A&A 389, 729-741 (2002)

DOI: 10.1051/0004-6361:20020626

## B-modes in cosmic shear from source redshift clustering

**P. Schneider**

^{1, 2}, L. van Waerbeke^{3, 4}and Y. Mellier^{3, 5}^{1}Institut f. Astrophysik u. Extr. Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

e-mail: peter@astro.uni-bonn.de

^{2}Max-Planck-Institut f. Astrophysik, Postfach 1317, 85741 Garching, Germany

^{3}Institute d'Astrophysique de Paris, 98 bis, boulevard Arago, 75014 Paris, France

^{4}Canadian Institute for Theoretical Astrophysics, 60 St Georges Str., Toronto, M5S 3H8 Ontario, Canada

^{5}Observatoire de Paris, DEMIRM/LERMA, 61 avenue de l'Observatoire, 75014 Paris, France

(Received 19 December 2001 / Accepted 19 April 2002 )

** Abstract **

Weak gravitational lensing by the large scale
structure can be used to probe the dark matter distribution in
the Universe directly and thus to probe cosmological
models. The recent detection of cosmic shear by several groups
has demonstrated the feasibility of this new mode of
observational cosmology. In the currently most extensive
analysis of cosmic shear, it was found that the shear field
contains unexpected modes, so-called , which are
thought to be unaccountable for by lensing. can in
principle be generated by an intrinsic alignment of galaxies
from which the shear is measured, or may signify some
remaining systematics in the data reduction and analysis. In
this paper we show that in fact *are produced* by
lensing itself. The effect comes about through the clustering
of source galaxies, which in particular implies an angular
separation-dependent clustering in redshift. After presenting
the theory of the decomposition of a general shear field
into E- and , we calculate their respective power
spectra and correlation functions for a clustered source
distribution. Numerical and analytical estimates of the
relative strength of these two modes show that the resulting
is very small on angular scales larger than a few
arcminutes, but its relative contribution rises quickly
towards smaller angular scales, with comparable power in both
modes at a few arcseconds. The relevance of this effect with
regard to the current cosmic shear surveys is discussed; it
can not account for the apparent detection of a
contribution on large angular scales in the cosmic shear
analysis of van Waerbeke et al. (2002).

**Key words:**cosmology

**--**gravitational lensing

**--**large-scale structure of the Universe

Offprint request: P. Schneider, peter@astro.uni-bonn.de

**©**

*ESO 2002*