http://arxiv.org/abs/2108.11400
The discovery of magnetic fields close to the M87 black hole using Very Long Baseline Interferometry by the Event Horizon Telescope collaboration utilized the novel concept of “closure traces”, that are immune to antenna-based corruptions. We take a fundamentally new approach to this promising tool of polarimetric interferometry. The corruption of measurements of polarized signals at the individual antennas are represented by general $2\times 2$ complex matrices, which are identified with gauge transformations belonging to the group $\textrm{GL}(2,\mathbb{C})$, so the closure traces now appear as gauge-invariant quantities. We apply this formalism to polarimetric interferometry and generalize it to any number of interferometer elements. Our approach goes beyond existing studies in the following respects: (1) we do not need auto-correlations, which are susceptible to large systematic biases, and therefore unreliable (2) we use triangular combinations of correlations as basic building blocks (analogous to the “elementary plaquettes” of lattice gauge theory), and (3) we use the Lorentz group and its properties to transparently identify a complete and independent set of invariants. This set contains all the information immune to corruption available in the interferometer measurements, thus providing robust constraints which would be important in future interferometric studies.
J. Samuel, R. Nityananda and N. Thyagarajan
Fri, 27 Aug 21
35/67
Comments: 9 pages (including references), 0 figures, submitted to Physical Review Letters. Contains appendices not included in the journal version