A Bayesian approach to modelling spectrometer data chromaticity corrected using beam factors -- I. Mathematical formalism

Abstract

Accurately accounting for spectral structure in spectrometer data induced by instrumental chromaticity on scales relevant for detection of the 21-cm signal is among the most significant challenges in global 21-cm signal analysis. In the publicly available EDGES low-band data set, this complicating structure is suppressed using beam-factor based chromaticity correction (BFCC), which works by dividing the data by a sky-map-weighted model of the spectral structure of the instrument beam. Several analyses of this data have employed models that start with the assumption that this correction is complete. However, while BFCC mitigates the impact of instrumental chromaticity on the data, given realistic assumptions regarding the spectral structure of the foregrounds, the correction is only partial. This complicates the interpretation of fits to the data with intrinsic sky models (models that assume no instrumental contribution to the spectral structure of the data). In this paper, we derive a BFCC data model from an analytic treatment of BFCC and demonstrate using simulated observations that, in contrast to using an intrinsic sky model for the data, the BFCC data model enables unbiased recovery of a simulated global 21-cm signal from beam-factor chromaticity corrected data in the limit that the data is corrected with an error-free beam-factor model.

26 pages, 8 figures; accepted for publication in MNRAS

References in corpus (16)

• PolyChord: nested sampling for cosmology
• Signature of Excess Radio Background in the 21-cm Global Signal and Power Spectrum
• Testing for calibration systematics in the EDGES low-band data using Bayesian model selection
• Results from EDGES High-Band: I. Constraints on Phenomenological Models for the Global $21$ cm Signal
• The REACH radiometer for detecting the 21-cm hydrogen signal from redshift 7.5 to 28
• Improved Measurement of the Spectral Index of the Diffuse Radio Background Between 90 and 190 MHz
• Spectral Index of the Diffuse Radio Background Between 50 and 100 MHz
• Astrophysical Constraints from the SARAS3 non-detection of the Cosmic Dawn Sky-Averaged 21-cm Signal
• Quantifying Ionospheric Effects on Global 21-cm Observations
• Formulating and critically examining the assumptions of global 21-cm signal analyses: How to avoid the false troughs that can appear in single spectrum fits
• Radiometric Measurements of Electron Temperature and Opacity of Ionospheric Perturbations
• Use of Time Dependent Data in Bayesian Global 21cm Foreground and Signal Modelling
• Contamination of the Epoch of Reionization power spectrum in the presence of foregrounds
• Global 21-cm signal extraction from foreground and instrumental effects III: Utilizing drift-scan time dependence and full Stokes measurements
• A Bayesian Calibration Framework for EDGES
• Analytic approximations of scattering effects on beam chromaticity in 21-cm global experiments

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• The EDGES measurement disfavors an excess radio background during the cosmic dawn
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• Rapid and Late Cosmic Reionization Driven by Massive Galaxies: a Joint Analysis of Constraints from 21-cm, Lyman Line & CMB Data Sets
• STARFIRE: An algorithm for estimating radio frequency interference in orbits around Earth
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• A general Bayesian model-validation framework based on null-test evidence ratios, with an example application to global 21-cm cosmology
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