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

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

Corresponding author: B. Ménard, menard@mpa-garching.mpg.de

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 .