Sensitivity Of A Low-Frequency Polarimetric Radio Interferometer

Context. The sensitivity of a radio interferometer is a key figure of merit (FoM) for a radio telescope. The sensitivity of a single polarized interferometer is typically given as an antenna effective area over a system temperature, A(e)/T-sys, assuming an unpolarized source. For a dual-polarized polarimetric interferometer intended to observe sources of unknown polarization, the state of polarization must not be assumed a priori. Furthermore, in contrast to the narrow field of view (FoV) of dish-based interferometers, the sensitivity of a polarimetric low-frequency radio interferometer warrants a careful review because of the very wide FoV of the dual-polarized antennas. A revision of this key FoM is particularly needed in the context of the Low-Frequency Square Kilometre Array (SKA-Low) where the sensitivity requirements are currently stated using A(e)/T-sys for a single-polarized antenna system, which produces ambiguity for off-zenith angles.Aims. This paper aims to derive an expression for the sensitivity of a polarimetric radio interferometer that is valid for all-sky observations of arbitrarily polarized sources, with neither a restriction on FoV nor with any a priori assumption regarding the polarization state of the source. We verify the resulting formula with an all-sky observation using the Murchison Widefield Array telescope.Methods. The sensitivity expression was developed from first principles by applying the concept of system equivalent flux density (SEFD) to a polarimetric radio interferometer (not by computing A(e)/T-sys). The SEFD was calculated from the standard deviation of the noisy flux density estimate for a target source due to system noise.Results. The SEFD for a polarimetric radio interferometer is generally not 1/root 2 of a single-polarized interferometer as is often assumed for narrow FoV. This assumption can lead to significant errors for a dual-polarized dipole based system, which is common in low-frequency radio astronomy: up to similar to 15% for a zenith angle with a coverage of 45 degrees and up to similar to 45% for 60 degrees coverage. The worst case errors occur in the diagonal planes of the dipole for very wide FoV. This is demonstrated through theory, simulation, and observations. Furthermore, using the resulting formulation, the calculation of the o ff-zenith sensitivity is straightforward and unambiguous.Conclusions. For wide FoV observations pertinent to a low-frequency radio interferometer such as SKA-Low, the narrow FoV and the single-polarized sensitivity expressions are not correct and should be replaced by the formula derived in this paper.