Polarization leakage in Epoch of Reionization windows: I. LOFAR
  observations of the 3C196 field
  Detection of the 21-cm signal coming from the epoch of reionization (EoR) is
challenging especially because, even after removing the foregrounds, the
residual Stokes $I$ maps contain leakage from polarized emission that can mimic
the signal. Here, we discuss the instrumental polarization of LOFAR and present
realistic simulations of the leakages between Stokes parameters. From the LOFAR
observations of polarized emission in the 3C196 field, we have quantified the
level of polarization leakage caused by the nominal model beam of LOFAR, and
compared it with the EoR signal using power spectrum analysis. We found that at
134--166 MHz, within the central 4$^\circ$ of the field the $(Q,U)\rightarrow
I$ leakage power is lower than the EoR signal at $k<0.3$ Mpc$^{-1}$. The
leakage was found to be localized around a Faraday depth of 0, and the rms of
the leakage as a fraction of the rms of the polarized emission was shown to
vary between 0.2-0.3\%, both of which could be utilized in the removal of
leakage. Moreover, we could define an `EoR window' in terms of the polarization
leakage in the cylindrical power spectrum above the PSF-induced wedge and below
$k_\parallel\sim 0.5$ Mpc$^{-1}$, and the window extended up to
$k_\parallel\sim 1$ Mpc$^{-1}$ at all $k_\perp$ when 70\% of the leakage had
been removed. These LOFAR results show that even a modest polarimetric
calibration over a field of view of $\lesssim 4^\circ$ in the future arrays
like SKA will ensure that the polarization leakage remains well below the
expected EoR signal at the scales of 0.02-1 Mpc$^{-1}$.
