mostly B- and C-class. These measurements typically assume an isothermal plasma, because the observations are not generally adequate to distinguish between this and a distribution of temperatures, which is more likely. That would easily be assessed with measurements of spectral lines formed at different temperatures.

Within AR cores, weaker “microflares,” e.g., flares of A-class or below are a lot more frequent than larger ones. They also have lower temperatures. This has been clearly shown with recent X-ray irradiance spectrometers, such as SphinX on board the CORONAS-PHOTON mission (see e.g., Mrozek et al., 2018) and in 2019/2020 by XSM on board Chandrayaan-2. Further, XSM has shown that microflares occur frequently also outside ARs, and their energies were found to be in the range 4 × 10²⁶–10²⁸ erg (Vadawale et al., 2021)¹. Kirichenko and Bogachev (2017) performed a statistical study of microflares of GOES class A0.01 to B using the SphinX full-Sun X-ray spectra and the Mg XII images from CORONAS-PHOTON, showing that they have a different relationship between X-ray flux and temperatures, compared to larger flares.

An understanding of the physics of microflares remains elusive, as key spatially-resolved spectroscopic observations have been lacking, and given that they have peak temperatures in the 4–8 MK range (see e.g., Feldman et al., 1996; Hannah et al., 2019; Mitra-Kraev and Del Zanna, 2019; Cooper et al., 2020; Vadawale et al., 2021¹) which have largely been unexplored by previous and current imaging spectrometers. Consequently, only a few models of microflare loops and associated events have been developed (see e.g., Testa and Reale, 2020; Joshi et al., 2021).

Some information has been provided with imaging spectroscopy of Bremsstrahlung emission with e.g., NuSTAR and FOXSI-2. A recent NuSTAR observation of a microflare was published by Cooper et al. (2020). The microflare was estimated to be approximately equivalent to a GOES 0.005 A-class flare, i.e., much weaker than the 0.1 A class microflares recently observed by FOXSI-2 (Athiray et al., 2020). This very weak NuSTAR event had an energy content of about 10²⁶ erg, i.e., close to those thought to occur in nanoflares, often quoted to be in the range 10²³–10²⁵ erg (although its definition is a bit artificial, as what really matters is energy per unit cross sectional area).

We note that microflares often are composed of a few loop structures which appear resolved at 1′′ resolution in Fe XVIII emission within the AIA 94 Å band (Del Zanna, 2012, 2013; Mitra-Kraev and Del Zanna, 2019). Therefore, although higher spatial resolution could show unresolved structures (if present), 1′′ resolution would be sufficient to follow the evolution of the main structures.

To summarize, we need observations in hot 5–10 MK lines with: (1) high spectral resolution (to resolve the hot lines from the background signal and measure Doppler shifts of the order of 10 km s⁻¹); (2) high sensitivity (to capture the faint emission during the impulsive phase and allow temporal resolutions of tens of seconds); (3) moderate/high spatial resolution (1′′ or better); (4) several ionization stages of the same element; (5) measurements of electron densities in the 10⁸–10¹³ cm⁻³ range. Plus of course a spatial coverage large enough to observe events. As microflares are normally composed of single loops with typical lengths of 50′′, they are easier to observe than bigger flares, which can be ten times (or more) larger.

A related important science problem is the cycle of evaporation and condensation of mass in the corona, and in particular in quiescent AR loops. Chromospheric evaporation signatures are expected to be in high-temperature lines, short-lived and very weak (see e.g., Patsourakos and Klimchuk, 2009). Such signatures (enhanced emission in the blue wing) have not been unambiguously observed yet. Therefore, also in this case high-sensitivity spectral observations of hot lines are needed.

An important point to make regards the “background” cooler emission. In the case of non-flaring emission, the intensity and temporal behavior of the hot and “background” emission will need to be combined with forward models. For the flaring emission, there is ample evidence that the cooler lines, e.g., those formed below 3 MK, are mostly not affected during the heating and initial cooling phase of an event. The post-flare loops are seen to be progressively filled in by the hot plasma, and it is only during the following cooling of the plasma that lower-temperature lines are observed, as e.g., shown in the case of a microflare by Mitra-Kraev and Del Zanna (2019). Therefore, with spatially-resolved spectroscopy, we do not expect the background emission to interfere with the emission of the 5–10 MK lines. The situation is more complex and unclear in the kernels of chromospheric evaporation, during the impulsive phase of a flare. Strongly enhanced emission in transition-region lines (see e.g., Testa et al., 2014) or coronal lines (see e.g., Del Zanna et al., 2011) has been observed alongside hot emission. As we have mentioned, Doppler flows and non-thermal broadenings are also present, so careful analyses will be required to disentangle any foreground emission for the cooler lines, and remove any cooler component from the few hot lines which may become blended.

The X-rays (5–20 Å) are rich in spectral lines emitted by hot plasma, from 3 to 15 MK, although most hot lines are blended, hence extremely high resolution spectroscopy is needed. That might not be enough to resolve the main lines whenever large non-thermal widths are present, as we have seen from early flare observations.

The X-rays are excellent for measuring the chemical abundances of hot plasma. They also allow estimates of non-thermal electrons via line ratio techniques (Dud́ık et al., 2019), although better diagnostics are available at shorter wavelengths, involving satellite lines (see e.g., the review by Del Zanna and Mason, 2018). The X-rays also provide electron density diagnostics but for the hot (10 MK) lines they are limited to high values (above 10¹² cm⁻³). Lines formed below 3 MK are not present in this wavelength range. Previous high-resolution spectroscopy in the X-rays has provided many important observations of flares and chromospheric evaporation, but has been limited by the lack of stigmatic imaging and relatively low sensitivity. The last solar spectra in this wavelength range were obtained by the SMM X-ray polychromator (Acton et al., 1980) Flat Crystal Spectrometers (FCS), which had a collimator of about 15′′ × 14′′.

The sounding rocket MaGIXS (led by A. Winebarger, MSFC, USA; see Kobayashi et al., 2011), will provide for the first time stigmatic imaging spectroscopy in the same spectral region, though at the expense of a small geometrical area. The design employs a Wolter-type grazing incidence telescope with mirrors developed at MSFC, the same as those used by the successful FOXSI flights. One of the limitations of these focusing mirrors is the moderate spatial resolution, in the range 5–10′′.

Many hot lines from six ionization stages of iron, from Fe xviii to Fe xxiii, are available in the soft X-rays (SXR) within a narrow (30 Å) spectral range. Most readers would be familiar with the Fe xviii observed with the AIA 94 Å band, and the Fe xxi in the AIA 131 Å band. The table highlights those that we consider our “primary” SXR lines, the strongest resonance lines from six ionization stages of iron, plus some density diagnostics.

The SXR spectral region has been used extensively in studies of laboratory plasma. It also showed its diagnostic power to perform time-resolved spectroscopy of stellar flares (see e.g., Del Zanna, 1995; Monsignori Fossi et al., 1996). However, the SXR have been largely unexplored in solar physics.

The hot soft X-ray lines were observed on the Sun for the first time in 1969 by the grazing incidence instrument on board OSO-5 (Kastner et al., 1974). A portion of their flare B is shown in Figure 2. After OSO-5, the same lines were observed during 2010–2014 by the SDO EVE MEGS-A spectrometer (Woods et al., 2012). Both instruments observed the full Sun. As significant low-T background emission from the quiet Sun and active regions is present, these high-T lines are clearly observed only in EVE spectra of larger flares. As an example, Figure 2 shows a portion of the SXR spectra during the peak phase of an M5-class flare (red) on 2010 Nov 6, with the pre-flare background spectrum in black.

The SXR also provide excellent electron density diagnostics around 10¹¹ cm⁻³ of high-T plasma, as discussed by e.g., Mason et al. (1984). The EVE medium (1 Å) resolution made electron density measurements achievable although difficult, as discussed, e.g., by Milligan et al. (2012), Del Zanna and Woods (2013), and Keenan et al. (2017). OSO-5 and EVE measurements indicate densities of solar flares in the range 10^11.5–10¹² cm⁻³, as reviewed in Del Zanna and Mason (2018). However, spatially resolved measurements of such a fundamental parameter obtained from high-T spectral lines have been lacking.

As with the X-rays, the SXR allow line to continuum measurements, i.e., diagnostics of absolute chemical abundances (relative to hydrogen) of hot plasma during flares, as shown, e.g., by Warren (2014) using EVE spectra of large flares. Such measurements are in principle also available in the UV (Feldman et al., 2003).

The SXR contain lines from dozens of ions formed from 0.1 to 12 MK, plus all Iron ionization stages from Fe viii to Fe xxiii. There are many diagnostics for the lower temperatures that are not discussed here, since this is not the focus of the paper. Covering temperatures from 0.1 to 12 MK in such a narrow region is a significant advantage over the other spectral ranges. We made a significant effort to review all the SXR lines taking into account a revision of available observations, to indicate which hot lines are likely to be blended with cooler lines. The main results are summarized in the Supplementary Material.

The identifications and atomic data for the cooler ions in the SXR still require a significant effort. We note that the strongest solar iron lines in the SXR were only identified recently by Del Zanna (2012) when benchmarking against laboratory and solar data a series of large-scale scattering calculations for the SXR. The new atomic data and identifications were introduced in CHIANTI version 8 by Del Zanna et al. (2015), but a large fraction of weaker lines still await firm identifications. Renewed efforts on measurements of laboratory plasma, such as those of Träbert et al. (2014) and on further atomic calculations should enable us to improve the completeness of the atomic data.

Doppler shifts of about 5 km s⁻¹ can easily be measured in the SXR, and large broadenings are relatively easy to measure in the against the background of cooler lines (which typically retain their small widths).

The first solar observations of the SXR range with an imaging spectrograph will be the upcoming flight of the Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS). EUNIS will cover the wavelength range 92–112 Å employing a dual multilayer PdB₄C stack with two reflectivity peaks (of about 0.1) centered on the Fe xviii 94 Å and Fe xix 108 Å lines, and a few Å wide. Note that multilayer coatings designed specifically to target a few hot lines can provide higher reflectivities, such as proposed for the Multi-slit Solar Explorer (MUSE) and in this paper. MUSE, described in De Pontieu et al. (2020), is designed to observe the SXR Fe xix 108.36 Å and Fe xxi 108.12Å lines (in addition to the strong coronal lines from Fe ix 171 and Fe xv 284 Å) with a large FOV (170′′ × 170′′) and a high resolution (0.4′′). The innovative and multiplexing design of this instrument will allow high cadence (12s) spectral observations in these four lines through the use of 37 slits (each spaced about 4.5′′ apart) covering a region of 170′′ × 170′′.

It is important to note that high spatial resolution can be achieved in the SXR with normal incidence. This has been shown by the two SXR channels of the SDO AIA (Lemen et al., 2012) telescopes, at 94 and 131 Å. Their sensitivity is high, due to good peak reflectances of the SXR multilayers (0.4 and 0.7, respectively, see Soufli et al., 2005), although obtained at the expense of narrow spectral bands. An additional advantage of the SXR is that the Zr front filters, employed for AIA for the first time in space, have shown minimal in-flight degradation (see e.g., Boerner et al., 2014), unlike nearly every filter adopted for EUV/UV instruments flown in space (see e.g., BenMoussa et al., 2013; Del Zanna and Mason, 2018). The main limitation of the SXR for a spectrometer has been the lack of multilayers with sufficiently high reflectances and wide spectral bands. A significant improvement has recently been obtained by Corso et al. (2021)² with multilayers of higher reflectances (0.25–0.4) at the specific wavelengths of the primary lines selected here.

The EUV has excellent diagnostics for lower-temperature plasma, up to about 4 MK, but there are only few “hot” lines. For example, the Hinode EIS instrument has provided excellent EUV observations of 1–4 MK plasma, but is “blind” until the very hot (about 15 MK) flare lines from Fe xxiii and Fe xxiv are observed (see e.g., Winebarger et al., 2012). These lines, as well as the low-temperature Fe xvii and Ca xvii lines require careful deblending from cooler lines, when their intensity is weak (see e.g., Young et al., 2007; Del Zanna, 2008; Warren et al., 2008; Del Zanna and Ishikawa, 2009; Del Zanna et al., 2011).

Within the EUV, there is also the strong Ca xviii 302.2 Å line, observed by e.g., Skylab NRL-SO82A (see e.g., Dere, 1978) and the SPIRIT slitless spectroheliograph on board CORONAS-F (Shestov et al., 2014). Another important hot line in the EUV is the Fe xix 592.2 Å line, which was first observed by the Skylab Harvard SO55 instrument, then by SoHO CDS, and more recently by the EUNIS-13 rocket flight (Brosius et al., 2014).

Currently, one advantage of the EUV over the X-rays is that high spatial resolution can be achieved with normal incidence, as shown, e.g., with the Hi-C sounding rocket, which obtained a spatial resolution of about 0.25′′(Kobayashi et al., 2014). Even higher resolutions are achievable in the UV, as e.g., shown by IRIS.

The main UV hot lines are Fe xix 1118.1 Å, Fe xx 721.5 Å, and Fe xxi 1354.1 Å. Several flare observations have been obtained with high-resolution imaging spectroscopy from e.g., SoHO SUMER (mostly of Fe xix and Fe xxi) and IRIS (Fe xxi) (see e.g., Kliem et al., 2002; Polito et al., 2015). Fe xxi was also observed earlier by SMM/UVSP. The Fe xviii 974 Å is another strong line, which was observed by SUMER (see e.g., Teriaca et al., 2012b), and is available to Solar Orbiter SPICE (Anderson et al., 2019). However, as we have mentioned, Fe xviii has a significant contribution from 3 to 4 MK emission and so its use for measuring high temperatures by itself is limited.

A significant improvement in terms of sensitivity and resolution over SUMER is the EUV Spectroscopic Telescope (EUVST, see Shimizu et al., 2019), an M-class mission recently selected by the Japanese Space Agency (JAXA). The EUVST has a high throughput and a high spatial resolution of 0.4′′, with a design based on the LEMUR instrument (Teriaca et al., 2012a): the optical components have a standard Mo/Si ML for the EUV: 170–215 Å, and a B₄C top layer providing good reflectances in three UV bands: 690–850, 925–1,085, and 1,115–1,275 Å. The strongest lines in the wavelength regions 463–542 and 557–637 Å would be observed in second order.

EUVST has been designed to address a broad range of science questions. The key requirement for EUVST is to obtain high-cadence, high-resolution observations in spectral lines formed from photospheric to flare temperatures. It will also be able to provide observations of iron lines formed in the 5–10 MK range, hence will be able to provide important contributions to the science topics mentioned here. However, with the exception of Fe xix, the lines from the other iron ions are intrinsically weaker than the resonance SXR lines, are observed in regions with lower sensitivities, and could be affected by photoabsorption in active regions. The planned EUVST spectral range is also limited in electron density diagnostics (see below). On the other hand, EUVST is excellent for measuring non-thermal widths and Doppler flows of a few km s⁻¹ (as it also has photospheric lines to measure rest wavelengths).

Finally, a few comments about the important issue of measuring electron densities from line ratios. There are plenty of diagnostics and measurements across different temperatures, as summarized in the review by Del Zanna and Mason (2018), but very few for hot (10 MK) plasma. We provide here a summary and further details on the hot plasma diagnostics, which were not all included in the review. There are measurements with SMM FCS from Fe xxi, Fe xxii lines in the X-rays around 9 Å(Phillips et al., 1996), which indicated densities of 10¹³ cm⁻³ during a flare. These lines are very weak and are difficult to measure though. Still within the X-rays, there are potentially a few density diagnostic ratios from Fe xix, Fe xxi, and Fe xxii, but these involve weak and often blended lines in a spectral region that is over-crowded even for the best crystal spectrometers, such as SMM FCS or the P78-1 SOLEX (McKenzie et al., 1980). Other density diagnostics involving satellite lines are available, but at wavelengths shorter than 2 Å. The He-like hot ions in the X-rays do provide density diagnostics, but only for densities above 10¹³ cm⁻³. At lower temperatures around 4 MK, Ne He-like lines have indicated densities of 10¹² cm⁻³ at the start of a flare (Wolfson et al., 1983).

Aside from the X-rays, the only other measurements of densities of hot plasma are those in the SXR, from OSO-5 (Mason et al., 1979; Mason et al., 1984) and EVE. These density diagnostics are well-known and well-studied in laboratory plasma (see e.g., Stratton et al., 1984). The atomic data and identifications for these n = 2 → n=2 transitions are well established. The best diagnostic ratios are those with the Fe xxi 102.2, 121.2, 142.2, 145.7 Å lines vs. the resonance line at 128.75 Å, as shown in Figure 3 (see also Table 1). They provide excellent measurements at relatively low densities, above 10¹⁰ cm⁻³. Other ratios involve Fe xix, Fe xx, and Fe xxii lines. There are also interesting ratios involving Fe xix lines, as shown in Figure 3: they are sensitive to very low densities, between 10⁸ and 10¹⁰ cm⁻³, which would be particularly important to investigate further. The variation in the Fe xix ratios is only 25% but measurable, especially if the multi-layers are fine-tuned to increase the signal in the weaker density-sensitive lines. It would therefore be possible to measure any densities from 10⁸ to 10¹³ cm⁻³ and above, observing both the Fe xix and Fe xxi line ratios. That would be quite an achievement.

There are in principle other density diagnostics at longer wavelengths. Within the EUV, a good density diagnostic above 10¹² cm⁻³ available at the EUVST wavelengths is the Fe xx 567.8/721.5 Å ratio, although it could be affected by neutral hydrogen absorption in active region observations. The 567.8 Å is intrinsically a relatively strong line, but will be observed in second order, where the sensitivity is low. Also, as the thermal width at 10 MK of the 567.8 line is 0.17 Å, the line will be blended with the strong Si vii 1135.4 Å transition.

There are also two other options outside the EUVST spectral range. One is the Fe xxi 786/1354 Å ratio, useful for densities higher than 10¹¹ cm⁻³. The other one, Fe xix 1,328/1,118 Å, is an excellent diagnostic for densities of 10¹¹ cm⁻³ or lower (see e.g., Feldman et al., 2000), although the 1,328 Å line is intrinsically very weak: at 10¹⁰ cm⁻³, its intensity is only 2% that of the 1,118 Å line, and decreases with density.

To illustrate the current capability for an imaging SXR spectrograph, an example (straw-man) instrument is presented. For high collecting area and resolution, the telescope mirror is a 20 cm diameter off-axis paraboloid with a focal length of 2 m that feeds a spectrograph with a magnification of 1.4, along the lines of the successful Hinode EIS. A back-illuminated CCD (or CMOS array) with 13.5 μm pixels at a distance of 1.4 m from the grating provides an image scale of 1′′/pixel. Reducing the spatial resolution from e.g., the 0.3′′ of the original LEMUR design not only increases the throughput but also significantly simplifies the thermal requirements for a more compact instrument. Clearly, a higher spatial resolution would be desirable, but would have to be evaluated in a trade-off study, to ensure that, depending on the size of the primary, sufficient signal can be obtained to achieve the science goals of a specific mission.

In a recent study, Corso et al. (2021)² produced a few new multilayers (ML), tuned to have peak reflectances in our primary SXR lines. We adopt two MLs: a 3-fold Mo/Si standard ML for the 126–150 Å range, and a new aperiodic B₄C/Y/B₄C/Pd for the 100–126 Å range. As the SXR hot primary lines cannot be observed with a single multilayer, we envisage that both the mirror and the grating would be segmented in two halves, each with a separate ML, as in the EIS instrument.

The spectral dispersion can be chosen to use one or two 2,048 × 2,048 pixel detectors to cover the wavelength region of interest. Holographic gratings with excellent micro-roughness on the scales relevant to obtaining high SXR reflectivity (0.3 nm on spatial scales of 0.01–1 um) have been demonstrated with line densities of 4,000/mm and a blaze to maximize throughput (the EUNIS flight grating has a density of 3,800 l/mm, the EIS one 4,200 l/mm). If used in first or second order, this would provide a dispersion of 12 or 24 mÅ/pixel and a wavelength range of 24 or 49 Å per detector, respectively. At the Nyquist limit, that provides a resolving power of R = 2,500 in first order (comparable to previous EUV spectrographs), or R = 5,000 in second order. We select the second option here, and use the grating efficiencies in second order calculated by Corso et al. (2021)², which are close to 40%. The second order with two 2,048 pixel detectors (as the Hinode EIS) provides a pixel size of 0.01 Å, corresponding to about 20 km s⁻¹. This means that Dopplershifts of 2–5 km s⁻¹ are measurable. We note that reconnection and associated flows are expected to be very fast (on short time scales) so even a resolution of a few tens of km s⁻¹ for the hot lines could be sufficient.

With a 0.01 Å slit, a 0.03 Å (or better) spectral resolution is achievable. The thermal FWHM of the Fe ions in the ranges 6–10 MK and 108–135 Å is 0.025–0.04 Å, so with such resolution the thermal width would be resolved. However, considering that significant non-thermal widths in the hot lines are likely present, a lower spectral resolution could be sufficient. In the plots that follow, we have adopted a 0.01 Å pixel resolution, included a thermal width of the lines (using their peak formation temperature), and added an instrumental FWHM of 0.025 Å.

An alternative option would be a 4,000/mm grating in first order, which would have higher efficiency (better than 50%) and would reduce the spectrograph size by 80%, at the expense of a 0.02 Å pixel resolution, which would still be acceptable.

For the detector, we have assumed an efficiency of 0.8, achievable with standard CCDs, such as the 4kx4k thinned back-illuminated CCDs used by AIA. We note that these CCDs have been proven very stable and higher efficiencies (0.85) have been achieved (Hi-C).

We have included a front filter, the same one used for the AIA 94 and 131 Å channels: a Zr filter, which has a transmission across the soft X-rays of about 0.4. We note that such filter includes a reduction of 15% due to the supporting mesh, although a mesh with a 95% transmission has been flown aboard Hi-C (see e.g., Kobayashi et al., 2014), so better transmission is achievable. We also note that the inclusion of a safety redundant filter in front of the detector would reduce by about 50% the signal we predict here. An alternative, adopted for the EUNIS-13 flight, would be not to use a front filter and use a KBr coated micro-channel plate (MCP) detector (not affected by visible light) instead of a CCD detector. In this case, the detected signal would be much higher than the values presented here.

Figure 4 shows the resulting effective area, which is the product of the filter transmission, the reflectivity of the primary, that of the grating, the grating efficiency, the geometrical area and the quantum efficiency of the detector. For comparison purposes, the same figure also shows the LEMUR (Teriaca et al., 2012a) effective area in the EUV and UV, scaled to the same geometrical area of each SXR channel. The figure clearly indicates that similar effective areas are achievable in the SXR and UV, for an equivalent aperture. As we have seen that the photons emitted by the hot lines in the SXR and UV are comparable, this indicates that similar numbers of detected photons are achievable either in the SXR or the UV. We note however that the EUVST baseline design assumes a large primary mirror with a 28 cm diameter, so its effective area is actually about a factor of four higher than what is shown in the EUV and UV panels in Figure 4. We also note that MUSE has a comparable effective area of 2 cm², while MaGIXS has a peak effective area of 0.03 cm² (Athiray et al., 2019).

To estimate the signal S detected (data numbers per second, DN/s) in a pixel we use:

where the terms convert the number of electrons produced in the CCD by a photon of wavelength λ (Å) into data numbers DN. I_r is the incident radiance, A_eff is the effective area, G is the gain of the camera, and Ω is the solid angle subtended by a pixel. We have assumed a gain of 6.3, the same as the EIS CCD.

We now return to the 10 MK simulation. The first radiance column in Table 1 shows that the Fe xix 1118.0 Å radiance is 0.23 erg cm⁻² s⁻¹ sr⁻¹, which is very close to the minimum values (0.22–0.5) recorded (with a total exposure of 2 h and only in some locations) by SUMER (Parenti et al., 2017).

The Fe xix 592.2 Å radiance is 0.24 erg cm⁻² s⁻¹ sr⁻¹, a value over 20 times lower than that measured with EUNIS-13 by Brosius et al. (2014), but not inconsistent with other EUNIS-13 observations, as we have mentioned.

Figure 5 shows the expected SXR count rates for the very weak 10 MK emission of Figure 1. The 10 MK spectrum has been added to that of an active region core, discussed in the Supplementary Material. Note that the units in the spectra are per pixel (0.01 Å) resolution, while Table 1 provides the total count rates in the lines.

As we have discussed, a good proxy for the 5–10 MK emission are Fe xix and higher ionization stages. The count rates in the Fe xix– Fe xxiii strongest lines are in the range 1.4–6.5. Such signals are easily measurable with a cadence of a few seconds and spatial averaging over ≃4′′. This is a major improvement over the 2 h exposures and spatial averaging obtained with SUMER in Fe xix (Parenti et al., 2017).

As we have mentioned, none of the previous observations of hot emission in AR quiescent cores were able to provide an indication of the distribution of temperatures above 5 MK. Upper limits in the 4–15 MK range have been provided by continuum emission or the Mg xii images. The few Fe xix observations from SUMER and CDS provide a similarly unclear picture. So it is possible that the count rates we estimate at 10 MK are either an over- or an under-estimate by a large margin. If say they were over-estimated by two orders of magnitude, a measureable signal of ≃100 DN/s could be obtained by an acceptable spatial averaging over ≃20′′ and a 2-min exposure.

The Fe xix 108.36 Å, Fe xx 121.85 Å, Fe xxi 128.75 Å, and Fe xxii 135.81 Å resonance lines are all excellent candidates. The Fe xix 108.36 Å has a small contribution from the quiescent AR core, which is questionable. The Fe xx 121.85 Å is super-imposed on an unidentified weak Fe xi transition which is currently expected at the same wavelength, although the quiet Sun spectra suggest that this is not the case (see the Supplementary Material). As there are many Fe xi transitions within the two SXR channels, it would be easy to deblend the Fe xi contribution, if the line was at that wavelength.

The Fe xxi 128.75 Å is unblended, while the Fe xxii 135.81 Å is blended on its red wing with a O vii 135.83 Å line. The O vii can accurately be estimated measuring other O vii transitions, such as the strong O vii 120.33 Å self-blend. Finally, the Fe xxiii could be deblended from the O vii and other lines.

To provide an estimate based on a numerical nanoflare simulation, we took the DEM distribution from the L = 120 Mm case as described by López Fuentes and Klimchuk (2015). This simulation is realistic in that it includes a variety of magnitudes and frequencies. The DEM distribution has large values at low temperatures, hence the simulation also naturally includes all the transition-region lines, as well as the coronal and the hot lines. As we would expect low densities around 10⁸ cm⁻³ for the hotter plasma and higher ones (10⁹ cm⁻³) for the coronal lines, we have adopted a constant pressure of 10^15.5 cm⁻³ K for the simulated spectra. Figure 6 and Table 1 show the expected SXR count rates. There is clearly a very strong signal in all the hot primary lines (i.e., from Fe xviii–Fe xxiii).

To estimate the signal for a very weak microflare, we consider the 0.005 A-class NuSTAR observations discussed by Cooper et al. (2020). The NuSTAR X-ray Bremsstrahlung emission was well fitted with an isothermal emission of 6.7 MK. The signal in the AIA 94 Å band, due to Fe xviii, was at the limit of detection. We converted the volume EM to a column emission measure EM = 1.18 × 10²⁷ (cm⁻⁵). Using our “coronal” abundances we expect about 3 DN/s/pixel due to Fe xviii in the AIA 94 Å band, close to what was observed. Figure 7 shows sections of our predicted SXR count rates for a density of 10¹¹ cm⁻³, added to those of the active region core discussed in the Supplementary Material. The total count rates are given in Table 1.

There is plenty of signal in all the resonance lines. They are not affected by the “background” emission, with the exception of Fe xxii, which is very weak given such a low temperature, and Fe xviii, as significant quiescent emission is expected to be present. Time-dependent ionization on a 1′′ spatial scale could be studied with exposure times of 1–10s.

The figure also shows the effect of an additional broadening of 200 km s⁻¹ FWHM, which would be easily measurable for the main Fe xviii, Fe xix, Fe xx, and Fe xxi lines, as no significant background emission from cooler lines is present. Much stronger broadenings would become difficult to observe, for this very weak hot emission.

Regarding density measurements, the comparisons with irradiance spectra shown in the Supplementary Material indicate that the Fe xix 119.98 Å and Fe xxi 121.21, 142.2 Å density-sensitive lines fall in regions relatively free of background emission. The Fe xxi 145.73 Å, on the other hand, is close to a Ni x line and would require background subtraction. The expected count rates indicate that even for this extremely weak microflare, densities could be measured with exposure times of about 100 s at 1′′ resolution.

As representative of a weak A class microflare, we have considered an isothermal plasma emission at 8 MK, an electron density of N_e = 10¹¹ cm⁻³, the Del Zanna (2013) coronal abundances and an emission measure EM = 10²⁹ cm⁻⁵. The microflare radiances are listed in Table 1. These parameters were chosen so as to reproduce the Fe xvii and Ca xvii radiances during the peak emission of a microflare recorded by EIS (Mitra-Kraev and Del Zanna, 2019). We note that the actual peak temperature of the post-flare loops was about 5 MK, although short-lived higher temperatures were probably present during the impulsive phase in one of the footpoints (see also Testa and Reale, 2020). Using the effective areas of the instruments, we found out that such a weak 8 MK microflare would be invisible to EIS in Fe xxiii and at the limit of detection for IRIS in the Fe xxi 1354.1 Å line (we estimate 3 IRIS DN/s in the line). On the other hand, it would have been well observed by the SDO AIA SXR bands, with about 200 DN/s in the Fe xviii 94 Å channel and 126 DN/s in Fe xxi within the 131 Å band.

Figure 8 shows the simulated SXR count rates (1′′ pixel) for the microflare case study, added to those of the active region core discussed in the Supplementary Material. The SXR channel provides very large count rates in all the primary lines, as listed in Table 1. For example, the Fe xxi 128.75 Å resonance line would produce 3.0 × 10³ DN/s. The Fe xix and Fe xxi density-sensitive lines are also strong, providing excellent density measurements with very short timescales of a second or so at 1′′ resolution. Larger (e.g., B-class) flares would require sub-second exposure times to avoid saturation.

The significant differences with the spectra of the sub-A class microflare are due not just to the increased emission measure, but also to the increased temperature, from 6.7 to 8 MK.