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Although observational data unequivocally point out to the presence ofchromospheres in red giant stars, no attempts have been made so far to modelthem using 3D hydrodynamical model atmospheres. We therefore compute anexploratory 3D hydrodynamical model atmosphere for a cool red giant in order tostudy the dynamical and thermodynamic properties of its chromosphere, as wellas the influence of the chromosphere on its observable properties. 3D radiationhydrodynamics simulations are carried out with the CO5BOLD model atmospherecode for a star with the atmospheric parameters (Teff=4010 K, log g=1.5,[M/H]=0.0), which are similar to those of the K-type giant star Aldebaran(alpha Tau). ... we compute the emergent continuum intensity maps at differentwavelengths, spectral line profiles of Ca II K, the Ca II infrared triplet lineat 854.2nm, and H alpha, as well as the spectral energy distribution (SED) ofthe emergent radiative flux. The initial model quickly develops a dynamicalchromosphere characterised by propagating and interacting shock waves. The peaktemperatures in the chromospheric shock fronts reach values on the order of upto 5000 K although the shock fronts remain quite narrow. Like for the Sun, thegas temperature distribution in the upper layers is composed of a coolcomponent due to adiabatic cooling in the expanding post-shock regions and ahot component due to shock waves. For this red giant model, the hot componentis a rather flat high-temperature tail, which nevertheless affects theresulting average temperatures significantly. The simulations show that theatmospheres of red giant stars are dynamic and intermittent. Consequently, manyobservable properties cannot be reproduced with one-dimensional static modelsbut demand for advanced 3D HD modelling. Furthermore, including a chromospherein the models might produce significant contributions to the emergent UV flux.

Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars VI. First chromosphere model of a late-type giant