Radiative hydrodynamics simulations of red supergiant stars. III. Spectro-photocentric variability, photometric variability, and consequences on Gaia measurements

Context. It has been shown that convection in red supergiant stars gives rise to large granules causing surface inhomogeneities together with shock waves in the photosphere. The resulting motion of the photocenter (on time scales ranging from months to years) could possibly have adverse effects on the parallax determination with Gaia. Aims. We explore the impact of the granulation on the photocentric and photometric variability. We quantify these effects in order to better characterize the error possibly altering the parallax. Methods. We use 3D radiative-hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code OPTIM3D to compute intensity maps and spectra in the Gaia G band [325-1030 nm]. Results. We provide astrometric and photometric predictions from 3D simulations of RSGs that are used to evaluate the degradation of the astrometric parameters of evolved stars derived by Gaia. We show from RHD simulations that a supergiant like Betelgeuse exhibits a photocentric noise characterised by a standard deviation of the order of 0.1 AU. The number of bright giant and supergiant stars whose Gaia parallaxes will be altered by the photocentric noise ranges from a few tens to several thousandths. The degradation of the astrometric fit due to the presence of this photocentric noise will be noticeable up to about 5 kpc for the brightest supergiants. Moreover, parallaxes of supergiants are affected by a error of the order of a few percents. We show that the photocentric noise, as predicted by the 3D simulation, does account for a substantial part of the supplementary 'cosmic noise' that affects Hipparcos measurements of Betelgeuse and Antares.