  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.
