Emission Line Intensity Ratios of Fe xxvi/ xxv/ xxiv in Solar Flares Observed by Hinotori

High-resolution spectra observed by the Solar X-ray spectrometer on board the Hinotori mission are revisited. Flat crystals slightly offset to the satellite spin axis produce automatic spectral scans for emission lines emerging from highly charged iron ions in solar flares every half-spin time period. All the downlinked data of the mission are converted to FITS format and major flare spectral data are revived as IDL save files in ISAS/DARTS. Based on these data sets, single-temperature fits are performed for the emission line complex of highly charged iron ions in the wavelength range of 1.75–1.95 Å and compared with theoretical predictions. Synthetic spectra with single electron temperatures estimated from j/w line-intensity ratios fit fairly well for Fe xxiv and Fe xxiii lines in the wavelength range of 1.85–1.88 Å, while intensity ratios of Fe xxv lines (x, y, z) and the inner-shell excitation line of Fe xxiv (q) to the Fe xxv resonance line (w) have systematic excesses. Empirical relations for the observed line ratios are derived. Ion fractions of Fe+25/Fe+24 estimated by intensity ratios of Lyα/w in the temperature range of log T e =7.25–7.45 are consistent with values in ionization equilibrium, and the remaining excesses of the Fe xxv line ratios may suggest problems with the atomic parameters or atomic modeling.


Introduction
High-resolution X-ray spectral data taken by the SOX (SOlar X-ray spectrometer) instrument on board Hinotori are revisited with the aim of providing easier access for scientific analysis.Hinotori was the last satellite mission launched in 1981 by the ISAS attached to the University of Tokyo, the current ISAS/ JAXA (Tanaka 1983).The SOX instrument on board accommodated two Bragg crystal spectrometers (SOX1 and SOX2) to observe the highly charged iron ion emission-line complex (Fe XXVI-Fe XXI, as well as Fe Kα and Kβ) in the wavelength range of 1.75-1.95Å (Tanaka et al. 1982a).Time series of solar-flare spectra with moderate and high resolutions were taken every half-spin period of the spinning satellite, and its spin axis was set about one degree off the solar disk center (Tanaka & Nishi 1978).Super hot components were discovered and confirmed as strong Fe XXVI emissions in solar flares (Tanaka et al. 1982b).Production rates for super hot components varied from flare to flare, and a distinct group of solar flares (Type A) was identified that effectively produce hotter thermal plasma of T e > 3 × 10 7 K (Tanaka 1987).The scientific discoveries and characteristics of high-resolution iron emission-line spectra observed by Hinotori/SOX were extensively reviewed and discussed by Tanaka (1986).
Raw spectral data sets of SOX were reduced and compiled in the Annals of Tokyo Astronomical Observatory, the current NAOJ (Tanaka et al. 1982a;Moriyama et al. 1983).These data sets were directly obtained from the original telemetry frame format data, and published only in the form of tables and diagrams.Reduced data were not stored in modern media.
Recently, the Data ARchives and Transmission System in ISAS (ISAS/DARTS) (Tamura et al. 2004;Miura et al. 2000) have archived the entire telemetry data from Hinotori in FITS files, and the SOX spectral data can be extracted using IDL.All the flare spectral data reduced by (Tanaka et al. 1982a) and Moriyama et al. (1983) are also regenerated and open on the site of ISAS/DARTS as IDL save files. 1n this paper, intensity ratios of Fe XXV lines, x/w, y/w, and z/w are revisited.Simple single-temperature analysis with theoretical atomic models from CHIANTI ver.10 (Del Zanna et al. 2021), and Bely- Dubau et al. (1982) are applied to these SOX flare data sets.Systematic deviations from theoretical line-intensity ratios are found to be decreased, but still remain in the CHIANTI atomic database.Correction factors are obtained and empirical relations for the observed line ratios are derived with help of these atomic models.The derived ion fraction of Fe +25 /Fe +24 , hereafter N(H)/N(He), is almost in ionization equilibrium (IE) in the later phases of solar flares.Causes and reasons for the remaining excesses in the intensity ratios of Fe XXV lines are discussed.

FITS and IDL Save File Database for SOX
Raw telemetry data from the Hinotori mission in FITS format are released in ISAS/DARTS (Tamura et al. 2004;Miura et al. 2000) with documents (in Japanese) explaining their data formats.These data are in the telemetry frame format, and they have been archived in the SIRIUS database at ISAS since the 1970s.2SOX spectral data are then extracted from time series of the entire Hinotori scientific data by dividing them at the half-spin time interval (Tanaka et al. 1982b).IDL procedures to get level 0 and level 1 SOX data are also released.The level 0 data are defined as spectra of counts Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
versus spectral bins, while the level 1 are calibrated spectra with intensity versus wavelength.Since SOX spectral data reveal essentially nothing outside flaring periods, the level 1 data can be created only during these flaring times.Level 1 data are created as IDL save files for major solar flares published by Tanaka et al. (1982a) and Moriyama et al. (1983).3

Line-intensity-ratio Analysis
Proper reproduction of SOX spectra from the newly created database is confirmed by applying single-temperature analysis to the 1981 October 7 flare (X3.6) that occurred at the east limb.Following Tanaka (1986), standard single-electron temperature analysis is applied to SOX1 and SOX2 spectral data independently.
The peak intensity ratio of the Fe XXVI Lyα 1 at 1.778 Å to Fe XXV satellite line complex at around 1.792 Å (J-satellites) gives the electron temperature for hydrogen (H)-like ions, T e (H) (Dubau et al. 1981), while the peak intensity ratio of the helium (He)-like resonance line (w) blended with numerous weak satellite lines at 1.8504 Å to the dielectronic satellite ( j) at 1.8659 Å gives the electron temperature for He-like ions, T e (He) (Bely-Dubau et al. 1982).Conventional notations are adopted from Gabriel (1972).He considered the mechanism of formation of the satellite lines situated on the long-wavelength side of the He-like resonance line, namely dielectronic recombination and inner-shell excitation of the Li-like ion, both of which involve the excitation of a K-shell electron, and the upper levels of the satellite transitions are auto-ionization levels located above the ground state of He-like ions.In his calculation of these transitions, he assigned lowercase letters, including the resonance, intercombination, and forbidden transitions of He-like ions.
Theoretical line peak intensities are obtained from synthetic spectra generated by the CHIANTI ver.10.02 database (Del Zanna et al. 2021).A total of 6029 emission lines from Fe XXI to Fe XXVI emerging in the wavelength range of 1.75-1.95Å are registered in the database.Synthetic spectra for H-and Helike emission lines in the wavelengths of 1.77-1.80Å are calculated with an instrumental width of 0.025 Å, a typical spectral resolution of SOX1 at these wavelengths.For higher resolution SOX2 spectra in the wavelength range of 1.84-1.88Å, synthetic spectra are generated with an instrumental resolution of 0.009 Å. Fe ion fractions are taken from the ionization equilibrium calculation database (file name; chianti.ioneq)included in the CHIANTI package (Dere et al. 2019).Continuum emissions in SOX spectra are linearly fit against wavelengths, and seven data bins centered at the apparent line peaks of w, x, y, q, j, and z (SOX2) and Lyα 1 (SOX1) are used for quadratic Gaussian fitting to get lineprofile parameters.They are used to obtain the observed line ratios, and to finalize the wavelength calibration and the instrumental width for theoretical synthetic spectra.Once T e (H) and T e (He) are obtained from the diagnostic line pair ratios, synthetic spectra for SOX1 in the wavelength range of 1.75-1.80Å are created with T e (H), and synthetic spectra for SOX2 in the wavelength range of 1.84-1.88Å are created with T e (He).Synthetic spectra for SOX1 in the wavelength range of 1.80-1.95Å are simply created with T e (He) obtained in SOX2 analysis and with SOX1 spectral resolution at the wavelength of w.The volume emission measure (EM) is deduced by adopting an Fe abundance of ò(Fe) = 7.47 (Scott et al. 2015).
Figure 1 shows spectra of the 1981 October 7 flare taken in the representative phases of the flare.Spectra in the top panel are obtained at around the end of the initial phases, when T e (H) starts to rise sharply.Middle panel spectra are from the maximum phase, when T e (H) reaches the highest value of the flare.Spectra in the bottom panel are observed in decay phases, showing uniform temperature T e (H) ∼ T e (He).Derived T e (H), T e (He), and log EM are indicated in Figure 1.Just note here that the energy ratio of hν/kT e (H) at Fe Lyα is 2-3 in large solar flares.This is essentially the same Figure 1 as in Tanaka (1986)ʼs paper.Solid lines in each panel of Figure 1 show synthetic spectra created with single temperatures of T e (H) and T e (He), respectively.Dashed lines show the contributions of individual strong lines, w, x, t, y, q, k + r, j, and z in SOX2 spectra.Synthetic isothermal spectra generally show good fits to the observed spectra.Derived electron temperatures T e (He) from CHIANTI ver.10.02 and those obtained from the atomic parameters of Bely- Dubau et al. (1982) are found to have a difference of Δlog T e ∼ 0.02 in the temperature range of log T e = 7.25-7.45,because the w line intensity is relatively enhanced due to a higher contribution of satellite lines in the CHIANTI model, which gives a lower T e (He) than that obtained from Bely- Dubau et al. (1982)ʼs atomic parameters.It is noted that the intrinsic widths of contribution function for j and w have Δlog T e 0.3, so that this difference is a systematic one coming from the difference of atomic models applied here.
Bely- Dubau et al. (1982) estimate transition rates for contributions to the Fe XXV lines from cascade, radiative recombination, dielectronic recombination of Fe XXVI, and inner-shell ionization of lithium (Li)-like Fe XXIV, and propose a method under isothermal condition to estimate electron temperature, T e (He), and the ion fractions of N(H)/N(He) and N(Li)/N(He), namely Fe +23 /Fe +24 .In this study, N(H)/N(He) is estimated from the x/w and Lyα 1 /w ratios.Tanaka (1986) notes the advantages of SOX1 observing the resonance lines of H-like and He-like Fe ions in the same spectrometer, and that both resonance lines have very similar excitation potentials, meaning that the intensity ratio depends very little on electron temperature.Therefore, ion fractions of N(H)/N(He) can be directly estimated from intensity ratios of these resonance lines.The derived electron temperatures, T e (He) and T e (H), together with N(Li)/N(He) and N(H)/N(He) are summarized in Table 1.
It is found in Table 1 that the derived values are consistent with those in the previous analysis (Tanaka 1986).Somewhat larger differences are found in T e (H), N(Li)/N(He), and N(H)/ N(He), and they come from poorer signal-to-noise (S/N) ratios of those weaker lines applied to the analysis.In this paper, the x line is used to derive the ratio of N(H)/N(He) instead of z, because y has a larger discrepancy with theoretical models than x and z, and for z, coupled contributions from N(H)/N(He) and N(Li)/N(He) have to be considered (Bely- Dubau et al. 1982) .
In Figure 1, it is also found that synthetic spectra created with a single temperature for T e (He) provides reasonably good fits for the Li-like lines, as well as for Fe XXIII (Be-like) lines in the wavelength range of 1.85-1.88Å, once the parameter T e (He) is determined from the j/w ratio.This is not exactly the case for BCS spectra of the 1989 April 1 flare (Dere et al. 2019).On the other hand, He-like ion lines (x, y, z) and the inner-shell excitation line of the Li-like ion (q) have intensity excesses compared to theoretical predictions.Comparing the synthetic spectra with (solid line) and without satellite lines of the unobserved energy levels (dashed line) to the observed spectrum, it is clear in Figure 1 that numerous weak satellites calculated using the CHIANTI contribute to the better fits of spectral shape in the entire wavelength range but cannot compensate for all these excesses.

Excesses of He-like Ion Emission Lines
Excesses of He-like ion line intensity are already found and discussed in the previous analysis (Tanaka 1986).It was proposed that the H-like and He-like ionization balance deviates from equilibrium during solar flares, since the ion fractions N(H)/N(He) derived from the z/w intensity ratio and from the resonance-line ratio, Lyα/w were satisfactory in agreement to show a discrepancy for the entire range of electron temperature, T e (He).
In the present paper, the empirical relationship among the line intensities of the He-like ion, w, x, y, and z, together with q (inner-shell excitation line of the Li-like ion) is obtained by comparing the observed line ratios to theoretical predictions calculated with the improved atomic database.
A total of 70 data points for the observed line-intensity ratios (x/w, y/w, q/w, j/w, and z/w) are otained from SOX spectra taken at and after the maximum phases of the 13 large flares listed in (Tanaka 1986)ʼs paper which are time-integrated for four satellite spin periods (60-80 s), which is much shorter than flare-cooling timescales (Cargill et al. 1994), during which coronal parts of flaring loops are filled with plasma almost at uniform temperature above 10 MK, and they are gradually cooling down by thermal conduction to the chromosphere.Single-temperature fittings are, then, applied to obtain T e (He) and T e (H) from SOX1 and SOX2, respectively (Bely- Dubau et al. 1982;Del Zanna et al. 2021), and the excesses of the observed line ratios in SOX2 spectra.See also Figure 4 of Tanaka (1986) showing thermal evolution of the 1981 October 7 flare presented in Figure 1 and Table 1.Multithermal characteristics of cooling-flare loops will be discussed in a later section.
In Figure 2, the observed line-intensity ratios, q/w, x/w, y/w, and z/w, are plotted against j/w.The plus marks in each panel show the observed line ratios with error bars estimated from the spectra shown in Figure 1.Error ranges are just derived from photon noise and, therefore, are thought to be minimal ranges.The spinning satellite usually excites nutation during high-speed recording of flare spectra on magnetic tapes on board, which degrades the uniformity of wavelength scans and time integration of SOX spectra.This effect is rather difficult to be evaluated quantitatively, but this might be one of the reasons why data points scatter wider than those expected from photon noises.Nevertheless, excesses of the line ratios are noticeable and constant (zeroth-order) and linear (first-order) corrections to the theoretical predictions are performed for spectral data apparently showing isothermal characteristics, T e (H) ∼ T e (He) (filled circles in Figure 2), the total number of which is 28 out of 70.The following summarizes the results of the regression analysis.The first line in every two lines of each equation for the excess line ratio indicates a constant factor correction, and the numbered second line represents the linear regression of j/w.Here, Δ(l/w) is defined as the observed excess ratio over the theoretical ratio; l w l w l w ) , where l is one of q, x, y, and z.Error ranges are estimated from the isothermal ensemble of 28 data sets showing T e (H) ∼ T e (He).
From CHIANTI ver.10.02 (Del Zanna et al. 2021), we get: q w j w 1.155 0.084 0.271 1.284 0.080 1 x w j w 1.097 0.076 0.149 1.168 0.075 2 1.198 0.060 0.030 1.212 0.060 3 From Bely- Dubau et al. (1982), we get: 1.381 0.104 0.459 1.598 0.096 5 x w j w 1.167 0.081 0.134 1.230 0.080 6  (1982)ʼs model may be due to a higher contribution of numerous weak satellite lines enhancing the intensities of the resonance line (w), if the unresolved n = 3 line contribution to the resonance line (w) tabulated in Bely- Dubau et al. (1982) is compared to the apparent line peak enhancement in the CHIANTI synthetic spectrum with and without lines of the unobserved energy levels, which can be seen in Figure 1.
Two dotted lines for linear corrections of two theoretical models having different atomic parameters are almost indistinguishable in each panel of Figure 2. The decrease of fitting residuals is negligibly small in the temperature range of log T e = 7.25-7.45,if the number of fitting parameters is increased from 1 (constant factor correction) to 2 (linear correction) in the CHIANTI model, while with Bely- Dubau et al. (1982)ʼs parameters, the residuals are slightly smaller for the case of linear correction, but still larger than those using CHIANTI.The above statements are also numerically supported by Akaike's information criterion (AIC; Akaike 1973;Sugiura 1978), which compares possible models with different numbers of free parameters, and determines the best optimized fit for the data.The AIC suggests, therefore, one parameter correction to the CHIANTI prediction is appropriate enough for the current data quality of the SOX instrument.Table 2 summarizes the best estimates for the observed line ratios based on this correction (thick solid lines in Figure 2).
In the bottom right panel of Figure 2, the z/w line ratios that were obtained from the core of the Perseus cluster observed by Hitomi SXS (Hitomi collaboration 2016, 2018a) are plotted with star marks.Clusters of galaxies are thought to be formed hierarchically, namely by the merger of smaller structures, and the merger shocks are considered to heat diffuse intergalactic gas to such high temperatures (Saradin 2003).The derived electron temperatures are converted to j/w ratios using the CHIANTI model (Del Zanna et al. 2021).Note that the abscissa is expanded and the theoretical ratios and regression lines are extrapolated in this panel.It should be noted that the line ratios obtained from obs23 (Hitomi Collaboration 2018a) regions are located clearly above the area where the observed values for solar flare are extrapolated, while the line ratio for obs1 is rather close to the lines for the corrected theoretical predictions.Quantitative discussion of the effect of optical derived from x/w or z/w ratios and N(Li)/N(He) from q/w; 2, derived from Lyα 1 /w ratios.Error ranges are estimated from photon statistics.
depth and resonant scattering in the Fe XXV w line, comparing with the results of optically thin model calculations may be a possible explanation (Hitomi Collaboration 2018b), as well as the atomic data and spectral modeling.

Contribution of Dielectronic Satellites
Spectral lines of He-like ions and their satellites are prominent features in astrophysical X-ray spectra.Gabriel & Jordan (1969) suggested the latter are the transitions of Li-like ions, and Gabriel (1972) calculated the wavelengths and intensities of these lines, followed by Bely-Dubau et al. (1982).Spectral lines created by radiative decays following dielectronic capture of free electrons into auto-ionizing levels play an important role, and Li-like ions give rise to many such lines as satellite to the He-like ion lines, often heavily blended with them.Given the lack of availability of measurement in the NIST database (Kramida et al. 2023), the number of lines of the observed energy levels in the CHIANTI database is limited, and most of the data for these satellite lines are based on theoretical calculations (Del Zanna et al. 2021).
The thin solid lines in each panel of Figure 2 show line ratios calculated using CHIANTI (Del Zanna et al. 2021) only including lines of the observed energy levels.Predictions for the theoretical line ratios (thin solid lines) are increased (move upward) in the panels for x/w and z/w, and they are decreased (move downward) in the q/w and y/w ratios.The contribution of line intensities with unobserved energy levels near w, mostly n 3 dielectronic satellites of Fe XXIV, exceeds those near the x and z lines, while the contribution relatively decreases for q and y lines located in the line-dense wavelength region near 1.86 Å.Therefore, the apparent excesses of x/w and z/w may further reduce or may be diminished in the lower temperature domain, but slopes along the horizontal axis of the j/w ratio seem different from the observed ones, i.e., these excesses may still remain at higher temperatures.On the other hand, excess q/w and y/w ratios  simply worsen the degree of discrepancy.It is noted again that in Figure 1 synthetic spectra created with lines of the observed energy levels alone cannot reproduce the entire observed spectral line profiles in the wavelength range of 1.84-1.88Å.Since a constant factor correction to CHIANTI ver.10.02 is optimal, and the correction factor is different from line to line, this may suggest that the problem is not satellite line modeling around the resonance line w.Roughly 20% and 16% excesses for the y and q line-intensity ratios are still larger than those for x and z indicating less than 10% excess, although Bely-Dubau et al. (1982) suggest some Fe XXIII lines lie blended with both q and y features, and the CHIANTI database lists a lot of relatively strong Fe XXIV lines around this wavelength, among which the transition 1s 2 3s 2 S 1/2 -1s2p( 3 P)3s 2 P 1/2 at 1.8591 Å is the strongest.

Effect of Differential Emission Measure (DEM)
A single-temperature plasma is a strong assumption for flare plasma even in its decaying phases.Temperature distribution along the flaring loops with different density integrated over the flaring loop volume can be considered here by introducing the concept of differential emission measure (DEM), following the formulation in Appendix.
If an electron temperature, t 0 , is obtained from a singletemperature analysis of the observed line ratio, and it is assumed that plasma has a DEM distribution as presented in Appendix in the decay phases of flare, then the parameter λ could be determined to keep the line ratio unchanged: The left panel of Figure 3 shows log ò(t)/log T e , temperature gradient of the emission lines concerned in the temperature range of log T e = 7.25-7.45,derived from synthetic spectra created with CHIANTI described in Section 3. In the case of the He-like ion, T e (He) is derived from the j/w ratio, while the intensity ratio of J-satellites over Lyα 1 is used to obtain T e (H).
The values of λ to keep these line ratios for temperature diagnostics unchanged are shown in the middle panel of Figure 3.For T e (He) and He-like ion lines, since the w line has the steepest power-law index α, and j has the most gentle β, the derived λ values are rather close to α.The variation of other line-intensity ratios, I l /I 1 , is as follows: where χ is the power-law index for Line l (l is one of q, x, y, and z), and Line 1 corresponds to w.The excess of intensity ratios for He-like ion lines over their resonance line w is plotted in the right panel of Figure 3 with the parameter λ determined in Equation (9).Since the power-law indices of these lines are larger than that of j, emissivity contributions of higher temperature plasma in these lines have more weight than that of j, which results in the deficit in intensity ratios of these lines.This situation, however, contradicts the observed tendency.All four of the line ratios in Figure 2 show excesses, rather than deficits.

Non-ionization Equilibrium (IE)
The empirical ion fraction of N(H)/N(He) can be obtained from the observed line ratios, Lyα/w, and x/w.H-like and Helike ion-resonance lines have similar excitation potentials so that the line ratio is almost independent of temperature (Tanaka 1986).The intensities of the x and w lines have contribution of recombining plasma from the H-like ions (Bely- Dubau et al. 1982).Figure 4 shows derived N(H)/N(He) ratios plotted against T e (H) (left) and T e (He) [∼T e (H)] (right).The ion fraction of N(Li)/N(He) derived from the q/w ratios are also plotted in Figure 4. Data points obtained from spectra showing T e (H) ∼ T e (He) are only plotted in the right panel.These panels are essentially the same as Figure 12 of Tanaka (1986), but a major difference is that x/w ratios are used in this study, instead of z/w ratios.The z line is usually stronger and more isolated than x, but its intensity has contributions from both N (Li)/N(He) and N(H)/N(He).
The data points (crosses) scatter rather widely for the ion fraction determined using Lyα/w ratios in Figure 4, which mainly comes from poor S/N ratios in the wavelength range around the Lyα line complex, and limited dynamic ranges for the strong w line intensity in SOX1.As a reference, error ranges for N(H)/N(He) and T e (H) estimated from photon statistics are indicated for the representative spectra in Figure 1.Accurate error ranges are again difficult to estimate and they could become still wider.
Discrepancies can be seen at first for the N(H)/N(He) ion fraction in the right panel of Figure 4, where only data with T e (He) ∼ T e (H) are plotted.Ion fractions derived from the resonance-line ratios distribute almost consistently along the IE condition, while those obtained from the x/w ratios show systematic excesses in the right panel by a couple of factors.The slope along T e (He) is also different from those of the IE curves, suggesting that the excess ion fractions might come from plasma in a non-IE state, e.g., recombining plasma, but the ratio of the resonance lines suggests that it is almost in IE.
A slight upward shift above the IE curves may indicate a slight overabundance of N(H) compared to N(He) in IE.It is noted, however, that the observed ion fraction derived from the resonance-line ratio could be almost consistent with IE values, as discussed in the previous subsection, if a multithermal emission measure is considered for apparently isothermal plasma in the later phases of solar flares, having less emission measure at higher temperatures.In the middle panel of Figure 3 for the case of T e (H) diagnostics, the Lyα 1 line has the largest power-law index, but the index for the He-like ion-resonance line w is smaller than that for the J-satellites.As a result, the ratio of Lyα 1 /w exceeds that for isothermal plasma shown in the right panel of Figure 3.The line excitation mechanism is similar for the Lyα and w lines, but the N (H)/N(He) ion fraction derived from the Lyα/w ratio tends to be overabundant above the IE condition for cooling plasma with the assumed DEM distribution.
The discrepancy between N(H)/N(He) ion fractions obtained from the two independent methods was not recognized in the previous analysis Tanaka (1986).Coupled ambiguities for the q and z line intensities observed in various flare phases might have obscured the fact in the previous analysis.
It is also found in this analysis that N(Li)/N(H) ratios also deviate from the IE curves.Antonucci et al. (1987) analyzed q/w ratios using Bely- Dubau et al. (1982)ʼs method, and proposed a revised ionization balance for Fe XXV, XXIV, and XXIII, among which N(Li)/N(He) is indicated by the dasheddotted line in Figure 4.The dotted line shows the same ratio adopted from Doyle & Raymond (1981).However, crosses in the right panel lie in parallel between the IE curves of Doyle & Raymond (1981) and CHIANTI (Dere et al. which simply reflects the fact in Figure 2 that the q/w ratio has a constant 16% excess compared to the j/w ratio. In the left panel plotted against T e (H), the data points indicated by thin open circles and crosses are those obtained from spectra showing T e (H) > T e (He).They deviate from the equilibrium values; N(H)/N(He) ratios cross the equilibrium curves downwards, and the N(Li)/N(H) ratios deviate upward in higher temperature ranges.These tendencies can also be explained assuming a multitemperature plasma, and no plasma is required to be in transient ionization.Besides, the excess of q/w suggests that plasma is ionizing in most of the ion-fraction calculations, while the excesses of x/w indicate that plasma is recombining.Therefore, the working hypothesis of non-IE plasma is not supported by the observations, and is, in fact, self contradictory.
In the same left panel of Figure 4, N(H)/N(He) ion fractions analyzed for the Perseus cluster core (Hitomi Collaboration 2018a), are also plotted (five-pointed star marks).The Lyα 1 /w intensity ratio is directly proportional to the N(H)/N(He) ion fraction, if an isothermal plasma is assumed.The stringency of the isothermal assumption and the ambiguity in the calculation of IE should be reconsidered in both plasmas.
Finally, line ratios to the resonance line of the He isoelectronic sequence (w) other than Fe can be sometimes recognized as slightly excessive in solar and astrophysical plasmas.He-like calcium (Ca XIX) is thought to be best studied in solar flares.Phillips et al. (2018) looked into Ca XIX/XVIII spectra between 3.17 and 3.21 Å obtained by DIOGENESS/ CORONAS-F and SOLFLEX/P78-1.It is noted that Figures 6-8 of Phillips et al. (2018) show slight intensity excesses of x and y lines compared to theoretical spectral fit with single T e determined by the k/w ratio.The He-like line ratio, z/w of O VII and Ne IX in stellar corona is obtained by XMM-Newton (Ness et al. 2003).It can be seen in Figure 6 compared to Figure 3 of Ness et al. (2003) that active stellar coronae having log T e > 6.6 seem to show excess z/w ratios plotted above the theoretical line ratios for log T e = 6.6.All these excesses are rather small, however, similar to the results of the present study for Fe ions, and various factors segregated from atomic physics should be more carefully considered, especially for the case of stellar coronal plasmas.(1982)ʼs method.Cross marks are from Lyα/w ratios for N(H)/N(He), and from q/w ratios for N(Li)/N(He) with CHIANTI (Del Zanna et al. 2021) .Lines show theoretical ion fractions in ionization equilibrium; solid lines from CHIANTI, chianti.ioneq(Dere et al. 2019), dashed lines (Jacobs et al. 1977), dotted lines (Doyle & Raymond 1981), and dashed-dotted lines (Antonucci et al. 1987).Three plus marks indicate ion fractions, N(H)/N(He) and their error ranges obtained from the spectra shown in Figure 1.Thick marks are data points showing T e (H) ∼ T e (He) in the left panel, and the same ones plotted in the right panel.Five-pointed star marks in the left panel are from Hitomi Collaboration (2018a).

Conclusion
The empirical line-intensity ratios of the Fe He-like ion are determined by best effort in Table 2. Large data scatter comes from poor S/N ratios in SOX spectra.A couple of causes and reasons are considered that modify theoretical ratios to the observed ratios.Qualitative analysis for plasma having a DEM distribution in IE cannot explain the tendency of the observed line ratios.Decaying flare plasma still in transient ionization also cannot explain the observations, because N(H)/N(He) is almost consistent with the ionization equilibrium condition, if the multithermal nature of flare plasma is considered for the Lyα 1 /w ratios.The simplest and most likely explanation is that atomic parameters for these lines still have an ambiguity of 9%-20%.Further precise measurements and modeling for the relevant atomic parameters are needed.

Figure 1 .
Figure 1.Iron spectra in three representative phases of the 1981 October 7 flare.Lower resolution spectra (SOX1) are at the left, higher resolution spectra (SOX2) are at the right.The ordination is intensity in units of photons cm −2 s −1 bin −1 .SOX1 spectra in the wavelengths of 1.75-1.80Å are shown 20 times enhanced in intensity; refer to the right-side ordinates.Identification of strong lines is shown in the middle panel.Synthetic spectra generated by CHIANTI ver.10.02 with isothermal assumption are shown by solid lines, and the contributions of individual strong lines, w, x, t, y, q, k + r, j, and z are shown by dotted lines in the SOX2 spectra.Electron temperature (T e [K]) and volume emission measure (EM [cm −3 ]) are indicated.Also see the text.
In Figure2, deviations from the theoretical ratios shown by thick solid lines (Del Zanna et al. 2021) and dashed lines (Bely-Dubau et al. 1982) are obvious.Excesses of the line ratios, namely corrections to the theoretical line ratios by constant factors, are plotted with the same line types as the theoretical models.Factors of 1.09-1.20 for CHIANTI ver. 10 (Del Zanna et al. 2021) and 1.17-1.59for the parameters of Bely-Dubau et al. (1982) are obtained as excesses for four lineintensity ratios over the resonance line of the He-like ion (w).The decrease of correction factors in CHIANTI ver.10.02 (Del Zanna et al. 2021) compared to those in Bely-Dubau et al.

Figure 2 .
Figure 2. Line-intensity ratios against j/w ratios.Filled circles are observed ratios obtained from spectra showing T e (H) ∼ T e (He).Three plus marks show line ratios and their error ranges obtained from spectra in Figure 1.Thick solid lines and dashed lines systematically deviated from the data points indicate theoretical ratios calculated with single-temperature models using CHIANTI (Del Zanna et al. 2021) and atomic parameters of Bely-Dubau et al. (1982), respectively.Upward-shifted thick solid and dashed lines show the regression lines applying constant excesses.Dotted lines show those of linear regression analyses shown in Equations (1)-(8) in the text.Thin solid lines indicate line ratios calculated by CHIANTI with lines of the observed energy levels only.Four five-pointed star marks plotted in the z/w panel are Hitomi results for the Perseus cluster core (Hitomi collaboration 2016, 2018a).See the details in the text.

Figure 3 .
Figure 3. (Left) Power-law indices of lines, log ò/log T e .(Middle) DEM parameter λ determined to keep the temperature diagnostic line pairs j/w and J-sat/Lyα 1 unchanged.(Right) Excess of line ratio, when the ratios of the temperature diagnostic line pairs are kept unchanged.Horizontal dashed-dotted line shows unity.Solid lines are for x/w, y/w, z/w, and q/w, and the dashed line is for Lyα 1 /w.

Figure 4 .
Figure 4. Ion fractions derived from the line-intensity ratios.Circles are from Bely-Dubau et al. (1982)ʼs method.Cross marks are from Lyα/w ratios for N(H)/N(He), and from q/w ratios for N(Li)/N(He) with CHIANTI (Del Zanna et al. 2021) .Lines show theoretical ion fractions in ionization equilibrium; solid lines from CHIANTI, chianti.ioneq(Dere et al. 2019), dashed lines (Jacobs et al. 1977), dotted lines (Doyle & Raymond 1981), and dashed-dotted lines (Antonucci et al. 1987).Three plus marks indicate ion fractions, N(H)/N(He) and their error ranges obtained from the spectra shown in Figure 1.Thick marks are data points showing T e (H) ∼ T e (He) in the left panel, and the same ones plotted in the right panel.Five-pointed star marks in the left panel are from Hitomi Collaboration (2018a).

Table 2
Best Estimates for Observed Line Ratios