Line formation in AGB atmospheres including velocity effects Molecular line profile variations of long period variables

Context. Towards the end of the evolutionary stage of the asymptotic giant branch (AGB) the atmospheres of evolved red giants are considerably influenced by radial pulsations of the stellar interiors and developing stellar winds. The resulting complex velocity fields severely affect molecular line profiles (shapes, time-dependent shifts in wavelength, multiple components) observable in near-infrared spectra of long period variables. Time-series high-resolution spectroscopy allows us to probe the atmospheric kinematics and thereby study the mass loss process. Aims. With the help of model calculations the complex line formation process in AGB atmospheres was explored with the focus on velocity effects. Furthermore, we aimed for atmospheric models which are able to quantitatively reproduce line profile variations found in observed spectra of pulsating late-type giants. Methods. Models describing pulsation-enhanced dust-driven winds were used to compute synthetic spectra under the assumptions of chemical equilibrium and LTE. For this purpose, we used molecular data from line lists for the considered species and solved the radiative transfer in spherical geometry including the effects of velocity fields. Radial velocities (RV) derived from Doppler-shifted (components of) synthetic line profiles provide information on the gas velocities in the line-forming region of the spectral features. In addition, we made use of radial optical depth distributions to give estimates for the layers where lines are formed and to illustrate the effects of velocities in the line formation process. Results. Assuming uniform gas velocities for all depth points of an atmospheric model we estimated the conversion factor between gas velocities and measured RVs to p = u(gas)/RV approximate to 1.2-1.5. On the basis of dynamic model atmospheres and by applying our spectral synthesis codes we investigated in detail the finding that various molecular features in AGB spectra originate at different geometrical depths of the very extended atmospheres of these stars. We show that the models are able to quantitatively reproduce the characteristic line profile variations of lines sampling the deep photosphere (CO Delta v = 3, CN) of Mira variables and the corresponding discontinuous, S-shaped RV curve. The global velocity fields (traced by different features) of typical long-period variables are also realistically reproduced. Possible reasons for discrepancies concerning other modelling results (e. g. CO Delta v = 2 lines) are outlined. In addition, we present a model showing variations of CO Delta v = 3 line profiles comparable to observed spectra of semiregular variables and discuss that the non-occurence of line doubling in these objects may be due to a density effect. Conclusions. The results of our line profile modelling are another indication that the dynamic models studied here are approaching a realistic representation of the outer layers of AGB stars with or without mass loss.