CMB statistical anisotropy, multipole vectors, and the influence of the dipole

A simple algorithm which gives the multipole vectors in terms of the roots of a polynomial is given. We find that the reported alignment of the low $l$ multipole vectors can be summarized as an orthogonality of these with the dipole direction. This orthogonality is not only present in $l=2$ and 3 but also for $l=5$ and higher. This alignment is likely due to nonlinearity in the data processing. Our results are based on the 3 yr Wilkinson Microwave Anisotropy Probe data, we also list corresponding results for the first year data.

Figure 1

Three year multipole vectors on the north galactic hemisphere, the line indicating the plane orthogonal to the dipole

Figure 2

First year multipole vectors from Tegmark et al. map

Figure 3

The Wehrl entropy for $1\le l\le 20$

Figure 4

First year multipole vectors using the ILC map