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Astron. Astrophys. 360, 1148-1156 (2000)

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5. Data analysis

There are a two main classes of diagnostic tecniques making use of EUV spectral line intensities to measure element abundances: one involving line ratios (see for example Young & Mason (1997 or Drake et al. 1997), and the other involving the DEM of the emitting plasma (see for example Pottasch 1963; Dupree 1972; Malinovsky & Heroux 1973; Feldman 1992; Fludra & Schmeltz 1995). The latter method allows to take into proper account the temperature dependence of the Contribution Functionof the emitting ions. Since we are studying lines emitted by ions formed at different temperatures, the latter method is more appropriate for our purposes.

The DEM diagnostic technique we adopt is described in full detail by Landi & Landini (1997). This diagnostic technique relies on an iterative procedure which calculates a temperature-dependent correction to an initial arbitrary DEM , until theoretical line intensities predicted through the resulting DEM agree with their observed values within the experimental uncertainties. The element abundance diagnostic technique adopted in the present work requires as input an adopted abundance dataset, and enables the determination of correction factors (a simple multiplicative constant) to single element abundances relative to an element, that is taken as reference.

We have used as starting values the coronal abundances of Feldman (1992). This dataset presents low-FIP element abundances enhanced by nearly a factor 4 relatively to photospheric values. During the present study the abundances of Fe has been taken as reference (correction equal to unity) and those of the other elements have been multiplied by the correction factor that gives the best fit.

5.1. DEM diagnostics

Fig. 6 and Fig. 7 display the resulting DEM curves for each of the two selected regions. The two regions present DEM curves showing qualitatively the same behaviour, with a large peak at around [FORMULA] K, and a high-temperature tail which rapidly decreases as temperature exceeds [FORMULA] K. Similar DEM curves have been found by a number of authors in the literature.

[FIGURE] Fig. 6. DEM for the He i selected region, as determined using three different ion fractions datasets as described in the text: RAY (full line), SHU (dotted line) and MAZ (dashed line).

[FIGURE] Fig. 7. DEM for the Fe ix selected region, as determined using three different ion fractions datasets as described in the text: RAY (full line), SHU (dotted line) and MAZ (dashed line).

From Fig. 6 and Fig. 7 it is evident that the use of different ion fraction datasets hugely affects the shape of the DEM curves at all temperatures. For example, in both the emitting regions the RAY and MAZ datasets provide similar curves at temperatures around 1-1.5[FORMULA] K, but large differences are found at transition region and chromospheric temperatures. On the contrary, SHU and RAY curves provide a reasonable good agreement at low temperatures, but heavily disagree at coronal temperatures, where the peak found in the SHU DEM curve is broader, lower and slightly hotter than the one found in the RAY results. No agreement at all is found between the SHU and MAZ results. Differences rise up to a factor 4.

These differences are directly related to the differences in the ion fractions. For instance, the DEM curve at coronal temperature is mainly dominated by the Fe lines and a few other hot ions, for which Mazzotta et al. (1998) and Arnaud & Raymond (1992) provide very similar ion fractions (see for example Fig. 2): this explains the agreement found between MAZ and RAY curves at coronal temperature. Shull & Steenberg (1982) ion fractions for coronal ions, based on less accurate ionization and recombination rates, are sometimes very different from the other two datasets, so that huge differences in the DEM are found.

Similarly, differences found between RAY and MAZ DEM curves at transition region temperatures may be explained by differences in the ion fractions for the neon and magnesium ions which determine the DEM at those temperatures (see for example Fig. 1).

It is therefore clear that ion fraction datasets are a critical parameter in the determination of DEM curves from EUV emission lines, and the choice of the adopted dataset can be the dominant source for uncertainties in the results. Given the considerable size of the differences, this is particularly important for theoretical models involving the DEM of the emitting plasma.

Unfortunately, the lack of an independent measurement of the DEM does not allow us to determine which of the adopted ion fraction datasets is more accurate and therefore recommendable for further DEM studies, or to point out ions for which new and improved calculations of ionization and recombination rates are required.

5.2. Abundance measurements

In order to determine the DEM curves displayed in Fig. 6 and Fig. 7 it has been necessary to correct the abundances of nearly all the elements in the dataset. Table 2 reports the correction factors to the Feldman (1992) abundances for each of the selected regions. The uncertainties of these factors are of the order of or smaller than 25%, and are given both by the uncertainties on the measured line fluxes and in the atomic data and transition probabilities used to calculate level populations (Eq. 2).


[TABLE]

Table 2. Correction factors to the Feldman (1992) element abundances for the He i (left) and Fe ix (right) emitting regions obtained using the three different ion fraction datasets RAY, SHU and MAZ. Fe abundance has been takes as reference. The FIP is in eV. The correction factors are multiplicative contants.


Table 2 shows that for each given ion fraction dataset, the two different regions show very similar correction factors, indicating that their element abundances are about the same despite their different position in the active region.

From Table 2 it is possible to see that the use of different ion fraction datasets may cause large differences in the abundance correction factors found in each of the two emitting regions.

The largest differences are reported for the two high-FIP elements oxygen and neon: while correction factors obtained from RAY and SHU are similar, differences of more than a factor 2 are found when they are compared to MAZ's values. It is important to note that the correction factors obtained from the MAZ ion fractions indicate also that a large correction in the relative O/Ne abundance is required, which is much greater than the value reported by Landi & Landini (1998b).

Sulphur (whose FIP is at the boundary between the high- and low-FIP classes) also shows that SHU ion fractions cause large differences in the abundance correction factors from MAZ and RAY results.

More limited differences are found for the low-FIP elements. The only exception to this is calcium, since its correction factor changes by a factor larger than 3 if MAZ ion fractions are used. It is possible to see that the use of MAZ data leads to a correction factor for calcium abundance similar to those of the other low-FIP elements, while the other two ion fraction datasets caused its value to be very large. The only calcium lines available in the CDS-NIS spectral range are due to Ca x. Anomalies in the behaviour of the Ca x lines have already been noted in previous studies (Landi & Landini 1998b and Del Zanna & Bromage 1999) and they were ascribed mostly to element abundance. These results show that ion fractions could be responsible for most of the calcium anomalies. The comparison with the behaviour of the other low-FIP elements seems to suggest that MAZ ion fractions for Ca x should be more reliable than the other two datasets, as abundances of elements belonging to the same FIP class are expected to to have qualitatively the same behaviour. This is consistent with the results of Smith et al. (1985), who pointed out that the dielectronic recombination rates used in the SHU and RAY are incorrect for the Ne-like ions, and that this altered the corresponding Na-like ion abundances. This might explain why results obtained with the MAZ dataset, who adopt different rates for Ne-like dielectronic recombination, show that Ca x is in better agreement with observations.

As in the DEM studies, these differences may be explained by comparisons between the ion fractions of the ions involved in the abundance measurements. Fig. 1 and Fig. 2 clearly show that huge changes are found for Ca x ion fraction between Mazzotta et al. (1998) data and those from Arnaud & Rothenflug (1985) and Shull & Steenberg (1982), which are similar; such discrepancies are found (although smaller in size) for several magnesium and neon ions.

The most important result shown in Table 2 is that the relative low-to-high FIP element abundance is heavily affected by changes in the ion fraction dataset. In particular, the use of RAY and SHU datasets show that the abundance for the high-FIP elements must be increased relative to the low-FIP elements' value, thus implying that the FIP effect is less effective than assumed by adopting the Feldman (1992) element abundances. On the contrary, results obtained using MAZ data show that the FIP effect is as strong as reported by Feldman (1992).

It is therefore clear that the ion fraction datasets are a very important source for uncertainty in quantitative FIP effect studies when EUV line intensities are used.

Unfortunately, it is not possible to carry out an independent check of the element abundances in the emitting plasma with the present data, so that it is not possible both to determine which of the ion fraction datasets is to be recommended for further studies, and to draw any quantitative conclusion on the element abundances and the FIP effect of the emitting regions.

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© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000
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