BP3M: Bayesian Positions, Parallaxes, and Proper Motions Derived from the Hubble Space Telescope and Gaia Data

We present a hierarchical Bayesian pipeline, BP3M, that measures positions, parallaxes, and proper motions (PMs) for cross-matched sources between Hubble Space Telescope (HST) images and Gaia-even for sparse fields (N-* < 10 per image)-expanding from the recent GaiaHub tool. This technique uses Gaia-measured astrometry as priors to predict the locations of sources in HST images, and is therefore able to put the HST images onto a global reference frame without the use of background galaxies/QSOs. Testing our publicly available code in the Fornax and Draco dwarf spheroidal galaxies, we measure PMs that are a median of 8-13 times more precise than Gaia DR3 alone for 20.5 < G < 21 mag. We are able to explore the effect of observation strategies on BP3M astrometry using synthetic data, finding an optimal strategy to improve parallax and position precision at no cost to the PM uncertainty. Using 1619 HST images in the sparse COSMOS field (median nine Gaia sources per HST image), we measure BP3M PMs for 2640 unique sources in the 16 < G < 21.5 mag range, 25% of which have no Gaia PMs; the median BP3M PM uncertainty for 20.25 < G < 20.75 mag sources is 0.44 mas yr(-1) compared to 1.03 mas yr(-1) from Gaia, while the median BP3M PM uncertainty for sources without Gaia-measured PMs (20.75 < G < 21.5 mag) is 1.16 mas yr(-1). The statistics that underpin the BP3M pipeline are a generalized way of combining position measurements from different images, epochs, and telescopes, which allows information to be shared between surveys and archives to achieve higher astrometric precision than that from each catalog alone.