Modeling atmospheric phase corruptions in high-frequency VLBI using Gaussian processes

TL;DR

The paper addresses atmospheric phase corruptions in high-frequency VLBI by jointly modeling station-based gain phases with the source visibility phases using Gaussian Processes. It leverages a half-integer Matérn kernel to enable a state-space representation and applies Kalman filtering for efficient marginalization of the gain phases, removing the need for a reference station. Through synthetic tests and an EHT 3C 279 analysis, the approach accurately recovers GP parameters and yields calibration consistent with established EHT-HOPS results. The method shows promise for extensions to frequency-dependent phase behavior and multi-frequency calibration, enhancing coherent integration for horizon-scale VLBI imaging.

Abstract

Using very long baseline interferometry (VLBI) observations at (sub)millimeter wavelengths, the Event Horizon Telescope (EHT) currently achieves the finest angular resolution of any astronomical facility, necessary for imaging the horizon-scale structure around supermassive black holes. A significant calibration challenge for high-frequency VLBI stems from rapid variations in the atmospheric water vapor content above each telescope in the array, which induce corresponding fluctuations in the phase of the correlated signal that limit the coherent integration time and thus the achievable sensitivity. In this paper, we introduce a model that describes station-based phase corruptions jointly with a parameterization for the source structure. We adopt a Gaussian Process (GP) prescription for the time evolution of these phase corruptions, which provides sufficient flexibility to capture even highly erratic phase behavior. The use of GPs permits the application of a Kalman filtering algorithm for numerical marginalization of these phase corruptions, which permits efficient exploration of the remaining parameter space. Our model also removes the need to specify an arbitrary ``reference station'' during calibration, instead establishing a global phase zeropoint by enforcing the GPs at all stations to have fixed mean and finite variance. We validate our method using a real EHT observation of the blazar 3C 279, demonstrating that our approach yields calibration solutions that are consistent with those determined by the EHT Collaboration. The model presented here can be straightforwardly extended to incorporate frequency-dependent phase behavior, such as is relevant for the frequency phase transfer calibration technique.

Figures (7)

• Figure 1: Synthetic data gain phases (top) and visibility phases (bottom) versus time for each station and baseline, respectively.
• Figure 2: Posterior distributions for the model parameters determined from fitting synthetic data. Left: Pairwise distributions for the coherence timescale parameters $\tau_i$. Center: Pairwise distributions for the phase fluctuation magnitude parameters $\sigma_i$. Right: Posterior distributions for the visibility phase parameters $\phi_{ij}$. For all 2D distributions, the red contours enclose 50% and 90% of the posterior probability. Blue lines represent the input values used when generating the synthetic data.
• Figure 3: Uncalibrated visibility phase versus time on each of the baselines in the EHT 3C 279 dataset; in each panel, the baseline is specified in the upper left-hand corner. Time is measured in UT hours since the start of 2017 April 5.
• Figure 4: Same as \ref{['fig:realdata_allscans']}, but showing now the unwrapped visibility phases for a single scan. Note that no single scan contained all 10 baselines shown in \ref{['fig:realdata_allscans']}, so we show here a scan containing only 6 baselines.
• Figure 5: Recovered station gain phases versus time for each of the stations participating in the scan whose visibility phases are shown in \ref{['fig:realdata_singlescan']}. The solid curve in each panel shows the median posterior value, and the shaded region indicates 90% confidence interval.