Synthetic photometry for carbon-rich giants II. The effects of pulsation and circumstellar dust

Context. Red giant stars approaching the end of the evolutionary phase of the asymptotic giant branch (AGB) are, inter alia, characterised by (i) pulsations of the stellar interiors; and (ii) the development of dusty stellar winds. Therefore, such very evolved objects cannot be adequately described with hydrostatic dust-free model atmospheres. Aims. By using self-consistent dynamic model atmospheres which simulate pulsation-enhanced dust-driven winds we studied in detail the influence of the above mentioned two effects on the spectral appearance of long period variables with carbon-rich atmospheric chemistry. While the pulsations lead to large-amplitude photometric variability, the dusty envelopes (resulting from the outflows which contain dust particles composed of amorphous carbon) cause pronounced circumstellar reddening. Methods. Based on one selected dynamical model which is representative of C-type Mira variables with intermediate mass loss rates, we calculated synthetic spectra and photometry for standard broad-band filters (Johnson-Cousins-Glass system) from the visual to the near-infrared. The synthetic photometry was subsequently compared with observational results. Results. Our modelling allows to investigate in detail the substantial effect of circumstellar dust on the resultant photometry. The pronounced absorption of amorphous carbon dust grains (increasing towards shorter wavelengths; Q(abs)/a proportional to lambda(-beta) with beta approximate to 1), leads to colour indices which are significantly redder than the corresponding ones based on hydrostatic dust-free models. Only if we account for this circumstellar reddening we get synthetic colours that are comparable to observations of evolved AGB stars. The photometric variations of the dynamical model were compared to observed lightcurves of the C-type Mira RU Vir which appears to be quite similar to the model (although the model is not a dedicated fit). We found good agreement concerning the principal behaviour of the BVRIJHKL lightcurves and also quantitatively fitting details (e. g. magnitude ranges, the amplitude decrease from visual to NIR, absolute magnitudes). The analysed model is able to reproduce the variations of RU Vir and other Miras in (J - H) vs. (H - K) diagrams throughout the light cycle (ranges, loops). Contrasting the model photometry with observational data for a variety of galactic C-rich giants in such colour-colour diagrams proved that the chosen atmospheric model fits well into a sequence of objects with increasing mass loss rates, i. e., redder colour indices. Conclusions. The comparison of our synthetic photometry with observational results provides a further indication that the applied dynamic model atmospheres represent the outer layers of pulsating and mass-losing C-rich AGB stars reasonably well.