Wilkinson Microwave Anisotropy Probe

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The low resolution (res 4) maps were used to study the influence of foregrounds on the polarization component of the WMAP data outside the Galactic plane.

A map for each differencing assembly and each year of data was produced by degrading the normal resolution (res9) maps to res 4. The res 9 processing mask was used to block out the Galactic plane, resulting in a set of 85 res 4 pixels that were completely unpopulated. These pixels were repopulated from the res 9 data. The reason for this two-step procedure was to assure that data omitted by the processing mask at res 9 were excluded from the small subset of res 4 pixels that overlap the boundary of the cut. This processing resulted in 30 maps (3 years times 10 D/A's).

The single-year, single-D/A maps were combined into one map for each frequency band using a weighted average. There are 5 such maps, each comprising three years of data. In this case, the res 4 Galactic plane remains unpopulated for the Stokes I and spurious (S) components, because of zero-point effects.

Both the single-year, single-D/A maps and the three-year band-averaged maps are available for download.

The spurious signal (S) is not a Stokes parameter, but rather, an apparent signal generated by differences in the two radiometers that compose a differencing assembly. This component is computed by the map-making process, as discussed in Jarosik, et.al., 2006.

The Stokes I and spurious (S) components included in the low-resolution map set are not suitable for direct use in analysis because of signal aliasing. Instead, their purpose is to help furnish a complete description of Stokes Q and U.

WMAP maps are stored in FITS binary table extensions. The maps are stored in the first extension in a file; the format of this table depends upon whether polarization maps have been included in the file. Some files also contain the polarization covariance matrices for the maps; if supplied these matrices are stored in a second binary table extension.

As previously stated, the first FITS extension contains the maps. These maps are in a nested HEALPix format, with each row representing a single pixel. There are either four or two columns depending upon whether or not polarization maps are included; these columns are:

TEMPERATURE	The Stokes I, or temperature, measurement in mK (thermodynamic).
Q_POLARISATION	The Stokes Q polarization measurement in mK (thermodynamic).
U_POLARISATION	The Stokes U polarization measurement in mK (thermodynamic).
SPUR_SIGNAL	The bandpass mismatch component.
N_OBS	The effective number of observations.

The column names were selected to be compatible with existing HEALPix software. The TEMPERATURE and N_OBS columns are the only columns that exist in files that do not contain polarization maps.

Some files that contain polarization maps contain a second FITS extension containing the 3x3 polarization noise covariance matrices for the pixels in the maps of the first FITS extension. These matrices are used in the map-making process and characterize the noise properties of the polarization maps. See section 3.4 of Jarosik, et.al., 2006 in the set of three year WMAP papers for more details. The columns of this extension are:

N_OBS	The effective number of observations as reported in the first extension. This is included here for completeness.
M11	The bandpass mismatch (SS) noise covariance term in units of N_Obs-style counts.
M12	The SQ noise covariance term in units of N_Obs-style counts.
M13	The SU noise covariance term in units of N_Obs-style counts.
M22	The QQ noise covariance term in units of N_Obs-style counts.
M23	The QU noise covariance term in units of N_Obs-style counts.
M33	The UU noise covariance term in units of N_Obs-style counts.

The covariance matrix of a pixel may be constructed by assembling the row elements into a 3x3 symmetric matrix with the form:

M11	M12	M13
M12	M22	M23
M13	M23	M33

The noise covariance matrices described above do not fully characterize the pixel-to-pixel noise in the res 4 maps. Therefore a more accurate, and much larger, inverse covariance matrix is supplied for each map as a separate product. This matrix consists of 12288x12288 elements in sixteen 3072x3072 blocks. The covariance matrices included in the map files comprise the diagonal elements of each of the blocks describing Q, U, and S coupling.

The elements corresponding to the Galatic plane pixels as defined by the processing mask were set to zero. Therefore, the matrices as supplied are singular. To make them non-singular, the row and the column corresponding to each zero element of the diagonal need to be deleted.

A small effect due to transmission imbalance between the A side and the B side of the instrument has been projected out of the inverse variance matrices as described in Section 3.5.1 of Jarosik et al. (2007).

See Jarosik, et.al., 2006 and Page, et.al., 2006 for more information.

Additional Information

• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Beam Profiles, Data Processing, Radiometer Characterization and Systematic Error Limits, N. Jarosik, et.al. (2006)
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis, G. Hinshaw, et.al. (2006)
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis, L. Page, et.al. (2006)
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology, D. Spergel, et.al (2006).
• WMAP Three Year Explanatory Supplement

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