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：我们提出了一种层次化贝叶斯流水线BP3M，用于测量哈勃空间望远镜（HST）图像与盖亚（Gaia）交叉匹配源的位置、视差和自行——即便对于稀疏天区（每张图像$N_*<10$）亦可适用——这是对近期GaiaHub工具的扩展。该技术利用盖亚测量的天体测量数据作为先验信息，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图像定位到全球参考框架上。在天炉座和天龙座矮球状星系上测试我们的公开代码后，我们测量了精度中位数比盖亚DR3单独测量高8-13倍的精确自行（适用于$20.5<G<21~\mathrm{mag}$）。通过合成数据探索观测策略对BP3M天体测量的影响，我们发现了一种最优策略，可在不增加自行不确定性的前提下提升视差和位置精度。利用稀疏COSMOS天区（每张HST图像中位数含9个盖亚源）的1619张HST图像，我们为$16<G<21.5~\mathrm{mag}$范围内的2640个独立源测量了BP3M自行，其中25%的源在盖亚中无自行数据；对于$20.25<G<20.75~\mathrm{mag}$的源，BP3M自行不确定度中位数为$0.44~$mas/yr，而盖亚为$1.03~$mas/yr；对于无盖亚自行的源（$20.75<G<21.5~\mathrm{mag}$），BP3M自行不确定度中位数为$1.16~$mas/yr。支撑BP3M流水线的统计方法是一种通用化途径，可整合来自不同图像、历元和望远镜的位置测量结果，从而在巡天与档案数据间共享信息，实现比单一星表更高的天体测量精度。