Mapping the 3D dark matter with weak lensing in COMBO-17

We present a three-dimensional (3D) lensing analysis of the z = 0.16 supercluster A901/2, resulting in a 3D map of the dark matter distribution within a 3 × 10⁵ [h^-1 Mpc]³ volume. This map is generated from a combined catalogue of 3D galaxy coordinates together with shear estimates, using R-band imaging and photometric redshifts from the COMBO-17 survey. We perform a χ² fit of isothermal spheres to the tangential shear pattern around each cluster as a function of redshift to estimate the 3D positions and masses of the main clusters in the supercluster from lensing alone. Motivated by the appearance of a second cluster behind A902 in galaxy number density, we also fit a two-cluster model to A902. We then present the first 3D map of the dark-matter gravitational potential field, Φ, from weak lensing using the Kaiser-Squires and Taylor inversion methods. These maps clearly show the potential wells of the main supercluster components, including the new cluster behind A902, and demonstrate the applicability of 3D dark-matter mapping and projection-free, mass-selected cluster finding to current data. Finally, we develop the halo model of dark matter and galaxy clustering and compare this with the auto- and cross-correlation functions of the 3D gravitational potential, galaxy number densities and galaxy luminosity densities measured in the A901/2 field. We find significant anticorrelations between the gravitational potential field and the galaxy number density and luminosities, as expected due to baryonic infall into dark-matter concentrations. We find good agreement with the halo model for the number densities and luminosity correlation functions, but some disagreement with the shape of the gravitational potential correlation function, which we attribute to finite-field effects.