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WMAP

Wilkinson Microwave Anisotropy Probe

The data made available through this page has been updated. The most recent version of this data may be accessed through /product/map/current/

Product Name
Foreground Reduced Sky Maps Per Differencing Assembly
Mission
WMAP
Coord. System
Galactic
Projection Type
HEALPix, nested, res 9 (Nside=512) and res 10 (Nside=1024)
Resolution
0.23°- 0.93° (frequency dependent)

Description

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:
M11M12M13
M12M22M23
M13M23M33

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:
QQQU
UQUU

Additional Information

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A service of the HEASARC and of the Astrophysics Science Division at NASA/GSFC
Goddard Space Flight Center, National Aeronautics and Space Administration
HEASARC Director: Dr. Alan P. Smale
LAMBDA Director: Dr. Eric R. Switzer
NASA Official: Dr. Eric R. Switzer
Web Curator: Mr. Michael R. Greason