## 3. Results## 3.1. Influence of SiO on stellar atmospheresAs mentioned in the previous section, we have calculated all model atmospheres with and without taking into account the opacity of SiO. By comparing the results it became possible to estimate, how important this molecule is for the atmospheric structure. Fig. 3 displays a temperature versus pressure plot for an object with , , solar mass and chemical composition. In addition to the models with and without SiO we also show the curve for an atmosphere that has been calculated neglecting the opacities of TiO as well as of SiO. This allows to compare the effects of those two molecules. As one can clearly see, the presence of TiO causes a substantial heating over a large region of the atmosphere. This is related to the fact that its strong bands are generally located at wavelengths shorter than the spectral maximum of the stellar radiation field (Gustafsson & Jorgensen 1994). On the other hand SiO with its main rotation-vibration transitions in the mid infrared tends to cool the surface layers and gives rise to a corresponding small back-warming effect, which is seen in Fig. 3 for regions deeper than about .
Another obvious result from Fig. 3 is that the influence of SiO
remains small in all layers, especially if one compares it with the
enormous changes produced by TiO (shown) or H ## 3.2. The intensity of SiO bands as a function of temperature and atmospheric extensionIn order to investigate the behavior of the intensity of the SiO
absorption we have calculated equivalent widths for several of the
corresponding molecular features using our synthetic spectra. The
following bandheads have been measured from our high resolution data:
of In Figs. 4 and 5 we present the intensity of the SiO absorption as a function of stellar temperature for different values of log (g). In Fig. 4, which displays the total equivalent width of the whole fundamental band (), one can see that the latter decreases monotonously with , if the gravitational acceleration remains constant. This trend is almost linear. Only for the coolest objects and the smallest log (g) values there seems to be some saturation effect. The situation is a little bit different for the sum of the equivalent widths corresponding to the , and bandheads of the main isotope, which is shown in Fig. 5 and will be called in the following text (L for the photometric L-band). As for the fundamental band, the SiO absorption always goes monotonously down with the temperature. But for the more extended atmospheres there appears a very strong decrease between and 4200 K, while the gradient is only weak for cooler and hotter stars. This behavior causes the curves to show some kind of "s-shape". It is not so well pronounced in objects with , where the decrease is much more linear. For the most compact atmospheres the largest gradient even seems to appear at .
In Figs. 4 and 5 it is also obvious that at every temperature the SiO absorption becomes smaller, if the gravitational acceleration grows. As it turned out in all of the investigated cases, the relation between the equivalent width of the SiO bands and log (g) is almost linear. Thus, the strongest SiO features are expected in very cool giants and supergiants, while they always will be relatively weak in dwarfs. From our observations of AGB stars (Aringer et al. 1995) we found
that the intensity ratios of the SiO bandheads show a large scatter,
if different objects are compared. For example, in our sample the
value of changes by a factor of more than 2.
This is partly related to the total amount of the SiO absorption. But
even if the latter remains constant, there is still a considerable
scatter left, which may be caused by a different
or log (g). In principle the ratio between the
intensities of any band originating from transitions to the
level and its hot bands (transitions involving
only vibrationally excited levels) will reflect the temperature at the
depth(s) of formation in the stellar atmosphere (primarily via the
Boltzmann factor). Since the latter may be a function of
and log (g), those parameters could also affect
the intensity ratios. In order to see, if this is true and if the SiO
features can be used for an independent determination of effective
temperature and gravitational acceleration, we compared the equivalent
widths (EW) of some bandheads. First we concentrated on the
The last two statements are also valid, if the study is extended to
the bandheads of the isotope Finally we have compared the total intensities of the fundamental and the first overtone bands. It turned out that for the ratio is almost independent of temperature and only determined by variations of the gravitational acceleration: For higher values of log (g) the transitions become weaker relative to the features. On the other hand, if the atmospheres become hotter than 3600 K, there exists no clear trend being caused by different values of either or log (g). Of course, the ratio of the equivalent widths is also correlated with the total intensity of the SiO absorption (in all bands). But the scatter around the corresponding relation is very large. However, there are again no systematic trends caused by temperature or gravitational acceleration. ## 3.3. Sphericity effectsSince we have calculated our synthetic atmospheres using spherical radiation transport routines, we are able to investigate deviations from plane parallel geometry. The latter are related to the fact that the structure of spherical models is a function of stellar mass (as oppose to the plane parallel models). As one would expect, we found the strongest sphericity effects in the SiO features of the most extended and least massive stars. On the other hand, for objects with high mass and/or gravity the spherical models approach the plane parallel ones. To give some typical numbers, for and solar chemical abundances the ratio between for a and for a star (which is almost plane parallel) varies from 1.02 to 1.6, the largest values corresponding to the highest effective temperatures. In objects with the sphericity effects never produce significant changes of the SiO opacities. This demonstrates that the intensity of the SiO features decreases as a function of stellar mass, although the effect does not become very important, since larger differences appear only in hotter models, where the bands are already weak. And in high gravity stars deviations from plane parallel geometry can be completely neglected. ## 3.4. Chemical abundancesIt is evident that changes of the chemical abundances may have a large impact on the formation of SiO and consequently on the appearance of the SiO features. Therefore we studied such effects starting with the metallicity. In Fig. 7, which presents as a function of , the different curves and symbols correspond to selected temperatures and gravitational accelerations. One can see that for all parameters the intensity of the bandheads increases steadily with log (Z) showing almost a linear growth. This means that stars belonging to the galactic population II will always have much weaker SiO features than those with solar metallicity.
A similar and also very strong effect can be obtained, if one changes only the silicon abundance, which is shown in Fig. 8. As a consequence in principle it should be possible to estimate this quantity from low or medium resolution spectroscopy in the photometric L-band. But in practice it is not that simple, because the intensity of the SiO bands also depends on , log (g) and log (Z), which are in general not precisely known, especially for the coolest giants.
Finally, we have also investigated the effects of variations in the C/O ratios. Such changes may occur in AGB objects, when they transform into carbon stars (e.g. Lambert 1994). We studied the range between (solar) and 0.9. We did not go to higher values, since it is not likely that the used chemical equilibrium routine still gives correct results, if one comes too close to . This is due to the neglect of typical S-type molecules like VO, YO, ZrO and LaO. For there will be a carbon rich environment, where almost no SiO forms (Jorgensen 1994b). Within the limits of our investigation, which covered only values of and log (g) that are typical for AGB stars, we did not find any systematic or strong variations of the SiO bands, reflecting that the SiO density is determined by the silicon abundance only. For some models there was a slight decrease with C/O and for others we even observed an increase. The latter may be due to changes of the atmospheric structure. ## 3.5. MicroturbulenceAs it has already been mentioned in the previous section, the appearance of the SiO bands at a low or medium resolution is also influenced by the microturbulence. In general their intensity increases, if the value of becomes larger, since many of the lines are saturated. As one would expect, the size of this effect depends on the original intensity of the SiO absorption and the most striking changes can be found for the very cool and extended atmospheres. For example, in an object, which is characterized by , , solar mass and chemical abundances, grows by a factor of approximately 2, if increases from 1.0 to 3.5 km/s. Of course, this is one of the models with the strongest variations. The corresponding value for a similar star with is still almost 2, but it drops quickly at higher temperatures. On the other hand, if is smaller than 20 Å, the influence of the microturbulence remains always negligible. Thus, one has only to worry about the values of very cool giants and supergiants. © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |