We have previously reported the discovery of strong gravitational lensing by faint elliptical galaxies using the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, and here we investigate their potential usefulness in placing 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 that use a spherical mass distribution having various profiles, both empirical and following those predicted by cold dark matter simulations. These models also include a gravitational shear term. The model parameters and associated errors have been derived by two-dimensional analysis of the observed 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 fitted 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, Lambda, using gravitational lenses. References: 20
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