Wilkinson Microwave Anisotropy Probe DR2

The data made available through this page has been updated. The most recent version of this data may be accessed through https://lambda.gsfc.nasa.gov/product/wmap/current/

Foreground Reduced Low Resolution Sky Maps

Coordinate System:
Projection Type:
0.23°- 0.93° (frequency dependent)
HEALPix, nested, res 4 (Nside=16)
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These low resolution maps were created by degrading the foreground reduced res 9 single year individual D/A polarization maps to res 4 using the QQ, QU, and UU covariance matrices, omitting pixel-to-pixel covariance.

The inverse covariance matrices were corrected using the standard polarization mask to ignore covariance with pixels within the cut. These matrices were also corrected for the effects of compression and foreground cleaning by increasing the noise per observation by a few percent; the noise per observation has been applied to the matrices.

Rows and columns that correspond to pixels in the polarization mask are zero, so that the matrices are singular as supplied. 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).

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.

Pixel noise in units of mK can be evaluated from N_obs with the expression σ = σ0 / sqrt(N_Obs) where

Differencing Assembly Frequency Band
Stokes I Stokes Q,U Stokes I Stokes Q,U
K1 1.4391 1.4551 1.4391 1.4551
Ka1 1.4638 1.4831 1.4638 1.4831
Q1 2.2449 2.2693 2.1898 2.2128
Q2 2.1347 2.1563
V1 3.3040 3.3305 3.1249 3.1501
V2 2.9458 2.9696
W1 5.8833 5.9179 6.5112 6.5484
W2 6.5324 6.5707
W3 6.8849 6.9246
W4 6.7441 6.7803

Some files that contain polarization maps contain a second FITS extension containing the #nxn# 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 or 2x2 symmetric matrix with the form:


The size of the matrix depends upon whether or not the spurious signal component is included.

The EE fit in the parameter likelihood computation required only the Q and U components of the Q and V maps. Therefore these are the only maps that were produced for this deliverable category. Since the Stokes I and N_Obs maps were not produced in this form, these fields have been zero'ed out in the map files available through LAMBDA.

Additional Information

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