A Hierarchical Bayesian Differential Calibration of the Gaia DR3 Parallax Zero Point Using Galactic Globular Clusters

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, $δZ(G,ν_{\rm eff})$, 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.