Estimating distances from parallaxes. VI: A method for inferring distances and transverse velocities from parallaxes and proper motions demonstrated on Gaia Data Release 3

Abstract: The accuracy of stellar distances inferred purely from parallaxes degrades rapidly with distance. Proper motion measurements, when combined with some idea of typical velocities, provide independent information on stellar distances. Here I build a direction- and distance-dependent model of the distribution of stellar velocities in the Galaxy, then use this together with parallaxes and proper motions to infer kinegeometric distances and transverse velocities for stars in Gaia DR3. Using noisy simulations I assess the performance of the method and compare its accuracy to purely parallax-based (geometric) distances. Over the whole Gaia catalogue, kinegeometric distances are on average 1.25 times more accurate than geometric ones. This average masks a large variation in the relative performance, however. Kinegeometric distances are considerably better than geometric ones beyond several kpc, for example. On average, kinegeometric distances can be measured to an accuracy of 19% and velocities (sqrt[vra^2 + vdec^2]) to 16 km/s (median absolute deviations). In Gaia DR3, kinegeometric distances are smaller than geometric ones on average for distant stars, but the pattern is more complex in the bulge and disk. With the much more accurate proper motions expected in Gaia DR5, a further improvement in the distance accuracy by a factor of (only) 1.35 on average is predicted (with kinegeometric distances still 1.25 times more accurate than geometric ones). The improvement from proper motions is limited by the width of the velocity prior, in a way that the improvement from better parallaxes is not limited by the width of the distance prior.