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

Aims. Although observational data unequivocally point to the presence of chromospheres in red giant stars, no attempts have been made so far to model them using 3D hydrodynamical model atmospheres. We therefore compute an exploratory 3D hydrodynamical model atmosphere for a cool red giant in order to study the dynamical and thermodynamic properties of its chromosphere, as well as the influence of the chromosphere on its observable properties. Methods. Three-dimensional radiation hydrodynamics simulations are carried out with the (COBOLD)-B-5 model atmosphere code for a star with the atmospheric parameters (T-eff approximate to 4010 K, log g = 1 : 5, [M/H] = 0 : 0), which are similar to those of the K-type giant star Aldebaran (alpha Tau). The computational domain extends from the upper convection zone into the chromosphere (7.4 >= log >= tau(Ross) >= 12 : 8) and covers several granules in each horizontal direction. Using this model atmosphere, we compute the emergent continuum intensity maps at different wavelengths, spectral line profiles of Ca II K, the Ca II infrared triplet line at 854.2 nm, and H alpha, as well as the spectral energy distribution (SED) of the emergent radiative flux. Results. The initial model quickly develops a dynamical chromosphere that is characterised by propagating and interacting shock waves. The peak temperatures in the chromospheric shock fronts reach values of up to 5000 K, although the shock fronts remain quite narrow. Similar to the Sun, the gas temperature distribution in the upper layers of red giant stars is composed of a cool component due to adiabatic cooling in the expanding post-shock regions and a hot component due to shock waves. For this red giant model, the hot component is a rather flat high-temperature tail, which nevertheless affects the resulting average temperatures significantly. Conclusions. The simulations show that the atmospheres of red giant stars are dynamic and intermittent. Consequently, many observable properties cannot be reproduced with static 1D models, but require advanced 3D hydrodynamical modelling. Furthermore, including a chromosphere in the models might produce significant contributions to the emergent UV flux.