The Scalar Perturbation Spectral Index ns: WMAP Sensitivity to Unresolved Point Sources

Abstract

Precision measurement of the scalar perturbation spectral index, ns, from the Wilkinson Microwave Anisotropy Probe (WMAP) temperature angular power spectrum requires the subtraction of unresolved point-source power. Here we reconsider this issue, attempting to resolve inconsistencies found in the literature. First, we note a peculiarity in the WMAP temperature likelihood's response to the source correction: cosmological parameters do not respond to increased source errors. An alternative and more direct method for treating this error term acts more sensibly, and also shifts ns by ~0.3 σ closer to unity. Second, we re-examine the source fit used to correct the power spectrum. This fit depends strongly on the Galactic cut and the weighting of the map, indicating that either the source population or masking procedure is not isotropic. Jackknife tests appear inconsistent, causing us to assign large uncertainties to account for possible systematics. Third, we note that the WMAP team's spectrum was computed with two different weighting schemes: uniform weights transition to inverse noise variance weights at l = 500. The fit depends on such weighting schemes, so different corrections apply to each multipole range. For the Kp2 mask used in cosmological analysis, we prefer source corrections A = 0.012 ± 0.005 µK^2 for uniform weighting and A = 0.015 ± 0.005 µK^2 for Nobs weighting. Correcting WMAP's spectrum correspondingly, we compute cosmological parameters with our alternative likelihood, finding ns = 0.970 ± 0.017 and σ8 = 0.778 ± 0.045. This ns is only 1.8 σ from unity, compared to the ~2.6 σ WMAP 3 year result. Finally, an anomalous feature in the source spectrum at nl < 200 remains in the 3 year data, most strongly associated with the W band. We note the implications of these results for the 5 year data.

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