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Precise subtraction of foreground sources is crucial for detecting andestimating 21cm HI signals from the Epoch of Reionization (EoR). We quantifyhow imperfect point source subtraction due to limitations of the measurementdataset yields structured residual signal in the dataset. We use the Cramer-Raolower bound, as a metric for quantifying the precision with which a parametermay be measured, to estimate the residual signal in a visibility dataset due toimperfect point source subtraction. We then propagate these residuals into twometrics of interest for 21cm EoR experiments - the angular and two-dimensionalpower spectrum - using a combination of full analytic covariant derivation,analytic variant derivation, and covariant Monte Carlo simulations. Thismethodology differs from previous work in two ways: (1) it uses informationtheory to set the point source position error, rather than assuming a globalroot-mean-square error, and (2) it describes a method for propagating theerrors analytically, thereby obtaining the full correlation structure of thepower spectra. The methods are applied to two upcoming low-frequencyinstruments: the Murchison Widefield Array and the Precision Array for Probingthe Epoch of Reionization. In addition to the actual antenna configurations, weapply the methods to minimally-redundant and maximally-redundantconfigurations. We find that for peeling sources above 1 Jy, the amplitude ofthe residual signal, and its variance, will be smaller than the contributionfrom thermal noise for the observing parameters proposed for upcoming EoRexperiments, and that optimal subtraction of bright point sources will not be alimiting factor for EoR parameter estimation. We then use the formalism toprovide an ab initio analytic derivation motivating the 'wedge' feature in thetwo-dimensional power spectrum, complementing previous discussion in theliterature.

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