Calibration techniques for 21-cm experiments with application to HERA: quasi-redundant calibration analysis.

Abstract

Upcoming 21 cm observations promise to open a new window in our understanding of the universe from the epoch of recombination down to redshift of z 1. However, measurements of 21 cm signals come at a high cost since the 21 cm signals are buried under galactic and extragalactic foregrounds that are 4 to 5 orders of magnitude brighter. To overcome this challenge, instruments with high sensitivity and large fields of view are required to detect 21 cm signals. Furthermore, robust techniques are required to perform high precision calibration and foreground removal. Studies have shown that per-frequency antenna gain calibration errors of 1 part 103 will easily swamp the desired signal if an incomplete point source catalogue is used in calibrating the 21 cm instruments. To enhance sensitivity and lower the computational cost, the design and construction of a new generation of 21 cm instruments characterized by maximally redundant array configuration has been under undertaken. The Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) has been successfully calibrated using redundancy in an array configuration, which assumes that in a perfect redundant array, nominally identical baselines measure the same sky signal. In this work, we show that imperfectly redundant arrays produce per-frequency antenna gain calibration errors that can swamp the 21 cm power spectrum measurement. For a test case done using the observed antenna gain auto-correlations from early HERA data, applying correlation calibration in a way that accounts for primary beam variations in the array improves the per-frequency antenna gain amplitude and phase residuals by a factor of 11:4 and 2159 over the redundant calibration for 5% noise level in primary beam variations adopted in simulations. Including 30 bright sources with known positions, significantly improves the per-frequency antenna gain amplitude and phase calibration errors by a factor of 16 and 2317 respectively over redundant calibration. The flexibility of correlation calibration will play a significant role in quantifying and mitigating the per-frequency antenna gain calibration errors that can make 21 cm power spectrum reconstruction impossible. Furthermore, correlation calibration will be useful in solving for instrumental parameters of 21-cm instruments such as Hydrogen Epoch of Reionization Array (HERA), Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX), Canada Hydrogen Intensity Mapping Experiment (CHIME), The Tianlai project and SKA-low.