  Foregrounds with polarization states that are not smooth functions of
frequency present a challenge to HI Epoch of Reionization (EoR) power spectrum
measurements if they are not cleanly separated from the desired Stokes I
signal. The intrinsic polarization impurity of an antenna's electromagnetic
response limits the degree to which components of the polarization state on the
sky can be separated from one another, leading to the possibility that this
frequency structure could be confused for HI emission. We investigate the
potential of Faraday rotation by the Earth's ionosphere to provide a mechanism
for both mitigation of, and systematic tests for, this contamination.
Specifically, we consider the delay power spectrum estimator, which relies on
the expectation that foregrounds will be separated from the cosmological signal
by a clearly demarcated boundary in Fourier space, and is being used by the
Hydrogen Epoch of Reionization Array (HERA) experiment. Through simulations of
visibility measurements which include the ionospheric Faraday rotation
calculated from real historical ionospheric plasma density data, we find that
the incoherent averaging of the polarization state over repeated observations
of the sky may attenuate polarization leakage in the power spectrum by a factor
of 10 or more. Additionally, this effect provides a way to test for the
presence of polarized foreground contamination in the EoR power spectrum
estimate.
