Gravitational Lensing by Dark Matter Halos with Non-universal Density Profiles

The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of matter in the universe. By comparing predicted strong lensing probabilities with observations, we can test the mass distribution of dark matter halos, in particular, the inner density slope. In this letter, unlike previous work that directly models the density profiles of dark matter halos semi-analytically, we generalize the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White (GNFW) models of three populations with slopes, $\alpha$, of about -1.5, -1.3 and -1.1 for galaxies, groups and clusters, respectively. This approach is an alternative and independent way to examine the slopes of mass density profiles of halos. We present calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant $\Lambda$. It is shown that the compound model of density profiles does not match well with the observed lensing probabilities derived from the Jodrell-Bank VLA Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey data. Together with the previous work on lensing probability, our results suggest that a singular isothermal sphere mass model of less than about $10^{13}h^{-1}M_{\sun}$ can predict strong lensing probabilities that are consistent with observations of small splitting angles.