A Hierarchical Bayesian Differential Calibration of the Gaia DR3 Parallax Zero Point Using Galactic Globular Clusters
Abstract
Globular clusters (GCs) occupy a broad range of stellar colors and magnitudes while sharing nearly the same distance. Gaia Data Release 3 parallaxes retain systematic zero-point residual variations for GCs, even after the correction by the widely used standard correction model (L21). We derive an empirical residual correction by the Hierarchical Bayesian Model, separating cluster-level offsets from the differential information carried by the member sequences. We first evaluate the L21 baseline at a fixed reference color, which assigns the remaining color-dependent correction to the residual model. Then we model the residual zero point, δZ(G,νeff), with B-splines functions in color and magnitude--color interaction terms. The uncorrected cluster residuals exhibit a negative offset of approximately $25−−40~μ{\rm as}$. The L21 baseline removes most of this offset but leaves coherent color- and magnitude-dependent structure. Applying the residual model brings the mean residuals close to zero, especially across most of the sampled color range. In five-fold cross-validation that excludes entire clusters from training, the correction modestly reduces the magnitude- and color-trend RMS relative to the L21 correction. The resulting model therefore provides a differential refinement of the \textit{Gaia} DR3 parallax zero-point within the calibrated domain for GCs, rather than an independent determination of its absolute value.
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BibTeX
@misc{ding2026hierarchical,
title = {{A Hierarchical Bayesian Differential Calibration of the Gaia DR3 Parallax Zero Point Using Galactic Globular Clusters}},
author = {Ye Ding and Shilong Liao and Qi Xu and Qiqi Wu and Keyu Zhu and Zhaoxiang Qi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36543},
eprint = {2610.36543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36543},
}
RIS
TY - UNPB
TI - A Hierarchical Bayesian Differential Calibration of the Gaia DR3 Parallax Zero Point Using Galactic Globular Clusters
AU - Ye Ding
AU - Shilong Liao
AU - Qi Xu
AU - Qiqi Wu
AU - Keyu Zhu
AU - Zhaoxiang Qi
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36543
UR - https://arxiv.org/abs/2610.36543
AB - Globular clusters (GCs) occupy a broad range of stellar colors and magnitudes while sharing nearly the same distance. Gaia Data Release 3 parallaxes retain systematic zero-point residual variations for GCs, even after the correction by the widely used standard correction model (L21). We derive an empirical residual correction by the Hierarchical Bayesian Model, separating cluster-level offsets from the differential information carried by the member sequences. We first evaluate the L21 baseline at a fixed reference color, which assigns the remaining color-dependent correction to the residual model. Then we model the residual zero point, δZ(G,ν_eff), with B-splines functions in color and magnitude--color interaction terms. The uncorrected cluster residuals exhibit a negative offset of approximately $25−−40~μ{\rm as}$. The L21 baseline removes most of this offset but leaves coherent color- and magnitude-dependent structure. Applying the residual model brings the mean residuals close to zero, especially across most of the sampled color range. In five-fold cross-validation that excludes entire clusters from training, the correction modestly reduces the magnitude- and color-trend RMS relative to the L21 correction. The resulting model therefore provides a differential refinement of the \textit{Gaia} DR3 parallax zero-point within the calibrated domain for GCs, rather than an independent determination of its absolute value.
ER -