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 dSphs, we measure accurate PMs that are a median of 8-13 times more precise than Gaia DR3 alone for $20.5<G<21~\mathrm{mag}$. 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 9 Gaia sources per HST image), we measure BP3M PMs for 2640 unique sources in the $16<G<21.5~\mathrm{mag}$ range, 25% of which have no Gaia PMs; the median BP3M PM uncertainty for $20.25<G<20.75~\mathrm{mag}$ sources is $0.44~$mas/yr compared to $1.03~$mas/yr from Gaia, while the median BP3M PM uncertainty for sources without Gaia-measured PMs ($20.75<G<21.5~\mathrm{mag}$) is $1.16~$mas/yr. 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.

翻译：我们提出一种层级贝叶斯管道BP3M，用于测量哈勃空间望远镜（HST）图像与Gaia交叉匹配源的位置、视差和自行——即使是稀疏场（每幅图像中$N_*<10$个源）也能实现——该研究从近期发布的GaiaHub工具扩展而来。该技术以Gaia测量的天体测量数据为先验，预测HST图像中源的位置，因此无需借助背景星系/类星体即可将HST图像纳入全球参考框架。在天炉座和天龙座矮椭球星系中测试我们公开的代码时，我们测量了精确的自行，其精度中位数比Gaia DR3单独测量结果高出8-13倍（对应$20.5<G<21~\mathrm{mag}$星等）。我们利用合成数据探索观测策略对BP3M天体测量的影响，发现一种最优策略可在不增加自行不确定度的前提下提升视差和位置精度。利用稀疏的COSMOS场（每幅HST图像中Gaia源的中位数为9个）中的1619幅HST图像，我们测量了$16<G<21.5~\mathrm{mag}$星等范围内2640个独立源的BP3M自行，其中25%的源没有Gaia自行数据；对于$20.25<G<20.75~\mathrm{mag}$星等的源，BP3M自行不确定度中位数为$0.44~$毫角秒/年，而Gaia为$1.03~$毫角秒/年；对于无Gaia自行测量的源（$20.75<G<21.5~\mathrm{mag}$），BP3M自行不确定度中位数为$1.16~$毫角秒/年。支撑BP3M管道的统计方法是一种整合不同图像、历元和望远镜位置测量结果的通用框架，可实现跨巡天项目与档案库的信息共享，从而获得比单一星表更高的天体测量精度。