7 Comparing theory and observations for the EUV lines

Fexiv gives rise to a number of strong lines in the extreme ultraviolet (EUV; 150-900  Å) portion of the solar spectrum, the strongest of which are illustrated in Fig. 3 and listed in Table 9. These lines have been measured in a number of solar spectra, and we will use the published catalogues of Malinovsky & Heroux (1973, hereafter MH73) and TN94. The latter spectrum was obtained by the SERTS-89 instrument, and a detailed comparison of the CH97 Fexiv model with these observations was presented in Sect. 13.6 of Y98, to which reference will be made in the following sections. In the following discussion we refer to wavelengths given in Table 9 rounded down to the nearest Angstrom; for example the intensity ratio $I_{ 252.20~{\rm\AA} }/I_{264.79~{\rm\AA}}$ is denoted as 252/264.

In comparing theory with observation, it is essential to consider the accuracy of the observed line intensities. The TN94 catalogue explicitly gives error bars for each observed line and these are used here. MH73 do not do this, but a discussion of the accuracy of the line intensities is given on p. 1019 of their work. Although some intensities may be accurate to only $\pm$50%, the stronger lines are accurate to $\approx \pm 20$%. Relative intensities of strong lines are expected to be rather more accurate than this. Here we will only use the measured intensities and not quote error bars, so the values just quoted should be borne in mind.

There are several line ratios that are suitable for determining the electron density and these will be discussed in Sect. 7.2. As a check on the accuracy of the atomic data, though, line ratios that are insensitive to the density will first be considered.

7.1 Density insensitive ratios

The importance of line ratios that are insensitive to the physical conditions in the solar atmosphere was stressed in Y98 with regard to the accuracy of both the atomic data and instrument calibration. In this work, such ratios were divided into branching ratios and density insensitive ratios. The branching ratios are those for which the two emission lines have a common emitting level in the ion, and so the ratio of their emissivities depends solely on the radiative data and the energy levels of the ion. A comparison amongst the different Fexiv models is given in Table 10, and the ratios derived from the TN94 and MH73 spectra are also given. Similar values to those from the CH97 model are found here, indicating good agreement between the two sets of radiative data. The discrepancy identified by Y98 between theory and observations for the 257/270 is still not fully resolved. MH73 flag the 252 line as being blended, but do not identify the other component. It is likely, however, that the Fexiv line lies in the wing of the stronger Fexiii 251.95Å line.

    

Table 9: Wavelengths and level identifications for the 3s²3p - 3s3p² and 3s²3p - 3s²3d EUV permitted transitions

Transition
Configurations	Terms	J-values	Indices	$\lambda$ (Å)
3s23p - 3s3p2	2P - 4P	1/2 - 1/2	1 - 3	444.22
		3/2 - 1/2	2 - 3	484.82
		1/2 - 3/2	1 - 4	429.57
		3/2 - 3/2	2 - 4	467.43
		3/2 - 5/2	2 - 5	447.36
	2P - 2D	1/2 - 3/2	1 - 6	334.18
		3/2 - 3/2	2 - 6	356.65
		3/2 - 5/2	2 - 7	353.84
	2P - 2S	1/2 - 1/2	1 - 8	274.20
		3/2 - 1/2	2 - 8	289.15
	2P - 2P	1/2 - 1/2	1 - 9	257.39
		3/2 - 1/2	2 - 9	270.52
		1/2 - 3/2	1 - 10	252.20
		3/2 - 3/2	2 - 10	264.79
3s23p - 3s23d	2P - 2D	1/2 - 3/2	1 - 11	211.32
		3/2 - 3/2	2 - 11	220.08
		3/2 - 5/2	2 - 12	219.13

   

Table 10: Emissivity ratios for lines with common upper levels

	Theory $^\dagger$			Observations
Ratio	CH97	B94	SMY99	MH73$^{\rm a}$	SERTS-89$^{\rm b}$
220/211	0.21	0.22	0.22	0.28	0.25 $\pm$ 0.07
252/264	0.24	0.25	0.24	0.26	0.18 $\pm$ 0.06
257/270	0.75	1.12	0.66	n/a	0.38 $\pm$ 0.09
289/274	0.089	0.28	0.061	0.060	0.072 $\pm$ 0.024
356/334	0.036	0.048	0.029	n/a	0.028 $\pm$ 0.010
$^\dagger$ Theoretical models CH97, B94, SMY99; see Sect. 5.2.
$^{\rm a}$ Malinovsky & Heroux (1973).
$^{\rm b}$ From Thomas & Neupert (1994).

Density insensitive ratios arise through similarities in the way two lines are excited, e.g., if two lines are principally excited from the ground level at all densities, then their ratio will be insensitive to density. Four such ratios were identified in Y98, and are listed in Table 11. Theoretical values are listed for each of the three Fexiv models considered here. These values have been compiled using a different method to that used by Y98 on account of the way the B94 data were presented. The value for the ratio is the value at $\log\,N_{\rm e}=10.0$ and $\log\,T=6.2$, while the upper and lower limits represent the maximum deviations from this value over densities of $8.0\le \log\,N_{\rm e}\le 12.0$ and temperatures of $6.0\le \log\,T\le 6.4$. Note that none of the ratios are strictly insensitive to density or temperature, but the variations are less than or comparable to the errors in the observations.

Based on the CH97 model, Y98 listed the 270/211 ratio as insensitive as it shows relatively small variation with density (Fig. 4). In the SMY99 model, however, the ratio shows significantly greater variability. The reason for this lies in the way the 270 line is excited. The upper level for the 270 transition is 9 (Table 9), and the ratio $\Upsilon_{2,9}/\Upsilon_{1,9}$ at $\log\,T=6.2$ is 1.71 from Table 7. The B94 and CH97 models contain upsilons from DK91 which give a ratio of $\Upsilon_{2,9}/\Upsilon_{1,9}=0.82$ at $\log\,T=6.2$. Thus the way the 270 line is excited is very different in the two cases, and leads to the 270/211 being density sensitive in the present case.

An interesting consequence of the change in behaviour of the 270 line is that the 274/270 ratio also now shows density sensitivity (Fig. 4). Y98 noted that the CH97 model gave the 274/270 ratio as insensitive, but that considerable variation was seen in observations, with values of between 1.3 and 2.3 quoted. As can be seen from Fig. 4, the ratio is now predicted to vary between 2.0 and 1.0, in excellent agreement with observations.

As another consequence of the change in behaviour of the 270 line, it is now found to be insensitive when taken relative to a sum of the 264 and 274 lines, and this ratio is now given in Table 11, where excellent agreement with the MH73 and SERTS-89 observations is found.

The 274/211 ratio was highlighted in Y98 as, although the lines are very strong in spectra from solar active regions, the observed ratio was almost a factor 3 discrepant with theory. This problem is not fully resolved here, but the new theoretical ratio is $\approx$ 50% higher than the previous values, and is similar to the MH73 observed value. The Fexiv 211 line was observed in second order by the SERTS instrument, and the question of whether the 1st-2nd order calibration may be in error has been raised in Brickhouse et al. (1995; Sect. 3.2.1) and Y98; Sect. 15.1. Brickhouse et al. suggest that the 2nd order lines may be too weak by around 50%, and we note this would lower the SERTS ratio to 0.67 in better agreement with the SMY99 model.

The 334/274 ratio found here is similar to that from the CH97 model, and agrees with the SERTS observations. The B94 ratio is, however, too high compared to observations. The 444/334 ratio is found to be higher than in the other models, in apparent disagreement with the SERTS-89 observations. However, in Sect. 15.1 of Y98 it was suggested that the SERTS-89 calibration should be revised for lines above 400Å, on the basis of several density insensitive line ratios not agreeing with observed values. The Fexiv 444/334 ratio (from the CH97 model) was one of only two that actually agreed with the original TN94 calibration. If we accept the revised calibration of Y98, then the SERTS-89 444/334 ratio becomes $0.036\pm 0.010$ - in better agreement with the new Fexiv model.

    

Table 11: Comparisons of density insensitive ratios for different models with observations

	Theoretical ratios$^\dagger$			Observed ratios
Lines	CH97	B94	SMY99	MH73$^{\rm a}$	SERTS-89$^{\rm b}$
270/211	$0.48_{-0.12}^{+0.13}\nu$	$0.42_{-0.10}^{+0.10}\nu$		0.28	0.48 $\pm$ 0.09
274/211	$0.36_{-0.08}^{+0.07}\nu$	$0.33_{-0.07}^{+0.06}\nu$	$0.53_{-0.03}^{+0.05}\nu$	0.60	1.01 $\pm$ 0.18
270/(264+274)			$0.26_{-0.01}^{+0.02}\nu$	0.26	0.24 $\pm$ 0.04
334/274	$0.68_{-0.13}^{+0.28}\nu$	$0.97_{-0.14}^{+0.30}\nu$	$0.64_{-0.04}^{+0.06}\nu$	n/a	0.62 $\pm$ 0.10
444/334	$0.015_{-0.004}^{+0.006}\nu$	$0.017_{-0.004}^{+0.004}\nu$	$0.028_{-0.009}^{+0.011}\nu$	n/a	0.018 $\pm$ 0.005
$^\dagger$ Theoretical models; CH97, B94, SMY99, see Sect. 5.2.
$^{\rm a}$ Malinovsky & Heroux (1973).
$^{\rm b}$ From Thomas & Neupert (1994).

Figure 4: Variation of the 270/211 and 274/270 ratios predicted from models; the solid line is present work; the dashed line is from CHIANTI/v1.0; the asterisks are from Bhatia et al. (1994)

  
7.2 Density diagnostics

Four useful density diagnostics were identified by Y98 and we provide comparisons of the three different models considered here in Fig. 5, while densities derived from the Malinovsky & Heroux and SERTS-89 observations are presented in Table 12.

The agreement between the four ratios is excellent, and of particular interest is the 264/274 ratio, which Y98 noted yielded a very low density of $\log\,N_{\rm e} \le 8.4$ when the CH97 model was used. The new model now gives a density in agreement with other Fexiv ratios (Table 12).

Figure 5: Comparisons of the Bhatia et al. (1994) (asterisks), CHIANTI/v1.0 (dashed line) and present (complete line) calculations for four density diagnostic line ratios

7.3 CDS observations

The Coronal Diagnostic Spectrometer (CDS) is one of the twelve instruments on board the Solar and Heliospheric Observatory (SOHO) and is described in Harrison et al. (1997). CDS observes at EUV wavelengths between 150 and 800Å. There are two separate spectrometers, the grazing incidence (GIS) and the normal incidence (NIS). Calibration for the GIS is complicated and still somewhat uncertain, and we will consider only NIS spectra.

The 353/334 density diagnostic lines are observed by NIS and, indeed, they form one of the key density diagnostics for observers. A check on the quality of the atomic data is possible by looking at regions of low density ( $\log\,N_{\rm e}\ \le\ 9$) where the 353/334 ratio is close to the low density limit.

The ideal place to find low densities is above the limb in closed field regions. Here the plasma is close to being isothermal with temperatures of $6.1\le\log\,T\le 6.3$, and so the Fexiv lines are very prominent - see Fig. 6. Several data-sets containing the Fexiv lines from such regions were selected and 353/334 ratios derived. The points in Fig. 7 show these values. Note that the NIS calibration was revised on 23-Dec.-98, and the values were derived with this new calibration.

Also plotted in this figure are horizontal lines representing the low density limits predicted by the three Fexiv models. The SMY99 and B94 models predict the same value, while the CH97 model gives a value a factor of 4 lower. Note that for the CH97 and SMY99 models, the low density limit was calculated at $\log\,T=6.2$ and $\log\,N_{\rm e}=1$, whereas the B94 value is the ratio value at $\log\,N_{\rm e}=8$, the lowest density considered by B94. The actual low density limit is likely to be marginally less.

The observations clearly show that the CH97 model disagrees with observations, being over a factor of 4 too low. Both the SMY99 and B94 models are in good agreement with the observed values.

    

Table 12: Densities deduced from the SERTS-89 observed intensities using the present SMY99 model. Densities are in cm^-3 and log T = 6.3

	SERTS-89$^{\rm a}$		MH73$^{\rm b}$
Ratio	Ratio	log$N_{\rm e}$	Ratio	log$N_{\rm e}$
219/211	$0.404\pm 0.082$	$9.48^{+0.11}_{-0.14}\nu$	0.186	9.01
264/274	$1.010\pm 0.168$	$9.36^{+0.20}_{-0.27}\nu$	0.826	9.05
353/334	$0.453\pm 0.073$	$9.50^{+0.13}_{-0.16}\nu$	n/a	-
447/444	$2.882\pm 0.743$	$9.60^{+0.53}_{-1.03}\nu$	n/a	-
$^{\rm a}$ From Thomas & Neupert (1994).
$^{\rm b}$ Malinvosky & Heroux (1973).

Figure 6: NIS spectrum in the range 330 to 360Å taken above an active region on the solar limb. The Fexiv 334.2 and 353.8Å lines are clearly seen

Figure 7: A comparison of the low density limits of the Fexiv 353/334 density diagnostic predicted by the three models considered here with observed values (stars in the figure) of the ratio in low density regions