Gravitational Lens Time Delays: A Statistical Assessment of Lens Model Dependences and Implications for the Global Hubble Constant

Time delays between lensed multiple images have been known to provide an interesting probe of the Hubble constant, but such application is often limited by degeneracies with the shape of lens potentials. We propose a new statistical approach to examine the dependence of time delays on the complexity of lens potentials, such as higher-order perturbations, non-isothermality, and substructures. Specifically, we introduce a reduced time delay and explore its behavior as a function of the image configuration that is characterized by the asymmetry and opening angle of the image pair. In particular we derive a realistic conditional probability distribution for a given image configuration. We find that the probability distribution is sensitive to the image configuration such that more symmetric and/or smaller opening angle image pairs are more easily affected by perturbations on the primary lens potential. On average time delays of double lenses are less scattered than those of quadruple lenses. Furthermore, the realistic conditional distribution allows a new statistical method to constrain the Hubble constant from observed time delays. We find that 15 published time delay quasars constrain the Hubble constant to be H_0=70+/-3 km/s/Mpc. While systematic errors coming from the heterogeneous nature of the quasar sample and the uncertainty of the input distribution of lens potentials should be considered, reasonable agreement with other estimates indicates the usefulness of our new approach as a cosmological and astrophysical probe, particularly in the era of large-scale synoptic surveys. (Abridged