Open AccessRandom‐walk statistics and the spherical harmonic representation of cosmic microwave background maps
Author(s) -
Stannard Andrew,
Coles Peter
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.1365-2966.2005.09627.x
Subject(s) - physics , cosmic microwave background , random walk , amplitude , random field , spherical harmonics , cmb cold spot , isotropy , gaussian , harmonic , statistical physics , computational physics , anisotropy , statistics , optics , quantum mechanics , mathematics
We investigate the properties of the (complex) coefficients obtained in a spherical harmonic representation of temperature maps of the cosmic microwave background (CMB). We study the effect of the coefficient phase only, as well as the combined effects of phase and amplitude. The method used to check for anomalies is to construct a ‘random walk’ trajectory in the complex plane where the step length and direction are given by the amplitude and phase (respectively) of the harmonic coefficient. If the fluctuations comprise a homogeneous and isotropic Gaussian random field on the sky, the path so obtained should be a classical ‘Rayleigh flight’ with very well known statistical properties. We illustrate the use of this random‐walk representation by using the net walk length as a test statistic, and apply the method to the coefficients obtained from a Wilkinson Microwave Anisotropy Probe ( WMAP ) preliminary sky temperature map.