Cluster Cores, Gravitational Lensing, and Cosmology

Many multiply--imaged quasars have been found over the years, but none so far with image separation in excess of $8\arcsec$. The absence of such large splittings has been used as a test of cosmological models: the standard Cold Dark Matter model has been excluded on the basis that it predicts far too many large--separation double images. These studies assume that the lensing structure has the mass profile of a singular isothermal sphere. However, such large splittings would be produced by very massive systems such as clusters of galaxies, for which other gravitational lensing data suggest less singular mass profiles. Here we analyze two cases of mass profiles for lenses: an isothermal sphere with a finite core radius (density $\rho \propto (r^2+r_{core}^2)^{-1})$, and a Hernquist profile ($\rho \propto r^{-1}(r+a)^{-3}$). We find that small core radii $r_{core} \sim 30 h^{-1}$ kpc, as suggested by the cluster data, or large $a \gsim 300 h^{-1}$ kpc, as needed for compatibility with gravitational distortion data, would reduce the number of large--angle splittings by an order of magnitude or more. Thus, it appears that these tests are sensitive both to the cosmological model (number density of lenses) and to the inner lens structure, which is unlikely to depend sensitively on the cosmology, making it difficult to test the cosmological models by large--separation quasar lensing until we reliably know the structure of the lenses themselves.