Probability Density of the Multipole Vectors for a Gaussian Cosmic Microwave Background
arXiv:0704.3657 · doi:10.1111/j.1365-2966.2007.12484.x
Abstract
We review Maxwell's multipole vectors, and elucidate some of their mathematical properties, with emphasis on the application of this tool to the cosmic microwave background (CMB). In particular, for a completely random function on the sphere (corresponding to the statistically isotropic Gaussian model of the CMB), we derive the full probability density function of the multipole vectors. This function is used to analyze the internal configurations of the third-year Wilkinson Microwave Anisotropy Probe quadrupole and octopole, and we show the observations are consistent with the Gaussian prediction. A particular aspect is the planarity of the octopole, which we find not to be anomalous.
12 pages, 7 figures, MNRAS style
References in corpus (10)
- Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
- Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
- Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
- The Uncorrelated Universe: Statistical Anisotropy and the Vanishing Angular Correlation Function in WMAP Years 1-3
- The Axis of Evil revisited
- Correlating anomalies of the microwave sky: The Good, the Evil and the Axis
- The Velocity Field of the Local Universe from Measurements of Type Ia Supernovae
- Cleaned Three-Year WMAP CMB Map: Magnitude of the Quadrupole and Alignment of Large Scale Modes
- CMB statistical anisotropy, multipole vectors and the influence of the dipole
- The impact of dipole straylight contamination on the alignment of low multipoles of CMB anisotropies