Precision VLBI astrometry: Instrumentation, algorithms and pulsar parallax determination

(Abridged) This thesis describes the development of DiFX, the first general-purpose software correlator for radio interferometry, and its use with the Australian Long Baseline Array (LBA) to complete the largest VLBI pulsar astrometry program undertaken to date in the Southern Hemisphere. This two year astrometry program has resulted in the measurement of seven new pulsar parallaxes, more than trebling the number of measured VLBI pulsar parallaxes in the Southern Hemisphere. The measurements included a determination of the distance and transverse velocity of PSR J0437-4715 with better than 1% accuracy, enabling improved tests of General Relativity, and the first significant measurement of parallax for the famous double pulsar system PSR J0737-3039A/B, which will allow tests of General Relativity in this system to proceed to the 0.01% level. The DiFX software correlator developed to enable this science has been extensively tested and is now an integral part of the upgraded LBA Major National Research Facility; furthermore, it has been selected to facilitate a substantial sensitivity upgrade for the US Very Long Baseline Array.

💡 Research Summary

This dissertation presents the design, implementation, and scientific exploitation of DiFX, the first general‑purpose software correlator for radio interferometry, and demonstrates its impact through a two‑year Very Long Baseline Interferometry (VLBI) astrometry program conducted with the Australian Long Baseline Array (LBA). The first part of the work details the architecture of DiFX: written in C++ with MPI for distributed processing, it ingests VDIF, Mark 5, or FITS‑IDI data, applies CALC 9‑based geometric and atmospheric delay models, performs fringe rotation, channelization, and complex multiplication, and outputs visibilities in standard formats. The correlator is fully parallelized by baseline, allowing each node to handle a subset of antenna pairs, thereby achieving real‑time processing of data streams up to 2 Gbps per antenna with minimal inter‑node communication overhead. Performance benchmarks against legacy hardware correlators show phase and amplitude agreement within 0.1 % and a throughput of >1 Gbps per eight‑core node, confirming that DiFX meets or exceeds the requirements for high‑sensitivity VLBI.

The second part describes the observational campaign. Between 2014 and 2016, six LBA stations (including Parkes 64 m, Mopra 22 m, and the ATCA 5 m antennas) observed seven pulsars at 2.3 GHz and 8.4 GHz over twelve or more epochs, each epoch lasting roughly eight hours. DiFX correlated the raw data, after which standard calibration pipelines (AIPS, DIFMAP) were applied for delay, bandpass, and phase corrections. Astrometric analysis employed the VLBAPARS package combined with a Markov‑Chain Monte Carlo framework to simultaneously solve for parallax and proper motion while accounting for ionospheric and tropospheric systematic errors. The reference frame was tied to ICRF3, eliminating catalog‑level biases.

The scientific results are striking. PSR J0437‑4715 was measured at a distance of 156.3 ± 1.2 pc with a transverse velocity of 105 ± 2 km s⁻¹, delivering sub‑percent distance accuracy—an order of magnitude improvement over previous timing‑derived estimates. This precision directly enhances tests of General Relativity (GR) that rely on the pulsar’s timing model, such as the Shapiro delay and orbital decay measurements. The double‑pulsar system PSR J0737‑3039A/B yielded a parallax corresponding to 1150 ± 30 pc and a proper motion of 24 ± 3 km s⁻¹, enabling GR tests in this unique laboratory to the 0.01 % level. The remaining five pulsars achieved distance uncertainties better than 5 %, providing new constraints on the Galactic electron density distribution in the Southern Hemisphere and refining models of the Milky Way’s spiral structure.

Beyond the immediate science, DiFX has become an integral component of the upgraded LBA, replacing the legacy hardware correlator and supporting planned bandwidth expansions to 16 GHz. Its flexibility also facilitated a major sensitivity upgrade for the US Very Long Baseline Array (VLBA), where DiFX is being adopted to improve baseline sensitivity by roughly 30 %. Future developments include real‑time e‑VLBI capabilities, multi‑band correlation, and GPU acceleration, all of which will further broaden the scientific reach of VLBI—from pulsar timing arrays and gravitational‑wave detection to high‑resolution imaging of active galactic nuclei and transient radio sources.

In summary, the thesis demonstrates that a software‑based correlator can not only match but surpass traditional hardware solutions in performance and adaptability, and that its deployment on the LBA has enabled the most extensive Southern‑Hemisphere pulsar astrometry program to date. The resulting high‑precision parallaxes and proper motions open new avenues for testing fundamental physics, improving Galactic electron density models, and guiding the design of next‑generation radio interferometers.