The Effect of $w-term$ on Visibility Correlation and Power Spectrum Estimation

Abstract

Visibility-visibility correlation has been proposed as a technique for the estimation of power spectrum, and used extensively for small field of view observations, where the effect of $w-term$ is usually ignored. We consider power spectrum estimation from the large field of view observations, where the $w-term$ can have a significant effect. Our investigation shows that a nonzero $w$ manifests itself as a modification of the primary aperture function of the instrument. Using a gaussian primary beam, we show that the modified aperture is an oscillating function with a gaussian envelope. We show that the two visibility correlation reproduces the power spectrum beyond a certain baseline given by the width, $U_w$ of the modified aperture. Further, for a given interferometer, the maximum $U_w$ remains independent of the frequencies of observation. This suggests that, the incorporation of large field of view in radio interferometric observation has a greater effect for larger observing wavelengths.

9 pages, 4 figures, 2 tables

References in corpus (10)

• The non-coplanar baselines effect in radio interferometry: The W-Projection algorithm
• On using visibility correlations to probe the HI distribution from the dark ages to the present epoch I: Formalism and the expected signal
• The multi-frequency angular power spectrum of the epoch of reionization 21 cm signal
• Power spectrum of HI intensity fluctuations in DDO 210
• A Study of ISM of Dwarf Galaxies Using HI Power Spectrum Analysis
• A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry
• Estimation of Cosmological Parameters from HI Observations of Post-reionization Epoch
• The Scale Height of NGC 1058 Measured from its HI Power Spectrum
• HI power spectrum of the spiral galaxy NGC628
• Magnetohydrodynamic turbulence in supernova remnants

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