Annu. Rev. Astron. Astrophys. 1998. 36: 599-654
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5.2. Gravitational Lensing

Gravitational lensing provides a powerful way to study the distribution of matter in the Universe through the deflection of light from distant sources. There are many aspects of lensing, but only a few have been studied with cosmological simulations. An excellent (though already dated) review was given by Blandford & Narayan (1992). Here we summarize applications of simulations in two areas: strong gravitational lensing (formation of double images and long arcs) and weak lensing by clusters.

Cen et al (1994a) used cosmological simulations to estimate the frequency distribution of splitting angles for background QSOs lensed by the mass in their simulations. Their work extended an analytic treatment by Narayan & White (1988) based on the Press-Schechter formalism. Cen et al showed that, when the power spectrum is normalized by the COBE anisotropy, the CDM model predicts many lenses of separations greater than 8 arcsec, which contradicts observations. Wambsganss et al (1995) reached a similar conclusion based on simulated maps of the sky lensed by the mass distribution in their CDM simulation. Bartelmann et al (1995) used realistic cluster potentials from cosmological simulations to study the formation of arcs. They showed that the asymmetric cluster potentials greatly increase the frequency of arcs compared with spherically symmetric models. Bartelmann & Steinmetz (1996) noted similarly that arcs form preferentially in clusters with substructure.

Kaiser & Squires (1993) developed a nonparametric method for reconstructing the projected mass distribution of clusters from the coherent weak distortions of background galaxies. Their work has inspired a large number of observational applications and theoretical tests and extensions. Bartelmann et al (1996) have proposed a reconstruction method for the projected mass distribution using chi-squared minimization of image stretching and magnification and tested it with simulations. Bartelmann (1995) used simulations to test the accuracy of cluster mass reconstructions, concluding that the Kaiser & Squires method and variants should provide accurate results. However, the smearing of images caused by atmospheric seeing causes a bias on the order of a factor of two that must be corrected (Wilson et al 1996a).

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