Peculiarities of phases of the WMAP quadrupole

Int.J.Mod.Phys.D17:179-194,2008 We present the analysis on the quadrupole phases of the Internal Linear Combination map, ILC(I) and (III) derived by the WMAP team (1 and 3-year data release). This approach allows us to see the global trend of non-Gaussianity of the quadrupoles for the ILC(III) map through phase correlations with the foregrounds. Significant phase correlations is found in between the ILC(III) quadrupole and the WMAP foregrounds phases for K-W band: the phases of the ILC(III) quadrupole xi_{2,1}, xi_{2,2} and those of the foregrounds at K-W bands Phi_{2,1}, Phi_{2,2} display significant symmetry: xi_{2,1}+Phi_{2,1} ~= xi_{2,2}+Phi_{2,2}, which is a strong indication that the morphology of the ILC(III) quadrupole is mere reflection of that the foreground quadrupole through coupling. To clarify this issue we exploit the symmetry of the CMB power, which is invariant under permutation of the index m=12. By simple rotation of the ILC(III) phases with the same angle we reach the phases of foreground quadrupole. We discuss possible sources of phase correlation and come to the conclusion that the phases of the ILC(III) quadrupole reflect most likely systematic effects such as changing of the gain factor for the 3-year data release with respect to the 1-year, rather than manifestation of the primordial non-Gaussianity.