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.
