CIRCUMSTELLAR DUST SHELLS AROUND LONG-PERIOD VARIABLES .1. DYNAMIC-MODELS OF C-STARS INCLUDING DUST FORMATION, GROWTH AND EVAPORATION

Dynamical models of circumstellar dust shells (CDS) around long-period and Mira variables are presented which include, consistently coupled, time-dependent hydrodynamics and a detailed treatment of the processes of formation, growth and evaporation of carbon grains. In this paper we study the limit case of isothermal shocks, which, nevertheless, yields a realistic picture of the dynamical interactions which determine the internal structure of the CDS. The first part of this paper comprises a description of our hydrodynamic code and of the modelling procedure. In the second part, we discuss in detail for one demonstrative model how dust formation and growth in interaction with the pulsating atmosphere are responsible for the development of a discrete structure of the CDS, in particular of a shell like distribution of the solid particles. Radiation pressure on the dust particles concentrated in these layers leads to the periodic generation of strong shock waves. The pulsation in the interior provides this process with the adequate physical conditions. Furthermore. we compare these models with a calculation where the dust component is represented schematically by a simple function accounting for the radiation pressure on dust. This approach which yields a reliable picture of the overall appearance, however, is not appropriate for a detailed modelling of the real structure of CDS.