Astrometry in crowded fields towards the Galactic bulge

Abstract

Context. The astrometry towards the Galactic bulge is hampered by high stellar crowding and patchy extinction. This effect is particularly severe for optical surveys such as the European Space Agency satellite Gala. Aims. In this study, we assess the consistency of proper motion measurements between optical (Gaia DR3) and near-infrared (VIRAC2) catalogues in comparison with proper motions measured with the Hubble Space Telescope (HST) observations in several crowded fields towards the Galactic bulge and in Galactic globular clusters. Methods. Assuming that the proper motion measurements are well characterised, the uncertainty-normalised proper motion differences between pairs of catalogues are expected to follow a normal distribution. A deviation from a normal distribution defines the inflation factor r. By multiplying the proper motion uncertainties with the appropriate inflation factor values, the Gaia (VIRAC2) proper motion measurements are brought into a 1σ agreement with the HST proper motions. Results. The inflation factor (r) depends on stellar surface density. For the brightest stars in our sample (G < 18), the dependence on G-band magnitude is strong, corresponding to the most precise Gaia DR3 proper motions. We used the number of observed Gaia DR3 sources as a proxy for the stellar surface density. Assuming that the HST proper motion measurements are well determined and free from systematic errors, we find that Gaia DR3 proper motion uncertainties are better characterised, having r < 1.5 in fields with a stellar number density with fewer than 200 Gaia DR3 sources per arcmin2, and are underestimated by up to a factor of 4 in fields with stellar densities higher than 300 sources per arcmin2. For the most crowded fields in VIRAC2, the proper motion uncertainties are underestimated by a factor of 1.1 up to 1.5, with a dependence on J-band magnitude. In all fields, the brighter sources have the higher r value. At the faint end (G > 19), the inflation factor is close to 1, meaning that the proper motions already fully agree with the HST measurements within 1σ. Conclusions. In the crowded fields common to both catalogues, VIRAC2 proper motions agree with HST proper motions and do not need an inflation factor for their uncertainties. Because of the depth and completeness of VIRAC2 in these fields, it is an ideal complement to Gaia DR3 for proper motion studies towards the Galactic bulge.