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

We use the statistics of strong gravitational lensing from the JVAS/CLASS 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 were typically {\it assumed} in order to constrain cosmological parameters. We use three different observables to obtain our constraints (total optical depth, and angular and redshift 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 SIS density profile and marginalizing over other relevant parameters, we find $152 {\rm km/s}\leq \sigma_* \leq 186 {\rm km/s}$ (68% CL), and $138 {\rm km/s}\leq \sigma_* \leq 206 {\rm km/s}$ (95% CL). Furthermore, if we instead assume a generalized NFW density profile and marginalize over other parameters, the slope of the profile is constrained to be $1.58\leq\beta\leq 1.98$ (95% CL), although in this case the total optical depth tends to favor somewhat lower values of $\beta$ than does the likelihood function based on angular splitting and redshift dependence of the lenses. 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.