How well do third-order aperture mass statistics separate E- and
  B-modes?
  With 3rd-order statistics of gravitational shear it will be possible to
extract valuable cosmological information from ongoing and future weak lensing
surveys which is not contained in standard 2nd-order statistics, due to the
non-Gaussianity of the shear field. Aperture mass statistics are an appropriate
choice for 3rd-order statistics due to their simple form and their ability to
separate E- and B-modes of the shear. However, it has been demonstrated that
2nd-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 2nd-order statistical
measures for cosmic shear. Whether the same developments are needed for
3rd-order shear statistics is largely determined by how severe this E-/B-mixing
is for 3rd-order statistics. We test 3rd-order aperture mass statistics against
E-/B-mode mixing, and find that the level of contamination is well-described by
a function of $\theta/\theta_{\rm min}$, with $\theta_{\rm min}$ being the
cut-off scale. At angular scales of $\theta > 10 \;\theta_{\rm min}$, the
decrease in the E-mode signal due to E-/B-mode mixing is smaller than 1
percent, and the leakage into B-modes is even less. For typical small-scale
cut-offs this E-/B-mixing is negligible on scales larger than a few arcminutes.
Therefore, 3rd-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.
