Bayes-SCF: A Bayesian filter to mitigate foreground leakage in the 21-cm power spectrum

Abstract

Missing channels in radio-interferometric visibility data can introduce systematic artefacts into the estimated 21-cm power spectrum. A common workaround is to first estimate the two-frequency correlation $C(\Delta \nu )$ and then Fourier-transform it to obtain the power spectrum $P(k_{\parallel })$. This procedure yields an unbiased estimate when the signal is statistically homogeneous (ergodic) along the line-of-sight, but it fails in the presence of non-ergodic foregrounds. Smooth Component Filtering (SCF) has recently been proposed as a solution to this problem, in which the dominant non-ergodic (spectrally smooth) component is removed prior to estimating $C(\Delta \nu )$. In existing implementations, the smooth component is estimated by convolving the visibilities with a Hann window along the frequency axis. We demonstrate that this Hann-based SCF performs adequately only when foregrounds are extremely spectrally smooth. It breaks down with increased flagging and when foregrounds exhibit spectral structures. We introduce a Bayesian extension, Bayes-SCF, based on Gaussian Process regression, which overcomes these limitations. Bayes-SCF models the smooth component via a covariance function with a fixed correlation length, enabling controlled and data-driven filtering. Using simulated data, we show that Bayes-SCF robustly recovers the input model 21-cm power spectrum in the presence of spectrally unsmooth foregrounds. The filter is demonstrated to work under different flagging patterns, including $80\%$ channels being randomly flagged. Bayes-SCF is also effective in a delay-spectrum approach. The primary trade-off introduced by the Bayesian framework is the increased computational cost; future work will focus on optimizing the algorithm and applying it to real Murchison Widefield Array data.

Accepted for publication in MNRAS. 22 pages, 25 figures, including appendices. The Bayes-SCF code is available at https://github.com/aecosmo/Bayes-SCF

References in corpus (19)

• Improved upper limits on the 21-cm signal power spectrum of neutral hydrogen at $\mathbf{z}\approx 9.1$ from LOFAR
• The Epoch of Reionization Window: I. Mathematical Formalism
• Deep multi-redshift limits on Epoch of Reionisation 21cm Power Spectra from Four Seasons of Murchison Widefield Array Observations
• The CMBR fluctuations from HI perturbations prior to reionization
• On using visibility correlations to probe the HI distribution from the dark ages to the present epoch I: Formalism and the expected signal
• Foregrounds for redshifted 21 cm studies of reionization: GMRT 153 MHz observations
• The multi-frequency angular power spectrum of the epoch of reionization 21 cm signal
• Characterizing Foreground for redshifted 21-cm radiation: 150 MHz GMRT observations
• The FHD/$\mathbf{\epsilon }$ppsilon Epoch of Reionization Power Spectrum Pipeline
• A Digital-Receiver for the Murchison Widefield Array
• A Tapered Gridded Estimator (TGE) for the Multi-Frequency Angular Power Spectrum (MAPS) and the Cosmological HI 21-cm Power Spectrum
• Statistical recovery of 21cm visibilities and their power spectra with Gaussian constrained realisations and Gibbs sampling
• Towards 21-cm Intensity Mapping at $z=2.28$ with uGMRT using the Tapered Gridded Estimator I: Foreground Avoidance
• Hydrogen intensity mapping with MeerKAT: Preserving cosmological signal by optimising contaminant separation
• The Tracking Tapered Gridded Estimator for the 21-cm power spectrum from MWA drift scan observations I: Validation and preliminary results
• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator III: Foreground removal
• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator -- IV. Wideband analysis
• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator II: Cross-polarization power spectrum
• Determining Ideal Fields for Epoch of Reionisation Science Using the 21 cm Line