Sensitivity of a low-frequency polarimetric radio interferometer

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