A re-analysis of the three-year WMAP temperature power spectrum and likelihood

Abstract

We analyze the three-year WMAP temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies: On large angular scales there is a small power excess in the WMAP spectrum (5-10% at l<~30) primarily due to likelihood approximation issues between 13 <= l <~30. On small angular scales there is a systematic difference between the V- and W-band spectra (few percent at l>~300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of over-subtraction of unresolved point sources. As far as the low-l bias is concerned, most parameters are affected by a few tenths of a sigma. The most important effect is seen in n_s. For the combination of WMAP, Acbar and BOOMERanG, the significance of n_s =/ 1 drops from ~2.7 sigma to ~2.3 sigma when correcting for this bias. We propose a few simple improvements to the low-l WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise regime. Finally, we make the products from the Gibbs sampling analysis publically available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.

14 pages, 7 figures. Accepted for publication in ApJ. Numerical results unchanged, but interpretation sharpened: Likelihood approximation issues at l=13-30 far more important than potential foreground issues at l <= 12. Gibbs products (spectrum and sky samples, and "easy-to-use" likelihood module) available from http://www.astro.uio.no/~hke/ under "Research"

References in corpus (26)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• A high resolution foreground cleaned CMB map from WMAP
• Extrapolation of Galactic Dust Emission at 100 Microns to CMBR Frequencies Using FIRAS
• A Full-Sky H-alpha Template for Microwave Foreground Prediction
• Estimating the Power Spectrum of the Cosmic Microwave Background
• High Resolution Observations of the CMB Power Spectrum with ACBAR
• A Measurement of the CMB <EE> Spectrum from the 2003 Flight of BOOMERANG
• A Measurement of the Angular Power Spectrum of the CMB Temperature Anisotropy from the 2003 Flight of Boomerang
• Power Spectrum of Primordial Inhomogeneity Determined from the 4-Year COBE DMR Sky Maps
• Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling
• Power spectrum estimation from high-resolution maps by Gibbs sampling
• A Maximum Likelihood Analysis of the Low CMB Multipoles from WMAP
• A measurement of the polarization-temperature angular cross power spectrum of the Cosmic Microwave Background from the 2003 flight of BOOMERANG
• Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background
• CMB component separation by parameter estimation
• The Age of the Universe and the Cosmological Constant Determined from Cosmic Microwave Background Anisotropy Measurements
• Exact likelihood evaluations and foreground marginalization in low resolution WMAP data
• Bayesian Power Spectrum Analysis of the First-Year WMAP data
• Cosmological Parameter Constraints as Derived from the Wilkinson Microwave Anisotropy Probe Data via Gibbs Sampling and the Blackwell-Rao Estimator
• A blind estimation of the power spectrum of CMB anisotropy from WMAP
• Point-Source Power in 3 Year Wilkinson Microwave Anisotropy Probe Data
• The Angular Power Spectrum of the First-Year WMAP Data Reanalysed

Cited by in corpus (63)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters
• Planck 2013 results. XXII. Constraints on inflation
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission
• Joint Bayesian component separation and CMB power spectrum estimation
• Planck 2013 results. XII. Component separation
• Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
• Increasing evidence for hemispherical power asymmetry in the five-year WMAP data
• Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Bayesian Estimation of CMB Polarization Maps
• Measuring the Speed of Dark: Detecting Dark Energy Perturbations
• A needlet ILC analysis of WMAP 7-year data: estimation of CMB temperature map and power spectrum
• Bayesian analysis of an anisotropic universe model: systematics and polarization
• Improved Measurements of the CMB Power Spectrum with ACBAR
• Estimating the large-scale angular power spectrum in the presence of systematics: a case study of Sloan Digital Sky Survey quasars
• On Minimally-Parametric Primordial Power Spectrum Reconstruction and the Evidence for a Red Tilt
• Bayesian Calibrated Significance Levels Applied to the Spectral Tilt and Hemispherical Asymmetry
• Broken Isotropy from a Linear Modulation of the Primordial Perturbations
• Cosmic Cartography of the Large-Scale Structure with Sloan Digital Sky Survey Data Release 6
• Planck Intermediate Results. IX. Detection of the Galactic haze with Planck
• MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio
• Testing Isotropy of Cosmic Microwave Background Radiation
• Parity Asymmetry in the CMBR Temperature Power Spectrum
• CMB anisotropy power spectrum using linear combinations of WMAP maps
• The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis
• Integrated Sachs Wolfe Effect and Rees Sciama Effect
• The inflationary gravitational-wave background and measurements of the scalar spectral index
• TEASING: a fast and accurate approximation for the low multipole likelihood of the Cosmic Microwave Background temperature
• Signals of Statistical Anisotropy in WMAP Foreground-Cleaned Maps
• A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data
• Using the cluster mass function from weak lensing to constrain neutrino masses
• CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator
• Non-Gaussian gravitational clustering field statistics
• An Improved Diffuse Foreground Subtraction by ILC method: CMB Map and Angular Power Spectrum using Planck and WMAP Observations
• The effect of asymmetric beams in the Wilkinson Microwave Anisotropy Probe experiment
• Extragalactic Point Source Search in WMAP 61 and 94 GHz Data
• A multi-level solver for Gaussian constrained CMB realizations
• Lensing as a Probe of Early Universe: from CMB to Galaxies
• A Global ILC Approach in Pixel Space over Large Angular Scales of the Sky using CMB Covariance Matrix
• Analysis of WMAP 7-year Temperature Data: Astrophysics of the Galactic Haze
• Angular power spectrum of CMB anisotropy from WMAP
• Effect of Foregrounds on the CMBR Multipole Alignment
• Cosmo++: An Object-Oriented C++ Library for Cosmology
• CMB Polarization and Temperature Power Spectra Estimation using Linear Combination of WMAP 5-year Maps
• Scale dependence of the primordial spectrum from combining the three-year WMAP, Galaxy Clustering, Supernovae, and Lyman-alpha forests
• Bayesian analysis of white noise levels in the 5-year WMAP data
• Marginal distributions for cosmic variance limited CMB polarization data
• Primordial anisotropies from cosmic strings during inflation
• Galaxy Formation and Dark Matter
• Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r
• Cosmological Parameters from a re-analysis of the WMAP-7 low resolution maps
• Model Independent Foreground Power Spectrum Estimation using WMAP 5-year Data
• On the regularity of the covariance matrix of a discretized scalar field on the sphere
• Extended Delta-map: a map-based foreground removal method for CMB polarization observations
• Application of Genetic Algorithm to Estimate the Large Angular Scale Features of Cosmic Microwave Background
• A Partial-Sky Gibbs ILC Approach for the Estimation of CMB Posterior over Large Angular Scales of the Sky