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Astron. Astrophys. 337, 149-177 (1998)

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6. Concluding remarks

Based on the hydrodynamics simulations presented in this work we have been able to explain the development of large detached dust shells and the corresponding loops in an IRAS two-color diagram as a natural consequence of long-term mass loss variations within a thermal pulse cycle of the central stellar object. Despite the fact that our simulations are only made for one particular AGB evolutionary track, we found very encouraging similarities with the observations existing so far. This is particularly true for the properties of the spectral energy distributions and the appearance of spatially resolved images of carbon stars with detached dust shells.

Although, in principle, a short mass loss "eruption" of sufficient strength and duration could also explain the existence of AGB stars with excess far infrared (FIR) emission, we have shown that for the mass loss law used in the present investigation, the short mass loss spikes associated with the helium shell flashes are not the reason for the formation of detached shells in our models. Their amplitude and duration is much too small. Likewise, interaction of the AGB wind with the interstellar medium turns out to be of minor importance in this context. Rather, high mass loss sustained for several ten thousand years, interrupted by extended minima with mass loss rates reduced by orders of magnitude (after a thermal pulse) produces the strong FIR excess and corresponding loops in the IRAS two-color diagram.

We conclude from our hydrodynamical simulations that the density enhancement generated by a short mass loss "eruption" broadens considerably as it moves towards the outer regions of the circumstellar shell due to the existence of substantial velocity gradients. It is therefore not considered as a likely cause for the observed very thin detached CO shells. However, the same simulations provide another mechanism creating thin shells of enhanced gas density, namely the interaction of winds of different velocity and density. Once the critical mass loss rate is exceeded, the "dust-driven", faster wind in the inner parts of the shells runs into the slower "shock-driven" wind in the outer parts, acting like a snow plow piling up matter in a thin shell at the interface between both type of winds (for details see Steffen & Schönberner 1998).

It should be noted that the models discussed here are far from being fully self-consistent: they cover only those parts of the circumstellar envelope that lie outside the sonic point and therefore cannot make predictions about the mass loss rate which depends on the conditions close to the stellar surface. Fully self-consistent theoretical models of circumstellar AGB shells require the incorporation of stellar pulsations, dust chemistry, multi-component hydrodynamics and stellar evolution.

While we do not intend to take up such an ambitious project, we plan several smaller steps to improve our model calculations for future applications. These include introducing a distribution of grain sizes , developing improved formulae for [FORMULA] and [FORMULA] based on more physical models, and the incorporation of an energy equation for the gas component . Based on the resulting improved models, CO dissociation and line formation computations could be performed to study the problem of the origin of thin detached CO shells in more detail.

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© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998