Measuring the reionization 21 cm fluctuations using clustering wedges

One of the main challenges in probing the reionization epoch using the redshifted 21 cm line is that the magnitude of the signal is several orders smaller than the astrophysical foregrounds. One of the methods to deal with the problem is to avoid a wedge-shaped region in the Fourier $k_{\perp} - k_{\parallel}$ space which contains the signal from the spectrally smooth foregrounds. However, measuring the spherically averaged power spectrum using only modes outside this wedge (i.e., in the reionization window), leads to a bias. We provide a prescription, based on expanding the power spectrum in terms of the shifted Legendre polynomials, which can be used to compute the angular moments of the power spectrum in the reionization window. The prescription requires computation of the monopole, quadrupole and hexadecapole moments of the power spectrum using the theoretical model under consideration and also the knowledge of the effective extent of the foreground wedge in the $k_{\perp} - k_{\parallel}$ plane. One can then calculate the theoretical power spectrum in the window which can be directly compared with observations. The analysis should have implications for avoiding any bias in the parameter constraints using 21 cm power spectrum data.