Non-Gaussian Spectra
ArXiv astro-ph/9610174 (1996)
Authors:
Pedro G Ferreira, Joao Magueijo
Abstract:
Gaussian cosmic microwave background skies are fully specified by the power
spectrum. The conventional method of characterizing non-Gaussian skies is to
evaluate higher order moments, the n-point functions and their Fourier
transforms. We argue that this method is inefficient, due to the redundancy of
information existing in the complete set of moments. In this paper we propose a
set of new statistics or non-Gaussian spectra to be extracted out of the
angular distribution of the Fourier transform of the temperature anisotropies
in the small field limit. These statistics complement the power spectrum and
act as localization, shape, and connectedness statistics. They quantify generic
non-Gaussian structure, and may be used in more general image processing tasks.
We concentrate on a subset of these statistics and argue that while they carry
no information in Gaussian theories they may be the best arena for making
predictions in some non-Gaussian theories. As examples of applications we
consider superposed Gaussian and non-Gaussian signals, such as point sources in
Gaussian theories or the realistic Kaiser-Stebbins effect. We show that in
these theories non-Gaussianity is only present in a ring in Fourier space,
which is best isolated in our formalism. Subtle but strongly non-Gaussian
theories are also written down for which only non-Gaussian spectra may accuse
non-Gaussianity.