System equivalent flux density of a low-frequency polarimetric phased array interferometer

Aims. This paper extends the treatment of system equivalent flux density (SEFD), discussed in our earlier to interferometric phased array telescopes. The objective is develop an SEFD formula involving only most fundamental assumptions that readily applicable interferometer radio observations. Our aim compare resultant expression against often-used root-mean-square (rms) approximation, ${\rm{SEFD}}_I^{{\rm{rms}}} = {1 \over 2}\sqrt {{\rm{SEFD}}_{XX}^{\rm{2}} + {\rm{SEFD}}_{YY}^{\rm{2}}} $, study inaccuracy I rms . Methods. We take into account all mutual coupling and noise within environment (intra-array coupling). intra-array included through realized resistance array, which accounts for noise. No assumption made regarding polarization (or lack thereof) sky nor orthogonality antenna elements. that, phasor representation, real imaginary components a given source are independent equally distributed (iid) with zero mean. Noise sources mutually correlated non-iid among themselves allowed, provided each iid. uncorrelated between entities separated by baseline distance, case Murchison Widefield Array (MWA) typically tens wavelengths or greater. By comparing resulting we proved always underestimates SEFD, leads overestimation sensitivity. Results. present generalized but has similar form result. Here, physical meaning lengths resistances have been such they also valid environment. simulated was validated using MWA observation Hydra-A galaxy at 154.88 MHz. observed XX on average higher 9% 4%, respectively, while YY lower 4% compared values pixels −12 dB beam width. errors due approximation nearly identical, mean difference images virtually 0%. result suggests derived expression, as well simulation approach, correct may be applied any pointing. As result, this method permits identification telescope pointing angles where (overestimates sensitivity). For example, (Az, ZA) (81°, 46°), underestimation calculation 7% −3 width, increases 23% At 199.68 MHz, (45°, 56.96°), reached 29% width 36% two different frequencies expected consistent proof.