Polarization leakage in epoch of reionization windows: III. Wide-field effects of narrow-field arrays

Leakage of polarized Galactic diffuse emission into total intensity can potentially mimic the 21-cm signal coming from the epoch of reionization (EoR), as both of them might have fluctuating spectral structure. Although we are sensitive to the EoR signal only in small fields of view, chromatic sidelobes from further away can contaminate the inner region. Here, we explore the effects of leakage into the 'EoR window' of the cylindrically averaged power spectra (PS) within wide fields of view using both observation and simulation of the 3C196 and NCP fields, two observing fields of the LOFAR-EoR project. We present the polarization PS of two one-night observations of the two fields and find that the NCP field has higher fluctuations along frequency, and consequently exhibits more power at high-$k_\parallel$ that could potentially leak to Stokes $I$. Subsequently, we simulate LOFAR observations of Galactic diffuse polarized emission based on a model to assess what fraction of polarized power leaks into Stokes $I$ because of the primary beam. We find that the rms fractional leakage over the instrumental $k$-space is $0.35\%$ in the 3C196 field and $0.27\%$ in the NCP field, and it does not change significantly within the diameters of $15^\circ$, $9^\circ$ and $4^\circ$. Based on the observed PS and simulated fractional leakage, we show that a similar level of leakage into Stokes $I$ is expected in the 3C196 and NCP fields, and the leakage can be considered to be a bias in the PS.