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 , \sigma _ { ap } = 247 \pm 35 km { s } ^ { -1 } , 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 H _ { 0 } from lens time delays .
This has required the development of a new lens code that is highly optimized for speed .
The minimum– \chi ^ { 2 } 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 H _ { 0 } =75 ^ { +7 } _ { -6 } km { s } ^ { -1 } { Mpc } ^ { -1 } ( 68 % CL ; \Omega _ { m } =0.3 , \Omega _ { \Lambda } =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 H _ { 0 } .
The lens galaxy G1 is \sim 5 times more massive than the secondary lens galaxy ( G2 ) , and has a mass density slope of \gamma _ { G 1 } ^ { \prime } = 2.03 ^ { +0.14 } _ { -0.14 } \pm 0.03 ( 68 % CL ) for \rho \propto r ^ { - \gamma ^ { \prime } } , very close to isothermal ( \gamma ^ { \prime } =2 ) .
After extinction-correction , G1 exhibits a smooth surface brightness distribution with an R ^ { 1 / 4 } 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 H _ { 0 } to be little affected by known systematic errors ( \lesssim 5 % ) .