Non-parametric maximum likelihood component separation for CMB polarization data

Abstract

Mitigation of the impact of foreground contributions to measurements of Cosmic Microwave Background (CMB) polarization is a crucial step in modern CMB data analysis and is of particular importance for a detection of large-scale CMB $B$ modes. A large variety of techniques, based on different assumptions and aiming at either a full component separation or merely cleaning the foreground signals from the CMB maps, have been described in the literature. In this work, we consider this problem within a unified framework based on the maximum likelihood principle, under the assumption that the signal at each frequency can be represented as a linear mixture of sky templates. We discuss the impact of various additional assumptions on the final outcome of the procedure. We find that the component separation problem can be fully solved in two specific situations: when we either know the frequency scaling of all the components or can correctly model them with a limited number of unknown parameters, as is the case in the parametric component separation techniques; or when we either know the statistical properties of all the components, the foregrounds and CMB, or can correctly model them with a limited number of parameters, as for instance in SMICA-like approaches. However, we also show that much less stringent assumptions are sufficient if we only aim at recovering the cleaned CMB signal. In particular, we discuss a ``minimally informed'' non-parametric method based on maximum likelihood. The method only assumes that the component properties are independent on the sky direction, at least over some region of the sky, and that the CMB covariance is known up to some limited number of parameters. We apply this method to recover the CMB $B$ modes polarization signal in the context of forthcoming CMB experiments and compare its performance with that of the standard parametric... (abridged)

References in corpus (25)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• The Simons Observatory: Science goals and forecasts
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Planck 2018 results. IV. Diffuse component separation
• Joint Bayesian component separation and CMB power spectrum estimation
• On Foreground Removal from the Wilkinson Microwave Anisotropy Probe Data by an Internal Linear Combination Method: Limitations and Implications
• The Python Sky Model: software for simulating the Galactic microwave sky
• Separation of anomalous and synchrotron emissions using WMAP polarization data
• CMB component separation by parameter estimation
• Maximum Likelihood algorithm for parametric component separation in CMB experiments
• A needlet ILC analysis of WMAP 7-year data: estimation of CMB temperature map and power spectrum
• Modeling Thermal Dust Emission with Two Components: Application to the Planck HFI Maps
• Sensitivity and foreground modelling for large-scale CMB B-mode polarization satellite missions
• Simple foreground cleaning algorithm for detecting primordial B-mode polarization of the cosmic microwave background
• Characterization of foreground emission at degree angular scale for CMB B-modes observations. Thermal Dust and Synchrotron signal from Planck and WMAP data
• Forecasting performance of CMB experiments in the presence of complex foreground contaminations
• Evidence for Line-of-Sight Frequency Decorrelation of Polarized Dust Emission in $Planck$ Data
• Impact of Galactic polarized emission on B-mode detection at low multipoles
• BeyondPlanck III. Commander3
• Characterizing bias on large scale CMB $B$-modes after galactic foregrounds cleaning
• On the Detection of CMB B-modes from Ground at Low Frequency
• Semi-blind Bayesian inference of CMB map and power spectrum
• A Statistical Analysis of the "Internal Linear Combination" Method in Problems of Signal Separation as in CMB Observations
• Constraints on the Optical Depth to Reionization from Balloon-Borne CMB Measurements

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