The excitation temperatures derived from the different bands are not in agreement with each other. We therefore suggest a two component model which could explain the spectra.
In the first component, corresponding to the region suggested by Justtanont et al. (1998), the CO2 exists in a dense quasi-static layer close to the star, the layer extending out to only a few stellar radii, resembling the warm, molecular-forming region suggested by Tsuji et al. (1997). CO2 is supposed to have a temperature of the order of and high densities. This would give rise to the band and the absorption at , a band which is now optically thick and which will appear differently depending on the physical conditions. As seen in Table 4, the number of molecules needed for the observed emission is too high compared to the number calculated from a spherically symmetric wind at a constant mass-loss rate. It is impossible to produce these fluxes from a small region close to the star extending out to, e.g., 3 stellar radii with the assumptions above. The number of excited molecules needed exceeds the expected number for a thermally populated level by several orders of magnitude.
More reasonable numbers will result from a high density layer with a density of more than , only extending out to a few stellar radii. A density enhancement of several orders-of-magnitude above the classical wind density, is required. In this case, the band will be formed in conditions in which collision are close to being dominant over radiative processes, cf. Sect. 4.2.
The second component, which has been argued for by Ryde et al. (1997), would be a region extending far out from the star. The colder emission is then supposed to originate from this tenuous region. The corresponding cold emission would be hardly detectable in the emission. Thus, as is seen in Table 4, assuming a much larger shell of CO2, extending out to several hundred stellar radii (finally limited by the photo dissociation by the interstellar UV field) the required degree of excitation in the upper level of the band would be some percent for all our stars, which is not unreasonable. The number of stellar IR photons per square centimetre and second is typically two orders of magnitude greater than the number of photons in the measured lines, which is reassuring.
The temperature and number of molecules required from the observed emission features are thus consistent with the location of the carbon dioxide in a circumstellar shell, extending typically out to stellar radii. This is also consistent with the chemical models of Willacy & Millar (1997) for oxygen-rich circumstellar envelopes, in which CO2 is formed in a region from around 100 to 1000 stellar radii. Abundances of other molecules in their models show good agreement with observations, which is reassuring. In these models carbon is provided by CO and CH4, and most carbon-bearing molecules are due to the breakdown of CH4. An important reaction for the present discussion is the one where some CO is destroyed at small radii by the reaction CO+OHCO2+H. Further out, all molecules will eventually be destroyed by photo-dialysis by the interstellar ultraviolet field.
R Cas is a special case (Fig. 1). Here, both absorption and emission are clearly seen. With the emission from the cold, second component filling in the absorption at in the red wing, the width of the absorption is consistent with . The residual emission in the band, after the absorption has been subtracted, is , which requires molecules. This is a reasonable number of excited molecules compared to the total number expected in a large shell, cf. Table 4.
As seen from Table 1, where the parameters of the stars discussed are given, the only parameter that is clearly different between the M giants with and without CO2 emission is the mass-loss rate. In the latter stars the high mass-loss rate seems to prevent the formation of the CO2 emission. This finding was also hinted at by Justtanont et al. (1998). They found that the equivalent widths of the CO2 feature are well and positively correlated with the dust feature. They indicate that the higher the mass-loss rate the smaller is the feature and thereby the less pronounced are CO2 features. This is consistent with our findings. Whether the correlation between mass-loss rate and the CO2 features has a simple physical origin is still uncertain. It seems, however, tempting to suggest that the stars with high mass-loss rates more easily accelerate winds from the stellar surface to velocities above the velocity of escape while stars with lower mass-loss rates produce less acceleration. For these stars much of the material levitated above the photosphere is stopped by gravity or shocks close to the star where it forms a relatively dense warm layer, where and dust may form and radiate.
The relative strengths of the band emission and the band emission are different in R Crt and R Dor. This difference in relative strengths is also seen in the six stars of Justtanont el al. (1998). This would be a natural consequence of the two component model. In an optically thin, one component model all molecules de-exciting from the and energy states will finally have to de-excite via the transition. This does not seem to occur according to the observations. A two component model with one of the bands being optically thick may solve this. It could also be explained if the resonance band is on the verge of becoming optically thick, thereby being weakened by self absorption. But in this case one would sooner expect a broader band which is not seen in the observations. Our high resolution observations also do not verify this.
© European Southern Observatory (ESO) 1999
Online publication: December 4, 1998