CMB multipole measurements in the presence of foregrounds

Abstract

Most analysis of Cosmic Microwave Background spherical harmonic coefficients a_lm has focused on estimating the power spectrum C_l=<|a_lm|^2> rather than the coefficients themselves. We present a minimum-variance method for measuring a_lm given anisotropic noise, incomplete sky coverage and foreground contamination, and apply it to the WMAP data. Our method is shown to constitute lossless data compression in the sense that the widely used quadratic estimators of the power spectrum C_l can be computed directly from our a_lm-estimators. As the Galactic cut is increased, the error bars Delta-a_lm on low multipoles go from being dominated by foregrounds to being dominated by sample variance from other multipoles, with the intervening minimum defining the optimal cut. Applying our method to the WMAP quadrupole and octopole, we find that their previously reported "axis of evil" alignment appears to be rather robust to Galactic cut and foreground contamination.

arXiv comment3-year WMAP results added, TOH foreground-cleaned 3-year map available at http://space.mit.edu/home/tegmark/wmap.html . 15 PRD pages, 7 figs. More multipoles available electronically from the authors on request

References in corpus (91)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Cosmological parameters from SDSS and WMAP
• The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications
• Gravity, Lorentz Violation, and the Standard Model
• Cosmological parameter analysis including SDSS Ly-alpha forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• Asymmetries in the CMB anisotropy field
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• A high resolution foreground cleaned CMB map from WMAP
• The significance of the largest scale CMB fluctuations in WMAP
• The axis of evil
• Is the low-l microwave background cosmic?
• How to measure CMB power spectra without losing information
• Limits on non-Gaussianities from WMAP data
• Dark Energy Anisotropic Stress and Large Scale Structure Formation
• A method for subtracting foregrounds from multi-frequency CMB sky maps
• Testing the cosmological principle of isotropy: local power spectrum estimates of the WMAP data
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• Foregrounds and Forecasts for the Cosmic Microwave Background
• Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy?
• On the large-angle anomalies of the microwave sky
• Could dark energy be vector-like?
• On Foreground Removal from the Wilkinson Microwave Anisotropy Probe Data by an Internal Linear Combination Method: Limitations and Implications
• Radical Compression of Cosmic Microwave Background Data
• Constraining the Topology of the Universe
• Spontaneous Isotropy Breaking: A Mechanism for CMB Multipole Alignments
• Power spectrum estimation from high-resolution maps by Gibbs sampling
• Measuring Statistical isotropy of the CMB anisotropy
• Suppressing CMB Quadrupole with a Bounce from Contracting Phase to Inflation
• Non-Gaussian Signatures in the Temperature Fluctuation Observed by the Wilkinson Microwave Anisotropy Probe
• A determination of the Spectra of Galactic components observed by WMAP
• CMB mapping experiments: a designer's guide
• A Low CMB Quadrupole from Dark Energy Isocurvature Perturbations
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Beam Profiles and Window Functions
• Creation of a Compact Topologically Nontrivial Inflationary Universe
• Is the Universe odd?
• Multiple inflation and the WMAP 'glitches'
• Low-order multipole maps of CMB anisotropy derived from WMAP
• The Statistical Significance of the Low CMB Mulitipoles
• Disformal Inflation
• Cosmic Microwave Background, Accelerating Universe and Inhomogeneous Cosmology
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• Possible Explanation to Low CMB Quadrupole
• Assessing the effects of foregrounds and sky removal in WMAP
• Constraints on mode couplings and modulation of the CMB with WMAP data
• The N-point correlation functions of the first-year Wilkinson Microwave Anisotropy Probe sky maps
• Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis
• Noncommutative Inflation and the CMB Multipoles
• Mapping the large-scale anisotropy in the WMAP data
• Primordial magnetic field and non-Gaussianity of the 1-year Wilkinson Microwave Anisotropy Probe (WMAP) data
• 2-point anisotropies in WMAP and the Cosmic Quadrupole
• On Precision Measurement of the Mean Curvature
• Stochastic Inflation and the Lower Multipoles in the CMB Anisotropies
• The Multipole Vectors of WMAP, and their frames and invariants
• Template fitting and the large-angle CMB anomalies
• Asymmetric inflation: exact solutions
• An inflation model with large variations in spectral index
• Microwave sky and the local Rees-Sciama effect
• Cosmological Acceleration and Gravitational Collapse
• CMB and foregrounds in WMAP first year data
• Examining the Effect of the Map-Making Algorithm on Observed Power Asymmetry in WMAP Data
• De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter
• A First Glimpse of String Theory in the Sky?
• Analysis of the Kamionkowski-Loeb method of reducing cosmic variance with CMB polarization
• The Local Shape of the Universe in the Inflationary Limit
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• Cosmic microwave background multipole alignments in slab topologies
• No Higher Criticism of the Bianchi Corrected WMAP Data
• The CMB Quadrupole in a Polarized Light
• Constraints on the solid dark universe model
• Measuring the Three Point Correlation Function of the Cosmic Microwave Background
• What do very nearly flat detectable cosmic topologies look like?
• Second-order gravitational effects of local inhomogeneities on CMB anisotropies in nonzero-Lambda flat cosmological models
• The Amplitude of Dark Energy Perturbations
• Probing the largest scale structure in the universe with polarization map of galaxy clusters
• Cosmological Structure Evolution and CMB Anisotropies in DGP Braneworlds
• Foreground analysis from the 1-year Wilkinson Microwave Anisotropy Probe (WMAP) data
• Topological signatures in CMB temperature anisotropy maps
• The Integrated Sachs-Wolfe effect as a probe of non-standard cosmological evolution
• Scale of Homogeneity of the Universe from WMAP
• Non-Gaussian Foreground Residuals of the WMAP First Year Maps
• Relativistic Effects of our Galaxy's Motion on Circles-in-the-sky
• Discrete Spectrum of Inflationary Fluctuations
• Detectability of Cosmic Topology in Generalized Chaplygin Gas Models
• Eccentric inflation and WMAP
• Cosmological Parameters and Cosmic Topology
• Double sneutrino inflation and its phenomenologies
• The synchrotron foreground and CMB temperature-polarization cross correlation power spectrum from the first year WMAP data
• Constraints from the Detection of Cosmic Topology on the Generalized Chaplygin Gas
• Astro-ph communication: Simulations of the WMAP Internal Linear Combination sky map

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• Signals of Statistical Anisotropy in WMAP Foreground-Cleaned Maps
• Can a primordial magnetic field originate large-scale anomalies in WMAP data?
• A model-independent test for scale-dependent non-Gaussianities in the CMB
• Testing gaussianity, homogeneity and isotropy with the cosmic microwave background
• Low-l CMB Analysis and Inpainting
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• Rogues' gallery: the full freedom of the Bianchi CMB anomalies
• Statistical Anisotropy and the Vector Curvaton Paradigm
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• Direction Dependence in Supernova Data: Constraining Isotropy
• A Theory of a Spot
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• Large scale alignment anomalies of CMB anisotropies: a new test for residuals applied to WMAP 5yr maps
• CMB map derived from the WMAP data through Harmonic Internal Linear Combination
• CMB Alignment in Multi-Connected Universes
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• Hierarchical Bayesian Detection Algorithm for Early-Universe Relics in the Cosmic Microwave Background
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• Is the cold spot responsible for the CMB North-South asymmetry?
• The One-dimensional Fourier Representation and Large Angular Scale Foreground Contamination in the 3-year Wilkinson Microwave Anisotropy Probe data
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• Stable indications of relic gravitational waves in Wilkinson Microwave Anisotropy Probe data and forecasts for the Planck mission
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• Hemispherical power asymmetry: parameter estimation from CMB WMAP5 data
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• Can one reconstruct masked CMB sky?
• Real space tomography of the primordial Universe with cluster polarization
• Testing the statistical isotropy of large scale structure with multipole vectors
• High-z Supernova Type Ia Data: non-Gaussianity and Direction Dependence
• Cosmic Covariance and the Low Quadrupole Anisotropy of the Wilkinson Microwave Anisotropy Probe (WMAP) Data
• Cross-correlation analysis of CMB with foregrounds for residuals
• Modelling the WMAP large-angle anomalies as an effect of a local density inhomogeneity
• A close examination of cosmic microwave background mirror-parity after Planck
• A search for concentric rings with unusual variance in the 7-year WMAP temperature maps using a fast convolution approach
• Testing Gaussianity in the WMAP data of OT foreground reduced map
• Examining statistical isotropy of CMB low multipoles from Planck PR4 data
• CMB low multipole alignments across WMAP and \emph{Planck} data releases
• Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy