The Impact of Modeling Errors on Interferometer Calibration for 21 cm
  Power Spectra
  We study the impact of sky-based calibration errors from source mismodeling
on 21\,cm power spectrum measurements with an interferometer and propose a
method for suppressing their effects. While emission from faint sources that
are not accounted for in calibration catalogs is believed to be spectrally
smooth, deviations of true visibilities from model visibilities are not, due to
the inherent chromaticity of the interferometer's sky-response (the "wedge").
Thus, unmodeled foregrounds, below the confusion limit of many instruments,
introduce frequency structure into gain solutions on the same line-of-sight
scales on which we hope to observe the cosmological signal. We derive analytic
expressions describing these errors using linearized approximations of the
calibration equations and estimate the impact of this bias on measurements of
the 21\,cm power spectrum during the Epoch of Reionization (EoR). Given our
current precision in primary beam and foreground modeling, this noise will
significantly impact the sensitivity of existing experiments that rely on
sky-based calibration. Our formalism describes the scaling of calibration with
array and sky-model parameters and can be used to guide future instrument
design and calibration strategy. We find that sky-based calibration that
down-weights long baselines can eliminate contamination in most of the region
outside of the wedge with only a modest increase in instrumental noise.
