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Instability of reconstruction of the low CMB multipoles

Instability of reconstruction of the low CMB multipoles We discuss the problem of the bias of the Internal Linear Combination (ILC) CMB map and show that it is closely related to the coefficient of cross-correlation K(ℓ) of the true CMB and the foreground for each multipole ℓ. We present analysis of the cross-correlation for the WMAP ILC quadrupole and octupole from the first (ILC(I)) and the third (ILC(III)) year data releases and show that these correlations are ∼ −0.52–0.6. Analysing 104 Monte Carlo simulations of the random Gaussian CMB signals, we show that the distribution function for the corresponding coefficient of the cross-correlation has a polynomial shape P(K, ℓ) ∝ (1 − K 2)ℓ−1. We show that the most probable value of the cross-correlation coefficient of the ILC and foreground quadrupole has two extrema at K ≃ ±0.58. Thus, the ILC(III) quadrupole represents the most probable value of the coefficient K. We analyze the problem of debiasing of the ILC CMB and pointed out that reconstruction of the bias seems to be very problematic due to statistical uncertainties. In addition, instability of the debiasing illuminates itself for the quadrupole and octupole components through the flip-effect, when the even ℓ + m modes can be reconstructed with significant error. This error manifests itself as opposite, in respect to the true sign of even low multipole modes, and leads to significant changes of the coefficient of cross-correlation with the foreground. We show that the CMB realizations, whose the sign of quadrupole (2, 0) component is negative (and the same, as for all the foregrounds), the corresponding probability to get the positive sign after implementation of the ILC method is about 40%. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Astrophysical Bulletin Springer Journals

Instability of reconstruction of the low CMB multipoles

Astrophysical Bulletin , Volume 63 (3) – Aug 29, 2008

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References (52)

Publisher
Springer Journals
Copyright
Copyright © 2008 by MAIK Nauka
Subject
Physics; Astronomy, Astrophysics and Cosmology
ISSN
1990-3413
eISSN
1990-3421
DOI
10.1134/S1990341308030024
Publisher site
See Article on Publisher Site

Abstract

We discuss the problem of the bias of the Internal Linear Combination (ILC) CMB map and show that it is closely related to the coefficient of cross-correlation K(ℓ) of the true CMB and the foreground for each multipole ℓ. We present analysis of the cross-correlation for the WMAP ILC quadrupole and octupole from the first (ILC(I)) and the third (ILC(III)) year data releases and show that these correlations are ∼ −0.52–0.6. Analysing 104 Monte Carlo simulations of the random Gaussian CMB signals, we show that the distribution function for the corresponding coefficient of the cross-correlation has a polynomial shape P(K, ℓ) ∝ (1 − K 2)ℓ−1. We show that the most probable value of the cross-correlation coefficient of the ILC and foreground quadrupole has two extrema at K ≃ ±0.58. Thus, the ILC(III) quadrupole represents the most probable value of the coefficient K. We analyze the problem of debiasing of the ILC CMB and pointed out that reconstruction of the bias seems to be very problematic due to statistical uncertainties. In addition, instability of the debiasing illuminates itself for the quadrupole and octupole components through the flip-effect, when the even ℓ + m modes can be reconstructed with significant error. This error manifests itself as opposite, in respect to the true sign of even low multipole modes, and leads to significant changes of the coefficient of cross-correlation with the foreground. We show that the CMB realizations, whose the sign of quadrupole (2, 0) component is negative (and the same, as for all the foregrounds), the corresponding probability to get the positive sign after implementation of the ILC method is about 40%.

Journal

Astrophysical BulletinSpringer Journals

Published: Aug 29, 2008

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