Closure invariants for polarised radio interferometric observations: a graph theoretical approach

TL;DR

This paper extends the mathematical framework of closure invariants in polarised radio interferometry to incomplete data scenarios, demonstrating their robustness and utility through simulations.

Contribution

It introduces a graph-theoretical formalism for closure invariants applicable to incomplete visibility data in polarised radio interferometry.

Findings

Closure invariants can be derived for incomplete graphs.

Invariants retain useful information despite noise.

The formalism is validated through simulations.

Abstract

Aperture synthesis observations with full polarisation have long been used to study the magnetic fields of synchrotron emitting sources. Recently proposed closure invariants give us a powerful method for extracting information from measured visibilities which are corrupted by antenna and polarisation dependent gains. In this paper, a formalism developed earlier for complete graphs (where all visibilities are available) is extended to incomplete graphs. The formalism provides a complete and independent set of closure invariants from the measured visibilities in a general situation where not all visibilities are available. We then show in a simulated, quasi-realistic case that the invariants developed here contain usable information even in the presence of noise.