Pixelated lenses and H₀ from time-delay quasars

Observed time delays between images of a lensed QSO lead to the determination of the Hubble constant by Refsdal's method, provided the mass distribution in the lensing galaxy is reasonably well known. Since the two or four QSO images usually observed are woefully inadequate by themselves to provide a unique reconstruction of the galaxy mass, most previous reconstructions have been limited to simple parameterized models, which may lead to large systematic errors in the derived H₀ by failing to consider enough possibilities for the mass distribution of the lens. We use nonparametric modeling of galaxy lenses to better explore physically plausible but not overly constrained galaxy mass maps, all of which reproduce the lensing observables exactly, and derive the corresponding distribution of H₀'s. Blind tests - in which one of us simulated galaxy lenses, lensing observables, and a value for H₀ and the other applied our modeling technique to estimate H₀ - indicate that our procedure is reliable. For four simulated lensed QSOs, the distributions of inferred H₀ have an uncertainty of ≃ 10% at 90% confidence. Application to published observations of the two best-constrained time-delay lenses, PG 1115+080 and B1608+656, yields H₀ = 61 ± 11 km s^-1 Mpc^-1 at 68% confidence and 61 ± 18 km s^-1 Mpc^-1 at 90% confidence.