Accounting for Noise and Singularities in Bayesian Calibration Methods for Global 21-cm Cosmology Experiments

Abstract

Due to the large dynamic ranges involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper we present three methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalisation to characterise a low noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalising the noise. The second method fits polynomials to the noise wave parameters by marginalising over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalised polynomial method. Running these methods on a suite of simulated datasets based on the REACH receiver design and a lab dataset, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an analytic estimate of the calibrator's noise. We find in the case of the measured lab dataset the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5% of the noise floor.

9 pages, 5 figures

References in corpus (35)

• Cosmology at Low Frequencies: The 21 cm Transition and the High-Redshift Universe
• An absorption profile centred at 78 megahertz in the sky-averaged spectrum
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• Enhanced global signal of neutral hydrogen due to excess radiation at cosmic dawn
• Concerns about Modelling of the EDGES Data
• Constraining the unexplored period between reionization and the dark ages with observations of the global 21 cm signal
• Design and characterization of the Large-Aperture Experiment to Detect the Dark Age (LEDA) radiometer systems
• Testing for calibration systematics in the EDGES low-band data using Bayesian model selection
• Too Hot, Too Cold or Just Right? Implications of a 21-cm Signal for Dark Matter Annihilation and Decay
• The redshifted 21-cm signal in the EDGES low-band spectrum
• Toward Empirical Constraints on the Global Redshifted 21 cm Brightness Temperature During the Epoch of Reionization
• Results from EDGES High-Band: I. Constraints on Phenomenological Models for the Global $21$ cm Signal
• Constraining Primordial Black Holes with the EDGES 21-cm Absorption Signal
• The REACH radiometer for detecting the 21-cm hydrogen signal from redshift 7.5 to 28
• SARAS 2: A Spectral Radiometer for probing Cosmic Dawn and the Epoch of Reionization through detection of the global 21 cm signal
• Calibration of the EDGES High-Band Receiver to Observe the Global 21-cm Signature from the Epoch of Reionization
• Absolute calibration of a wideband antenna and spectrometer for sky noise spectral index measurements
• Bayesian model selection without evidences: application to the dark energy equation-of-state
• Results from EDGES High-Band: III. New Constraints on Parameters of the Early Universe
• Astrophysical Constraints from the SARAS3 non-detection of the Cosmic Dawn Sky-Averaged 21-cm Signal
• SARAS 3 CD/EoR Radiometer: Design and Performance of the Receiver
• Results from EDGES High-Band: II. Constraints on Parameters of Early Galaxies
• Bayesian noise wave calibration for 21-cm global experiments
• A Bayesian Calibration Framework for EDGES
• Global 21-cm signal extraction from foreground and instrumental effects IV: Accounting for realistic instrument uncertainties and their overlap with foreground and signal models
• Bayesian Data Analysis for Sky-averaged 21-cm Experiments in the Presence of Ionospheric Effects
• The effects of the antenna power pattern uncertainty within a global 21 cm experiment
• Bayesian evidence-driven diagnosis of instrumental systematics for sky-averaged 21-cm cosmology experiments
• Calibration Error in 21-centimeter Global Spectrum Experiments
• Receiver design for the REACH global 21-cm signal experiment
• Measuring Noise Parameters Using an Open, Short, Load, and 1/8-wavelength Cable as Source Impedances
• A Bayesian Method to Mitigate the Effects of Unmodelled Time-Varying Systematics for 21-cm Cosmology Experiments
• Modelling a Hot Horizon in Global 21 cm Experimental Foregrounds
• A new technique to measure noise parameters for global 21-cm experiments

Cited by in corpus (3)

• Rapid and Late Cosmic Reionization Driven by Massive Galaxies: a Joint Analysis of Constraints from 21-cm, Lyman Line & CMB Data Sets
• The magnitude of the dark ages 21-cm signal in the context of existing early and late time constraints on $\Lambda$CDM
• Capturing System Drift with Time Series Calibration for Global 21-cm Cosmology Experiments