Detecting dark photon dark matter with Gaia-like astrometry observations

A class of dark photon dark matter models with ultralight masses would lead to oscillation of a test body through a coupling with baryons or $B-L$ charge. This periodical oscillation of an observer results in swing of a star's apparent position due to the effect of aberration of light, which could be probed with high-precision astrometry observations of stars in the Milky Way. We propose to use the observations of stellar positions of a number of stars by Gaia to search for this kind of dark photon dark matter. We show that this astrometry method is able to give promising sensitivities to search for the dark photon dark matter in the mass range of $10^{-23}\sim10^{-21}$ eV.