A&A 456, 1001-1012 (2006)
Observatoire de Genève, 51 chemin de Maillettes, 1290 Sauverny, Switzerland
Received 9 January 2006 / Accepted 8 March 2006
Aims. We investigate the non-equilibrium chemistry of the inner winds of AGB stars for different stages of stellar evolution, choosing a standard AGB stellar model and changing photospheric C/O ratios, to describe winds of M, S, and C stars. Chemical formation pathways for several important molecules and the chemistry of S stars and its implications for the nature of the dust forming in these objects are discussed.
Methods. The inner wind standard model (gas density, temperature, and velocity) is derived from taking into account the effect of shocks induced by stellar pulsation on the gas. The chemistry consists of 68 elements and molecules and 752 chemical reactions. Molecular concentration profiles are derived by solving a system of non-linear, stiff, ordinary, coupled differential equations applied to the wind model gas parameters.
Results. We find that unexpected molecules are present in the inner winds, as a result of non-equilibrium chemistry due to shock propagation. In particular, there exists a group of molecules always formed in the inner wind of AGBs, whatever the stage of evolution of the star, i.e., CO, HCN, CS, and SiO, while other groups of species are typical of a O-rich or C-rich chemistry. The shocked regions above the photosphere, where thermal equilibrium does not apply, act as true molecular factories.
Key words: stars: AGB and post-AGB - stars: late-type - astrochemistry
It is usually thought that the chemical composition of these layers results from the state of evolution of the star on the AGB, that is, the carbon-to-oxygen (C/O) ratio of the stellar photosphere. However, while it is reasonable to apply thermal equilibrium (hereafter, TE) in the photosphere because of the very large gas temperatures and densities, and then derive TE photospheric molecular abundances, this assumption does not hold for the gas layers above the photosphere through which shocks propagate. Indeed, the parameters of the post-shock gas will span wide ranges of values on very short time scales, and the chemistry will adapt to these strong variations. The first evidence of non-TE in the inner wind of AGBs was given by the observations of a few molecules which were not expected to form under TE, e.g., the ISO SWS detection of CO2 by Justtanont et al. (1996) in the O-rich AGB star NML Cygni. Theoretical models of the inner wind of AGBs which take into account the non-equilibrium chemistry induced by shock activity have been developed by Willacy & Cherchneff (1998, hereafter WC98) for the carbon-rich star IRC+ 10216 and by Duari et al. (1999, hereafter DCW99) for the O-rich Mira IK Tau. The latter study was able to explain the formation of carbon-bearing species such as HCN and CO2 above the O-rich stellar photosphere. The presence of HCN in the inner envelope of AGBs was further confirmed by its detection at sub-millimeter wavelengths in the S star Cygni (Duari & Hatchell 2000). Both theoretical studies showed that the inner winds of AGB stars experience a non-equilibrium chemistry active in levitating regions of gas whose parameters are favorable to the formation of molecules, resulting in the "extended atmosphere'' observed by Tsuji et al. (1997) and Perrin et al. (2004). In particular, they showed that some molecules detected in the outer envelope of AGBs (for example, HCN in O-rich and S stars and CS and SiO in C-rich AGBs) and thought to form at large stellar radii are in fact formed in the post-shocked layers and are ejected in the outer wind as "parent'' molecules.
Table 1: Pre-shock, shock front, and excursion (post-shock) gas temperature and number density as a function of position in the envelope and shock strengths. M is the Mach number (= / ) associated with each shock speed.
In this paper, we study the impact of stellar evolution and photospheric C/O ratio variations on the chemistry of the inner envelope of AGB stars to investigate molecular formation and the chemical changes responsible for the formation of various types of dust (silicates for O-rich AGBs and amorphous carbon and silicon carbide for carbon stars). We investigate in particular C/O ratios very close to unity to discuss the chemistry of S stars. Finally, we wish to highlight possible observable molecular tracers for O-rich and C-rich objects in view of the new observing opportunities coming on line with the HIFI spectrometer on board of the Herschel satellite and ALMA. Indeed, the very high resolution of HIFI coupled to a frequency coverage in the Far-Infrared (FIR) and the submillimeter will allow the detection of the rotational transitions associated with the low lying vibrational states of molecules (e.g., the low energy bending modes of heavy molecules Cernicharo 1999) and the resolution of line profiles, thus providing information on the physical conditions, the dynamics, and the chemical composition of the inner winds of AGB stars. In a complementary way, ALMA will allow spatially resolved studies of nearby AGB stellar envelopes. It is therefore crucial to try and understand the chemistry acting in these inner regions from a theoretical point of view.
Section 2 gives a summary of the approach and model adopted for the study. In Sect. 3, we describe the chemistry at play. Results are fully presented and discussed in Sect. 4, in particular the presence of a group of species common to all AGB stars, molecules typical of a O-rich and C-rich chemistry, the important role of a few atomic species and radicals, and finally, the inner chemistry of S stars and its implication in dust formation. A summary and conclusions are given in Sect. 5.
In our model, the inner layers are shocked periodically and levitate above the photosphere before falling down to their initial position due to stellar gravity. We assume that the first shock steepens at 1 and further propagates outwards. We consider an initial shock velocity of 25 km s-1 at 1 , a reasonable hypothesis on the ground of available measurements. This shock velocity value generates an inner envelope temperature and density profiles of the shocked, gravity-bound layers close to the photosphere (Cherchneff et al. 1992; WC98). Placing ourselves in a Lagrangian frame, we apply a non-equilibrium chemistry following the formalism of Cherchneff (1996) and WC98. Analytical parameters describing the inner layers are listed in Table 1, and Fig. 1 shows the gas trajectories above the photosphere for the initial shock velocity considered in our model of TX Cam. Each trajectory corresponds to a specific radius and shock velocity in the envelope and is made of gas excursions which repeat themselves at each stellar pulsation. An excursion represents the trajectory of the postshock gas as a function of the pulsation phase of the star.
|Figure 1: Trajectories of the gas parcels induced by an initial 25 km s-1 shock as a function of position in the envelope, shock strength, and stellar pulsation phases. Arrows show the various shock positions.|
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We choose 5 values of C/O ratios typical of stars ascending the AGB: for Mira-type stars, we set C/O equal to 0.75 and 0.9; for S stars, we investigate values of C/O ratios equal to 0.98 (SE stars), 1, and 1.01 (SC stars); and finally, we choose C/O = 1.1 for carbon-rich AGBs. The extreme carbon star IRC+ 10216 (C/O = 1, 5) has been studied in detail by WC98.
For each value of the C/O ratio, we run our set of non-linear, stiff, ordinary differential equations in one gas excursion and over three pulsation periods starting at 1 , to check for gas parameters and helium abundance periodicity. We then move to the next closest radius, re-scale the results to the new local pre-shock gas density and run our system again over three pulsation periods. This approach has been followed from 1 to 5 , assuming that dust condensation does not occur before 5 and using the gas parameters given in Table 1. Although using a Lagrangian formalism, we can, at the end of the calculations, derive Euler-type profiles for our species abundances which can be directly compared to observations.
Table 2: Chemical species considered in the present inner wind model: elements are He, H, O, C, N, Si, and S.
We list in Table 3 a sample of species abundances at 1 resulting from the non-equilibrium chemistry induced by the propagation of the 25 km s-1 shock and present in the post-shock gas, for the two most extreme values of C/O ratios. We also list the expected abundances from TE calculations for comparison.
Our calculations show an interesting and unexpected result: whatever the enrichment in carbon of the star, i.e., the C/O ratio, the atomic and molecular content of the gas layers just above the stellar photosphere is very much the same, and in many cases, totally different from what would be expected from TE calculations. Indeed, we see that the abundances of the listed molecules span very similar ranges for C/ and C/ (see for example, HCN, CS, CN, SiS, and SiO). Even molecules like C2H2, H2O, CO2, HS, OH, and SO show maximum differences in abundance ratios ranging from 10 to 60. This homogeneity of the molecular content has never been considered before and in part determines the nature of the molecules that can form at larger radii. The presence of unexpected molecules close to the photosphere for specific C/O ratios was already discussed by WC98. In their study of the extreme carbon star IRC+ 10216 (C/), they showed that SiO formation was triggered by the presence of water H2O and the hydroxyl radical OH very close to the photosphere, the later reacting with atomic Si to form SiO.
A first important result of this study is the confirmation that TE does not hold once shocks have propagated and that the O-rich or C-rich character of the envelope of an AGB star, present in the photosphere, vanishes just above the photosphere and develops again further out in the shocked molecular layers. Indeed, we will see in Sects. 4.3 and 4.4 that this character results from the destruction and/or formation of certain molecules at a few stellar radii.
Table 3: Species abundances in the post-shock gas at 1 for TE calculations and non-equilibrium chemistry.
Our calculations point to the fact that at least four molecules among those listed in Table 3, whose abundances between 1 and 5 do not change drastically with C/O ratios, exist. They are CO, SiO, HCN, and CS, and their calculated abundances with respect to the total gas number density are listed in Table 4 as a function of C/O ratios and position in the flow. These four molecules form in high quantities whatever the C/O ratio, a fact which implies that the chemical processes responsible for formation/destruction of these species work with the same efficiency whatever the oxygen and carbon photospheric content of the star. Apart from those four species, two molecules, CN and HCO, also show abundances that stay almost constant when changing the C/O ratio (for CN, abundance values range from at 1 to at 5 for all C/O ratios, while for HCO, abundance values vary from at 1 to at 5 ). Below, we study in detail the chemistry at play for CO, SiO, HCN, and CS and compare our results to available observational data.
Table 4: Abundances between 1 to 5 for molecules common to all AGB, whatever the C/O ratio.
Out of thermodynamical equilibrium, carbon monoxide is formed from
the trimolecular reaction
As already stressed by WC98 in their study of IRC+ 10216, the
chemistry of SiO is linked to the presence of the hydroxyl radical
OH, which is formed from shock chemistry in the inner wind. We
confirm this chemical formation route for SiO for the various C/O
ratios of our study. Indeed, the reaction
Our derived, almost constant, high SiO abundances (about ) before condensation of dust for TX Cam (C/ ) are in good agreement with the abundances derived from thermal mm line emission observations of Miras by González Delgado et al. (2003) and Schöier et al. (2004). For carbon stars, we see that the present SiO abundances decrease with increasing C/O ratios and radius, with a minimum value at the dust formation radius of about . For IRC+ 10216 (C/), WC98 found an abundance at of , confirming these trends. These values are in good agreement with the mm survey of several carbon stars, including IRC+ 10216, carried by Woods et al. (2003). From the chemistry, we should therefore expect higher SiO abundances in the inner wind of O-rich stars than in their carbon counterparts, a fact that was already observed by Bujarrabal et al. (1994).
HCN is another example of the importance of the chemistry of shocks just above the photosphere. For
all the C/O ratios of this study, the formation mechanism of HCN is directly linked to its radical CN by
For IRC+ 10216, several vibrational transitions of HCN have been observed with the ISO SWS in absorption between 2.5 and 3.6 m and in emission around 14 m by Cernicharo et al. (1999), who derived a HCN abundance of , in good agreement with the calculated value of WC98 ( at 4 and before dust condensation). Aoki et al. (1998, Paper II, 1999) also observed the same HCN transitions in several carbon stars (of type SC (C/ ) and N (C/ )) along with CH vibration-rotations transitions between 3.3 and 3.8 m with the ISO SWS. Therefore, the simultaneous detection of HCN and CH in the flow supports the validity of our chemical channels for HCN formation.
For O-rich stars and S stars, HCN has long been detected at mm wavelengths. The HCN abundance observed by Olofsson et al. (1991) in TX Cam and by Lindqvist et al. (1988) in several other O-rich Miras could not be reconciled with theoretical models of the outer envelopes, including photo-dissociation processes. They argued that the observed CN/HCN ratio in these stars implied an inner wind origin. The more recent mm survey of Bieging et al. (2000), including 30 AGB stars of spectral type M, S, and C, confirms the presence of HCN in O-rich Miras and in S stars and the need of an internal origin for HCN to explain the observed HCN line intensity ratios. In particular, they found that M and S stars present a strong correlation between HCN/SiO integrated line intensity ratios and mass loss, pointing to the fact that HCN must form near the stellar photosphere for these stars. Furthermore, their integrated line intensity ratio for HCN and SiO show a trend of increasing values from M to C stars, with almost similar values for S and M stars. Our present results show the same trend if one considers HCN to SiO abundance ratios at 5 as a function of C/O ratios, with closer values between M and S stars. Hence, we confirm that HCN is present in both M, S, and C stars, with maximum abundances for S stars, and that it is formed in the inner winds of these objects. Finally, high excitation ro-vibrational transitions of HCN were also detected in the S star Cygni (C/ ) (Duari & Hatchell 2000), implying the presence of HCN at radii <20 to satisfy excitation requirements.
Inspection of Table 4 shows that CS forms in quantities comparable to those of HCN and should be present
with high abundance values in all AGB stars. For all C/O ratios, the dominant formation pathway to CS close to the star occurs
in the fast chemistry zone of the gas parcel excursion and corresponds to
On the observational front, infrared fundamental and first-overtone bands were detected by Aoki et al. (1998, Paper II) with the ISO SWS in the SC star WZ Cas and the N star TX Psc. At millimeter wavelengths, Olofsson et al. (1998) studied a large sample of oxygen and carbon stars and reported detection of CS lines in all carbon objects and in a few oxygen-rich stars. They derived CS to CO line intensity ratios that are much higher for C stars than for M objects by a factor of 8. Although no direct comparisons can be made as our calculations use a unique stellar model, our results support this trend for radii >3 , with CS to CO abundance ratios higher by a factor of 4 in carbon stars than in O-rich Miras. Furthermore, in their theoretical model of the outer chemistry of the carbon star IRC+ 10216, Millar et al. (2001) argue for the need of CS injection from the inner envelope to match CS abundances derived by mm line observations.
From the results above, we see that some molecules are common to the
inner gas layers of any AGB stars, and should further travel through
the intermediate and outer envelopes untouched, except for SiO,
whose abundance is expected to be depleted because of its role in
the nucleation of dust and its further freezing on grain surfaces in
the intermediate wind of O-rich stars. On the other hand, some other
molecules are only present in the inner winds of stars of specific
stellar type. In this section, we investigate the formation
processes of those species for oxygen-rich objects.
|Figure 2: OH abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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|Figure 3: H2O abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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The present calculations show that the hydroxyl radical OH plays an
important role in the inner wind of AGBs as a trigger to molecular
formation. Indeed, we saw in Sect. 4.2 that OH is responsible for
the formation of CO and SiO in both O-rich and carbon inner
envelopes. We will see below that it is also responsible for CO2formation in O-rich stars. The abundances of OH as a function of C/O
ratio and stellar radius are shown in Fig. 2. At 1 ,
is present in any AGB with abundances extremely different from those
predicted by TE equilibrium calculations and forms at small phases
of the gas excursion (shortly after the passage of the shock) by the
Water forms at any phase of the pulsation and any radius in the flow from reaction
H2O abundances are shown in Fig. 3. In the case of TX Cam (C/ ), the calculated abundance is in the inner wind. From Reaction 16, we see that H2O abundances are highly dependent on OH and its formation efficiency. At any radius and for any C/O ratio, the net rate for H2O formation is always positive while that of OH is negative, implying a constant conversion of OH into H2O in the wind. For C/, the OH abundance at 1 is larger by a factor of 10 than for C/, while H2 abundances are comparable, resulting in a higher formation rate for water in O-rich AGBs. In C-stars, the gradual depletion of atomic oxygen in the flow results in very low OH abundances for R > 1 and a failure to sustain H2O formation (see Fig. 3).
Observation of H2O IR transitions in O-rich AGBs with the ISO
SWS/LWS was reported by various authors (Neufeld et al. 1996; Tsuji
et al. 1997; Truong-Bach et al. 1999; Yamamura et al. 1999; Markwick
Millar 2000; Tsuji 2000; Ryde
Eriksson 2002), and our
present model values are in good agreement with abundances derived
from ISO data (Truong-Bach et al.) and from modeling of the 183 GHz
water maser emission line by González-Alfonso & Cernicharo
|Figure 4: CO2abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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|Figure 5: SO abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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SO has long been detected in the outer envelope of O-rich Miras at
mm wavelengths (Omont et al. 1993; Bujarrabal et al. 1994). Willacy
Millar (1997) modeled the chemistry of the outer envelopes of
several O-rich AGBs, including TX Cam, for which they found a SO
abundance lower than that observed by Bujarrabal et al. They assumed
no SO injection from the inner wind at large radii but in-situ
formation processes only. Our model abundances of SO are illustrated
in Fig. 5, and our model value for TX Cam at 5
Assuming that SO is injected to large radii in
the envelope, this value added to that derived from local formation
processes could boost the outer SO abundance to better match the
observed value of
derived by Bujarrabal et al. In our
model, SO is formed at high gas density and temperature from the
As for SO2, the main formation channel in this study is
The detection of SO2 with the ISO SWS in several O-rich AGBs by
Yamamura et al. (1999) implies a formation site close to the star
and an abundance spanning the range 10-8-10-7, slightly
below SO values. Hence, our model fails in reproducing observations,
partly due to the limited number of reactions involved in the SO2formation scheme and the lack of measured reaction rates. Other
formation processes must then be advocated. The absence of a
chromosphere and the assumption of neutral shocks in our model
excludes ion-neutral reactions and photo-processes, in particular
photo-dissociation, which could play a role in the chemistry of some
species such as SO2.
|Figure 6: HS abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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Finally, we present our results for HS in Fig. 6. We can see that HS
is present in all stars at 1 ,
but that its abundance
decreases with radius, slowly in O-rich and S stars, but very
rapidly, to become negligible at 2 ,
for carbon stars.
Very much like the CN/HCN and SiO/SiO2 couples, in the gas
excursions, HS and H2S are coupled by the reaction
Yamamura et al. (2000, Paper I) report the identification of ro-vibrational lines of HS in the IR spectrum of the S star R Andromedae. They derive an excitation temperature of 2200 K and a HS/H abundance of , and they found that the lines must come from a thin gas layer above the photosphere because of the lack of various velocity or temperature components in the HS lines. We see from Fig. 6 that the HS abundance with respect to H2 for a C/ drops from at 1 to at 2.5 to reach 10-10 at 5 . These abundances are in excellent agreement with the value derived by Yamamura et al., and we confirm the confinement of the HS distribution in the inner wind. As for H2S, we find that its distribution follows that of HS, and that the molecule is present in the inner wind of M and SE stars, but with lower abundances ranging from to 10-9.
We turn now to carbon-rich AGBs and present and discuss results for the most important molecules typical of a carbon-rich stellar environment.
Acetylene C2H2 is an extremely important molecule in the wind
of carbon-rich AGBs as it plays different roles depending on its
position in the flow. Close to the star, it is conjectured that
C2H2 triggers the formation of dust nucleation clusters such
as large polycyclic aromatic hydrocarbons (PAHs) (Cherchneff et al.
1992; Cherchneff 1996; Cau 2002) and later contributes to the
cluster growth via addition onto its surface. At larger radii,
C2H2 is photo-dissociated to give rise to its radical C2H
and a complex carbon chemistry leading to the formation of
cyanopolyyne molecules and carbon chains (Cherchneff et al. 1993;
Glassgold 1993; Millar et al. 2000).
|Figure 7: C2H2 abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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|Figure 8: SiS abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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Absorption bands of acetylene around m have been detected with the ISO SWS by Aoki et al. (1999) in several carbon stars and by Cernicharo et al. (1999) in IRC+ 10216. The latter derived a C2H2 abundance of in gas layers at temperatures 1700 K located between 1 and 3 . The model acetylene abundance calculated by WC98 is 10 times larger, but this discrepancy could stem from the nucleation and condensation of dust, with possible deposition of C2H2 on the grain surfaces. There may also be additional destruction processes not considered in our neutral chemistry (see Sect. 4.5).
The chemistry of silicon sulphide SiS is linked to that of hydrogen
sulfide HS and atomic Si, and results are illustrated in Fig. 8. Its
dominant formation process at small radii for all C/O ratios
involves the destruction of HS via
SiS has long been observed at mm wavelengths in AGB stars. In particular, Bujarrabal et al. (1994) report its detection in some O-rich AGBs, including TX Cam and IK Tau, and in most of the carbon AGBs of their survey. They derived a higher SiS abundance in C stars (on average, ) than in M stars ( ), a trend confirmed by our present calculations. Their derived SiS abundances for IK Tau and TX Cam are always larger than those in our model, which predicts SiS as a parent molecule, but with inner abundance values injected at large radii much smaller than those observed in the outer stellar envelope. For TX Cam, our model abundance at 5 is , while that of Bujarrabal et al. is 10-6. However, our small inner abundances are not inconsistent with the picture that local chemical processes at large radii involving ion-molecule reactions must be efficient in building the SiS abundance derived from mm line observations.
Observations of carbon stars by Woods et al. (2003) report the detection of SiS in their star sample with abundances ranging from to . The present model abundance calculated for our synthetic stellar model is at 5 , therefore slightly higher than the observed values. This discrepancy can be due to either our estimated chemical reaction rates for Si chemistry, which could possibly be fine-tuned for better matches, or to a depletion effect of SiS due to freeze-out of the molecules on grains in the intermediate envelope. Both aspects should be further studied.
Finally, Aoki et al. (1998) report the detection of SiS first overtone bands in the 6.7 m region with the ISO SWS for the SC stars WZ Cas, but the bands could not be detected in the N stars of the sample. Our model predicts SiS values very similar for SC and N stars at small radii, confirming SiS as a parent molecule in these objects.
We see from above that in both O-rich and C-rich AGBs, some elements, namely S and Si, play a crucial role in the formation or destruction of various key molecules, in particular SiO, CS, SiS and C2H2. Silicon abundances are illustrated in Fig. 9 as a function of C/O ratio and position, and sulphur abundances are presented in Fig. 10. From our model, based on neutral chemistry, we find that Si and S have much lower abundances at 1 than given by TE calculations for any C/O ratio. For carbon stars however, the Si abundance increases with radius to reach high values, whilst the abundance in M Miras keeps dropping.
the dominant Si-bearing species is SiO, and Si
destruction stems from Reaction 5, while some Si returns to the gas
via the opposite reaction. However, at larger radii, the dominant
destruction process for SiO is not the reverse of Reaction 5
anymore, but Reaction 6 becomes responsible for SiO2 formation.
Thus, Si is not returned to the gas, and its abundance drops to
negligible values. For carbon stars, SiO2 formation is not
favoured, and the reverse of Reaction 5 continues to return Si at
large radii, resulting in higher Si abundances.
|Figure 9: Si abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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|Figure 10: S abundances versus C/O ratio (curve labels) and stellar radius. TE abundances are also plotted on the left-hand side of the radius axis for comparison.|
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Fine structure lines in emission of iron, sulphur, and silicon were detected in a sample of seven O-rich and C-rich AGBs by Aoki et al. (1998, Paper II) with the ISO SWS. They reported detection of emission lines in three objects only, the M star 30g Her and the carbon stars TX Psc and WZ Cas. In particular, the [SI] 25 m line was detected in TX Psc along with the [FeI] 24 m and the [FeII] 26 m lines, whereas the [SiII] 34.8 m line and two [FeII] at 26 m and 35.3 m were detected in 30g Her. Neutral lines were thus observed in carbon stars when emission lines from ions were detected in M stars, reflecting the presence of a harsher environment in oxygen stars, possibly coming from chromospheric activity. Hass & Glassgold (1993) have also observed the [SiII] fine structure lines in the O-rich supergiant Orionis whereas Castro-Carrizo et al. (2001) and Fong et al. (2001) report no detection of FIR atomic fine structure lines with the ISO LWS/SWS in oxygen and carbon-rich AGBs.
At a first glance, these observations appear to contradict our model results. However, as mentioned before, we consider a neutral chemistry in our calculations, as we wish to understand the dominant chemical processes at play in molecular formation. We should also include photo-ionization processes coming from chromospheric UV in M stars and photo-dissociation processes stemming from the soft UV radiation field of the star for carbon AGBs. Indeed, the detection in 30g Her of [SiII] lines implies that Si must be present in the inner wind, a result in contradiction with that of our model. However, Si ions could come from the photo-dissociation of SiO (SiO has a dissociation energy of 8 eV, close to the ionization potential of iron, whose ions are observed in 30g Her) and the further ionization of Si atoms. As for carbon stars, neutral sulphur atoms could result from the photo-dissociation of SiS, as suggested by Oaki et al. (1998, Paper II).
An enhancement of atomic sulphur in the inner wind of carbon stars will result in the destruction of some of the acetylene formed close to the star, following Reaction 29, which would then reduce the gas C2H2 content. As seen above, the C2H2 abundance in IRC+ 10216 derived by Cernicharo et al. (1999) is 10 times smaller than the model value calculated by WC98, a result coherent with the existence of possible additional destruction channels for acetylene in the inner wind. Atomic sulphur would also react with molecular ions such as CH+, HCN+, and OH+ to produce HS+ and therefore enhance the abundances of HS and HS2 in the gas. On the other hand, we conjecture that the presence of Si ions in M stars would not much alter our neutral chemistry results, as Si+ is expected to react with carbon chains, which are under-abundant in the inner wind, to form species of the silicon carbide family SiCx/SiCxH. Si+ will also transfer charge with other atomic species like Na or Mg. A proper chemical model including chromospheric effects (photo-ionization, photo-dissociation, and ion-neutral reactions), as well as the chemistry involving metals would confirm or disprove the above conjectures.
Table 5: Species present in the inner wind of S stars as a function of C/O ratios and position.
The dominant molecules formed in the inner wind of S stars in our calculations are listed in Table 5 as a function of C/O ratio and position in the inner wind. For our SE star, that is C/ , the molecular and atomic content of the inner envelope is close to that of O-rich Miras. For SC stars, i.e., C/ , the inner wind chemical composition is very similar to that of C-rich AGBs. However, for C/, we see that the inner wind has a chemical composition typical of both O-rich and C-rich AGB stars, with the presence of two shells, one close to the star with an O-rich molecular content, the second at larger radii and rich of C2H2, SiS, and Si atoms, species typical of carbon stars. Therefore, the molecular content of S stars seems to be highly sensitive to the C/O ratio and its vicinity to unity.
Although a C/O ratio of 1 is unlikely to be represented by observable S stars, the above trends are interesting in terms of dust formation scenarios in AGB stars. In O-rich stars, we saw above that SiO forms constantly in the inner gas layers with high abundances, along with SiO2, which is present in small abundances of . Although the dust nucleation and condensation in O-rich AGBs has not yet been tackled in the inner, shocked regions, we know from the 9.7 m and 17.5 m features and the 33.6, 40.5, and 43 m emission bands that the nature of the dust formed is a mixture of amorphous silicate material (mainly Olivine [MgFeSiO4]) and crystalline silicates (forsterite [Mg2SiO4], enstatite [MgSiO3], diopside [CaMgSi2O6], and water, Demyk et al. 2000). Under TE, the first condensate at high temperatures is corundum (Al2O3) followed by various silicates. However, out of equilibrium, Donn & Nuth (1985) reported that results of nucleation experiments on refractory materials were in disagreement with predictions of TE condensation schemes, a fact later confirmed by Rietmeijer et al. (1999). Furthermore, these experiments conducted with mixed Mg-SiO and Fe-SiO systems indicated that at high temperatures (T > 950 K), pure (SiO)xclusters were more stable than mixed metal-SiO clusters. Although the chemical scheme for (SiO)x cluster formation in our present model is not considered, the high abundances of SiO formed in our gas and the trend of SiO conversion into SiO2 at 3 are coherent with the above picture.
For carbon-rich AGBs, we know that acetylene plays an important role in the dust nucleation and condensation stage, and the large C2H2 abundances found in this study comfirm this scenario.
For S stars however, the situation is far more complex. Skinner et al. (1990) report in their study of the IR spectrum of a large sample of S stars all possible dust configurations: some SE stars show clear silicate features, whilst other SE stars have the SiC 11.3 m feature in their spectrum along with the silicate bands, some SC stars show the SiC feature only and other SC stars have both SiC and silicate bands. We suggest from our study that most of these configurations could be explained by the gradually changing C/O ratio of the star. For example, from inspection of Table 5, we see that SE stars showing the SiC feature could be stars with a C/O ratio very close to but less than unity. The two-shell configuration mentioned above could lead to a first phase of carbon dust formation expelled in the flow prior to silicate formation.
As for SC stars with silicates bands, the explanation is less straightforward and different scenarios may play a role, including that of the presence of a companion star. Yamamura et al. (2000, Paper II) studied the near IR spectrum of V778 Cygni, a well-known silicate carbon star and showed that the ISO/SWS and IRAS/LRS spectra of the silicate emission bands were identical, implying no variation of the features over a 14 year period. They derived a silicate dust temperature of 600 K and some O-rich molecules were tentatively detected (H2O and CO2). They ruled out the evolutionary scenario which predicts a possible fossil O-rich component coming from the previous Miras state of the star because the silicate bands would show some variation in this case due to a temperature change of the O-rich shell resulting from expansion. They further suggested the presence of an O-rich circumstellar disk around a companion star, located at 12 and constantly replenished with silicate material, to explain this steady behavior.
From our present study, we follow the suggestions of Skinner et al. (1990) and conjecture that carbon stars with silicate features could be SC stars with C/O very close to unity for which the inner envelope shows a mixture of both O-rich and C-rich molecules. It is important to recall that the envelope region studied in this paper comprises gas layers which are gravitationally bound to the star in which the gas stays for a long period of time (several pulsation periods, that is, period 14 years) with very specific ranges of parameters favorable to dust nucleation and condensation. Based on temperature constraints, dust formation could occur at any radius between 3 and 10 , depending on the physical parameters of the star (in particular, the effective temperature and the shock velocity). The temperature of the gas excursions at the onset of dust formation can drop as low as 600 K in the adiabatic cooling post-shock region. At the outer edge of our inner wind, the freshly formed dust would drive the wind via radiation pressure on grains. A constantly replenished shell of dust arises from this scenario, and its composition varies depending on the non-expanding inner wind molecular composition. Those regions will experience slow and gradual changes in chemical composition when the photospheric C/O ratio changes from 0.98 to 1.01 over a period typical of that of thermal pulses, i.e., years. As seen from Table 5, the chemical composition of the inner wind can be dual for a long period of time compared to dust condensation time scales, with a mixture of O-rich and C-rich dust precursors. It is then reasonable to suggest that a two component (silicate-carbon) dust may form when the C/O ratio approaches unity on the AGB. We by no means dispute the presence of disks in the environment of some stellar objects, but since there is no observational proof of a companion for V778 Cygni, more efforts should be dedicated to investigating the evolutionary scenario for this star with appropriate circumstellar and dust formation models.
We have presented a chemical study of the quasi-static molecular layers, or extended atmosphere, or inner wind, of AGB stars, with a special emphasis on the interplay between stellar evolution and chemical composition. We summarize below the major findings:
The author wishes to thank A. G. G. M. Tielens for helpful comments on this study and A. Maeder for his careful reading of the manuscript.