# The scalar perturbation spectral index n\_s: WMAP sensitivity to unresolved point sources

Source: [The scalar perturbation spectral index n\_s: WMAP sensitivity to unresolved point sources](<https://www.sota2.com/research/paper/68fa27e62c2a3760193c58cb>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:48.489Z

Authors: K. M. Huffenberger, H. K. Eriksen, F. K. Hansen, A. J. Banday, K. M. Gorski

Published: 2007-10-10T17:34:32.000Z

## Abstract

Precision measurement of the scalar perturbation spectral index, n\_s, from the Wilkinson Microwave Anisotropy Probe temperature angular power spectrum requires the subtraction of unresolved point source power. Here we reconsider this issue. 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 n\_s by ~0.3 sigma 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 muK^2 for uniform weighting and A = 0.015 +/- 0.005 muK^2 for N\_obs weighting. Correcting WMAP's spectrum correspondingly, we compute cosmological parameters with our alternative likelihood, finding n\_s = 0.970 +/- 0.017 and sigma\_8 = 0.778 +/- 0.045 . This n\_s is only 1.8 sigma from unity, compared to the ~2.6 sigma WMAP 3-year result. Finally, an anomalous feature in the source spectrum at l\<200 remains, most strongly associated with W-band.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0710.1873>)

[PDF](<https://arxiv.org/pdf/0710.1873.pdf>)