A Spherical Harmonic Analysis of the Ooty Wide Field Array (OWFA) Visibility Signal

TL;DR

This paper develops a spherical harmonic formalism to relate OWFA's measured visibilities to the sky's angular power spectrum, validating it with simulations and comparing it to flat sky approximations.

Contribution

It introduces a new spherical harmonic analysis framework for OWFA visibilities, including analytical window functions and validation against simulations.

Findings

The formalism accurately relates visibilities to the sky's multipoles.

Comparison shows the spherical harmonic approach outperforms flat sky approximation at large baselines.

The method is validated with simulations, confirming its reliability.

Abstract

Considering redshifted $21$-cm intensity mapping with the upcoming OWFA whose field of view subtends $\sim 57^{\circ}$ in the N-S direction, we present a formalism which relates the measured visibilities to the spherical harmonic coefficients of the sky signal. We use this to calculate window functions which relate the two-visibility correlations {\it i.e.} the correlation between the visibilities measured at two baselines and two frequencies, to different multipoles of the multi-frequency angular power spectrum $C_{\ell}(\nu_1,\nu_2)$. The formalism here is validated using simulations. We also present approximate closed form analytical expressions which can be used to calculate the window functions. Comparing the widely adopted flat sky approximation, we find that its predictions match those of our spherical harmonic formalism to within $16 \%$ across the entire OWFA baseline range. The match improves at large baselines where we have $< 5 \%$ deviations.