Three-dimensional hydrodynamical simulations of red giant stars: semi-global models for interpreting interferometric observations

Context. Theoretical predictions from models of red giant branch stars are a valuable tool for various applications in astrophysics ranging from galactic chemical evolution to studies of exoplanetary systems. Aims. We use the radiative transfer code OPTIM3D and realistic 3D radiative-hydrodynamical (RHD) surface convection simulations of red giants to explore the impact of granulation on interferometric observables. We assess how 3D simulations of surface convection can be validated against observations. Methods. We computed intensity maps for the 3D simulation snapshots in two filters, the optical at 5000 +/- 300 angstrom and the K band 2.14 +/- 0.26 mu m FLUOR filter, corresponding to the wavelength-range of instruments mounted on the CHARA interferometer. From the intensity maps, we constructed images of the stellar disks and account for center-to-limb variations. We then derived interferometric visibility amplitudes and phases. We study their behavior with position angle and wavelength, and compare them with CHARA observations of the red giant star HD 214868. Results. We provide average limb darkening coefficients for different metallicities and wavelengths ranges. We explain prospects for detecting and characterizing granulation and center-to-limb variations of red giant stars with today's interferometers. Regarding interferometric observables, we find that the effect of convective-related surface structures depends on metallicity and surface gravity. We provide theoretical closure-phases that should be incorporated into the analysis of red giant planet companion closure phase signals. We estimate 3D-1D corrections to stellar radii determination: 3D models are similar to 3.5% smaller to similar to 1% larger in the optical than 1D, and roughly 0.5 to 1.5% smaller in the infrared. Even if these corrections are small, they are needed to properly set the zero point of effective temperature scale derived by interferometry and to strengthen the confidence of existing red giant catalogs of calibrating stars for interferometry. Finally, we show that our RHD simulations provide an excellent fit to the red giant HD 214868 even though more observations are needed at higher spatial frequencies and shorter wavelength.