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

Attempts to constrain the Hubble constant using the strong gravitational lens system Q0957+561 are limited by systematic uncertainties in the mass model, since the time delay is known very precisely. One important systematic effect is the mass-sheet degeneracy, which arises because strong lens modeling cannot constrain the presence or absence of a uniform mass sheet κ, which rescales H 0 by the factor (1 – κ). In this paper, we present new constraints on the mass sheet derived from a weak-lensing analysis of the Hubble Space Telescope imaging of a 6 arcmin square region surrounding the lensed quasar. The average mass sheet within a circular aperture (the strong lens model region) is constrained by integrating the tangential weak gravitational shear over the surrounding area. We find the average convergence within a 30'' radius around the lens galaxy to be κ(<30'') = 0.166 ± 0.056 (1σ confidence level), normalized to the quasar redshift. This includes contributions from both the lens galaxy and the surrounding cluster. We also constrain a few other low-order terms in the lens potential by applying a multipole aperture mass formalism to the gravitational shear in an annulus around the strong-lensing region. Implications for strong lens models and the Hubble constant are discussed in an accompanying paper.