Article révisé par les pairs
Résumé : Aims. Surface brightness asymmetries are a very common feature of stars. Among other effects they cause a difference between the projected barycentre and photocentre. The evolution of those surface features makes this difference time-dependent. In some cases, e.g. for supergiant stars, the displacement can be a non-negligible fraction of the star radius R, and if R > 1 AU, of the parallax. Methods. We investigate the impact of surface brightness asymmetries on both the Gaia astrometric solution and the data processing flow with a theoretical approach. Results. We show that when the amplitude of the displacement is comparable to the epoch astrometric precision, the resulting astrometric solution of a genuine single star may be, in some cases, of low quality (with some parameters up to 10σ off). In this case, we provide an analytical prediction of the impact of the photocentre motion on both χ 2 and the uncertainty in the astrometric parameters. Non-single star solutions are found, if allowed for the closest stars. A closer look at the parameters of the orbital solutions reveals however that they are spurious (since the semi-major axis is smaller than either its error or the stellar radius). It is thus possible to filter out those spurious orbital solutions. Interestingly, for the stocastic solutions, the stochastic noise appears to be a good estimate of the photocentric noise. © 2011 ESO.