Observing and modeling the dynamic atmosphere of the low mass-loss C-star R Sculptoris at high angular resolution

Context. We study the circumstellar environment of the carbon-rich star R Sculptoris using the near- and mid-infrared high spatial resolution observations from the ESO-VLTI focal instruments VINCI and MIDI, respectively. Aims. These observations aim at increasing our knowledge of the dynamic processes in play within the very close circumstellar environment where the mass loss of AGB stars is initiated. Methods. We first compare the spectro-interferometric measurements of the star at different epochs to detect the dynamic signatures of the circumstellar structures at different spatial and spectral scales. We then interpret these data using a self-consistent dynamic model atmosphere to discuss the dynamic picture deduced from the observations. Since the hydrodynamic computation needs stellar parameters as input, a considerable effort is first applied to determining these parameters. Results. Interferometric observations do not show any significant variability effect at the 16 m baseline between phases 0.17 and 0.23 in the K band, and for both the 15 m baseline between phases 0.66 and 0.97 and the 31 m baseline between phases 0.90 and 0.97 in the N band. We find fairly good agreement between the dynamic model and the spectrophotometric data from 0.4 to 25 mu m. The model agrees well with the time-dependent flux data at 8.5 mu m, whereas it is too faint at 11.3 and 12.5 mu m. The VINCI visibility measurements are reproduced well, meaning that the extension of the model is suitable in the K-band. In the mid-infrared, the model has the proper extension to reveal molecular structures of C2H2 and HCN located above the stellar photosphere. However, the windless model used is not able to reproduce the more extended and dense dusty environment. Conclusions. Among the different explanations for the discrepancy between the model and the measurements, the strong nonequilibrium process of dust formation is one of the most probable. The transition from windless atmospheres to models with considerable mass-loss rates occurs in a very narrow range of stellar parameters, especially for the effective temperature, the C/O ratio, and the pulsation amplitude. A denser sampling of such critical regions of the parameter space with additional models might lead to a better representation of the extended structures of low mass-loss carbon stars like R Sculptoris. The complete dynamic coupling of gas and dust and the approximation of grain opacities with the small-particle limit in the dynamic calculation could also contribute to the difference between the model and the data.