Wilkinson Microwave Anisotropy Probe

The foreground reduced skymaps were produced by removing a foreground model from the 'unreduced' maps using the Foreground Template Model discussed in Hinshaw, et.al., 2006 and Page, et.al, 2006; see those papers for details. Briefly, synchrotron, free-free, and dust emission templates were modeled and then subtracted from the single year 'unreduced' maps. The goal was to produce a set of maps with the foreground removed while retaining WMAP's noise characteristics.

Because the K and Ka maps were used to produce the foreground models, only Q, V, and W band foreground reduced maps were created and delivered to LAMBDA.

As with the 'unreduced' maps, full three year maps were produced by performing a weighted, pixel-by-pixel, mean of the three single year maps; the N_Obs measurement was used to weight this mean. The N_Obs measurements were added together to produce the final, three year, N_Obs measurement.

The same foreground template model was used to produce foreground reduced high resolution (res 10) V and W maps.

WMAP maps are stored in FITS binary table extensions. The maps are stored in the first extension in a file; the number of columns in 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. The number of columns depends upon which maps are included; these columns may be:

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 for I, Q, U, and N_Obs maps 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. The Q_POLARISATION and U_POLARISATION exist in files containing polarization maps; the names were selected to be compatible with existing HEALPix software. The SPUR_SIGNAL columns exists only in polarization map files that contain an 'S' map.

The WMAP skymaps used the HEALPix nested pixel ordering scheme in Galactic coordinates. For the convenience of users who do not have HEALPix software installed, we provide a series of FITS sky map files that give the sky coordinates of each pixel center for various resolutions.

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

	σ0 For Each Differencing Assembly
	K1	Ka1	Q1	Q2	V1	V2	W1	W2	W3	W4
Stokes I	1.436	1.470	2.254	2.141	3.314	2.953	5.899	6.565	6.926	6.761
Stokes Q,U	1.453	1.488	2.278	2.163	3.341	2.975	5.929	6.602	6.964	6.800
The table of noise levels, σ0, for the full-resolution, foreground-reduced maps were updated on 2 June 2009 to correct an error. The previously posted values were inadvertantly copied from the 3-year release.

Some files that contain polarization maps contain a second FITS extension containing the 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 Jarosik, et.al., 2007 and in Hinshaw, et.al., 2008 for more details. There are two forms of this matrix, depending upon whether or not the bandpass mismatch term (S map) has been included in the file.

If the S map is supplied then 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 for a pixel may then be constructed by assembling the row elements into a 3x3 symmetric matrix with the form:

M11	M12	M13
M12	M22	M23
M13	M23	M33

If, on the other hand, the S map is not supplied then the columns of this extension are:

QQ	The QQ noise covariance term in units of N_Obs-style counts.
QU	The QU noise covariance term in units of N_Obs-style counts.
UU	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 2x2 symmetric matrix with the form:

QQ	QU
UQ	UU

Additional Information

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results, G. Hinshaw, et.al. (2008)
• WMAP Five Year Explanatory Supplement

Back to Product Page