Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Beam Profiles, Data Processing, Radiometer Characterization and Systematic Error Limits

TL;DR

This paper presents the three-year Wilkinson Microwave Anisotropy Probe (WMAP) data release, detailing improvements in instrument modeling, data processing, and systematic error control. Key contributions include updated radiometer gain models, refined beam and window-function determinations using six seasons of Jupiter data, and a maximum-likelihood framework for producing Stokes I, Q and U sky maps along with the inverse pixel-pixel noise matrix. The work also explains sidelobe corrections, polarization handling, and an end-to-end validation via spin-synchronous checks and year-to-year null tests, demonstrating high reproducibility and controlled systematics. Collectively, these advancements enable more precise CMB analyses and tighter constraints on cosmological parameters from the 3-year data set.

Abstract

The WMAP satellite has completed 3 years of observations of the cosmic microwave background radiation. The 3-year data products include several sets of full sky maps of the Stokes I, Q and U parameters in 5 frequency bands, spanning 23 to 94 GHz, and supporting items, such as beam window functions and noise covariance matrices. The processing used to produce the current sky maps and supporting products represents a significant advancement over the first year analysis, and is described herein. Improvements to the pointing reconstruction, radiometer gain modeling, window function determination and radiometer spectral noise parametrization are presented. A detailed description of the updated data processing that produces maximum likelihood sky map estimates is presented, along with the methods used to produce reduced resolution maps and corresponding noise covariance matrices. Finally two methods used to evaluate the noise of the full resolution sky maps are presented along with several representative year-to-year null tests, demonstrating that sky maps produced from data from different observational epochs are consistent.

Figures (16)

• Figure 1: The temperature of the middle of the B side primary mirror vs. the Sun azimuth in the spacecraft coordinate system. The red data were taken during the first year of observations, the black during the second and the blue during the third. The similarity between the three indicates that the screening of the cold optics from solar radiation is still effective during the second and third years of operation.
• Figure 2: Comparison of the hourly gain determinations (black) based on measurement of the CMB dipole to two different versions of the radiometer gain model. These data are for the V223 detector and the time range spans the three years of WMAP science data collection. The blue lines are the original gain model derived by fitting the initial 310 days of data. The light blue region, to the left of the vertical red line, indicates the time range used to fit the model. The dark blue region, to the right of the red vertical line, is this model as originally fit, applied to the remainder of the data. The orange line is the new form gain model fit to all three years of data. The updated gain model is a significantly better fit to the hourly gain measurements. Note that the difference between the models contains a component roughly linear in time.
• Figure 3: Difference between the temperature sky maps produced using two different gain models. Raw data from from the V2 differencing assembly for year-1 was processed both with the original (year-1) and the improved (3-year) gain models. The map projection shown is in ecliptic rather than Galactic coordinates. The observed quadrupolar feature arises from imperfect subtraction of the velocity induced dipole signal in maps processed with the year-1 gain model. Similar features are observed in similarly constructed difference maps for many of the DAs.
• Figure 4: Amplitude of the quadrupole difference between temperature maps produced using the original and improved gain models. The horizontal axis is the difference between the mean slopes of the gain models. Each black symbol represents one Differencing Assembly. The line is a fit to these points constrained to pass through the origin and has a slope of $9.9~\hbox{$\mu$\rm K}/(\%\;\hbox{yr}^{-1})$. The red symbols are estimates of the amplitude of residual quadrupolar artifacts in the temperature maps after application of the improved gain model. Note that these values are distributed around zero indicating that the phases of the estimated residuals are random and should not bias the measured sky quadrupole.
• Figure 5: Noise and Filter Properties of the W11 Radiometer. The top panel displays the measured autocorrelation function of the W11 radiometer noise (black diamonds) and the parameterized fit to these data (red line) as described in § \ref{['sec:TOD_power_spectra']}. The data point at $\Delta t= 0$ with value 1 has been omitted for clarity. The remaining plots illustrate the steps used to form the $N_{\rm tt}^{-1}$ filters used in the conjugate gradient map solution, described in § \ref{['sec:map_evaluation']}. The second panel displays the noise power spectral density obtained from a Fourier transform of the parameterized noise autocorrelation function, while the third panel shows the reciprocal of this function. The last panel presents the $N_{\rm tt}^{-1}$ filter function obtained via a Fourier transform of the reciprocal noise power spectral density, again with the data point at $\Delta t = 0$ and value 1 omitted for clarity.