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Astron. Astrophys. 348, L17-L20 (1999)

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2. Time-dependent model atmosphere

A time-dependent model of the dynamical atmosphere of an AGB star with solar element abundances has been calculated by means of the CHILD -code developed by Fleischer et al. (1992). The code solves the coupled equation system describing time-dependent hydrodynamics, radiative transfer, chemistry, and dust formation in a self-consistent way. However, the model shown in Fig. 1 turns out to be dust-free. Consequently, the pure effect of the stellar pulsation (as simulated by the piston approximation) is studied. The composition of the gas is calculated by assuming chemical equilibrium and the radiative transfer problem is solved in grey approximation. In contrast to Fleischer et al. (1992), Planck mean gas opacities have been used, based on the line data for TiO, CO, H2O and SiO beside several continuum opacity sources. The stellar parameters have not been chosen to describe any specific star, but just represent a typical model.

[FIGURE] Fig. 1. Radial structure of an oxygen-rich time-dependent model at one instant of time (full line: velocity u, dashed line: gas density [FORMULA]). Model parameters: [FORMULA]K, [FORMULA], [FORMULA], [FORMULA], piston amplitude [FORMULA]km s-1, pulsation period [FORMULA]d.

Since radiation pressure on molecules fails to accelerate the gas substantially ([FORMULA]), no further disturbances are introduced into the velocity field and the model exhibits a rather simple saw-tooth-like velocity structure and a step-wise decreasing density profile (see also Fleischer et al. 1992, Höfner et al. 1998). Due to the propagating shocks caused by the pulsation, a considerable time-dependent levitation of the atmosphere is achieved, i.e. the density is much larger than in the initial hydrostatic model (see top panels of Fig. 2).

[FIGURE] Fig. 2. Molecular number densities in the hydrostatic case (l.h.s.) and in the time-dependent hydrodynamic case (r.h.s.). The upper panel shows the temperature (full black) and the gas density (dashed grey = static, full grey = dynamic). The radial distance is given in units of the stellar radius [FORMULA] of the initial model. The model parameters are the same as in Fig. 1.

The analysis of the composition of the gas in chemical equilibrium (Fig. 2, r.h.s.) reveals two distinct regions with enhanced molecular particle densities: a region close to the star ([FORMULA]) and a region further out ([FORMULA], slightly dependent on the considered molecule). The second maximum is not present in the static model (l.h.s.) and is situated in a post-shock region. The polyatomic molecules are more strongly affected by the levitation since their concentrations depend on a larger power of the density. In comparison to the static model, the total amounts of molecules have increased by about [FORMULA] for CO, [FORMULA] for SiO, but by factors of about 5, 50, and 300 for CO2, H2O, and SO2, respectively.

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© European Southern Observatory (ESO) 1999

Online publication: July 16, 1999