The Multipole Vectors of WMAP, and their frames and invariants

Abstract

We investigate the Statistical Isotropy and Gaussianity of the CMB fluctuations, using a set of multipole vector functions capable of separating these two issues. In general a multipole is broken into a frame and $2\ell-3$ ordered invariants. The multipole frame is found to be suitably sensitive to galactic cuts. We then apply our method to real WMAP datasets; a coadded masked map, the Internal Linear Combinations map, and Wiener filtered and cleaned maps. Taken as a whole, multipoles in the range $\ell=2-10$ or $\ell=2-20$ show consistency with statistical isotropy, as proved by the Kolmogorov test applied to the frame's Euler angles. This result in {\it not} inconsistent with previous claims for a preferred direction in the sky for $\ell=2,...5$. The multipole invariants also show overall consistency with Gaussianity apart from a few anomalies of limited significance (98%), listed at the end of this paper.