Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars I. Atmospheric structure of a giant located near the RGB tip

Context. Red giant stars are important tracers of stellar populations in the Galaxy and beyond, thus accurate modeling of their structure and related observable properties is of great importance. Three-dimensional (3D) hydrodynamical stellar atmosphere models offer a new level of realism in the modeling of red giant atmospheres but still need to be established as standard tools. Aims. We investigate the character and role of convection in the atmosphere of a prototypical red giant located close to the red giant branch (RGB) tip with atmospheric parameters, T-eff = 3660 K, log g = 1.0, [M/H] = 0.0. Methods. Differential analysis of the atmospheric structures is performed using the 3D hydrodynamical and 1D classical atmosphere models calculated with the (COBOLD)-B-5 and LHD codes, respectively. All models share identical atmospheric parameters, elemental composition, opacities and equation-of-state. Results. We find that the atmosphere of this particular red giant consists of two rather distinct regions: the lower atmosphere dominated by convective motions and the upper atmosphere dominated by wave activity. Convective motions form a prominent granulation pattern with an intensity contrast (similar to 18%) which is larger than in the solar models (similar to 15%). The upper atmosphere is frequently traversed by fast shock waves, with vertical and horizontal velocities of up to Mach similar to 2.5 and similar to 6.0, respectively. The typical diameter of the granules amounts to similar to 5Gm which translates into similar to 400 granules covering the whole stellar surface. The turbulent pressure in the giant model contributes up to similar to 35% to the total (i.e., gas plus turbulent) pressure which shows that it cannot be neglected in stellar atmosphere and evolutionary modeling. However, there exists no combination of the mixing-length parameter, alpha(MLT), and turbulent pressure, P-turb, that would allow to satisfactorily reproduce the 3D temperature-pressure profile with 1D atmosphere models based on a standard formulation of mixing-length theory.