The importance of wide-field foreground removal for 21 cm cosmology: a demonstration with early MWA epoch of reionization observations

In this paper we present observations, simulations, and analysis demonstrating the direct connection between the location of foreground emission on the sky and its location in cosmological power spectra from interferometric redshifted 21 cm experiments. We begin with a heuristic formalism for understanding the mapping of sky coordinates into the cylindrically averaged power spectra measurements used by 21 cm experiments, with a focus on the effects of the instrument beam response and the associated sidelobes. We then demonstrate this mapping by analyzing power spectra with both simulated and observed data from the Murchison Widefield Array. We find that removing a foreground model that includes sources in both the main field of view and the first sidelobes reduces the contamination in high k(parallel to) modes by several per cent relative to a model that only includes sources in the main field of view, with the completeness of the foreground model setting the principal limitation on the amount of power removed. While small, a percent-level amount of foreground power is in itself more than enough to prevent recovery of any Epoch of Reionization signal from these modes. This result demonstrates that foreground subtraction for redshifted 21 cm experiments is truly a wide-field problem, and algorithms and simulations must extend beyond the instrument's main field of view to potentially recover the full 21 cm power spectrum.