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Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
Grain J., Tristram M., Stompor R.
Physical Review D 79 (2009) 123515 (30 p.) - http://hal.in2p3.fr/in2p3-00434062
Planète et Univers/Astrophysique/Cosmologie et astrophysique extra-galactique
Physique/Astrophysique/Cosmologie et astrophysique extra-galactique
Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
J. Grain1, 2, M. Tristram3, R. Stompor2
1 :  IAS - Institut d'astrophysique spatiale
CNRS : UMR8617 – INSU – Université Paris XI - Paris Sud
bat. 121 91405 ORSAY CEDEX
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
3 :  LAL - Laboratoire de l'Accélérateur Linéaire
CNRS : UMR8607 – IN2P3 – Université Paris XI - Paris Sud
Centre Scientifique d'Orsay B.P. 34 91898 ORSAY Cedex
We extend the pure pseudo-power-spectrum formalism proposed recently in the context of the Cosmic Microwave Background polarized power spectra estimation by Smith (2006) to incorporate cross-spectra computed for multiple maps of the same sky area. We present an implementation of such a technique, paying particular attention to a calculation of the relevant window functions and mixing (mode-coupling) matrices. We discuss the relevance and treatment of the residual $E/B$ leakage for a number of considered sky apodizations as well as compromises and assumptions involved in an optimization of the resulting power spectrum uncertainty. In particular, we investigate the importance of a pixelization scheme, patch geometry, and sky signal priors used in apodization optimization procedures. In addition, we also present results derived for more realistic sky scans as motivated by the proposed balloon borne experiment EBEX. We conclude that the presented formalism thanks to its speed and efficiency can provide an interesting alternative to the CMB polarized power spectra estimators based on the optimal methods at least on angular scales smaller than ~10 degrees. In this regime, we find that it is capable of suppressing the total variance of the estimated $B$-mode spectrum to within a factor of ~2 of the variance due to only the sampling and noise uncertainty of the B-modes alone, as derived from the Fisher matrix approach.

Articles dans des revues avec comité de lecture
Physical Review D (Phys. Rev. D)
Publisher American Physical Society
ISSN 1550-7998 (eISSN : 1550-2368)
123515 (30 p.)

LAL 09-204
31 pages, 24 figures, typos corrected on Eq. 32, Appendix C clarified, published in Physical Review D
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