Measuring the Galaxy-Galaxy-Mass Three-point Correlation Function with Weak Gravitational Lensing

We discuss the galaxy-galaxy-mass three-point correlation function and show how to measure it with weak gravitational lensing. The method entails choosing a large of pairs of foreground lens galaxies and constructing a mean shear map with respect to their axis, by averaging the ellipticities of background source galaxies. An average mass map can be reconstructed from this shear map and this will represent the average mass distribution around pairs of galaxies. We show how this mass map is related to the projected galaxy-galaxy-mass three-point correlation function. Using a large N-body dark matter simulation populated with galaxies using the Halo Occupation Distribution (HOD) bias prescription, we compute these correlation functions, mass maps, and shear maps. The resultant mass maps are distinctly bimodal, tracing the galaxy centers and remaining anisotropic up to scales much larger than the galaxy separation. At larger scales, the shear is approximately tangential about the center of the pair but with small azimuthal variation in amplitude. We estimate the signal-to-noise ratio of the reconstructed mass maps for a survey of similar depth to the Sloan Digital Sky Survey (SDSS) and conclude that the galaxy-galaxy-mass three-point function should be measurable with the current SDSS weak lensing data. Measurements of this three-point function, along with galaxy-galaxy lensing and galaxy auto-correlation functions, will provide new constraints on galaxy bias models. The anisotropic shear profile around close pairs of galaxies is a prediction of cold dark matter models and may be difficult to reconcile with alternative theories of gravity without dark matter.