The wedge bias in reionization 21-cm power spectrum measurements

A proposed method for dealing with foreground emission in upcoming 21-cm observations from the epoch of reionization is to limit observations to an uncontaminated window in Fourier space. Foreground emission can be avoided in this way, since it is limited to a wedge-shaped region in k_∥, k_⊥ space. However, the power spectrum is anisotropic owing to redshift-space distortions from peculiar velocities. Consequently, the 21-cm power spectrum measured in the foreground avoidance window - which samples only a limited range of angles close to the line-of-sight direction - differs from the full redshift-space spherically averaged power spectrum which requires an average over all angles. In this paper, we calculate the magnitude of this `wedge bias' for the first time. We find that the bias amplifies the difference between the real-space and redshift-space power spectra. The bias is strongest at high redshifts, where measurements using foreground avoidance will overestimate the redshift-space power spectrum by around 100 per cent, possibly obscuring the distinctive rise and fall signature that is anticipated for the spherically averaged 21-cm power spectrum. In the later stages of reionization, the bias becomes negative, and smaller in magnitude (≲20 per cent).