CIRCUMSTELLAR DUST SHELLS AROUND LONG-PERIOD VARIABLES .3. INSTABILITY DUE TO AN EXTERIOR KAPPA-MECHANISM CAUSED BY DUST FORMATION

Dynamical models of circumstellar dust shells (CDS) around very luminous carbon-rich long-period variables are presented which include time-dependent hydrodynamics and a detailed treatment of the processes of formation, growth and evaporation of the dust grains. In contrast to our previous calculations, where we assumed that the sinusoidally moving inner boundary simulates the interior pulsation of the star, we now present model calculations, where the velocity of the inner boundary is equal to zero. A new nonlinear effect arises because of the dust opacity: By the backwarming due to the formation of a discrete dust layer, small-amplitude waves are initiated in the innermost region which provide a density enhancement necessary for a new dust formation and growth cycle. It is shown how this mechanism starts in an initially hydrostatic atmosphere and how it is self-maintaining due to the induced waves. Hence, the circumstellar shell mimics a pulsating atmosphere, although this effect is caused by an instability due to the dust formation process. Furthermore, it is shown that this modeling approach yields stationary dust-driven wind models as a limiting case. However, this is only achieved if the dust opacity is neglected in the determination of the temperature in radiative equilibrium or if dust formation is so ineffective that no relevant backwarming occurs. Since very high luminosities and low temperatures are needed for the exterior cc-mechanism to occur by itself, the pure effect as described in this paper probably will not show up in general but only for objects at the very end of their AGE evolution. However, as AGE stars are usually pulsating objects, a complex interaction between the pulsation and the exterior kappa-mechanism is likely to occur in a broader range of parameters.