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Astron. Astrophys. 347, 617-629 (1999)

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3. Atomic data

3.1. Model atom for Fe I

The level energies [FORMULA], degeneracies [FORMULA] and Einstein coefficients [FORMULA] for the lowest 200 states (ordered by energy) of the neutral iron atom have been obtained from the NIST  3 (Fuhr et al. 1988) and from KURUCZ 's database 4 (Kurucz 1988). Both databases agree with each other concerning the electronic configurations and the energies of these levels. However, the Einstein coefficients may differ substantially. KURUCZ 's list includes many more lines (especially forbidden transitions) for highly excited states, whereas the NIST database has more data for lines among low levels. We have taken KURUCZ 's line-list as the starting point and have added/replaced all Einstein coefficients listed by NIST with [FORMULA]. Four fine-structure lines (2-1, 3-1, 3-2, 7-6) have also been included with Einstein coefficients taken from Hollenbach & McKee (1989).

Fig. 2 gives an impression of the complexity of the radiative line data for Fe I. According to our working definition Eqs. (8) to (10), there are 4 fine-structure, 2420 forbidden and 1289 permitted lines in the Fe I model atom covering wavelengths between 2140 Å and 89 µm. Note that in order to account for the first (semi-)permitted line (4375.9 Å) the model atom has to include at least 36 levels (the [FORMULA]-level located at 22845.9 cm-1 [FORMULA] 2.8 eV).

[FIGURE] Fig. 2. Types of radiative transitions between the lowest 90 states (ordered by energy) of Fe I (cross: fine-structure, open circle: forbidden, full circle: permitted, dot: no radiative transition). The higher levels [FORMULA] are not depicted.

An ionisation potential of [FORMULA]eV is assumed and the partition function of Fe II is chosen to be 30. The photo-ionisation cross sections are assumed to vary with frequency as


The threshold cross sections [FORMULA] are adopted from (Vernazza et al. 1981) for the levels listed therein and is assumed to be equal to [FORMULA] for all other levels. The latter is chosen such that the total direct recombination rate


equals [FORMULA] at 10000 K, which agrees with the known rate (Landini & Fossi 1990). The rates of collisional de-excitation and collisional ionisation are calculated according to


where [FORMULA], [FORMULA] and [FORMULA], [FORMULA] denote the rate coefficients for electron and heavy particle impact, respectively. The heavy particle density is approximated by [FORMULA], where [FORMULA] and [FORMULA] are the total number densities of hydrogen and helium nuclei. Collisional de-excitation rates for both electron and heavy particle impact for transitions among lower levels have been summarised by Hollenbach & McKee (1989) for neutral and singly ionised atoms including Fe I. We have adopted their rates for the transitions 2-1, 3-1, 3-2, 6-1, 7-1, 7-6 and have completed the missing rates among the 10 lowest levels ([FORMULA]) by assuming [FORMULA] and [FORMULA] with respect to the nearest given rate. Electron collision rates for transitions which have a permitted radiative counterpart are calculated according to the van Regemorter-formula (van Regemorter 1962). For all other transitions we assume a constant collision strength of [FORMULA] which is related to the de-excitation rate coefficient by


All missing heavy particle collision rate coefficients [FORMULA] are assumed to be [FORMULA].

The collisional ionisation rates are calculated from


Eq. (20) yields the correct total collisional ionisation rate by electron impact [FORMULA] in LTE as published by Landini & Fossi (1990). Parameters are [FORMULA]K and [FORMULA]. [FORMULA] is the partition function. The collisional ionisation rates for heavy particle impact [FORMULA] are assumed to be [FORMULA] times the electron rates as is true for hydrogen (Drawin 1969).

3.2. Model atom for Fe II

The positive iron atom is modelled without continuum since the high ionisation potential of 16.16 eV is assumed to prevent considerable ionisation of Fe II in the investigated parameter regime of this paper. The total particle density of Fe II atoms is assumed to be given by [FORMULA] from the solution of the statistical equations for Fe I.

Extensive atomic data (radiative + collisional) for many astrophysically interesting positive ions have recently been published in the CHIANTI database (Dere et al. 1997). Besides the level energies, degeneracies, transition wavelengths and Einstein coefficients, these data include electron collision rates according to a 5-parameter fit as a function of temperature (Burgess & Tully 1992), which provides an excellent base for non-LTE investigations in a wide temperature range.

The Fe II CHIANTI data set comprises 142 levels with energies up to 93487.6 cm-1([FORMULA] eV), 1268 radiative transitions (1098 Å to 87.3 µm) and collision rates for transitions from all levels down to the lowest 35 levels. We have completed the missing collision rates by the van Regemorter-formula (van Regemorter 1962) for permitted transitions and by assuming a constant collision strength of [FORMULA] otherwise. All heavy particle collision rate coefficients [FORMULA] are assumed to be [FORMULA].

We find 12 fine-structure, 246 forbidden and 1010 permitted transitions in the database (see Fig. 3). In order to catch the first permitted lines (2600.2 and 2626.5 Å) the Fe II model atom must include the [FORMULA] level [FORMULA] (located at 38450.0 cm-1 [FORMULA] 4.8 eV).

[FIGURE] Fig. 3. Types of radiative transitions within the lowest 90 states (ordered by energy) of Fe II (cross: fine-structure, open circle: forbidden, full circle: permitted, dot: no radiative transition). The higher levels [FORMULA] (not depicted) mainly possess permitted radiative transitions.

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© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999