Wilkinson Microwave Anisotropy Probe (WMAP) First Year Observations: TE Polarization

TL;DR

This work analyzes WMAP one-year polarization data to characterize TE correlations using three independent TE estimators (two-point correlation, quadratic estimator, and pixel-space templates) and foreground separation across five bands. The TE signal on degree scales agrees with adiabatic CMB predictions with no free parameters, while a pronounced large-scale excess points to reionization, yielding an optical depth around tau ~ 0.16–0.17. A model-independent estimate corroborates the Lambda-CDM result, reinforcing that the observed TE imprint reflects an extended and complex ionization history rather than a single instantaneous event. The results highlight early reionization as a key feature of cosmic history and demonstrate robust foreground handling, setting the stage for future full-sky polarization maps and spectra.

Abstract

The Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the full sky in Stokes I, Q, and U parameters at frequencies 23, 33, 41, 61, and 94 GHz. We detect correlations between the temperature and polarization maps significant at more than 10 standard deviations. The correlations are present in all WMAP frequency bands with similar amplitude from 23 to 94 GHz, and are consistent with a superposition of a CMB signal with a weak foreground. The fitted CMB component is robust against different data combinations and fitting techniques. On small angular scales theta < 5 deg, the WMAP data show the temperature-polarization correlation expected from adiabatic perturbations in the temperature power spectrum. The data for l > 20 agree well with the signal predicted solely from the temperature power spectra, with no additional free parameters. We detect excess power on large angular scales (theta > 10 deg) compared to predictions based on the temperature power spectra alone. The excess power is well described by reionization at redshift 11 < z_r < 30 at 95% confidence, depending on the ionization history. A model-independent fit to reionization optical depth yields results consistent with the best-fit LambdaCDM model, with best fit value tau = 0.17 +- 0.04 at 68% confidence, including systematic and foreground uncertainties. This value is larger than expected given the detection of a Gunn-Peterson trough in the absorption spectra of distant quasars, and implies that the universe has a complex ionization history: WMAP has detected the signal from an early epoch of reionization.

Figures (9)

• Figure 1: Geometry for Stokes $Q$ and $U$ parameters. WMAP measures polarization by differencing two orthogonal polarization channels, then solving for $Q$ and $U$ as the spacecraft compound spin projects the OMT onto the sky at different angles $\gamma$ relative to the Galactic meridians. All analysis uses coordinate-independent quantities $Q^\prime$ and $U^\prime$ defined with respect to the great circle connecting a pair of pixels (see text).
• Figure 2: Temperature-polarization correlation function for WMAP co-added QVW data. The gray band shows the 68% confidence interval for similar co-added data taken from Monte Carlo simulations without polarization. The inset shows data for $\theta < 10\arcdeg$. The data are inconsistent with no temperature-polarization cross-correlations at more than 10 standard deviations. Note that the data are not independent between angular bins.
• Figure 3: Angular templates for potential systematic errors caused by bandpass mismatch between the 2 radiometers in each differencing assembly. We fit this template to the correlation functions from each DA to detect or limit systematic errors related to bandpass mismatch in the main beam. The effect is significant only in K and Ka bands, which have the brightest unpolarized foregrounds.
• Figure 4: Fitted CMB (left) and foreground (right) components from a multi-frequency decomposition of the measured two-point correlation functions. Top panels show the IQ (TE) correlation, while bottom panels show IU (TB). The CMB component is shown in units of thermodynamic temperature, while the foreground is shown in antenna temperature evaluated at 41 GHz. Different colors show the effect of using different temperature maps in the cross-correlation, or including different polarization frequency channels in the CMB-foreground decomposition. "Co-Add" refers to a noise-weighted linear combination of the correlation functions computed for individual frequency channels. "Fit" refers to a 2-component fit (Eq. \ref{['gal_fit_eqn']}) using the specified polarization frequency channels. The grey band shows the 68% confidence interval for the CMB component for the KKaQVW fit (which has the smallest statistical uncertainty) assuming CMB temperature anisotropy and instrument noise, but no CMB polarization. "Combination" and "COBE-DMR" replace the temperature map in Eq. \ref{['IQ_def']} with maps with reduced foreground emission: either the WMAP internal linear combination map or the COBE-DMR map of the CMB temperature. "MEM Model" and "ILC Residual" replace the temperature map in Eq. \ref{['IQ_def']} with maps dominated by foreground emission: either the WMAP maximum-entropy foreground model or the residual map produced by subtracting the internal linear combination map from the individual temperature maps at each frequency. The fitted CMB component is stable as different frequency channels and data sets are analyzed. Foreground emission is faint compared to the cosmic signal.
• Figure 5: Diagonal elements of the covariance matrix for the $c_l^{TE}$ polarization cross-power spectrum. Points show the diagonal elements computed from 7500 Monte Carlo simulations. The solid line shows the analytical model (Eq. \ref{['covar_diag']}). Note we multiply ${\bf M}_{ll}$ by $\left( \frac{l+1}{2 \pi} \right)^2$ to match the units in Figures \ref{['te_adiabatic_fig']} and \ref{['te_data_vs_model']}.