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Astron. Astrophys. 342, 799-808 (1999)

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5. Conclusions

We found that in contrast to the SRb stars in our sample the Miras show a very large scatter of the equivalent widths of the SiO bandheads at [FORMULA]m. Despite their cool temperatures some of them have only weak or no SiO absorption. This seems to be related to their strong pulsations producing a large variability of the bands, which has already been observed by Rinsland & Wing (1982).

When comparing the [FORMULA]-values with other stellar properties we found that there is a general decrease with longer pulsation period, bluer IRAS (12-25) color and maybe with a cooler temperature of the first blackbody from a fit to the overall energy distribution, which is attributed to the photosphere. However, all of these trends may only reflect the different properties of the Miras and SRb stars in our sample. We did not discover any correlation of the SiO band intensities with the effective temperatures derived from (J-K), or with the (K-12) color and the IRAS-LRS class, both of which can be regarded as a rough measure for the thickness of the circumstellar shell. But in this context it should be kept in mind that our sample of objects is quite small and all statistical results will be affected by the strong variability of the SiO bands in Mira stars. Thus, it is necessary to confirm this work with a larger number of [FORMULA]m spectra and to complement it using time-dependent observations as they have been obtained by the ISO-SWS (e.g. Hron et al. 1998).

In order to reproduce the SiO bands of very cool and extended objects, as they are discussed in this work, one has to use spherical radiative transfer based on a spherical model structure. In addition, the influence of the SiO absorption on the definition of a pseudo-continuum must be taken into account. We want to emphasize again that these two things are not important for more compact and warmer stars like M dwarfs and early M giants, where we found a good agreement between the predictions made in Paper I and the observations (see Paper I). Nevertheless, even after including sphericity into the spectral synthesis and correcting for the SiO absorption in the continuum points the spectra calculated from hydrostatic MARCS atmospheres are only able to explain the objects in our sample with the most intense SiO features ([FORMULA]Å). They fail completely when it comes to Miras with weak or no SiO bands. However, these stars are dominated by dynamical phenomena and consequently they cannot be described by hydrostatic structures.

Our dynamical atmospheres still have some shortcomings like a grey radiative transfer or the somewhat artificial simulation of the pulsation as a sinusoidally moving piston at the inner boundary. In addition, at the moment the models exist only for a limited number of combinations of stellar parameters. Nevertheless, we have shown that in principle they are able to explain the whole range of equivalent widths of the observed SiO bandheads and their variations.

Thus, we conclude that hydrostatic atmospheres cannot explain the SiO bands of cool extended giants without introducing additional features, which are not part of the self-consistent solution (like the "warm molecular envelope" proposed by Tsuji et al. 1997). In contrast, the dynamical models do not need such assumptions to reproduce the observations. In the future it will therefore be very important to develop more realistic dynamical atmospheres to understand the complex relation between fundamental stellar parameters, pulsation, mass loss, dust formation and the observed spectra.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999