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 lumino us carbon-rich long-period variables are presented which include time- dependent hydrodynamics and a detailed treatment of the processes of f ormation, growth and evaporation of the dust grains. In contrast to ou r previous calculations, where we assumed that the sinusoidally moving inner boundary simulates the interior pulsation of the star, we now p resent model calculations, where the velocity of the inner boundary is equal to zero. A new nonlinear effect arises because of the dust opac ity: By the backwarming due to the formation of a discrete dust layer, small-amplitude waves are initiated in the innermost region which pro vide a density enhancement necessary for a new dust formation and grow th cycle. It is shown how this mechanism starts in an initially hydros tatic atmosphere and how it is self-maintaining due to the induced wav es. Hence, the circumstellar shell mimics a pulsating atmosphere, alth ough 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 i s 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 lumi nosities and low temperatures are needed for the exterior cc-mechanism to occur by itself, the pure effect as described in this paper probab ly 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 obje cts, a complex interaction between the pulsation and the exterior kapp a-mechanism is likely to occur in a broader range of parameters.