Early-Type Galaxies, Dark Halos, and Gravitational Lensing Statistics

We present calculations of the expected statistics of gravitational lensing of quasars in the Hubble Space Telescope snapshot survey. We first model early-type (elliptical and SO) galaxies using their observed surface brightness profiles and dynamically inferred mass-to-light ratios. Our work improves upon previous calculations, which have generally approximated the galaxy potentials by isothermal spheres. For standard cosmologies, the predicted number of lensed quasars in the survey is 1.1-2.8, 98% of which have image separations less than 2", compared to the four lenses observed, two of which have separations greater than 2". These constant mass-to-light ratio models are rejected. Even in an extreme model in which every early-type galaxy is assumed to reside in a dense cluster, the probability of producing lenses with greater than 2" separation is too small. Clusters are inefficient in enlarging the image separations because too much fine tuning between the cluster mass profile and the galaxy position within the cluster is required. The predicted number of lenses and their image separations agree well with the observations (at the ∼30% level) if a dark isothermal halo component is added to the early-type galaxies. The halo component must have a core radius small enough to yield an effectively flat rotation curve and a velocity dispersion σ* ≳ 270 km s-1 for an Lsun galaxy. The observed lensing statistics strongly favor the hypothesis that dark halos are generically present in early-type galaxies. Although stars dominate the mass at small radii and determine the lensing cross section, the dark matter at larger radii increases the typical image separation and enhances the lensing probability through the magnification bias. Models with a cosmological constant λ produce more lens systems, but with similar image separations to standard models. Models with nonzero λ therefore overpredict the number of small-separation lenses if there are no dark halos or overpredict the total number of lenses if a halo component is included. The observations constrain λ to be ≲ 0.7, so that a cosmological constant no longer provides an attractive solution for the "age problem" of the universe. These conclusions are robust with respect to uncertainties in the model parameters.