The multipole vectors of the Wilkinson Microwave Anisotropy Probe, and their frames and invariants
Abstract
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.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- September 2005
- DOI:
- 10.1111/j.1365-2966.2005.09310.x
- arXiv:
- arXiv:astro-ph/0502574
- Bibcode:
- 2005MNRAS.362..838L
- Keywords:
-
- cosmic microwave background;
- Astrophysics
- E-Print:
- 9 pages. Submitted to MNRAS