Probing red supergiant dynamics through photo-center displacements measured by Gaia

International audienceContext. Red supergiant (RSGs) are cool massive stars in a late phase of their evolution when the stellar envelope becomes fully convective. They are the brightest stars in the universe at infrared light and can be detected in galaxies far beyond the Local Group, allowing for accurate determination of chemical composition of galaxies. The study of their physical properties is extremely important for various phenomena including the final fate of massive stars as type II supernovae and gravitational wave progenitors. Aims. We explore the well-studied nearby young stellar cluster χ Per, which contains a relatively large population of RSG stars. Using Gaia EDR3 data, we find the distance of the cluster ( d = 2.260 ± 0.020 kpc) from blue main sequence stars and compare with RSG parallax measurements analysing the parallax uncertainties of both groups. We then investigate the variability of the convection-related surface structure as a source for parallax measurement uncertainty. Methods. We use state-of-the-art three-dimensional radiative hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code OPTIM3D to compute intensity maps in the Gaia G photometric system. We calculate the variabiltiy, as a function of time, of the intensity-weighted mean (or the photo-center) from the synthetic maps. We then select the RSG stars in the cluster and compare their uncertainty on parallaxes to the predictions of photocentre displacements. Results. The synthetic maps of RSG show extremely irregular and temporal variable surfaces due to convection-related dynamics. Consequentially, the position of the photo-center varies during Gaia measurements between 0.033 and 0.130 AU (≈1 to ≈5% of the corresponding simulation stellar radius). We argue that the variability of the convection-related surface structures accounts for a substantial part of the Gaia EDR3 parallax error of the RSG sample of χ Per. Conclusions. We suggest that the variation of the uncertainty on Gaia parallax could be exploited quantitatively using appropriate RHD simulations to extract, in a unique way, important information about the stellar dynamics and parameters of RSG stars