Strong lensing constraints on the velocity dispersion and density profile of elliptical galaxies

We use the statistics of strong gravitational lensing from the Cosmic Lens All-Sky Survey to impose constraints on the velocity dispersion and density profile of elliptical galaxies. This approach differs from much recent work, where the luminosity function, velocity dispersion and density profile have been typically assumed in order to constrain cosmological parameters. It is indeed remarkable that observational cosmology has reached the point where we can consider using cosmology to constrain astrophysics, rather than vice versa. We use two different observables to obtain our constraints: total optical depth and angular distributions of lensing events. In spite of the relatively poor statistics and the uncertain identification of lenses in the survey, we obtain interesting constraints on the velocity dispersion and density profiles of elliptical galaxies. For example, assuming the singular isothermal sphere density profile and marginalizing over other relevant parameters, we find 168 less than or equal to sigma(*) less than or equal to 200 km s(-1) (68 per cent confidence level), and 158 less than or equal to sigma(*) less than or equal to 220 km s(-1) (95 per cent confidence level). Furthermore, if we instead assume a generalized Navarro-Frenk-White density profile and marginalize over other parameters, the slope of the profile is constrained to be 1.50 less than or equal to beta less than or equal to 2.00 (95 per cent confidence level). We also constrain the concentration parameter as a function of the density profile slope in these models. These results are essentially independent of the exact knowledge of cosmology. We briefly discuss the possible impact on these constraints of allowing the galaxy luminosity function to evolve with redshift, and also possible useful future directions for exploration.