The Role of the Instrumental Response in 21 cm EoR Power Spectrum Gridding Analyses

Abstract

Reconstruction of the sky brightness measured by radio interferometers is typically achieved through gridding techniques, or histograms in spatial Fourier space. For Epoch of Reionisation (EoR) 21 cm power spectrum measurements, extreme levels of gridding resolution are required to reduce spectral contamination, as explored in other works. However, the role of the shape of the Fourier space spreading function, or kernel, also has consequences in reconstructed power spectra. We decompose the instrumental Murchison Widefield Array (MWA) beam into a series of Gaussians and simulate the effects of finite kernel extents and differing shapes in gridding/degridding for optimal map making analyses. For the MWA, we find that the kernel must extend out to 0.001--0.0001% of the maximum value in order to measure the EoR using foreground avoidance. This requirement changes depending on beam shape, with compact kernels requiring far smaller extents for similar contamination levels at the cost of less-optimal errors. However, simple calibration using pixelated degridding results, regardless of shape of the kernel, cannot recover the EoR due to catastrophic errors caused by the pixel resolution. Including an opaque horizon with widefield beams also causes significant spectral contamination via a beam--horizon interaction that creates an infinitely extended kernel in Fourier space, which cannot be represented well. Thus, our results indicate that simple calibration via degridded models and optimal map making for extreme widefield instrumentation are not feasible.

arXiv commentAccepted in ApJ. 16 pages, 6 figures

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• Direct Optimal Mapping for 21cm Cosmology: A Demonstration with the Hydrogen Epoch of Reionization Array
• Multi-frequency angular power spectrum of the 21~cm signal from the Epoch of Reionisation using the Murchison Widefield Array
• Aliasing from Galactic Plane Setting in Widefield Radio Interferometry
• The impact of lunar topography on the 21-cm power spectrum for grid-based arrays : Insights for the Dark-ages EXplorer (DEX)