An Image-based Tapered Gridded Estimator (ITGE) for the angular power spectrum

Abstract

We present the Image-based Tapered Gridded Estimator (ITGE) to measure the angular power spectrum $(C_{\ell })$ of the sky signal directly from the visibilities measured in radio-interferometric observations. The ITGE allows us to modulate the sky response through a window function which is implemented in the image plane, and it is possible to choose a wide variety of window functions. In the context of the cosmological HI 21-cm signal, this is useful for masking out the sky signal from specific directions which have strong residual foregrounds. In the context of the ISM in external galaxies, this is useful to separately estimate the $C_{\ell }$ of different parts of the galaxy. The ITGE deals with gridded data, hence it is computationally efficient. It also calculates the noise bias internally and exactly subtracts this out to give an unbiased estimate of $C_{\ell }$. We validate the ITGE using realistic VLA simulations at $1.4\mathrm{GHz}$. We have applied the ITGE to estimate the $C_{\ell }$ of HI 21-cm emission from different regions of the galaxy NGC 628. We find that the slope of the measured $C_{\ell }$ in the outer region is significantly different as compared with the inner region. This indicates that the statistical properties of ISM turbulence possibly differ in different regions of the galaxy.

12 pages, 7 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnrasl.oxfordjournals.org/

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• Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using $150\mathrm{MHz}$ GMRT observations
• Probing early universe through redshifted 21-cm signal: Modelling and observational challenges
• Calibration requirements for Epoch of Reionization 21-cm signal observations -- II. Analytical estimation of the bias and variance with time-correlated residual gains
• The Tracking Tapered Gridded Estimator (TTGE) for the power spectrum from drift scan observations
• Calibration requirement for Epoch of Reionization 21-cm signal observation -- III. Bias and variance in uGMRT ELAIS-N1 field power spectrum