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Astron. Astrophys. 338, 1102-1108 (1998)

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2. Atomic data and theoretical ratios

2.1. Fe XIII

The diagnostic potential of Fe XIII emission lines, due to 3s 23p 2-3s 3p 3 transitions, was first noted by Flower & Pineau des Forets (1973) and Flower & Nussbaumer (1974). The latter presented possible electron density sensitive emission line ratios calculated using electron excitation rates generated in the Distorted Wave approximation. Subsequently this ion has been used successfully for a density diagnostic of active regions and flares (see for example, Dere et al. 1979, Dere 1982). More recently Keenan et al. (1995) used Fe XIII emission lines to infer electron densities for solar active regions and for two stars, [FORMULA] Cen and Procyon.

The model ion for Fe XIII , used by Keenan et al. (1995), consisted of the eight energetically lowest LS states 3s 23p 2 [FORMULA],[FORMULA] and 1S0; 3s 3p 3 [FORMULA], [FORMULA], 1D2, 3S1 and 1P1, making a total of 14 fine-structure levels. Using the model ion above together with the statistical equilibrium code of Dufton (1977) relative Fe XIII level populations and hence emission-line strengths were calculated as a function of electron density at the temperature of maximum fractional abundance of Fe XIII , Log Te=6.2 K(Arnaud & Rothenflug, 1985).

By using the same theoretical data as Keenan et al. (1995) we will examine the ratio;

R1 = I(3s23p2 3P1 - 3s3p3 [FORMULA])/I(3s23p2 3P0 - 3s3p3 3D1)

= I(359.64Å)/I(348.18Å).

2.2. O IV

Ions in the boron isoelectronic sequence are frequently used for diagnostic purposes, as first outlined by Flower & Nussbaumer (1975). Subsequent papers based on B-like ions include Vernazza & Mason (1978), Doschek (1984), and Dwivedi & Gupta (1992, 1994).

The ratio we will examine in this work is;

R2= I(1407.39Å)/I(1401.16Å).

Both these lines belong to the transition [FORMULA] [FORMULA] [FORMULA] [FORMULA] which produces lines at 1407.4, 1404.8, 1401.1, 1399.7 and 1397.2Å.

The atomic data adopted in the calculation of the O IV I(1407.39Å)/I(1401.16Å) intensity ratio are as discussed in the paper by O'Shea et al. (1996) with the exception of the Einstein A-coefficients for the 2s 22p 2P-2s 2p 2 4P inter-combination lines. These are the transitions that produce the range of O IV lines between 1397 and 1407Å. Brage et al. (1996) have recently recalculated radiative rates for these transitions, and shown that the data of Nussbaumer & Storey (1982) employed by O'Shea et al. are in error. The results of Brage et al. were therefore used in the line ratio calculations, although it should be noted that these lead to theoretical values for most line ratios within a few percent of those of O'Shea et al. and Cook et al. (1995). This is not the case for line ratios involving the O IV 1404.81Å transition, where the Brage et al. diagnostics are up to [FORMULA]20% different. However we do not employ the 1404.81Å line as a diagnostic, as it is blended with a S IV transition at 1404.77Å (Cook et al. 1995).

The model ion used for calculating the theoretical line ratios of O IV consisted of the 15 energetically lowest fine-structure levels, namely 2s 22p [FORMULA]; 2s 2p 2 [FORMULA], [FORMULA], [FORMULA], [FORMULA]; 2p 3 [FORMULA], [FORMULA] and [FORMULA].

As the theoretical data for O IV and Fe XIII used in this work came from the Keenan et al. group working in Queen's University Belfast (QUB), results from these data will be referred to subsequently as the QUB results.


The second source of theoretical line ratios used in this work come from the CHIANTI database. CHIANTI consists of a collection of critically evaluated data necessary to calculate the emission line spectrum of an astrophysical plasma (Dere et al., 1997). It consists of a database of atomic energy levels, electron collisional excitation rates and atomic radiative data such as oscillator strengths and A-values. A set of programs written in IDL (Interactive Data Language) uses these data to solve the statistical equilibrium equations providing theoretical line intensity ratios, synthetic spectra and the differential emission measure. The collisional data comes from a number of sources which employed both R-matrix and distorted wave calculations. In general, the excitation rates used by both O'Shea et al. (1996) and Keenan et al. (1995) are similar to those used by the CHIANTI project. For example the O IV atom of both groups used the R-matrix excitation rates from Zhang et al. (1994). However for Fe XIII , CHIANTI used excitation rates calculated using the Distorted Wave approximation while Keenan et al. (1995) used the excitation rates from Tayal (1995) which were calculated using the R-matrix method. Energies are typically taken from databases of observed energy levels (see Dere et al. 1997 for details) and supplemented by the best theoretical estimates available. CHIANTI does not include proton excitation rates which may be important for fine structure transitions in highly ionised systems. As shown above these were included for the O IV atomic data used by O'Shea et al. (1996). For the O IV model atom the 125 lowest energy levels were used, while for Fe XIII the lowest 27 levels were used.

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Online publication: September 17, 1998