2. Modelling method and parameters
We solve the coupled system of radiation hydrodynamics and time-dependent dust formation (cf. Höfner et al. 1995) employing an implicit numerical method and an adaptive grid (for details of the numerical technique see Dorfi & Feuchtinger 1995). The gas dynamics including self-gravity is described by the equations of continuity, motion and energy, and the radiation field by the grey moment equations of the radiative transfer equation. The energy exchange between matter and radiation adopts a LTE source function which could result in overestimating the cooling rates behind radiative shocks. Considering C-rich stars we assume the formation of amorphous carbon grains. The extinction efficiency of the grains ( ; a: grain radius, T: temperature) is based on the optical constants of Maron (1990).
The pulsation of the long-period variable (LPV) is simulated by a sinusoidal motion of the inner boundary which is located below the stellar photosphere (). Since the radiative flux is kept constant at this point the luminosity at the inner boundary varies according to .
The models are characterized by the following set of parameters: stellar mass , luminosity , effective temperature and the carbon-to-oxygen abundance ratio (all abundances except carbon are assumed as solar) of the hydrostatic initial model as well as the piston parameters period P and velocity amplitude . For the models presented in this paper (except series P) we have calculated from and using the radius-luminosity-mass relation of Iben (1984) with and as in Bowen & Willson (1991) together with and have chosen P according to a period-luminosity relation for Miras (Feast et al. 1989). The physical parameters are selected to demonstrate the effects of time-dependent dust formation in LPV atmospheres which leads to a sample biased towards relatively high values. In this context we want to emphasize that the conclusions drawn from our calculations of C-rich objects may not be directly applicable to the large group of O-rich AGB stars.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998