2004MNRAS.354..343T

We present a numerical method to estimate the lensing parameters and the Hubble constant H₀from quadruply imaged gravitational lens systems. The lens galaxy is modelled using both separable deflection potentials and constant mass-to-light ratio profiles, while possible external perturbations have been taken into account by introducing an external shear. The model parameters are recovered by inverting the lens and the time-delay ratio equations and imposing a set of physically motivated selection criteria. We investigate correlations among the model parameters and the Hubble constant. Finally, we apply the codes to the real lensed quasars PG 1115+080 and RX J0911+0551, and combine the results from these two systems to get H₀= 56±23 km/s/Mpc. In addition, we are able to fit to the single systems a general elliptical potential with a non-fixed angular part, and then we model the two-lens systems with the same potential and a shared H₀: in this last case, we estimate H₀= 49⁺⁶_–11km/s/Mpc.