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

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4. Calculation of the composition of the gas

A consistent non-LTE modelling of Fe I and Fe II cannot be performed on its own, but must be part of a larger model which includes the determination of the Fe I/Fe II ratio and especially the electron density, which enters into the calculation of the collision rates.

We consider a mixture of the elements H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ca, and Fe with solar abundances according to Anders & Grevesse (1989, "Photosphere"-column). The neutral atoms are modelled with continuum, the ions without continuum. Table 1 summarises the references for the respective model atoms. The line data have been taken mainly from the KURUCZ and the CHIANTI databases. The collisional de-excitation rates for neutral atoms are calculated similarly as stated in Sect. 3.1. The collisional rates for ions are adopted from the CHIANTI database. Photo-ionisation cross sections for all states of all atoms other than H I and Fe I have been obtained from the OPACITY PROJECT  5 (Seaton et al. 1994) and smoothed to a 10 Å-wavelength grid. We noticed that the OP threshold wavelengths are not very accurate (usually too short) and have scaled the cross sections as a function of wavelength according to the threshold wavelengths derived from the level energies and the ground state ionisation potentials (Allen 1973). Collisional ionisation rates are calculated according to Eq. (20) with the parameters [FORMULA] and [FORMULA] given by Landini & Fossi (1990).


[TABLE]

Table 1. Overview of model atoms.
Notes:
*) fine-structure + forbidden + permitted
(1) OPACITY PROJECT (Seaton et al. 1994) with corrected threshold wavelengths (see text)
(2) Luttermoser & Johnson (1992)
(3) Vernazza et al. (1981)
(4) CHIANTI database (Dere et al. 1997)
(5) KURUCZ 's line-list (Kurucz 1988)
(6) Hollenbach & McKee (1989)
(7) Mendoza (1983)
(8) R. Sutherland (1997, priv. comm.)


To summarise, the model atoms for species other than Fe I and Fe II contain between 5 and 30 levels, usually covering all known states with excitation energies lower than [FORMULA]9 eV or (in case of Na I, Mg I, Al I and Si I) at least all states with excitation energies [FORMULA] 78% of the ionisation potential (exceptions: Ne I, Ne II, Ca II). The model atoms include all fine-structure and forbidden cooling lines, and collision rates listed by Hollenbach & McKee (1989), as well as the highly excited states with a considerable number of permitted transitions.

The concentration of 96 neutral diatomic and polyatomic molecules are calculated with respect to the total neutral atom densities by assuming chemical equilibrium. The electron density [FORMULA] and the total neutral atom densities [FORMULA] are found by a Newton-Raphson iteration involving all elements under consideration in order to achieve the conditions of charge and particle conservation, respectively.

For practical reasons, it was not possible to use the full model atoms as described in Table 1 during the Newton-Raphson iteration. We have instead used truncated model atoms during this iteration (5-level-atoms for H, He I and C I, 3-level-atom for Na, 1-level-atom for all other atoms) which preliminarily determines the electron, ion, atom and molecule densities. In a second step, the full neutral atom models are calculated, and the atom and ion densities are corrected accordingly. In a third step, the ion model atoms are calculated.

According to the assumptions outlined, all results of the model calculations (including the Fe I and Fe II heating/cooling rates) depend on the following local parameters: [FORMULA], T, [FORMULA] and [FORMULA]. The total hydrogen particle [FORMULA] is proportional to the mass density [FORMULA] ([FORMULA]), where [FORMULA] and [FORMULA] are the mass and the abundance of element El with respect to hydrogen.

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© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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