  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.
