Three‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Polarization Analysis

Abstract

The Wilkinson Microwave Anisotropy Probe ( WMAP ) has mapped the entire sky in five frequency bands between 23 and 94 GHz with polarization-sensitive radiometers. We present 3 year full-sky maps of the polarization and analyze them for foreground emission and cosmological implications. These observations open up a new window for understanding how the universe began and help set a foundation for future observations. WMAP observes significant levels of polarized foreground emission due to both Galactic synchrotron radiation and thermal dust emission. Synchrotron radiation is the dominant signal at l < 50 and ν ≲ 40 GHz, while thermal dust emission is evident at 94 GHz. The least contaminated channel is at 61 GHz. We present a model of polarized foreground emission that captures the large angular scale characteristics of the microwave sky. After applying a Galactic mask that cuts 25.7% of the sky, we show that the high Galactic latitude rms polarized foreground emission, averaged over l = 4-6, ranges from ≈5 μK at 22 GHz to ≲0.6 μK at 61 GHz. By comparison, the levels of intrinsic CMB polarization for a ΛCDM model with an optical depth of τ = 0.09 and assumed tensor-to-scalar ratio r = 0.3 are ≈0.3 μK for E-mode polarization and ≈0.1 μK for B-mode polarization. To analyze the maps for CMB polarization at l < 16, we subtract a model of the foreground emission that is based primarily on a scaling WMAP 's 23 GHz map. In the foreground-corrected maps, we detect l ( l + 1) C /2π = 0.086 ± 0.029 (μK) 2 . This is interpreted as the result of rescattering of the CMB by free electrons released during reionization at z r = 10.9 for a model with instantaneous reionization. By computing the likelihood of just the EE data as a function of τ we find τ = 0.10 ± 0.03. When the same EE data are used in the full six-parameter fit to all WMAP data (TT, TE, EE), we find τ = 0.09 ± 0.03. Marginalization over the foreground subtraction affects this value by δτ < 0.01. We see no evidence for B modes, limiting them to l ( l + 1) C /2π = -0.04 ± 0.03 (μK) 2 . We perform a template fit to the E-mode and B-mode data with an approximate model for the tensor scalar ratio. We find that the limit from the polarization signals alone is r < 2.2 (95% CL), where r is evaluated at k = 0.002 Mpc -1 . This corresponds to a limit on the cosmic density of gravitational waves of Ω GW h 2 < 5 × 10 -12 . From the full WMAP analysis, we find r < 0.55 (95% CL) corresponding to a limit of Ω GW h 2 < 1 × 10 -12 (95% CL). The limit on r is approaching the upper bound of predictions for some of the simplest models of inflation, r ~ 0.3.