A ug 2 00 4 Strong Gravitational Lenses in a Cold Dark Matter Universe

We present theoretical and observational studies of strong gravitational lenses produced by clusters of galaxies. Our purpose is to test the Cold Dark Matter (CDM) model at small and highly nonlinear scales where it has been claimed that the CDM model may confront several difficulties. We concentrate our attention on the statistics of strong gravitational lenses because the strong lensing is sensitive to the mass distributions of central, high-density regions of lensing clusters where the cold and collisionless hypotheses on dark matter are crucial. We use two complementary statistics, lensed arcs and quasars, to probe the mass distributions. First, we construct a triaxial lens model, and develop a new method to include triaxiality of dark halos in the lens statistics. We find that the effect of triaxiality is significant; it enhances lensing probabilities by a factors of a few to ten, assuming the degree of triaxiality predicted in the CDM model. Thus it is essential to take triaxiality into account in the lens statistics. In particular, we argue that both central concentration and large triaxiality of dark halos are required to reproduce the observed number of arcs in clusters; thus the result can be interpreted as a strong evidence for the cold and collisionless dark matter. One of the most notable advantages of the triaxial modeling over the spherical modeling is that the triaxial modeling allows us to predict image multiplicities. We find that the CDM halos predict significant fraction (more than 20%) of naked cusp lenses, unlike lensing by isothermal galaxies where naked cusp configurations are rare. In addition, we point out the image multiplicities depend strongly on the central concentration of dark halos. Therefore we propose image multiplicities as a new powerful test of the CDM model. While many lensed arcs are known, no quasar strongly lensed by clusters of galaxies has been discovered. We searched for large-separation lensed quasars from the data of the Sloan Digital Sky Survey, and succeeded in discovering the first large-separation lensed quasar SDSS J1004+4112. The system consists of four lensed images of a quasar at z = 1.73. We identify the lensing cluster at z = 0.68, from the deep imaging and spectroscopy of galaxies in the cluster. We calculate the expected probabilities and image multiplicities for lensed quasars in the SDSS, and find that the discovery of the large-separation quadruple lens SDSS J1004+4112 is quite consistent with the theoretical predictions based on the CDM model.