Astron. Astrophys. 335, L69-L72 (1998)

3. Model atmospheres

To calculate the structure of the atmosphere and circumstellar envelope (density, temperature, degree of condensation, etc.) as a function of time we solve the coupled system of grey radiation hydrodynamics and time-dependent dust formation. Details about physical and numerical aspects of the modelling method can be found in previous papers (Höfner & Dorfi 1997 and references therein). The stellar pulsation of the LPV is simulated by a variable inner boundary (piston) located beneath the photosphere.

The models presented here have been improved compared to those of Höfner & Dorfi (1997) by introducing a more realistic treatment of the gas opacity. Most time-dependent dynamical models use a constant value for the absorption coefficient of the gas. Our present models are calculated using Planck mean absorption coefficients based on the SCAN molecular line data (Jorgensen 1997). As discussed by Höfner et al. (1998) the gas opacity plays a crucial role with regard to the atmospheric structure and, consequently, the near-IR properties of the models.

We selected one particular model with the following parameters: K and (for the hydrostatic initial model) and (corresponding to log), = 1.4, a pulsation period of and a piston velocity amplitude of 4 km/s. With regard to period, bolometric luminosity and amplitude and mass loss rate, the selected model is quite comparable to R Scl. R Scl's corresponding parameters are , 5700 (Whitelock et al. 1997), approximately 0:m 5 (from the VJHKL data) and /yr (from the IRAS colours using Ivezi & Elitzur 1995). The C/O ratio is also close to the values found by Lambert et al. (1986). However, we want to emphasize that it is not our aim to make a specific model for R Scl or to determine its fundamental parameters but rather to compare hydrodynamic and hydrostatic results, and to give a first comparison between the predictions of these models and ISO observations.

For the purpose of comparing synthetic spectra based on hydrostatic and hydrodynamical models, we also computed two hydrostatic models using the MARCS program (Gustafsson et al. 1975) in an updated version (Jorgensen et al. 1992) which includes spherical geometry and opacity sampling treatment of approximately 100 million molecular lines, and which is particularly suitable for carbon stars. The two models computed for the minimum and the maximum luminosity of R Scl have = 2930 K and 2650 K, respectively, C/O=1.40, log, and solar metallicity. If one adopts 2930 K as at maximum luminosity (Dyck et al. 1996), the models cover the temperature range expected during a pulsational cycle.

Especially in the upper layers of the atmosphere - which are severely affected by the pulsation-induced shock waves - the dynamical models show a complex structure. This is also reflected by the partial pressures of various molecules (cf. Fig. 2). Such structures give rise to qualitatively new predictions for the spectrum and we therefore emphasize the theoretical consistency in contrast to a hydrostatic approach when considering pulsating AGB stars.

Fig. 2. Gas pressure versus gas temperature for two phases of the hydrodynamical model. The full line corresponds to maximum light (), the dash-triple-dot line to minimum light (). The `steps' in the gas pressure indicate shock waves. Dashed, dotted, and dashed-dotted lines show the partial pressures of C2H2, C3 and C2, respectively, in the maximum-light model. Note two distinct maxima in the partial pressure of C2H2 at T=1500 K and T=2100 K, caused by a shock.

© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998
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