Astronomy and Astrophysics – Astrophysics
Scientific paper
2004-10-26
Mon.Not.Roy.Astron.Soc. 364 (2005) 929-933
Astronomy and Astrophysics
Astrophysics
5 pages, 1 figure, uses mn.sty. Version accepted for publication in MNRAS. Includes toy models of non-random walks
Scientific paper
10.1111/j.1365-2966.2005.09627.x
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.
Coles Peter
Stannard Andrew
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