Introduction

Most long-period variables (LPVs) are surrounded by extended dusty circumstellar shells accompanied by considerable mass loss, which is often large enough to influence their evolution and to provide substantial amounts of chemically processed material to the ISM (Lafon & Berruyer 1991). Due to the improved instrumental capabilities at infrared and longer wavelengths a large amount of observational data is available for these objects (for a review see Habing 1990). On the other hand based on the progress in theoretical dynamical modelling of LPV atmospheres achieved during the last years (e.g. Bowen 1988, Fleischer et al. 1992) a detailed comparison of theory and observations seems to become accessible now.

The modelling method

Dynamical model calculations

Our approach for the dynamical modelling of circumstellar dust shells of LPVs, which is described in detail in Fleischer et al. 1992, comprises the explicit solution of the hydro-equations in spherical symmetry adopting Lagrangian coordinates, the treatment of radiative transfer by the Eddington approximation for a spherical grey atmosphere according to Lucy (1976), the description of postshock cooling of the gas either by limiting cases (e.g. isothermal shocks) or by cooling functions, and the consistent detailed treatment of the formation, growth and destruction of carbon grains by means of a moment method (cf. Gauger et al. 1990).