Quadratic estimator for CMB cross-correlation

Abstract

The Quadratic Maximum Likelihood estimator can be used to reconstruct the Cosmic Microwave Background (CMB) power spectra with minimal error bars. Still, it requires an accurate estimate of the datasets noise covariance matrix in order to be corrected for spurious bias. We describe an extension of this method to cross-correlation, thus removing noise bias and mitigating the impact of systematic effects, providing they are uncorrelated. This estimator is tested on two simulation surveys at large and intermediate angular scales, respectively corresponding to satellite and ground-based CMB experiments. The analysis focuses on polarization maps, over a wide range of noise levels from 0.1 to 50 muK.arcmin. We show how this estimator minimizes the increase of variance due to polarization leakage between E and B modes. We compare this method with the pure pseudo-spectrum formalism which is computationally faster but less optimal, especially on large angular scales.

arXiv comment12 pages, 11 figures. Xpure (pixel optimisation for pure pCl) analysis added. The code is available on GitLab: https://gitlab.in2p3.fr/xQML

References in corpus (33)

• Planck 2015 results. XIII. Cosmological parameters
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Quintessence and the Rest of the World
• Wilkinson Microwave Anisotropy Probe (WMAP) First Year Observations: TE Polarization
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Cosmological Signature of New Parity-Violating Interactions
• Mission design of LiteBIRD
• Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth
• How to measure CMB power spectra without losing information
• Likelihood Analysis of CMB Temperature and Polarization Power Spectra
• Fast estimation of polarization power spectra using correlation functions
• Planck intermediate results. XLVII. Planck constraints on reionization history
• Myths and Truths Concerning Estimation of Power Spectra
• Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field
• Benchmark Parameters for CMB Polarization Experiments
• E/B decomposition of finite pixelized CMB maps
• How to measure CMB polarization power spectra without losing information
• The Cosmic Microwave Background and Helical Magnetic Fields: the tensor mode
• Exploring Cosmic Origins with CORE: Survey requirements and mission design
• Effects of Cosmological Magnetic Helicity on the Cosmic Microwave Background
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
• A general solution to the E-B mixing problem
• Faraday Rotation of the Cosmic Microwave Background Polarization and Primordial Magnetic Field Properties
• Signatures of kinetic and magnetic helicity in the CMBR
• Hybrid Estimation of CMB Polarization Power Spectra
• Harmonic E/B decomposition for CMB polarization maps
• Large-scale CMB temperature and polarization cross-spectra likelihoods
• Primordial B-mode Diagnostics and Self Calibrating the CMB Polarization
• CMB EB and TB cross-spectrum estimation via pseudo-spectrum techniques
• A comparison of CMB Angular Power Spectrum Estimators at Large Scales: the TT case
• Separating E from B
• Prospects for next generation Cosmic Microwave Background experiments

Cited by in corpus (17)

• A unified pseudo-$C_{\ell }$ framework
• Planck intermediate results. LVII. Joint Planck LFI and HFI data processing
• Cosmological parameters derived from the final (PR4) Planck data release
• Planck constraints on the tensor-to-scalar ratio
• Reionization optical depth determination from Planck HFI data with ten percent accuracy
• CMB spectral distortions revisited: a new take on $\mu$ distortions and primordial non-Gaussianities from FIRAS data
• Planck constraints on cross-correlations between anisotropic cosmic birefringence and CMB polarization
• Likelihood methods for CMB experiments
• LiteBIRD Science Goals and Forecasts. A Case Study of the Origin of Primordial Gravitational Waves using Large-Scale CMB Polarization
• ECLIPSE: a fast Quadratic Maximum Likelihood estimator for CMB intensity and polarization power spectra
• Testing CMB Anomalies in E-mode Polarization with Current and Future Data
• Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum
• Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum
• Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys
• Unraveling the CMB lack-of-correlation anomaly with the cosmological gravitational wave background
• Constraints on primordial non-Gaussianity from Quaia
• Modeling optical systematics for the Taurus CMB experiment