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20th of October 2021
ATNF Colloquium
Towards a General Theory of Closure Invariants in Radio Interferometry
Nithyanandan Thyagarajan (Space & Astronomy, CSIRO)
Abstract: Recent "planet-scale" very long baseline interferometry (VLBI) efforts at millimetre wavelengths have resulted in the first detailed images near the event horizon of the supermassive black hole (SMBH) at the centre of M87 by the Event Horizon Telescope (EHT) collaboration. Calibration of the radio signals received by such widely separated VLBI stations is one of the key challenges in the accurate reconstruction of images. Closure phases and amplitudes in co-polar interferometry, have long provided calibration-independent observables immune to multiplicative, station-dependent corruptions. Very recently, "closure traces" for full polarimetric interferometry have been introduced and used in the recent study of the magnetic field structures around the M87 central black hole. So far, a systematic method for explicitly exhibiting a full set of invariants has still remained unclear. Using the mathematical framework of the gauge theories of particle physics and Lorentz transformations, I will describe a general formalism, applicable to interferometer arrays of arbitrary size, that uses only triangular combinations of correlations as basic building blocks to precisely isolate a complete and independent set of invariants, and unifies the treatment for all closure invariants, from which the closure phases and closure amplitudes familiar in co-polar interferometry naturally emerge. These results can find significant applications in ongoing and future (including space-based) observations of SMBHs using the current and the next-generation EHT (ngEHT), and more generally, polarimetric radio interferometry.

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