A&A 409, 411-421 (2003)

DOI: 10.1051/0004-6361:20031095

## Measuring with higher-order quasar-galaxy correlations induced by weak lensing

**B. Ménard**

^{1, 2}, M. Bartelmann^{1}and Y. Mellier^{2, 3}^{1}Max-Planck-Institut für Astrophysik, PO Box 1317, 85741 Garching, Germany

^{2}Institut d'Astrophysique de Paris, 98bis Bld. Arago, 75014 Paris, France

^{3}LERMA, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, France

(Received 21 August 2002 / Accepted 20 May 2003)

** Abstract **

Via the magnification bias, gravitational lensing by large-scale
structures causes angular cross-correlations between distant quasars and
foreground galaxies on angular scales of arcminutes and above. We
investigate the three-point cross-correlation between quasars and galaxy
pairs measurable via the second moment of the galaxy counts around quasars
and show that it reaches the level of a few per cent on angular scales near
one arcminute. Combining two- and three-point correlations, a skewness
parameter can be defined which is shown to be virtually independent of the
shape and normalisation of the dark-matter power spectrum. If the galaxy
bias is linear and deterministic, the skewness depends on the cosmic matter
density parameter
only; otherwise, it can be used to probe the
non-linearity and stochasticity of the bias. We finally estimate the
signal-to-noise ratio of a skewness determination and find that a sample of
about twenty thousand distant quasars e.g. from the Sloan Digital Sky Survey
should suffice for a direct measurement of
.

**Key words:**cosmology: gravitational lensing

**--**cosmology: large-scale structure of Universe

Offprint request: B. Ménard, menard@mpa-garching.mpg.de

**©**

*ESO 2003*