Relations between three-point configuration space shear and convergence statistics

Details Relations between three-point configuration space shear and convergence statistics Relations between three-point configuration space shear and convergence statistics

2011-05-11

arxiv.org/abs/1105.2309v1

Astronomy and Astrophysics, Volume 533, 2011, id.A48

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

17 pages, 5 figures, submitted to A&A

Scientific paper

10.1051/0004-6361/201117236

With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.

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