The impact of modelling errors on interferometer calibration for 21 cm power spectra

Abstract

We study the impact of sky-based calibration errors from source mismodeling\non 21\\,cm power spectrum measurements with an interferometer and propose a\nmethod for suppressing their effects. While emission from faint sources that\nare not accounted for in calibration catalogs is believed to be spectrally\nsmooth, deviations of true visibilities from model visibilities are not, due to\nthe inherent chromaticity of the interferometer's sky-response (the "wedge").\nThus, unmodeled foregrounds, below the confusion limit of many instruments,\nintroduce frequency structure into gain solutions on the same line-of-sight\nscales on which we hope to observe the cosmological signal. We derive analytic\nexpressions describing these errors using linearized approximations of the\ncalibration equations and estimate the impact of this bias on measurements of\nthe 21\\,cm power spectrum during the Epoch of Reionization (EoR). Given our\ncurrent precision in primary beam and foreground modeling, this noise will\nsignificantly impact the sensitivity of existing experiments that rely on\nsky-based calibration. Our formalism describes the scaling of calibration with\narray and sky-model parameters and can be used to guide future instrument\ndesign and calibration strategy. We find that sky-based calibration that\ndown-weights long baselines can eliminate contamination in most of the region\noutside of the wedge with only a modest increase in instrumental noise.\n