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

TL;DR

The paper presents the three-year Wilkinson Microwave Anisotropy Probe (WMAP) polarization analysis, delivering full-sky polarization maps across five frequency bands and a foreground-modeling framework to separate Galactic emission from the CMB. By extending mapmaking to include intricate instrument systematics, and applying joint TT–E–B power-spectrum analyses with precise foreground templates, the study robustly detects low-ℓ E-mode polarization tied to reionization and places upper limits on primordial gravitational waves. Foreground subtraction via KD3Pol and masking enables a credible measurement of the EE spectrum at $\ell\lesssim 10$, yielding $\tau ≈ 0.089 \pm 0.030$, while BB remains undetected with $\mathcal{B}_\ell^{BB}$ consistent with zero; tensor-to-scalar limits improve when TT data are included, constraining $r < 0.55$ (95% CL). The work demonstrates the critical role of Galactic foreground modeling in CMB polarization and sets the stage for future, more sensitive searches for B-mode signals in the early universe.

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 three-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 the universe. WMAP observes significant levels of polarized foreground emission due to both Galactic synchrotron radiation and thermal dust emission. The least contaminated channel is at 61 GHz. Informed by a model of the Galactic foreground emission, we subtract the foreground emission from the maps. In the foreground corrected maps, for l=2-6, we detect l(l+1) C_l^{EE} / (2 pi) = 0.086 +-0.029 microkelvin^2. This is interpreted as the result of rescattering of the CMB by free electrons released during reionization and corresponds to an optical depth of tau = 0.10 +- 0.03. We see no evidence for B-modes, limiting them to l(l+1) C_l^{BB} / (2 pi) = -0.04 +- 0.03 microkelvin^2. We find that the limit from the polarization signals alone is r<2.2 (95% CL) corresponding to a limit on the cosmic density of gravitational waves of Omega_{GW}h^2 < 5 times 10^{-12}. From the full WMAP analysis, we find r<0.55 (95% CL) corresponding to a limit of Omega_{GW}h^2 < 10^{-12} (95% CL).

Figures (28)

• Figure 1: A model of the ionization history of the universe. The line marked "x" is the ionization fraction, $x=n_e/n$ where $n_e$ is the number of electrons and $n=11.2\omega_b(1+z)^3~{\rm m^{-3}}$ is the number of protons with $\omega_b$ the baryon density. From quasar absorption systems we know the universe has been fully ionized since at least $z\approx6$. Between $6\la z\la30$ the first generation of stars ionized the universe. We show a possible model inspired by holder/etal:2003. The history for this period is uncertain though the reionization produces a characteristic signature in the CMB polarization. For $30<z<2000$, we show decoupling as described in peebles:POPC. The line marked $\tau$ is the net optical depth, $\tau(z)$. The dashed curves are the integrands in the numerator (bottom) and denominator (top) of equation \ref{['eq:ih']} (divided by 200) for the $100<z<2000$ region. By eye, one can see that the ratio of the integrals at the maximum, and thus the fractional polarization, is $\approx5$%. The vertical line marks the redshift of decoupling, $z_{dec}=1088$, at the maximum of the visibility function (not shown).
• Figure 2: Top: Map of Tau A in Galactic coordinates at 41 GHz in Stokes $I$, $Q$, $U$, $P$, smoothed to $1^{\circ}$. Since Tau A is polarized parallel to the Galactic plane it is negative in $Q$ and small in $U$. Bottom: Map of Centaurus A in Stokes $I$, $Q$, $U$, and $P$. For both sets of plots, Stokes $I$ is scaled logarithmically and all the others are scaled linearly. The scaling in mK is indicated above the grayscale wedge for each panel. A map of the noise bias has been subtracted from the P images.
• Figure 3: P and $\gamma$ maps for K, Ka, and Q bands in Galactic coordinates. See bennett/etal:2003 for features and coordinates. There is only one polarization map for K and Ka bands. For Q band, there are two maps which have been coadded. The maps are smoothed to $2^{\circ}$. The polarization vectors are plotted whenever a r4 HEALPix pixel (see §\ref{['sec:mask']}, roughly $4\deg\times4\deg$) and three of its neighbors has a signal to noise (P/N) greater than unity. The length of the arrow is logarithmically dependent on the magnitude of $P$. Note that $P$ is positive. Maps of the noise bias have been subtracted in these images.
• Figure 4: Similar to Figure \ref{['fig:pgmaps1']} but for V and W bands. The two V-band maps have been coadded as have the four W-band maps. The relatively higher noise in the ecliptic plane is evident. Maps of the noise bias have been subtracted in these images.
• Figure 5: A Lambert azimuthal equal area projection of the Galactic poles ( left: north) showing the K-band polarization. The circumference of each map is at zero Galactic latitude. The convention in this plot is to use bars to indicate the polarization direction. It is clear that the polarization extends to high Galactic latitudes. A map of the noise bias is subtracted from this image.