Values of H-0 from models of the gravitational lens 0957+561

The lensed double QSO 0957 + 561 has a well-measured time delay and hence i s useful for a global determination of H-0. Uncertainty in the mass distrib ution of the lens is the largest source of uncertainty in the derived H-0. We investigate the range of H-0 produced by a set of lens models intended t o mimic the full range of astrophysically plausible mass distributions, usi ng as constraints the numerous multiply imaged sources that have been detec ted. We obtain the first adequate fit to all the observations only if we in clude effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart fr om circular symmetry as well. Lens models that are consistent with observat ions to 95% confidence level (CL) indicate H-0 = 104(-23)(+31)(1 - <(kappa) over bar>(30 ")) km s(-1) Mpc-l. Previous weak-lensing measurements constra in the mean mass density within 30 " of G1 to be <(kappa)over bar>(30 ") = 0.26 +/- 0.16 (95% CL), implying H-0 = 77(-24)(+29) km s(-1) Mpc(-1) (95% C L). The best-fitting models span the range 65-80 km s(-1) Mpc(-1). Further observations will shrink the confidence interval for both the mass model an d <(kappa)over bar>(30 "). The range of H-0 allowed by the full gamut of ou r lens models is substantially larger than that implied by limiting conside ration to simple power-law density profiles. We therefore caution against u sing simple isothermal or power-law mass models to derive H-0 from other ti me-delay systems. High signal-to-noise ratio imaging of multiple or extende d lensed features will greatly reduce the H-0 uncertainties when fitting co mplex models to time-delay lenses.