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Astron. Astrophys. 329, 291-314 (1998)

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3. Method of analysis

The quality of the SERTS-89 spectrum has meant that for a lot of the transition region and coronal ions we have several lines identified for a single species, thus allowing a detailed comparison of theory with observations. One such attempt at a detailed comparison is that of Brickhouse et al. (1995) who studied only the iron ions and used every observed line to compare with theory. Fig. 1 of their work shows a comparison assuming an electron density of 1010cm-3 for all the ions, while in Fig. 6 of their work they use density diagnostic pairs for the ions to estimate average electron densities. In each case we see a large spread in derived values.

In this work, we argue that while every line in the spectrum for a given ion should be used they should not be used in an average sense but instead be used firstly as a check on both the atomic data and the instrument calibration and secondly as a means of determining plasma parameters such as density and emission measure.1 The first step in this process is to look for density insensitive line ratios. These come in two forms and we will differentiate branching ratios from ratios whose insensitivity stems from, e.g., the lines being principally excited from the same lower level (these we will refer to as simply density insensitive ratios). The reason for this differentiation is that the atomic data required to predict branching ratios are simply the transition probabilities which can generally be calculated to accuracies of [FORMULA] %. For density insensitive ratios we need to have estimates of the electron excitation rates which are rather more difficult to calculate and so less accurate (typically 30% or less).

The use of ratios insensitive to the electron density as a means of determining the calibration of solar EUV instrumentation has been discussed by Neupert & Kastner (1983) where references to earlier work can be found. The quality of atomic data for many ions has improved substantially since this work, so allowing far more density insensitive ratios to be identified, while the CHIANTI database ensures that all of this data is easily accessible.

The advantage of density insensitive ratios over branching ratios lies in the fact that they can span large regions in wavelength, whereas lines related by branching ratios tend to lie close to one another (usually within 20 Å). As an example, one can see the five Fe XIV branching ratios in Table 18 which each involve lines within 23 Å of each other, whereas the density insensitive ratios presented in Table 19 involve lines separated by up to 110 Å. A disadvantage is that the density insensitive ratios are often not strictly density insensitive and may also show some temperature sensitivity.

In choosing density sensitive ratios to study, we try to avoid any redundancy in the lines. For example, for lines a, b and c, say; if a and b are related by a branching ratio and agree well with theory, and if a and c are density sensitive and yield a density of 10 [FORMULA] cm-3, say, then we can immediately guess that the [FORMULA] ratio will also yield a density of around this value. The most extreme example of this removal of redundancy can be seen in Fe XIII where, starting from the observed 23 lines, we reduce the number of density diagnostic ratios down to 4 which are shown in Table 20. The consistency between these ratios is reasonable and contrasts strongly with Fig. 6 of Brickhouse et al. (1995) where they show densities spanning 3 orders of magnitude. The reason for this difference is that our method eliminates weak lines or lines inconsistent with theory at the initial density-insensitive ratio stage. Thus, the lines we use to predict densities are typically strong lines that are known to be consistent with theory in terms of insensitive ratios.

We choose to go through the different ions by iso-electronic sequence, each of which commands a section to itself, and discuss each ion within the sequence separately. The exceptions to this are the iron and nickel ions which are rather more complex and deserving of a separate section. Each section has three tables displaying branching ratios, density insensitive ratios and density sensitive ratios. An explanation of the symbols used in these tables is given in Sect. 5.

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997
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