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

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.