Impact of instrument and data characteristics in the interferometric reconstruction of the 21 cm power spectrum

TL;DR

This paper analyzes how instrument and data choices affect the interferometric measurement of the 21 cm power spectrum, emphasizing window functions' role in reconstructing the signal and managing foreground leakage.

Contribution

It provides a detailed assessment of window functions in interferometric 21 cm cosmology, highlighting their dependence on instrument characteristics and analysis parameters, with practical implications for HERA.

Findings

Long-baseline observations increase low-k tails, facilitating foreground leakage.

Bandwidth and frequency taper choices can reduce window function tails.

Window functions enable accurate power spectrum reconstruction in simulations.

Abstract

Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process. In a delay-based analysis, the mapping between instrumental and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on these window functions. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that long-baseline observations correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage, whilst an informed choice of bandwidth and frequency taper can reduce said tails. With simple test cases and realistic simulations, we show that, apart from tracing mode mixing, the window functions help accurately reconstruct the power spectrum estimator of simulated visibilities. The window functions depend strongly on the beam chromaticity, and less on its spatial structure - a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low-k power to avoid foreground leakage. The window functions presented here correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and will be used in future analyses to confront theoretical models and data directly in cylindrical space.