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Astron. Astrophys. 357, 180-196 (2000)

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5. Conclusions

We have applied two different computer codes to study the time-dependent hydrodynamics of circumstellar gas/dust shells of AGB stars in their final stages of evolution. A two-component radiation hydrodynamics code was combined with detailed stellar evolution calculations in order to study the dynamical response of the AGB wind envelope and the emergent spectral energy distribution to temporal changes of the stellar luminosity and mass loss rate driven by helium-shell flashes. A completely independent one-component, high-resolution Godunov-type hydrodynamics code was used to refine the results obtained with the two-component code which suffers from considerable numerical diffusion.

We verified that a presumed short episode of high mass loss translates into a correspondingly narrow, high-density shell moving through the circumstellar envelope, provided that the mass loss rate, and hence the outflow velocity, is essentially constant during the mass loss `eruption'. In the absence of an initial velocity gradient across the shell, the signature of the `eruption' is not broadened significantly as it recedes from the star at highly supersonic speed. In principle, this scenario remains a viable explanation for the existence of the very thin molecular shells around some carbon-rich AGB stars, although is is not clear what causes the required very short event ([FORMULA] yrs) of extremely high mass loss rate ([FORMULA]). Moreover, the total amount of dust ejected during the `eruption' turned out to be insufficient to account for the observed excess emission at [FORMULA] 100 µm. A rather high dust-to gas ratio of [FORMULA] has to be postulated to correct this problem, which may be taken as another argument against the mass loss `eruption' scenario.

We discovered that an alternative mechanism producing very thin shells of greatly enhanced gas density can operate in the dusty outflows from AGB stars: the interaction of a faster inner wind running into a slower outer wind, sweeping up matter at the interface between both type of winds. Based on different numerical simulations and on a simple analytical model, we have shown that this mechanism easily leads to the formation of very thin shells without the need to invoke large variations of the mass loss rate on very short time scales. According to our simulations, the thin shells of wind-compressed gas are produced at some time during the steady recovery from mass loss `interruption' after a helium-shell flash. In this situation, the `present' mass loss rate and outflow velocity are relatively high, in contradiction with observational evidence indicating very low `present' [FORMULA] and [FORMULA] in all known objects with detached molecular shells. We therefore do not consider this scenario a likely explanation for the presently known sample of objects with circumstellar CO shells. In principle, this type of two-wind interaction should nevertheless work, possibly producing similar gas shells around some AGB stars with attached dust shells, which might, however, be difficult to detect.

Finally, we demonstrate that a typical helium-shell flash can trigger a mass loss `eruption' which in turn gives rise to a short phase of high outflow velocity and subsequent two-wind interaction, leading to the formation of a thin compressed gas shell. This scenario combines the advantages of the two scenarios mentioned before and avoids their problems. In particular, it explains in a natural way why the mass loss rate and the outflow velocity will be very low a few thousand years after the formation of the compressed gas shell: the stellar luminosity, and hence also the mass loss rate, are expected to decline sharply after a helium-shell flash. In consequence, a detached dust shell is produced which contains enough `cool' dust to account for the observed IRAS colors of TT Cyg or S Sct, including the excess emission at [FORMULA] 100 µm. At the same time, the pulsational properties of AGB stars in the luminosity minimum are expected to be `irregular' or `semiregular', matching observations.

We point out that it is not necessary to invoke unknown physical processes for this scenario to operate. All that is needed is a sufficiently strong luminosity peak during the helium-shell flash, which is entirely plausible according to detailed stellar evolution models, and a concomitant increase of mass loss rate and outflow velocity. All "thermal pulses" should produce a detached dust shell, but not all of them will have the right properties to produce a pronounced thin gas shell.

As the main result of this work, we conclude that the CO shell seen around the semiregular, optically visible carbon star TT Cygni is very likely the striking manifestation of a recent helium-shell flash.

To confirm this conclusion, improved stellar evolution calculations including a consistent treatment of nucleosynthesis, `dredge-up', and mass loss (e.g. according to the fitting formula by Arndt et al. 1997) will be an essential prerequisite for future hydrodynamical models of the impact of helium-shell flashes on the circumstellar environment. Augmented by CO dissociation and line formation calculations, such future models might provide important new information on the time dependence of luminosity and mass loss rate during a thermal pulse cycle.

Similarly, further observations are necessary to confirm that the scenario proposed here really is the correct explanation. In contrast to the mass loss `eruption' scenario, substantial amounts of gas and dust should exist outside the CO shell of TT Cyg according to the ideas put forward in this work. This difference provides one possibility to discriminate between the two scenarios by means of future observations.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000