Statistical strong lensing II. Cosmology and galaxy structure with time-delay lenses

Context. Time-delay lensing is a powerful tool for measuring the Hubble constant H-0. However, in order to obtain an accurate estimate of H-0 from a sample of time-delay lenses, very good knowledge of the mass structure of the lens galaxies is needed. Strong lensing data on their own are not sufficient to break the degeneracy between H-0 and the lens model parameters on a single object basis. Aims. The goal of this study is to determine whether it is possible to break the H-0-lens structure degeneracy with the statistical combination of a large sample of time-delay lenses, relying purely on strong lensing data with no stellar kinematics information. Methods. I simulated a set of 100 lenses with doubly imaged quasars and related time-delay measurements. I fitted these data with a Bayesian hierarchical method and a flexible model for the lens population, emulating the lens modelling step. Results. The sample of 100 lenses on its own provides a measurement of H-0 with 3% precision, but with a -4% bias. However, the addition of prior information on the lens structural parameters from a large sample of lenses with no time delays, such as that considered in Paper I, allows for a 1% level inference. Moreover, the 100 lenses allow for a 0.03 dex calibration of galaxy stellar masses, regardless of the level of prior knowledge of the Hubble constant. Conclusions. Breaking the H-0-lens model degeneracy with lensing data alone is possible, but 1% measurements of H-0 require either many more than 100 time-delay lenses or knowledge of the structural parameter distribution of the lens population from a separate sample of lenses.