Alternative Multipole Vectors for the CMB Temperature Fluctuations

We introduce new, low-l, multipole vectors for the CMB temperature fluctuations. A very strong alignment of the quadrupole and octopole vectors is observed as well as a remarkably low declination of these vectors with respect to the galactic plane. The temperature fluctuations, ∆T (Ω), of the CMB radiation are traditionally decomposed according to ∆T (Ω) = ∑ lm almYlm(Ω) (1) where al−m = (−1) ma∗lm reflects the reality of ∆T (Ω). For each l there are thus 2l + 1 independent real parameters which can be utilized in general to construct l uncorrelated unit vectors and one common overall amplitude. In [1] a method to construct such multipole vectors was introduced and the properties of these vectors were studied in [1, 2]. In particular, it turned out that the l = 2 and 3 multipole vectors possess quite unusual correlations which are unexpected for a statistically isotropic sky with Gaussian random alm, 〈alma ∗ lm〉 = Clδll′δmm′ . The multipole vectors presented in [1] where obtained by the construction of symmetric traceless rank-l tensor representation of the spherical harmonics Ylm and it remains to be seen to what extent the above mentioned correlations depend on these particularly chosen multipole vectors. To study this question we introduce an alternative set of multipole vectors whose directions point towards the maxima and minima of ∆Tl(Ω) ≡ ∑ m almYlm(Ω). Utilizing the alm in Table II of [3], obtained from a foreground cleaned [4] CMB map one obtains in galactic coordinates (l, b) the following unit vectors: n̂1 = (157 ◦.03, 6◦.29), n̂2 = (63 ◦.33, 30◦.41), (2) in the quadrupole sector and n̂a = (145 ◦.97, 10◦.59), n̂b = (14 ◦.59, 29◦.75), n̂c = (82 ◦.09, 17◦.93), (3)