Multipole invariants and non-Gaussianity

Details Multipole invariants and non-Gaussianity Multipole invariants and non-Gaussianity

2004-07-05

arxiv.org/abs/astro-ph/0407081v2

Mon.Not.Roy.Astron.Soc. 362 (2005) L16-L19

Astronomy and Astrophysics

Astrophysics

Scientific paper

10.1111/j.1745-3933.2005.00065.x

We propose a framework for separating the information contained in the CMB multipoles, $a_{\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map.

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