Maxwell's Multipole Vectors and the CMB

Abstract

The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative approach as a starting point, the present article develops a fast algorithm for computing multipole vectors, with an exposition that is both simpler and better motivated than in the author's previous work. Tests show the resulting algorithm, coded up as a Mathematica notebook, to be both fast and robust. This article serves to announce the free availability of the code. The algorithm is then applied to the much discussed anomalies in the low-ell CMB modes, with sobering results. Simulations show the quadrupole-octopole alignment to be unusual at the 98.7% level, corroborating earlier estimates of a 1-in-60 alignment while showing recent reports of 1-in-1000 (using non-unit-length normal vectors) to have unintentionally relied on the near orthogonality of the quadrupole vectors in one particular data set. The alignment of the quadrupole and octopole vectors with the ecliptic plane is confirmed at better than the 2sigma level.

v2. Explains anomalous 99.9% result as combined effect of quadrupole-octopole alignment and near orthogonality of quadrupole vectors in DQT data set; textual improvements; 8 pages

References in corpus (9)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Asymmetries in the CMB anisotropy field
• A high resolution foreground cleaned CMB map from WMAP
• The significance of the largest scale CMB fluctuations in WMAP
• Is the low-l microwave background cosmic?
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• On Foreground Removal from the Wilkinson Microwave Anisotropy Probe Data by an Internal Linear Combination Method: Limitations and Implications
• Polynomial Interpretation of Multipole Vectors
• Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere

Cited by in corpus (8)

• Large-angle anomalies in the CMB
• Large-scale alignments from WMAP and Planck
• Testing gaussianity, homogeneity and isotropy with the cosmic microwave background
• Large scale alignment anomalies of CMB anisotropies: a new test for residuals applied to WMAP 5yr maps
• Large scale directional anomalies in the WMAP 5yr ILC map
• Searching for hidden mirror symmetries in CMB fluctuations from WMAP 7 year maps
• Dodecahedral topology fails to explain quadrupole-octupole alignment
• A Large Scale Pattern from Optical Quasar Polarization Vectors