Abstract. We present a new generation of model atmospheres for AGB stars which combine time-dependent dynamics and frequency-dependent radiative transfer. This allows us to take both the effects of pulsation (shock waves, stellar winds) and the complex influence of molecular opacities into account. In the case of C-rich stars, the models also include a self-consistent time-dependent description of dust formation. We investigate the influence of frequency-dependent radiative transfer on the energy and momentum balance of the atmosphere and compare our new models to existing grey dynamical models as well as to classical hydrostatic model atmospheres. We stress the importance of non-grey radiative transfer for obtaining realistic density-temperature structures even in highly dynamical models, discussing both the resulting observable properties and the wind characteristics. Presenting synthetic spectra, we argue that the current dynamical models represent an important step in a process leading from a qualitative to a quantitative description of atmospheres and winds of pulsating AGB stars.

Abstract.We have calculated synthetic opacity sampling spectra for carbon-rich Asymptotic Giant Branch (AGB) stars based on dynamic model atmospheres which couple time-dependent dynamics and frequency-dependent radiative transfer, as presented in the third paper of this series. We include the molecules CO, CH, CN, C 2 , CS, HCN, C 2 H 2 and C 3 in our calculations, both when computing the atmospheric structures, and the synthetic spectra. A comparison of the synthetic spectra with various observed colours and spectra in the wavelength range between 0.5 and 25 µm of TX Psc, WZ Cas, V460 Cyg, T Lyr and S Cep is presented. We obtain good agreement between observations gathered at different phases and synthetic spectra of one single hydrodynamical model for each star in the wavelength region between 0.5 and 5 µm. At longer wavelengths our models showing mass loss offer a first self-consistent qualitative explanation of why a strong feature around 14 µm, which is predicted by all hydrostatic models as well as dynamical models showing no mass loss, is missing in observed AGB carbon star spectra.

Abstract. Atmospheres of evolved AGB stars are heavily affected by pulsation, dust formation and mass loss, and they can become very extended. Time series of observed high-resolution spectra proved to be a useful tool to study atmospheric dynamics throughout the outer layers of these pulsating red giants. Originating at various depths, different molecular spectral lines observed in the near-infrared can be used to probe gas velocities there for different phases during the lightcycle. Dynamic model atmospheres are needed to represent the complicated structures of Mira variables properly. An important aspect which should be reproduced by the models is the variation of line profiles due to the influence of gas velocities. Based on a dynamic model, synthetic spectra (containing CO and CN lines) were calculated, using an LTE radiative transfer code that includes velocity effects. It is shown that profiles of lines that sample different depths qualitatively reproduce the behaviour expected from observations.

Abstract. We present self-consistent dynamical models for dust-driven winds of carbon-rich AGB stars. The models are based on the coupled system of frequency-dependent radiation hydrodynamics and time-dependent dust formation. We investigate in detail how the wind properties of the models are influenced by the micro-physical properties of the dust grains that are required by the description of grain formation. The choice of dust parameters is significant for the derived outflow velocities, the degrees of condensation and the resulting mass-loss rates of the models. In the transition region between models with and without massloss the choice of micro-physical parameters turns out to be very significant for whether a particular set of stellar parameters will give rise to a dust-driven mass-loss or not. We also calculate near-infrared colors to test how the dust parameters influence the observable properties of the models, however, at this point we do not attempt to fit particular stars.

Cool giant stars are highly dynamical objects, and complex micro-physical processes play an important role in their extended atmospheres and winds. The interpretation of observations, and in particular of high-resolution IR spectra, requires realistic self-consistent model atmospheres. Current dynamical models include rather detailed micro-physics, and the resulting synthetic spectra compare reasonably well with observations. A transition from qualitative to quantitative modelling is taking place at present. We give an overview of existing dynamical model atmospheres for AGB stars, discussing recent advances and current trends in modelling. When comparing synthetic spectra and other observable properties resulting from dynamical models with observations we focus on the near-and mid-IR wavelength range.