Journal Article

Higher order statistics for three-dimensional shear and flexion

Dipak Munshi, Thomas Kitching, Alan Heavens and Peter Coles

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 416, issue 3, pages 1629-1653
Published in print September 2011 | ISSN: 0035-8711
Published online September 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.18434.x
Higher order statistics for three-dimensional shear and flexion

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We introduce a collection of statistics appropriate for the study of spinorial quantities defined in three dimensions, focusing on applications to cosmological weak gravitational lensing studies in three dimensions. In particular, we concentrate on power spectra associated with three- and four-point statistics, which have the advantage of compressing a large number of typically very noisy modes into a convenient data set. It has been shown previously by Munshi & Heavens that, for non-Gaussianity studies in the microwave background, such compression can be lossless for certain purposes, so we expect the statistics we define here to capture the bulk of the cosmological information available in these higher order statistics. We consider the effects of a sky mask and noise, and use Limber’s approximation to show how, for high-frequency angular modes, confrontation of the statistics with theory can be achieved efficiently and accurately. We focus on scalar and spinorial fields including convergence, shear and flexion of three-dimensional weak lensing, but many of the results apply for general spin fields.

Keywords: gravitational lensing: weak; methods: analytical; methods: numerical; methods: statistical; large-scale structure of Universe

Journal Article.  15945 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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