The visibility based Tapered Gridded Estimator (TGE) for the redshifted 21-cm power spectrum

TL;DR

This paper introduces an improved Tapered Gridded Estimator (TGE) for 21-cm power spectrum analysis, which reduces computation, suppresses outer field contributions, and accurately estimates the power spectrum and its variance using simulations.

Contribution

The paper extends the TGE method to 3D for 21-cm power spectrum estimation, incorporating noise bias subtraction and variance prediction validated by simulations.

Findings

Accurately recovers input power spectra from simulations.

Provides analytic variance predictions that match simulation results.

Effectively suppresses outer field contributions in power spectrum estimation.

Abstract

We present the improved visibility based Tapered Gridded Estimator (TGE) for the power spectrum of the diffuse sky signal. The visibilities are gridded to reduce the computation, and tapered through a convolution to suppress the contribution from the outer regions of the telescope's field of view. The TGE also internally estimates the noise bias, and subtracts this out to give an unbiased estimate of the power spectrum. An earlier version of the 2D TGE for the angular power spectrum $C_{\ell}$ is improved and then extended to obtain the 3D TGE for the power spectrum $P({\bf k})$ of the 21-cm brightness temperature fluctuations. Analytic formulas are also presented for predicting the variance of the binned power spectrum. The estimator and its variance predictions are validated using simulations of $150 \, {\rm MHz}$ GMRT observations. We find that the estimator accurately recovers the input model for the 1D Spherical Power Spectrum $P(k)$ and the 2D Cylindrical Power Spectrum $P(k_\perp,k_\parallel)$, and the predicted variance is also in reasonably good agreement with the simulations.