The Hubble Constant from the Gravitational Lens

We present a refined gravitational lens model of the four-image lens system B1608+656 based on new and improved observational constraints: (i) the three independent time-delays and flux-ratios from Very Large Array (VLA) observations, (ii) the radio-image positions from Very Large Baseline Array (VLBA) observations, (iii) the shape of the deconvolved Einstein Ring from optical and infrared Hubble Space Telescope (HST) images, (iv) the extinction-corrected lens-galaxy centroids and structural parameters, and (v) a stellar velocity dispersion, σap = 247± 35 km s , of the primary lens galaxy (G1), obtained from an echelle spectrum taken with the Keck–II telescope. The lens mass model consists of two elliptical mass distributions with power-law density profiles and an external shear, totaling 22 free parameters, including the density slopes which are the key parameters to determine the value of H0 from lens time delays. This has required the development of a new lens code that is highly optimized for speed. The minimum–χ model reproduces all observations very well, including the stellar velocity dispersion and the shape of the Einstein Ring. A combined gravitational-lens and stellar dynamical analysis leads to a value of the Hubble Constant of H0=75 +7 −6 km s −1 Mpc (68% CL; Ωm=0.3, ΩΛ=0.7). The non-linear error analysis includes correlations between all free parameters, in particular the density slopes of G1 and G2, yielding an accurate determination of the random error on H0. The lens galaxy G1 is ∼5 times more massive than the secondary lens galaxy (G2), and has a mass density slope of γ G1 = 2.03 +0.14 −0.14±0.03 (68% CL) for ρ ∝ r ′ , very close to isothermal (γ=2). After extinction-correction, G1 exhibits a smooth surface brightness distribution with an R profile and no apparent evidence for tidal disruption by interactions with G2. Given the scope of the observational constraints and the gravitational-lens models, as well as the careful corrections to the data, we believe this value of H0 to be little affected by known systematic errors (. 5%). Subject headings: gravitational lensing — cosmology: distance scale — galaxies: elliptical and lenticular, cD — galaxies: structure — galaxies: kinematics and dynamics