Investigation of Gravitational Lens Mass Models

We have previously reported the discovery of strong gravitational lensing by faint elliptical galaxies using the WFPC2 on HST and here we investigate their potential usefulness in putting constraints on lens mass models. We compare various ellipsoidal surface mass distributions, including those with and without a core radius, as well as models in which the mass distributions are assumed to have the same axis ratio and orientation as the galaxy light. We also study models which use a spherical mass distribution having various profiles, both empirical and following those predicted by CDM simulations. These models also include a gravitational shear term. The model parameters and associated errors have been derived by 2-dimensional analysis of the observed HST WFPC2 images. The maximum likelihood procedure iteratively converges simultaneously on the model for the lensing elliptical galaxy and the lensed image components. The motivation for this study was to distinguish between these mass models with this technique. However, we find that, despite using the full image data rather than just locations and integrated magnitudes, the lenses are fit equally well with several of the mass models. Each of the mass models generates a similar configuration but with a different magnification and cross-sectional area within the caustic, and both of these latter quantities govern the discovery probability of lensing in the survey. These differences contribute to considerable cosmic scatter in any estimate of the cosmological constant using gravitational lenses.