Spectral calibration requirements of radio interferometers for epoch of reionisation science with the SKA
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Spectral features introduced by instrumental chromaticity of radio interferometers have the potential to negatively impact the ability to perform Epoch of Reionisation and Cosmic Dawn (EoR/CD) science. We describe instrument calibration choices that influence the spectral characteristics of the science data, and assess their impact on EoR/CD statistical and tomographic experiments. Principally, we consider the intrinsic spectral response of the antennas, embedded within a complete frequency-dependent primary beam response, and instrument sampling. The analysis is applied to the proposed SKA1-Low EoR/CD experiments. We provide tolerances on the smoothness of the SKA station primary beam bandpass, to meet the scientific goals of statistical and tomographic (imaging) of EoR/CD programs. Two calibration strategies are tested: (1) fitting of each fine channel independently, and (2) fitting of an nth-order polynomial for each ~ 1 MHz coarse channel with (n+1)th-order residuals (n = 2, 3, 4). Strategy (1) leads to uncorrelated power in the 2D power spectrum proportional to the thermal noise power, thereby reducing the overall sensitivity. Strategy (2) leads to correlated residuals from the fitting, and residual signal power with (n+1)th-order curvature. For the residual power to be less than the thermal noise, the fractional amplitude of a fourth-order term in the bandpass across a single coarse channel must be <2.5% (50 MHz), <0.5% (150 MHz), <0.8% (200 MHz). The tomographic experiment places constraints on phase residuals in the bandpass. We find that the root-mean-square variability over all stations of the change in phase across any fine channel (4.578 kHz) should not exceed 0.2 degrees.
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