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

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1. Introduction

Investigations on the thermal energy balance of gases can provide important scientific insight into various long-standing astrophysical problems, as for example the formation of chromospheres, the propagation of shock waves, and the generation of stellar winds.

The starting point of a thermodynamical description of the nebular-like gases in chromospheres and stellar winds is the determination of the important radiative heating/cooling rates , which are usually the leading terms in the energy equation. The iron group ions and especially the neutral iron atom have special properties concerning their possible efficiency as heating or cooling agents:
1) Iron possesses numerous electronic states at low excitation energies which can be easily (de-)excited by collisions. 2) Thousands of permitted, forbidden and fine-structure lines cause a strong coupling between the radiation field and the level populations. Lines of iron are visible in almost every astronomical object. 3) Iron is a fairly abundant element not much depleted by molecule formation. These facts alone immediately suggest that iron could be important for the energy balance of the gas.

Nevertheless, the role of iron as a contributor to the radiative heating and cooling in cool star winds has scarcely been investigated 1. Vernazza et al. (1981) computed radiative heating/cooling rates including a 15-level-atom plus continuum for Fe I for the solar chromosphere based on a semi-empirical model, where the temperature structure is chosen to best match the observations. Hollenbach & McKee (1989) modelled J shocks 2 in molecular clouds including 15 fine-structure and forbidden Fe I and Fe II cooling lines.

Carpenter et al. (1997) observed and modelled Fe I and Fe II UV lines of the carbon star TX Psc which provided various informations about the properties of its outer atmosphere, as for example the velocity and ionisation structures, and the line formation mechanisms (thermal excited or fluorescent). Recently, Aoki et al. (1998) detected surprisingly strong emission in infrared fine-structure lines in both carbon-rich and oxygen-rich AGB stars. They found that the C-stars mainly show Fe I emission lines, whereas the M-stars apparently show mainly Fe II lines. An explanation for the strength of the lines in LTE was difficult to achieve, as the authors were forced to assume very high densities around these stars.

In this paper, we investigate the efficiency of radiative heating and cooling by Fe I and Fe II. We calculate the total heating/cooling rates under various density, temperature and radiation field conditions. The paper is organised as follows. In Sect. 2, the basic equations and assumptions are outlined. Sect. 3 describes the model atoms for Fe I and Fe II. Sect. 4 summarises the methods used for the computational solution of the statistical equations and describes how the calculations for iron are embedded in a larger steady-state non-LTE model of the gas. In Sect. 5, the results for various gas densities, temperatures and background radiation fields are presented and discussed. Sect. 6 contains some general remarks on the importance of the different types of spectral lines and includes some generalisations concerning other atoms. Our conclusions are outlined in Sect. 7.

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© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999