Beyond the horizon: Quantifying the full sky foreground wedge in the cylindrical power spectrum

Abstract

One of the main obstacles preventing the detection of the redshifted 21-cm signal from neutral hydrogen in the early Universe is the astrophysical foreground emission, which is several orders of magnitude brighter than the signal. The foregrounds, due to their smooth spectra, are expected to predominantly occupy a region in the cylindrical power spectrum known as the foreground wedge. However, the conventional equations describing the extent of the foreground wedge are derived under a flat-sky approximation. This assumption breaks down for tracking wide-field instruments, thus rendering these equations inapplicable in these situations. In this paper, we derive equations for the full sky foreground wedge and show that the foregrounds can potentially extend far beyond what the conventional equations suggest. We also derive the equations that describe a specific bright source in the cylindrical power spectrum space. The validity of both sets of equations is tested against numerical simulations. Many current and upcoming interferometers (e.g., LOFAR, NenuFAR, MWA, SKA) are wide-field phase-tracking instruments. These equations give us new insights into the nature of foreground contamination in the cylindrical power spectra estimated using wide-field instruments. Additionally, they allow us to accurately associate features in the power spectrum to foregrounds or instrumental effects. The equations are also important for correctly selecting the "EoR window" for foreground avoidance analyses, and for planning 21-cm observations. In future analyses, it is recommended to use these updated horizon lines to indicate the foreground wedge in the cylindrical power spectrum accurately. The new equations for generating the updated wedge lines are made available in a Python library, pslines.

20 pages, 13 figures, and 2 tables; accepted for publication in Astronomy and Astrophysics (A&A)

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• Improved upper limits on the 21-cm signal power spectrum at $z=17.0$ and $z=20.3$ from an optimal field observed with NenuFAR
• Spectral modelling of Cygnus A between 110 and 250 MHz. Impact on the LOFAR 21-cm signal power spectrum
• Near-field imaging of local interference in radio interferometric data: Impact on the redshifted 21 cm power spectrum
• Detecting galaxy-21-cm cross-correlation during reionization
• First upper limits on the 21-cm signal power spectrum of neutral hydrogen at $z=9.16$ from the LOFAR 3C196 field
• Robust direction-dependent gain-calibration of beam-modelling errors far from the target field
• Separating Angular and Radial Modes with Spherical-Fourier Bessel Power Spectrum on All Scales and Implications for Systematics Mitigation
• Extracting the Epoch of Reionization Signal with 3D U-Net Neural Networks Using Data-driven Systematic Effect Model
• The impact of lunar topography on the 21-cm power spectrum for grid-based arrays : Insights for the Dark-ages EXplorer (DEX)
• Mitigating incoherent excess variance in high-redshift 21 cm observations with multi-output cross-Gaussian process regression
• Seeing Wiggles without Seeing Wiggles: BAO Recovery in 21 cm Intensity Mapping with Deep Learning