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 HI 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 (∆ν) with respect to ∆ν =| ν a − ν b |, and we use this to estimate P (k). Using simulations of 150 MHz GMRT observations, we find that this estimator is able to recover P (k) with an accuracy of 5 − 20% over a reasonably large k range even when the data in 80% randomly chosen frequency channels is flagged.

Predictions for measuring the 21-cm multifrequency angular power spectrum using SKA-Low

“…which can be estimated from the observed visibilities. Following the prescription in Bharadwaj et al (2018), it is possible to avoid noise bias C N ℓ (ν 1 , ν 2 ) and obtain an unbiased estimate of C ℓ (ν 1 , ν 2 ) from the measured visibilities. However, the noise contributions still persist in the error estimates and this cannot be avoided.…”

“…As mentioned earlier, it is possible to avoid the noise bias Cℓ N (ν, ν) (Bharadwaj et al 2018) by subtracting out the contribution of the self-correlation of visibility from itself. This also leads to a loss of a part of the signal.…”

Data Analysis for Precision 21 cm Cosmology

“…In the case of 21 cm interferometers, the synthesized beam of an instrument has considerable structure, which makes point source removal much more complicated (Pindor et al 2011). Thus, the projecting out of point sources generally requires a forward-modelling effort, where point source catalogs are propagated through a simulation of instrument visibilities, which are then subtracted from the data (Bernardi et al 2011;Sullivan et al 2012).…”

Calibration requirements for Epoch of Reionization 21-cm signal observations -- II. Analytical estimation of the bias and variance with time-correlated residual gains

“…Bharadwaj & Sethi (2001) shows that visibility correlation directly measures the power spectrum. This method and its variants (Datta et al (2007); Choudhuri et al (2014Choudhuri et al ( , 2016Choudhuri et al ( , 2019; Bharadwaj et al (2019) etc.) have been used to estimate the angular power spectrum of the diffused galactic foreground (Ghosh et al 2012;Choudhuri et al 2017b;Chakraborty et al 2019a;Choudhuri et al 2020) as well as the power spectrum of H i distribution in nearby galaxies (Dutta et al 2009;Dutta & Bharadwaj 2013;Nandakumar & Dutta 2020).…”

“…These foreground emissions include the radiation from the compact sources such as the radio galaxies as well as the diffuse synchrotron and freefree emissions from the Galaxy (Santos et al 2005;Ali et al 2008;Ghosh et al 2012;Ali et al 2016;Choudhuri et al 2020). Different techniques are discussed in the literature to mitigate the effect of foreground: foreground avoidance (Datta et al 2010), foreground mitigation (Choudhuri et al 2017a), foreground suppression (Choudhuri et al 2016(Choudhuri et al , 2019Bharadwaj et al 2019) are a few. In practice various foreground removal algorithms are investigated with the LOFAR-EoR data (FastICA 1 , GMCA 2 and GPR 3 ) in Hothi et al (2021).…”