4.1. The relation of CO shells and detached dust shells
In the pure mass loss `eruption' models investigated in Sect. 3.1, gas and dust are ejected simultaneously. Due to the dust drift relative to the gas, however, the peak of the dust density is not strictly co-spatial with that of the gas density. The separation of the two distributions increases with radial distance. However, the effect is rather small, and we may assume that gas and dust are essentially collocated. The assumed low mass loss rates before and after the `eruption' imply that almost all of the circumstellar dust is concentrated in the thin, detached shell. In principle, this is in agreement with the observed spectral energy distributions of S Sct and TT Cyg which exhibit excess emission in the far IR, indicative of a detached dust shell. Quantitatively, however, the total amount of ejected dust turned out to be insufficient to account for the observed excess emission at 100 µm. According to our models, a rather high dust-to gas ratio of has to be postulated to correct this problem, which may be taken as one argument against the mass loss `eruption' scenario.
In our simulations of two-wind interaction during the quiet phase of steadily increasing mass loss rate described in Sect. 3.2, the thin shell of wind-compressed gas marks the leading edge of material expelled with a higher wind velocity and lower density. It is produced at some time during the recovery from mass loss `interruption' after a helium-shell flash. Depending on the variation of (and the dust-to-gas ratio) during the thermal pulse, the onset of the faster wind can happen at different phases of the cycle: for the final pulses in our example it happens about 50 000 years before the rapid drop of the mass loss rate due to the following thermal pulse (cf. Fig. 7), while for the earlier pulses it happens at successively later phases (for even earlier pulses there is no fast wind at all). According to this scenario, the shells are found at different positions within the dust-rich regions. Hence, the formation of wind-compressed gas shells is not necessarily related to the occurrence of detached dust shells, and vice versa (a detached dust shell is created when decreases abruptly, while a compressed gas shell is formed when exceeds some critical limit). In contrast, the observations mentioned in the introduction indicate a simultaneous occurrence of detached dust shells and molecular CO shells in all known examples, while in the framework of the pure two-wind interaction scenario this coincidence should be more the exception than the rule. We therefore do not consider this scenario a likely explanation for the presently known objects with circumstellar CO shells. On the other hand, the type of two-wind interaction discussed here should nevertheless work. Then it is inevitable to conclude that similar gas shells should also exist around some AGB stars with attached dust shells, namely those that have recovered from the low mass loss phase and have just exceeded the critical wind density. It might be, however, that a compressed gas shell cannot be detected in CO emission when the dust shell is `attached'.
The third scenario , where two-wind interaction is initiated by a mass loss `eruption', which in turn is triggered by the onset of a helium-shell flash (see Sect. 3.3), combines the advantages of the two scenarios discussed before and avoids their problems. First, it is clear that a few thousand years after the formation of the compressed gas shell the mass loss rate will be very low, since both the stellar luminosity, and hence also the mass loss rate, are known to decline sharply after a helium-shell flash (cf. Fig. 11). This naturally explains the low rates of the `present' mass loss observed for all objects with CO shells. Likewise, it is natural to expect the pulsational properties of AGB stars in the luminosity minimum to be `irregular' or `semiregular'. Second, in contrast to the mass loss `eruption' scenario, the thermal emission now is not only due to the dust in the compressed shell but also comes from the dust farther out, which has been ejected during the phase of relatively high mass loss rate before the occurrence of the helium-shell flash. In this case, there is enough `cool' dust to account for the observed excess emission at 100 µm.
Fig. 14 shows the track of the system AGB star+dusty envelope in the IRAS two-color diagram during the time interval yrs yrs covering the helium-shell flash investigated in Sect. 3.3. According to two-component hydrodynamics / radiative transfer simulations with DEXCEL, the helium-shell flash gives rise to an extended loop in the IRAS two-color diagram, reflecting the detachment of the dust shell and the subsequent resumption of significant mass loss. The observed IRAS colors of TT Cyg (as given by Olofsson et al. 1996) agree closely with the computed colors at yrs (position `11' in Figs. 11, 12, and 14), when the mass loss rate is at its minimum and the compressed gas shell has moved out to cm. This is in almost perfect agreement with the shell radius given by Olofsson et al. (1998) which is based on a distance to TT Cyg of kpc. Using the (uncertain) Hipparcos distance of pc, the observed shell has a radius of cm, for which the model colors do not match the observed ones (position `6' in Fig. 14). In this case, one has to conclude that the drop of the mass loss rate after the helium-shell flash has actually been faster than in the model. This might indicate that TT Cyg is somewhat more massive than our model AGB star (higher stellar core mass implies shorter interpulse time scales), or that the employed stellar evolution sequence still has some deficiencies in describing the mass loss behavior during a helium-shell flash. Within the uncertainties of the Hipparcos parallax, however, the present model seems already close to reality, explaining both the observed dust emission and the geometry of the CO shell.
4.2. Emission and dissociation of CO
It is beyond the scope of the present work to estimate quantitatively the CO emission to be expected from the shells of enhanced gas density seen in our simulations. The main question is whether CO can survive in these shells without being substantially dissociated by the interstellar radiation field before reaching the observed radial distance.
In the case of the mass loss `eruption' scenario, we can use the CO dissociation computations for detached circumstellar shells by Liu (1997) to estimate the CO lifetime. In order to explain the CO shell around TT Cyg, we have to assume a mass ejection with and duration yrs (cf. Sect. 3.1). At the inner edge of such a thick shell, it seems marginally possible for CO to survive for 7 000 yrs, the estimated age of TT Cyg's CO shell, even for a homogeneous medium.
In the two-wind interaction scenarios, the situation is somewhat different. Here we start out with an essentially steady state wind of moderate density, . Assuming a homogeneous medium, CO can survive out to cm in such a situation (Mamon et al. 1988). The two-wind interaction mechanism building up the compressed shell operates within this circumstellar envelope, and hence the CO should be well shielded against photodissociation by interstellar radiation until the shell reaches this radial distance. Beyond this point, shielding will be inefficient and CO should dissociate quickly. However, there are strong indications that the medium in these shells is highly clumpy. As mentioned above, our model results do not support the idea that the clumps are the results of Rayleigh-Taylor instabilities in the interaction zone. Possibly, the origin of the clumps is related to the dust formation process in the innermost parts of the wind. Anyway, shielding becomes more efficient and the lifetime of CO against dissociation is considerably longer in a clumpy medium (see Olofsson et al. 1996, Liu 1997). Therefore, clumpy CO shells should exist well beyond cm.
4.3. CO shells around oxygen-rich AGB stars?
Up to now, CO shells have not been discovered around oxygen-rich AGB stars. We can only speculate about possible reasons.
In principle, the same mechanism invoked for the explanation of the CO shells seen around carbon stars should also work for oxygen-rich stars. However, the radiation pressure on silicate dust is less efficient, and the outflow velocities during the "dust driven" periods are lower than for carbon stars. For this reason, we do not see the formation of compressed gas shells in the simulations done so far with silicate dust, except for marginal density enhancements associated with the final two pulses. Certainly, the chemistry and optical properties are different for oxygen-rich and carbon-rich dust, and the same will be true for the relation between the stellar parameters and the mass loss rate, , for oxygen-rich and carbon-rich AGB stars. Note also that AGB stars with oxygen-rich circumstellar dust in general are in an earlier stage of evolution and hence have a smaller core mass than carbon stars, implying a lower average luminosity and a longer interpulse period of these objects. Lower stellar luminosity combined with lower dust opacity may be the reason why helium-shell flashes (which according to detailed stellar evolution calculations do occur also for M stars) may not result in mass loss `eruptions' and associated wind acceleration of sufficient strength.
© European Southern Observatory (ESO) 2000
Online publication: May 3, 2000