Kavli Affiliate: Jacqueline N. Hewitt
| First 5 Authors: Adélie Gorce, Samskruthi Ganjam, Adrian Liu, Steven G. Murray, Zara Abdurashidova
| Summary:
Combining the visibilities measured by an interferometer to form a
cosmological power spectrum is a complicated process in which the window
functions play a crucial role. In a delay-based analysis, the mapping between
instrumental space, made of per-baseline delay spectra, 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 spectrum measured by an
interferometer, we assess the impact of instrument characteristics and analysis
choices on the estimator by deriving its exact window functions, outside of the
delay approximation. Focusing on HERA as a case study, we find that
observations made with long baselines tend to correspond to enhanced low-k
tails of the window functions, which facilitate foreground leakage outside the
wedge, whilst the choice of bandwidth and frequency taper can help narrow them
down. With the help of simple test cases and more realistic visibility
simulations, we show that, apart from tracing mode mixing, the window functions
can accurately reconstruct the power spectrum estimator of simulated
visibilities. We note that the window functions depend strongly on the
chromaticity of the beam, 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 in this
work 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 can be used in future analyses to confront theoretical models
and data directly in cylindrical space.
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