Probabilistic methods for radio interferometry data analysis

Doctoral Thesis


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University of Cape Town

Probability theory provides a uniquely valid set of rules for plausible reasoning. This enables us to apply this mathematical formalism of probability, also known as Bayesian, with greater flexibility to problems of scientific inference. In this thesis, we are concerned with applying this method to the analysis of visibility data from radio interferometers. Any radio interferometry observation can be described using the Radio Interferometry Measurement Equation (RIME). Throughout the thesis, we use the RIME to model the visibilities in performing the probabilistic analysis. We first develop the theory for employing the RIME in performing Bayesian analysis of interferometric data. We then apply this to the problem of super-resolution with radio interferometers by performing model selection successfully between different source structures, all smaller in scale than the size of the point spread function (PSF) of the interferometer, on Westerbork Synthesis Radio Telescope (WSRT) simulations at a frequency of 1.4 GHz. We also quantify the change in the scale of the sources that can be resolved by WSRT at this frequency, with changing signal-to-noise (SNR) of the data, using simulations. Following this, we apply this method to a 5 GHz European VLBI Network (EVN) observation of the flaring blazar CGRaBS J0809+5341, to ascertain the presence of a jet emanating from its core, taking into account the imperfections in the station gain calibration performed on the data, especially on the longest baselines, prior to our analysis. We find that the extended source model is preferred over the point source model with an odds ratio of 109 : 1. Using the flux-density and shape parameter estimates of this model, we also derive the brightness temperature of the blazar (10¹¹-10¹² K), which confirms the presence of a relativistically boosted jet with an intrinsic brightness temperature lower than the apparent brightness temperature, consistent with the literature. We also develop a Bayesian criterion for super-resolution in the presence of baseline-dependent noise and calibration errors and find that these errors play an important role in determining how close one can get to the theoretical super-resolution limit. We then proceed to include fringe-fitting, the process of solving for the time and frequency dependent phase variations introduced by the interstellar medium and the Earth's atmosphere, in our probabilistic approach. Fringe-fitting is one of the first corrections made to Very Long Baseline Interferometry (VLBI) observations, and, by extending our method to include simultaneous fringefitting and source structure estimation, we will be able to perform end-to-end VLBI analysis using our method. To this end, we estimate source amplitude and fringe-fitting phase terms (phase offsets and delays) on 43 GHz Very Long Baseline Array and 230 GHz Event Horizon Telescope (EHT) simulations of point sources. We then perform model selection on a 5 μas extended Gaussian source (one-fourth the size of the PSF) on a synthetic 230 GHz EHT observation. Finally we incorporate turbulent time-varying phase offsets and delays in our model selection and show that the delays can be estimated to within 10-16 per cent error (often better than contemporary software packages) while simultaneously estimating the extended source structure.