The impact of point source subtraction residuals on 21 cm Epoch of Reionization estimation

Precise subtraction of foreground sources is crucial for detecting and estimating 21cm HI signals from the Epoch of Reionization (EoR). We quantify how imperfect point source subtraction due to limitations of the measurement dataset yields structured residual signal in the dataset. We use the Cramer-Rao lower bound, as a metric for quantifying the precision with which a parameter may be measured, to estimate the residual signal in a visibility dataset due to imperfect point source subtraction. We then propagate these residuals into two metrics of interest for 21cm EoR experiments - the angular and two-dimensional power spectrum - using a combination of full analytic covariant derivation, analytic variant derivation, and covariant Monte Carlo simulations. This methodology differs from previous work in two ways: (1) it uses information theory to set the point source position error, rather than assuming a global root-mean-square error, and (2) it describes a method for propagating the errors analytically, thereby obtaining the full correlation structure of the power spectra. The methods are applied to two upcoming low-frequency instruments: the Murchison Widefield Array and the Precision Array for Probing the Epoch of Reionization. In addition to the actual antenna configurations, we apply the methods to minimally-redundant and maximally-redundant configurations. We find that for peeling sources above 1 Jy, the amplitude of the residual signal, and its variance, will be smaller than the contribution from thermal noise for the observing parameters proposed for upcoming EoR experiments, and that optimal subtraction of bright point sources will not be a limiting factor for EoR parameter estimation. We then use the formalism to provide an ab initio analytic derivation motivating the 'wedge' feature in the two-dimensional power spectrum, complementing previous discussion in the literature.