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Astron. Astrophys. 319, 648-654 (1997)

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1. Introduction

The investigation of mass loss on the AGB is essential for understanding the late stages of stellar evolution of low and intermediate mass stars. A large number of detailed observational and theoretical programs have been devoted to this subject during the last few years (see e.g. Habing 1996 for a recent review). From these studies it has become clear that the interaction of pulsation and dust formation plays a key role for the mass loss phenomenon. Strong shock waves caused by the stellar pulsation lead to a levitation of the stellar atmosphere, providing a cool and dense environment as required for an efficient formation and growth of dust grains. The newly formed dust grains are accelerated by the stellar radiation field and initiate a slow massive outflow by transfering momentum to the surrounding gas.

Models of increasing complexity have been constructed to investigate this process in detail. Wood (1979) and Bowen (1988) have studied the mass loss of dynamical models introducing a parameterized opacity to describe the effects of dust formation in the circumstellar envelope. Bowen & Willson (1991) discuss the implications of their models for the mass loss during AGB evolution ("superwind"). Recently, Blöcker (1995) has used a modified version of Reimers' law based on the models of Bowen (1988) to describe mass loss in his calculations of stellar evolution on the AGB. The dynamical models of Fleischer et al. (1992) include a time-dependent description of dust formation and reveal complex phenomena like a discrete spatial structure of the circumstellar dust shell and multiperiodicity. Radiative transfer calculations by Winters et al. (1994, 1995) based on these models predict that these features will affect observable properties like brightness profiles or near-IR lightcurves. Observations seem to confirm these phenomena (e.g. Le Bertre 1992).

In the preceeding paper of this series (Höfner et al. 1995) we have presented for the first time dynamical models of the circumstellar envelope obtained by solving radiation hydrodynamics together with a detailed time-dependent description of the dust component. We have investigated the limiting case of purely dust driven winds and the dust-induced [FORMULA] -mechanism (cf. Fleischer et al. 1995). In the present paper we include the effects of stellar pulsation in our calculations by applying a piston and a variable luminosity at the inner boundary (Sect.  2).

In contrast to other papers on comparable models (e.g. Fleischer et al. 1992, Winters et al. 1994, 1995, Höfner et al. 1996) which highlight certain physical (or numerical) aspects of the problem with relatively few examples we want to present a systematic investigation of how the resulting properties depend on various physical parameters of the models. In particular we concentrate on two aspects: (i) the time-dependent behaviour (periodicity) which - in combination with detailed observations - could in principle help to constrain physical parameters of individual stars (Sect.  3) and (ii) time-averaged mass loss characteristics of a sample of models which satisfy a radius-luminosity-mass relation and a period-luminosity relation (Sect.  4). We compare our results to mean mass loss-period relations for Mira variables and discuss the implications of our models for stellar evolution on the AGB.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998