Bayesian polarization calibration and imaging in very long baseline interferometry

TL;DR

This work tackles the challenge of obtaining reliable polarimetric VLBI images by introducing a Bayesian polarization calibration and imaging method implemented in the resolve framework. It jointly infers antenna-based gains $\mathbf{G}$, polarization leakages $\mathbf{D}$, and Stokes images $\mathbf{I}$ under a forward RIME-based model, with Gaussian-process priors and variational inference to propagate calibration uncertainties into the images. Key contributions include enforcing the polarization constraint $I \ge \sqrt{Q^2+U^2+V^2}$, enabling multi-source/multi-IF calibration, and delivering uncertainty-quantified, physically plausible high-resolution polarimetric images, demonstrated on synthetic VLBA 15 GHz data and real 3C273 (15 GHz) and OJ287 (86 GHz) observations. The results show consistency with traditional leakage solutions while achieving super-resolution and robust D-term/gain estimates, highlighting the method's potential for next-generation arrays and RM-oriented analyses; the pipeline is publicly available for broad use.

Abstract

Extracting polarimetric information from very long baseline interferometry (VLBI) data is demanding but vital for understanding the synchrotron radiation process and the magnetic fields of celestial objects, such as active galactic nuclei (AGNs). However, conventional CLEAN-based calibration and imaging methods provide suboptimal resolution without uncertainty estimation of calibration solutions, while requiring manual steering from an experienced user. We present a Bayesian polarization calibration and imaging method using Bayesian imaging software resolve for VLBI data sets, that explores the posterior distribution of antenna-based gains, polarization leakages, and polarimetric images jointly from pre-calibrated data. We demonstrate our calibration and imaging method with observations of the quasar 3C273 with the VLBA at 15 GHz and the blazar OJ287 with the GMVA+ALMA at 86 GHz. Compared to the CLEAN method, our approach provides physically realistic images that satisfy positivity of flux and polarization constraints and can reconstruct complex source structures composed of various spatial scales. Our method systematically accounts for calibration uncertainties in the final images and provides uncertainties of Stokes images and calibration solutions. The automated Bayesian approach for calibration and imaging will be able to obtain high-fidelity polarimetric images using high-quality data from next-generation radio arrays. The pipeline developed for this work is publicly available.

Figures (10)

• Figure 1: Comparison between the ground truth image (left panel) convolved with the nominal CLEAN beam with the uniform weighting and the posterior mean resolve polarization reconstruction (right panel) with EVPAs with colors corresponding to the fractional linear polarization $P_{\text{frac}}$. The contours represent the total intensity of corresponding images.
• Figure 2: Comparison between the D-term posterior using resolve and ground truth D-terms from the synthetic data. Contours show 1$\sigma$ and 2$\sigma$ cumulative regions of resolve posterior D-terms using Gaussian kernel density estimation. The plus signs correspond to the ground truth D-terms.
• Figure 3: Comparison between the 3C273 VLBA CLEAN and resolve posterior mean linear polarization reconstructions at 15 GHz. Colored ticks indicate EVPAs, with colors corresponding to the fractional linear polarization $P_{\text{frac}}$. The contours representing the total intensity of corresponding images increase by a factor of 2, starting from 1$\%$ of the peak CLEAN total intensity.
• Figure 4: Comparison among the OJ287 GMVA+ALMA CLEAN, ehtim, and resolve posterior mean linear polarization reconstructions at 86 GHz. Colored ticks indicate EVPAs, with colors corresponding to the fractional linear polarization $P_{\text{frac}}$. The contours representing the total intensity of the corresponding images increase by a factor of 2, starting from 10$\%$ of the peak resolve posterior mean total intensity. All images were processed by Gaussian interpolation.
• Figure 5: Posterior amplitude gains of the OJ287 GMVA+ALMA observation using resolve. The solid line represents the amplitude gain posterior mean with a semi-transparent standard deviation. Each row represents an individual antenna with corresponding abbreviated name in the bottom left corner of each RCP plot.