Astronomy and Astrophysics – Astrophysics
Scientific paper
2005-02-25
Schneider P., & Watts P., 2005, A&A 432, 3, 783
Astronomy and Astrophysics
Astrophysics
14 pages, 1 figure. To be published in A&A
Scientific paper
10.1051/0004-6361:20041923
Galaxy-galaxy lensing (GGL) measures the 2-point cross-correlation between galaxies and mass in the Universe. In this work we seek to generalise this effect by considering the third-order correlations between galaxies and mass: galaxy-galaxy-galaxy lensing. Third-order correlations in the cosmic shear field have recently been reported in the VIRMOS-DESCART and CTIO surveys. Such data should also be ideal for measuring galaxy-galaxy-galaxy lensing. Indeed, the effects of these higher-order correlations may have already been detected in recent studies of galaxy-galaxy lensing. In this paper we lay out the basic relations for third-order cross correlations and their projections and introduce a new set of scale dependent third-order bias parameters. We define three new observables: two galaxy-shear-shear correlation functions, $G_{\pm}$, and a galaxy-galaxy-shear correlation, ${\cal G}$. We relate these to the various projected cross-bispectra and give practical estimators for their measurement. We note that the observational signature of these correlators is simply the excess shear-shear correlation measured about foreground galaxies (for $G_{\pm}$) and the average tangential shear around foreground galaxy pairs (for $\cal G$). Finally we derive expressions for the third order aperture mass statistics in terms of both the cross-bispectra and the real-space correlation functions. (Abridged)
Schneider Peter
Watts Peter
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