Wilkinson Microwave Anisotropy Probe

The TE, TB, EE, and BB power spectra are computed using a pseudo-C_l estimator for the region outside the 5yr polarization mask in P and outside the analysis mask in T. For the temperature-polarization cross spectra (TE and TB), foreground-cleaned V and W bands are used for T, foreground-cleaned Q, V, and W bands are used for polarization, and uniform weighting is used for multipole l <= 500, and Nobs weighting is used for l > 500. These TE and TB spectra are derived from data files released with version 4.1 of the WMAP likelihood code. The polarization auto spectra (EE and BB) also use foreground-cleaned Q, V, and W bands, but they use uniform weighting at all l.

Unbinned TE, TB, EE, and BB power spectra are provided as tables containing the following columns:

1. the multipole moment l
2. the power spectrum in units of μK²
3. the error derived from the diagonal elements of the covariance matrix in units of μK²
4. the portion of column 3 attributed to measurement errors
5. the portion of column 3 attributed to cosmic variance, assuming the best-fit ΛCDM model.

The diagonal elements provide an estimate of the error, but should not be used as exact error bars. The complete Fisher matrix should be used for that purpose.

Binned versions of the TE, TB, EE, and BB power spectra are also available in separate ASCII files with the following columns:

1. the mean multipole moment l
2. the smallest l contributing to the bin
3. the largest l contributing to the bin
4. the power spectrum in units of μK²
5. the error for the binned value, computed from the diagonal elements of the covariance matrix in units of μK²
6. the portion of column 5 attributed to measurement errors in units of μK²
7. the portion of column 5 attributed to cosmic variance in units of μK², assuming the best-fit ΛCDM model.

The EE and BB spectra bins are noise-weighted averages; the TE and TB spectra bins are straight averages. The binned cross spectra (TE and TB) are given in the form
(l + 1) C_l / 2 π
while the binned auto spectra (TT, EE, and BB) are multiplied by an additional factor of l to give
l (l + 1) C_l / 2 π

Also available are the BB power spectra before coadding frequences (Q, V, and W bands) as a table containing the following columns:

1. the multipole moment
2. the Q band power spectrum, in units of μK²
3. the Q band error derived from the diagonal elements of the covariance matrix attributed to measurement errors, in units of μK²
4. the V band power spectrum, in units of μK²
5. the V band error derived from the diagonal elements of the covariance matrix attributed to measurement errors, in units of μK²
6. the W band power spectrum, in units of μK²
7. the W band error derived from the diagonal elements of the covariance matrix attributed to measurement errors, in units of μK²

Like the other spectra, these are supplied in the form
l (l + 1) C_l / 2 π

Additional Information

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters, D. Larson, et.al. (2010)
• WMAP Seven Year Explanatory Supplement

Back to Product Page