FiveYear Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Bayesian Estimation of Cosmic Microwave Background Polarization Maps
Abstract
We describe a sampling method to estimate the polarized cosmic microwave background (CMB) signal from observed maps of the sky. We use a MetropoliswithinGibbs algorithm to estimate the polarized CMB map, containing Q and U Stokes parameters at each pixel, and its covariance matrix. These can be used as inputs for cosmological analyses. The polarized sky signal is parameterized as the sum of three components: CMB, synchrotron emission, and thermal dust emission. The polarized Galactic components are modeled with spatially varying powerlaw spectral indices for the synchrotron, and a fixed power law for the dust, and their component maps are estimated as byproducts. We apply the method to simulated lowresolution maps with pixels of side 7.2 deg, using diagonal and full noise realizations drawn from the WMAP noise matrices. The CMB maps are recovered with goodness of fit consistent with errors. Computing the likelihood of the Emode power in the maps as a function of optical depth to reionization, τ, for fixed temperature anisotropy power, we recover τ = 0.091 ± 0.019 for a simulation with input τ = 0.1, and mean τ = 0.098 averaged over 10 simulations. A "null" simulation with no polarized CMB signal has maximum likelihood consistent with τ = 0. The method is applied to the fiveyear WMAP data, using the K, Ka, Q, and V channels. We find τ = 0.090 ± 0.019, compared to τ = 0.086 ± 0.016 from the templatecleaned maps used in the primary WMAP analysis. The synchrotron spectral index, β, averaged over high signaltonoise pixels with standard deviation σ(β) < 0.25, but excluding ~6% of the sky masked in the Galactic plane, is 3.03 ± 0.04. This estimate does not vary significantly with Galactic latitude, although includes an informative prior.
WMAP is the result of a partnership between Princeton University and NASA's Goddard Space Flight Center. Scientific guidance is provided by the WMAP Science Team.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 2009
 DOI:
 10.1088/0004637X/701/2/1804
 arXiv:
 arXiv:0811.4280
 Bibcode:
 2009ApJ...701.1804D
 Keywords:

 cosmic microwave background;
 cosmology: observations;
 methods: statistical;
 polarization;
 radio continuum: ISM;
 Astrophysics
 EPrint:
 11 pages, 9 figures, matches version accepted by ApJ