Nonsingular density profiles of dark matter halos and Strong   gravitational lensing
  We use the statistics of strong gravitational lenses to investigate whether mass profiles with a flat density core are supported. The probability for lensing by halos modeled by a nonsingular truncated isothermal sphere (NTIS) with image separations greater than a certain value (ranging from zero to ten arcseconds) is calculated. NTIS is an analytical model for the postcollapse equilibrium structure of virialized objects derived by Shapiro, Iliev & Raga. This profile has a soft core and matches quite well with the mass profiles of dark matter-dominated dwarf galaxies deduced from their observed rotation curves. It also agrees well with the NFW (Navarro-Frenk-White) profile at all radii outside of a few NTIS core radii. Unfortunately, comparing the results with those for singular lensing halos (NFW and SIS+NFW) and strong lensing observations, the probabilities for lensing by NTIS halos are far too low. As this result is valid for any other nonsingular density profiles (with a large core radius), we conclude that nonsingular density profiles (with a large core radius) for CDM halos are ruled out by statistics of strong gravitational lenses. 
Da-Ming Chen