Astron. Astrophys. 348, L17-L20 (1999)

4. Discussion

The dynamical model presented here in fact exhibits a molecular "layer" at with a total hydrogen particle density of . This total amout of levitated gas due to pulsations (also the calculated CO and H₂O column densities) agree reasonably well with the lower limits inferred from the observations (Table 1). In contrast, the concentrations of the CO₂ and SO₂ molecules (i.e. ) are not sufficient to explain the strength of the observed molecular bands. This different degree of agreement for different molecules provides a strong argument for chemical non-equilibrium effects. Especially for SO₂, the discrepancy is out of reach in the framework of equilibrium chemistry. Recently, Duari et al. (1999) have reported on higher CO₂ concentrations, if time-dependent shock-chemistry is considered.

A better agreement between theory and observations might be achieved if a lower kinetic gas temperatures close to the star was assumed. A gas temperature being 500 K lower than the grey equilibrium temperature of our model increases the column densities of CO, H₂O, CO₂ and SO₂ by factors of 1.03, 3.9, 4.2 and 2.5, respectively, and also lowers the rotational excitation temperatures, since they remain coupled to in the relevant density range. Support for this idea comes from frequency-dependent radiative transfer calculations, which in fact show that the temperature in the outer parts of stellar atmospheres can be much lower than expected from the grey solution. A balancing of radiative heating and cooling in C-star envelopes leads to similar conclusions (Woitke & Sedlmayr 1999).

The stellar parameters (e.g. the surface gravity) have probably an important effect on the resultant total amount of levitated gas and their influence should be investigated more thoroughly. Furthermore, a larger pulsation amplitude should amplify the effect demonstrated in this letter, although the formation of molecular layers also occurs in case of very weak pulsations, since even small-amplitude waves steepen into strong shocks when they propagate through the exponential photospheric density gradient. Furthermore, dust formation will very likely increase the total amount of levitated gas (see e.g. Fleischer et al. 1992, Feuchtinger et al. 1993). A simultaneous occurence of dust and molecular layers is suggested from an observed correlation between the CO₂ 15 µm band and the 13 µm dust feature (Justtanont et al. 1998). The role of dust formation and the influence of the stellar parameters will be investigated in a forthcoming paper.

© European Southern Observatory (ESO) 1999

Online publication: July 16, 1999
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