Impact on EoR Power Spectrum of Calibration of Ionospheric Parameters for SKA1-LOW

Abstract

In this brief note I compare different proposed SKA1-LOW array layouts for the task of performing an Epoch of Reionisation (EoR) power spectrum analysis, in the context of the ability of the data to estimate ionospheric phase parameters. I outline an approach that computes the Fisher Information of the amplitude of parameters describing an ionospheric model that are contained within the extended baseline data towards high SNR calibration sources. Distributed pierce points through the ionosphere sample the distortion pattern adequately and allow for precise estimation of model parameters. The parameter uncertainties are then propagated through a statistical model for the distribution of point sources across the field-of-view to compute the covariance of the data due to an imprecisely-estimated ionosphere. This data covariance is then propagated into the two-dimensional power spectrum, as a metric used for EoR estimation, to determine the impact in wavenumber space. Despite yielding the same number of pierce points towards the ionosphere with redundant information (same pierce points), the superstation design provides additional sensitivity, yielding more precise calibration and consequently less impact on the EoR power spectrum at 50 MHz and 150 MHz. At higher frequencies (250 MHz), the reduced field-of-view yields calibration improvement for arrays that sample the ionospheric pierce points more completely, with less calibrators available. This note does not make any assessments of the relative science capabilities of the arrays (e.g. reduced sensitivity to EoR power spectrum due to relocation of core sensitivity to non-core sensitivity).