Detection of (dark) matter concentrations via weak gravitational lensing

The distortion of images of faint background galaxies by (weak) gravitationallensing can be used to measure the mass distribution of the deflector. Theimage distortions can be used to define a weighted mean of the mass inside acircular aperture, as was first suggested by Kaiser. The aperture mass can beused to {\it detect} dark matter concentrations. Keeping in mind thatwide-field cameras will become increasingly available, this method can be usedto search for mass concentrations on wide-field images. To do this, theaperture mass measure is generalized to account for different weightingfunctions. For each such weighting function, a signal-to-noise ratio can becalculated. For an assumed mass profile of the density concentrations, theweighting function can be chosen such as to maximize the resultingsignal-to-noise ratio. Numerical simulations which adopt parameterscharacteristic of 4-m class telescopes are then used to show that dark haloswith a velocity dispersion in excess of $\sim 600$\ts km/s can be reliablydetected as significant peaks in the signal-to-noise map. The effects of seeingand an anisotropic PSF are then investigated and shown to be less importantthan might be feared. It is thus suggested that the method of aperture massmeasures developed here can be used to obtain a mass-selected sample of darkhalos, in contrast to flux-selected samples. Shear fields around high-redshiftbright QSOs as detected by Fort et al. provide a first successful applicationof this strategy. The simplicity of the method allows its routine applicationto wide-field images of sufficient depth and image quality.Comment: 24 pages, Plain-Tex, no macros needed, including 10 figures, submitted to Monthly Notices of the Royal Astronomical Society; the result (15) and (16) of the paper was derived previously by Kaiser et al. (1994); proper reference is now give