Spectral calibration requirements of radio interferometers for Epoch of
  Reionisation science with the SKA
  Spectral features introduced by instrumental chromaticity of radio
interferometers have the potential to negatively impact the ability to perform
Epoch of Reionisation (EoR) and Cosmic Dawn (CD) science using the redshifted
neutral hydrogen emission line from the early Universe. We describe instrument
calibration choices that influence the spectral characteristics of the science
data, and assess their impact on EoR statistical and tomographic experiments.
Principally, we consider the intrinsic spectral response of the receiving
antennas, embedded within a complete frequency-dependent primary beam response,
and frequency-dependent instrument sampling. We assess different options for
bandpass calibration. 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) EoR 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 array 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 stringent 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.
