Open AccessThe multipole vectors of the Wilkinson Microwave Anisotropy Probe , and their frames and invariants
Author(s) -
Land Kate,
Magueijo João
Publication year - 2005
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2005.09310.x
Subject(s) - multipole expansion , physics , cmb cold spot , cosmic microwave background , euler angles , anisotropy , isotropy , consistency (knowledge bases) , planck , computational physics , sky , astrophysics , range (aeronautics) , optics , geometry , quantum mechanics , mathematics , materials science , composite material
We investigate the statistical isotropy (SI) and Gaussianity of the cosmic microwave background fluctuations, using a set of multipole vector functions capable of separating these two issues. In general a multipole is broken into a frame and 2ℓ− 3 ordered invariants. The multipole frame is found to be suitably sensitive to Galactic cuts. We then apply our method to real Wilkinson Microwave Anisotropy Probe ( WMAP ) data sets; a co‐added masked map, the interlinear combinations map, and Wiener filtered and cleaned maps. Taken as a whole, multipoles in the range ℓ= 2–10 or ℓ= 2–20 show consistency with SI, as proved by the Kolmogorov test applied to the Euler angles of the frame. This result is not inconsistent with previous claims for a preferred direction in the sky for ℓ= 2, …, 5 . The multipole invariants also show overall consistency with Gaussianity apart from a few anomalies of limited significance (98 per cent), listed at the end of this paper. However, we stress that this method in practice is very limited by noise.