Calibration and 21-cm Power Spectrum Estimation in the Presence of
  Antenna Beam Variations
  Detecting a signal from the Epoch of Reionisation (EoR) requires an exquisite
understanding of galactic and extra-galactic foregrounds, low frequency radio
instruments, instrumental calibration, and data analysis pipelines. In this
work we build upon existing work that aims to understand the impact of
calibration errors on 21-cm power spectrum (PS) measurements. It is well
established that calibration errors have the potential to inhibit EoR
detections by introducing additional spectral features that mimic the structure
of EoR signals. We present a straightforward way to estimate the impact of a
wide variety of modelling residuals in EoR PS estimation. We apply this
framework to the specific case of broken dipoles in Murchison Widefield Array
(MWA) to understand its effect and estimate its impact on PS estimation.
Combining an estimate of the percentage of MWA tiles that have at least one
broken dipole (15%-40%) with an analytic description of beam errors induced by
such dipoles, we compute the residuals of the foregrounds after calibration and
source subtraction. We find that that incorrect beam modelling introduces bias
in the 2D-PS on the order of $\sim 10^3\, \mathrm{mK}^2 \,h^{-3}\,
\mathrm{Mpc}^{3}$. Although this is three orders of magnitude lower than
current lowest limits, it is two orders of magnitude higher than the expected
signal. Determining the accuracy of both current beam models and direction
dependent calibration pipelines is therefore crucial in our search for an EoR
signal.
