A Tapered Gridded Estimator (TGE) for the multifrequency angular power spectrum (MAPS) and the cosmological H i21-cm power spectrum

Abstract

In this work, we present a new approach to estimate the power spectrum P(k) of redshifted H i 21-cm brightness temperature fluctuations. The MAPS C_ℓ(ν_a, ν_b) completely quantifies the second-order statistics of the sky signal under the assumption that the signal is statistically homogeneous and isotropic on the sky. Here, we generalize an already existing visibility based estimator for C_ℓ, namely TGE, to develop an estimator for C_ℓ(ν_a, ν_b) . The 21-cm power spectrum is the Fourier transform of C_ℓ(Δν) with respect to Δν = │ν_a − ν_b│, and we use this to estimate P(k). Using simulations of |150 \, {\rm MHz}150MHz| GMRT observations, we find that this estimator is able to recover P(k) with an accuracy of |5\text{--}20 {{\ \rm per\ cent}}5–20 per cent| over a reasonably large k range even when the data in |80 {{\ \rm per\ cent}}80 per cent| randomly chosen frequency channels are flagged.