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Astron. Astrophys. 323, 202-210 (1997)

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4. Discussion

In this section we want to compare our results to other work done on the SiO features of late type giants. First we start with the observations from Rinsland & Wing (1982), who investigated the [FORMULA] and [FORMULA] bandheads at 4 µm. Their spectra have only a rather low resolution of about 500, but they cover a large number of objects allowing a study of stars with very different properties. In Fig. 9 we compare their measurements to our calculations showing the equivalent widths as a function of spectral type. As one can see, the agreement between observations and models is quite good, especially if one takes into account the uncertainties of the stellar parameters. The plot includes mainly III-giants, since we could determine their effective temperatures and gravitational accelerations as a function of spectral type using different measurements of angular diameters taken from the literature and estimating their mass (Blackwell et al. 1990, Bonnell & Bell 1993, Di Benedetto & Rabbia 1987, Drake & Smith 1991, Ridgway et al. 1982). This is much more difficult for the very luminous stars. Nevertheless, also for a few of these objects - like [FORMULA] Ori - it was possible to compare our results to the data from Rinsland and Wing. And the agreement was again satisfactory. Unfortunately, this is not true for the very extended coolest giants with [FORMULA], where the predicted SiO absorption is always much stronger (50 % and more) than the observed one. As an example we have included the II-giants [FORMULA] Peg and [FORMULA] Per in Fig. 9, the latter being a semiregular variable and most probably also an AGB star, which is the case for many of these objects. The situation becomes even worse, if one looks at Mira, where Rinsland and Wing found an intense variation of the SiO bands connected to the stellar pulsation. Sometimes this causes the features almost to disappear. Of course, such a behavior can not be explained by our hydrostatic models. Even if temperature changes are taken into account, we never get a complete extinction of the SiO features.

[FIGURE] Fig. 9. The equivalent widths of the [FORMULA] and [FORMULA] bandheads of the main SiO isotope, which have been measured by Rinsland and Wing (1982) for K and M giants (full symbols), are compared to our theoretical values (open symbols). They are presented as a function of spectral type for class III (circles) and II (triangles). The corresponding effective temperatures and gravitational accelerations are taken from the literature (see text). One can see that the agreement between observations and models is quite good for the III-giants, whereas the predicted bands of the II-giants are too strong.

Aringer et al. (1995) observed the first overtone bands of supposed AGB stars at a medium resolution of approximately 4000. Their spectra cover the wavelength range between 3.95 and 4.10 µm including the [FORMULA], [FORMULA] and [FORMULA] bandheads of the main isotope. They investigated a sample of 23 oxygen-rich very cool giants, which are mainly Mira and semiregular variables. Confirming the results from Rinsland and Wing they found that many Mira stars have only a weak or no SiO absorption. They also suspect a connection with the stellar pulsation, since the semiregular variables with their much smaller photometric amplitudes always show strong SiO features. In addition there seems to be a correlation between the disappearance of the bands and the occurrence of Brackett- [FORMULA] emission, which is caused by shocks propagating through the atmosphere. The latter are also a consequence of stellar pulsation. However, even the strongest bands measured by Aringer et al. are still much weaker than our predictions for the effective temperatures and gravitational accelerations usually related to AGB stars. Thus, it is again confirmed that hydrostatic equilibrium models do not work for this type of objects. A detailed discussion of the observations by Aringer et al. will be given in the second paper of this series. A possible explanation for the comparatively weak SiO bands in AGB stars is the impact of dynamical atmospheres. Unfortunately, a self-consistent description of the different phenomena like pulsation, mass loss and dust formation including also molecular opacities does not exist at the moment. But it may be possible to calculate exploratory spectra based on available simple (concerning opacities and coupling of the phenomena) models (e.g. Höfner & Dorfi 1997) in order to estimate the effects.

It should be mentioned that the discrepancies between our models and the observations of AGB stars can not be explained by a wrong value of [FORMULA]. In order to get the right intensities one needs microturbulent velocities of less than 1 km/s, which is in contradiction with high resolution measurements. Our adopted [FORMULA] of 2.5 km/s seems to be appropriate (e.g. Tsuji et al. 1994).

Although it was not our aim to reproduce detailed line profiles, we have compared our results to several selected high resolution spectra (Ridgway et al. 1984, KPNO FTS archive). As a typical example we show in Fig. 10 FTS data for the K5III giant [FORMULA] Tau and a corresponding synthetic SiO spectrum, which has been calculated assuming a model atmosphere with [FORMULA], [FORMULA], [FORMULA] and solar chemical abundances. These values are very close to the real properties of the star (Bonnell & Bell 1993, Di Benedetto & Rabbia 1987, Ridgway et al. 1982), which is also true for our adopted [FORMULA] of 2.5 km/s. The plot covers two different wavelength ranges one including the [FORMULA] bandhead of 28 SiO and the other one situated in a region with just a few strong SiO lines. Taking into account the uncertainties of the stellar parameters, the presence of spectral features produced by other species in the stellar as well as in the Earth's atmosphere and our simple treatment of the line profiles (see sect. 2) the agreement between the FTS data and our calculation is satisfactory. Similar results were also obtained for other K and early M giants (e.g. [FORMULA] Boo), whereas it was again not possible to reproduce the spectra of very extended and cool objects, because the predicted SiO absorption for those stars came out too strong. In Fig. 10 there seems to be some discrepancy concerning the line widths, since our lines generally appear narrower than the observed ones. This may be due to the lower resolution of the FTS spectra ([FORMULA]) and the already mentioned simple treatment of the profiles, which could also cause an underestimation of the intensity for the outermost edge of the bandheads, where the density of the lines is extremely high. Nevertheless, this will have almost no influence on the appearance of medium or low resolution spectra (i.e. it could be simulated by a small change of [FORMULA]).

[FIGURE] Fig. 10. The observed high resolution spectrum of [FORMULA] Tau (full line) and a synthetic SiO spectrum for [FORMULA], [FORMULA], solar mass and chemical abundances (dashed line). A wavelength range including the [FORMULA] bandhead of 28 SiO and another one, which is situated in a region between two bandheads, are shown.

In a recent paper Tsuji et al. (1994) analysed high resolution FTS data of the SiO first overtone lines of six late type M giants and two M supergiants. They determined silicon abundances and isotopic ratios by using several different methods including a semi-empirical curve-of-growth analysis and synthetic spectra from model atmospheres. Since their work is dedicated to the study of individual lines, their fits to the profiles are much better than ours. However, they were also not able to reproduce the intensities for the most extended and coolest objects (e.g. RX Boo), although the discrepancies appear to be smaller than in our case and they could even reproduce the observed spectrum of the semiregular variable R Lyr. But this is caused by the fact that they used f -values, which are too weak compared to the new data by Langhoff & Bauschlicher (1993) (see also the appendix in Tsuji et al.). As a consequence, their adopted silicon abundances have to be decreased by a factor of around two in order to fit the observed spectra without any changes in the atmospheric parameters. This causes the values to be sub-solar for the late M giants. On the other hand our work has shown that there are still a lot of problems concerning the model atmospheres of cool extended stars making the interpretation of spectral data very difficult. And this is especially true for the determination of absolute chemical abundances, although in principle the SiO bands may be a very good indicator for silicon, as we have demonstrated in the last section.

If one wants to study the fundamental transition bands of SiO, the existing observational data are only poor. This is caused by the fact that up to now it was very difficult to obtain spectra of the wavelength range around 8 µm with ground based telescopes. As a consequence many of the measurements come from space- or airborne instruments. Cohen et al. (1992) have published mid infrared spectra for K and early M giants obtained with the Kuiper Airborne Observatory. They found that all objects including even the hottest ones with a spectral type of K1 III ([FORMULA] Boo) show a considerable SiO absorption at 8 µm. The features become stronger, if one goes from K to M stars. These results and a rough estimation of the observed band intensities agree with our models. On the other hand Vardya et al. (1986) report the detection of SiO emission in the IRAS LRS spectra of several Mira variables. Of course, such a behavior can not be explained by our classical model atmospheres, which produce strong fundamental absorption bands for very cool and extended stars. Thus, we might face a similar situation as for the first overtone transitions in AGB objects, where the observed absorption features are much weaker than the predicted ones. This could also be caused by some additional emission, as it was proposed by Tsuji et al. (1994). However, any identification of the fundamental bands based only on IRAS LRS spectra should be regarded as uncertain. First they are situated close to the blue edge of the reliable part of the LRS spectra (Joint IRAS Science Working Group 1988) and second the 9.7 µm silicate dust feature extends into the corresponding wavelength range (Simpson 1991), both making a definition of the continuum very difficult.

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Online publication: June 5, 1998