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Astron. Astrophys. 339, 811-821 (1998)

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4. Discussion

4.1. SiO abundances

The SiO abundances inferred from our models for the observed SiO (v=0, J=2-1 and J=3-2) line intensities seem to be consistent with those expected for stars with C/O = 0.95 - 1.00, which is the range expected for S stars. Sharp & Wasserburg (1995) have considered the composition of the gas and dust condensates in AGB star atmospheres in this range, and note that SiO should take up essentially all O not in CO, with SiO falling to near zero abundance only at C/O = 1.00. We assume that our program stars have silicon abundances equal to the solar value, Si/Htot = 3.6[FORMULA] (Anders & Grevesse 1989). Then, if Si is fully associated with O as SiO, and all H is in H2, the maximum SiO abundance, X(SiO), is 7.1[FORMULA]. For comparison, our lower limits on X(SiO) for the constant abundance models (column 6 of Table 3) are in the range (0.4 - 5)[FORMULA], except for [FORMULA] Gru with [FORMULA] (SiO) = 5[FORMULA], i.e., well below the upper limit set by the abundance of Si. The presumably more realistic models, with an exponential decline in X(SiO) with increasing distance from the star, yield central abundances an order of magnitude larger, [FORMULA] = (0.4 - 8)[FORMULA] (again, except for [FORMULA] Gru at 3[FORMULA]). These values would imply that between 5% and [FORMULA]100% of Si is in gas-phase SiO in the inner envelope, in the zone where dust condensation occurs.

This range of SiO abundances for the exponential model is consistent with values expected if SiO is formed under conditions of thermodynamic equilibrium, for reasonable stellar parameters. For example, the TE chemical models calculated by Latter (in BL) predict that X(SiO) is on the order of a few [FORMULA] for C/O [FORMULA] 0.97, T [FORMULA] 2300 K, and n[FORMULA] cm-3. The C/O ratio inferred for the S stars classified by Ake (1979) and by Keenan & Boeshaar (1980) with abundance indices like those of our program stars, are in this range, C/O = 0.95 - 0.97. The temperature classes range from S4 to S8 (see Table 1), which according to Ake (1979) correspond to color temperatures in the range 3200 - 1800 K. The photospheric temperature is not, of course, representative of the gas temperature in the extended atmosphere in which the SiO is assumed to form, which is likely to be cooler than the photosphere. The spectral classifications at least imply temperatures sufficiently low to permit formation of SiO at large abundances (i.e., approaching the limit set by the Si abundance and the available free O).

The model SiO abundances also suggest that if TE chemistry is the formation mechanism, then the total density in the relevant part of the stellar atmosphere must be in the vicinity of [FORMULA] cm-3 and cannot be much lower (e.g., 1010 cm-3). The inferred SiO abundances could then be used to constrain atmospheric models for these stars.

An important caveat in considering the TE chemical models for forming SiO, however, is whether TE is even relevant. All of the program stars are variables, and like other red giants, presumably have pulsation-driven shocks periodically passing through their extended atmospheres. If so, the effects of shocks on the atmospheric chemistry may be substantial. As an example, Willacy & Cherchneff (1998) have calculated molecular abundances in gas undergoing periodic shocks in a carbon-rich stellar atmosphere (specifically, for IRC+[FORMULA]216). They find that, in the carbon-rich case (C/O = 1.5), the SiO abundance is strongly enhanced over the TE value, by one or two orders of magnitude depending on the shock velocity. Thus, in the case of carbon stars the SiO abundance is probably determined by shock processes, not TE chemistry near the photosphere.

It is not clear whether this conclusion would apply to S (or M) stars, however. In carbon stars, Si is mainly in atomic Si and in SiS, with SiO a very minor carrier of Si. In S (and M) stars, SiO is predicted to be a major form of gas-phase silicon. Detailed calculations of the chemical effects of shocks in M and S stars would be of great interest.

The anomalously low SiO abundance derived for [FORMULA] Gru is noteworthy. Sahai (1992) discovered that the CO emission for the circumstellar envelope of this star was bipolar in morphology and that the CO J=2-1 and 1-0 lines showed relatively broad wings. He argued that these wings and the CO morphology implied that a fast bipolar outflow was being collimated by a dense torus of gas within the slower, presumably older outflow. If the interaction of these velocity components produces shocks, our analysis would suggest that SiO abundance is lowered as a result. The location of such shocks would presumably be in the extended circumstellar envelope, however, not in the stellar atmosphere. Alternatively, if the bipolar envelope is an indication that [FORMULA] Gru is already evolving off the AGB, there may simply be little circumstellar molecular gas in the vicinity of the star, due to a cessation of mass loss.

4.2. Composition of the dust

The type of dust formed is obviously related to the composition of the gas in AGB star atmospheres, as well as to the temperature and pressure. With the special chemical properties of S stars, especially C/O near 1, the character of the circumstellar dust is of interest for comparison with the molecular composition of the gas. Sharp & Wasserburg (1995) predicted that with 0.95 [FORMULA] (C/O) [FORMULA] 1.00, silicates and oxides should condense, but not graphite or silicon carbide grains. (They note, however, that the sensitivity of their calculations to the somewhat uncertain thermodynamic data for grain condensation makes quantitative prediction difficult in this range of C/O.)

One set of observational data on the nature of circumstellar dust are the IRAS LRS spectra. Chen & Kwok (1993) made a detailed examination of the spectra for all known S stars in the LRS database, including the stars in our sample. Four stars (ST Sco, RT Sco, W Aql, and [FORMULA] Gru) have class E spectra, i.e., showing the 9.7 micron silicate feature in emission. Three stars (R Gem, DK Vul, and RZ Sgr) are in class F, indicating a featureless dust continuum. (We note that the LRS spectra are not of uniformly good quality. The S/N ratio of the spectrum of DK Vul is rather low and may admit a weak 9.7 micron emission feature masked by noise.) None of these stars is classified as having an 11.3 micron silicon carbide feature (class C) or a stellar continuum (class S). The preponderance of class E LRS spectra is qualitatively consistent with our 100% detection rate of SiO and the relatively large inferred abundances of SiO, and with the absence of SiC emission features at 11.3 microns. The case of the featureless dust continuum (class F) is less clear. RX Sgr has an apparently featureless continuum with good S/N in the LRS spectrum, yet it also displays a well-detected SiO line and a relatively high inferred SiO abundance. Evidently the presence of SiO in the gas phase is no guarantee that the 9.7 micron silicate feature will be seen. The 3 stars in our present sample which Chen & Kwok (1993) classify as having F type LRS spectra are among the higher photospheric temperature classes (S4 or S5) in our sample. Higher gas temperature may favor the formation of oxide grains (e.g., Al2O3) rather than silicates, so that the 9.7 micron feature is suppressed because of a difference in grain composition (see Sharp & Wasserburg 1995; Sedlmayr & Krueger 1997).

4.3. Formation of HCN

Finally, we consider the problem of the detection of HCN in some S stars. In our present sample, we find a weak detection of HCN J=1-0 in RT Sco, and a strong detection in W Aql. The latter star was also detected by BL, as well as 3 others (R And, S Cas, and [FORMULA] Cyg). Thus, 5 S stars out of 15 surveyed for HCN emission are detected in the J=1-0 line.

The HCN abundance is uncertain because the molecular distribution is unknown. If we assume that HCN is formed close to the star, and is photodissociated at a radius given by (2), we infer initial abundances of at least a few [FORMULA] with respect to H2. Such large HCN abundances cannot easily be explained by gas phase TE chemistry. From the models of Latter (cf. BL), there is perhaps only a small corner of parameter space that could accommodate the inferred abundances of both SiO and HCN in this picture, i.e., if C/O [FORMULA] 0.97, T [FORMULA] 1300 K, and ntot [FORMULA] [FORMULA] cm-3. The inferred SiO abundance is a fairly strong constraint that C/O [FORMULA] 0.97, which is also consistent with the spectroscopic abundance indices (Ake 1979, Keenan & Boeshaar 1980). It could be that Eq. (2) underestimates the HCN photodissociation radius, [FORMULA]. If so, our values for the HCN abundances in Table 3 would be too large. Eq. (2) was derived for carbon stars, but S stars may have lower dust/gas ratios than is typical of carbon stars (cf BL; Sahai & Liechti 1995). Thus it seems at least as likely that Eq. (2) overestimates [FORMULA] as underestimates it. Interferometric images of the HCN emission would be very helpful to settle this question.

At such low gas temperatures, however, grain condensation is likely to be an important process, and could enhance HCN formation in the gas. Sharp (1988) argued that removal of O by condensation of silicate and/or oxide grains effectively raises the gas C/O and hence promotes the formation of HCN. This mechanism should be most effective for S stars with C/O [FORMULA] 0.95 - 0.97. The star [FORMULA] Cyg may be problematic, since it has strong HCN emission (cf. BL) but a relatively low C/O index, probably with C/O [FORMULA] 0.9 (Keenan & Boeshaar 1980).

A second possibility, also invoked to explain the presence of HCN in M-type stars is that HCN is formed by photochemical reactions in the outer envelope (Nercessian et al. 1989; Charnley et al. 1995; Willacy & Millar 1997). It is not clear that this mechanism is consistent with the expected abundances of likely precursor molecules, i.e., CHn, n = 2,3,4. Even in the C-rich model of Willacy & Cherchneff (1998), the TE abundances of CHn species are low and are not enhanced by shocks (except CH4 in relatively strong shocks). One would expect that CHn abundances are correspondingly much lower in the case of C/O [FORMULA] 0.97, typical of S stars, than in the case C/O = 1.5. Thus, a photochemical origin for HCN leads to the problem of the formation of the precursor simple hydrocarbons, CHn.

One may also speculate about the effects of shocks in generating HCN directly in S stars. The calculations of Willacy & Cherchneff (1998) find that in the carbon-rich case (C/O = 1.5), shocks destroy HCN, and lower the abundance by about a factor of 6 compared to the TE values. In the absence of detailed calculations for C/O [FORMULA] 1, it is difficult to predict whether HCN might be enhanced by shocks, but this mechanism does not appear promising as an explanation for the presence of detectable HCN in [FORMULA]30% of S stars surveyed.

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© European Southern Observatory (ESO) 1998

Online publication: October 22, 1998