## How well do third-order aperture mass statistics separate E- and B-modes?

^{1} Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85740 Garching bei München, Germany

e-mail: xun@mpa-garching.mpg.de
^{2} Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK
^{3} Argelander-Institut für Astronomie (AIfA), Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

Received: 4 September 2013

Accepted: 25 November 2013

With third-order statistics of gravitational shear it will be possible to extract valuable cosmological information from ongoing and future weak lensing surveys that is not contained in standard second-order statistics because of the non-Gaussianity of the shear field. Aperture mass statistics are an appropriate choice for third-order statistics because of their simple form and their ability to separate E- and B-modes of the shear. However, it has been demonstrated that second-order aperture mass statistics suffer from E-/B-mode mixing because it is impossible to reliably estimate the shapes of close pairs of galaxies. This finding has triggered developments of several new second-order statistical measures for cosmic shear. Whether the same developments are needed for third-order shear statistics is largely determined by how severe this E-/B-mixing is for third-order statistics. We tested third-order aperture mass statistics against E-/B-mode mixing and found that the level of contamination is well described by a function of *θ* */* *θ*_{min}, where *θ*_{min} is the cutoff scale. At angular scales of *θ* *>* 10 *θ*_{min}, the decrease in the E-mode signal due to E-/B-mode mixing is lower than 1 percent, and the leakage into B-modes is even less. For typical small-scale cutoffs this E-/B-mixing is negligible on scales larger than a few arcminutes. Therefore, third-order aperture mass statistics can safely be used to separate E- and B-modes and infer cosmological information, for ground-based surveys as well as forthcoming space-based surveys such as *Euclid*.

Key words: gravitational lensing: weak / methods: statistical / large-scale structure of Universe / cosmological parameters

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