Optical interferometry and Gaia measurement uncertainties reveal the physics of asymptotic giant branch stars.

Context. Asymptotic giant branch stars are cool luminous evolved stars that are well observable across the Galaxy and populating Gaia data. They have complex stellar surface dynamics Aims. On the AGB star CL Lac, it has been shown that the convection-related variability accounts for a substantial part of the Gaia DR2 parallax error. We observed this star with the MIRC-X beam combiner installed at the CHARA interferometer to detect the presence of stellar surface inhomogeneities. Methods. We performed the reconstruction of aperture synthesis images from the interferometric observations at different wavelengths. Then, we used 3D radiative hydrodynamics simulations of stellar convection with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the spectral channels of MIRC-X observations. Then, we determined the stellar radius and compared the 3D synthetic maps to the reconstructed ones focusing on matching the intensity contrast, the morphology of stellar surface structures, and the photocentre position at two different spectral channels, 1.52 and 1.70 micron, simultaneously. Results. We measured the apparent diameter of CL Lac at two wavelengths and recovered the radius using a Gaia parallax. In addition to this, the reconstructed images are characterised by the presence of a brighter area that largely affects the position of the photocentre. The comparison with 3D simulation shows good agreement with the observations both in terms of contrast and surface structure morphology, meaning that our model is adequate for explaining the observed inhomogenities. Conclusions. This work confirms the presence of convection-related surface structures on an AGB star of Gaia DR2. Our result will help us to take a step forward in exploiting Gaia measurement uncertainties to extract the fundamental properties of AGB stars using appropriate RHD simulations.