Values of H0 from models of the gravitational lens 0957+561

The lensed double QSO 0957 + 561 has a well-measured time delay and hence is useful for a global determination of H-0. Uncertainty in the mass distribution 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 to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply imaged sources that have been detected. We obtain the first adequate fit to all the observations only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models that are consistent with observations 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 constrain 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% CL). 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 and <(kappa)over bar>(30 "). The range of H-0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power-law density profiles. We therefore caution against using simple isothermal or power-law mass models to derive H-0 from other time-delay systems. High signal-to-noise ratio imaging of multiple or extended lensed features will greatly reduce the H-0 uncertainties when fitting complex models to time-delay lenses.