Improved Constraints on the Gravitational Lens Q0957+561. II. Strong Lensing

We present a detailed strong lensing analysis of a Hubble Space Telescope/Advanced Camera for Surveys legacy data set for the first gravitational lens, Q0957+561. With deep imaging we identify 24 new strongly lensed features, which we use to constrain mass models. We model the stellar component of the lens galaxy using the observed luminosity distribution and the dark matter halo using several different density profiles. We draw on the weak lensing analysis by Nakajima et al. to constrain the mass sheet and environmental terms in the lens potential. Adopting the well-measured time delay, we find H{sub 0} = 85{sup +14}{sub -13} km s{sup -1} Mpc{sup -1} (68% CL) using lensing constraints alone. The principal uncertainties in H{sub 0} are tied to the stellar mass-to-light ratio (a variant of the radial profile degeneracy in lens models). Adding constraints from stellar population synthesis models, we obtain H{sub 0} = 79.3{sup +6.7}{sub -8.5} km s{sup -1} Mpc{sup -1} (68% CL). We infer that the lens galaxy has a rising rotation curve and a dark matter distribution with an inner core. Intriguingly, we find the quasar flux ratios predicted by our models to be inconsistent with existing radio measurements, suggesting the presence of substructure in the lens.