HAL : in2p3-00434062, version 1
 arXiv : 0903.2350
 Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approachGrain J., Tristram M., Stompor R.Physical Review D 79 (2009) 123515 (30 p.) - http://hal.in2p3.fr/in2p3-00434062
 Statistiques/Applications 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 http://www.ias.u-psud.fr CNRS : UMR8617 – INSU – Université Paris XI - Paris Sud bat. 121 91405 ORSAY CEDEX France 2 : APC - UMR 7164 - AstroParticule et Cosmologie http://www.apc.univ-paris7.fr/ 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 France 3 : LAL - Laboratoire de l'Accélérateur Linéaire http://www.lal.in2p3.fr/ CNRS : UMR8607 – IN2P3 – Université Paris XI - Paris Sud Centre Scientifique d'Orsay B.P. 34 91898 ORSAY Cedex France
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.