Statistical strong lensing. III. Inferences with complete samples of lenses

Abstract: Context. Existing samples of strong lenses have been assembled by giving priority to sample size, at the cost of having a complex selection function. With the advent of the next generation of wide-field photometric surveys, however, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness. Aims. There are two main advantages of working with a complete sample of lenses. First, it is possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. This work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features. Methods. I introduced a general formalism for the statistical analysis of a sample of strong lenses with known selection function, then tested it on simulated data. The simulation consists of a population of $10^5$ galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of $\sim10^3$ strong lenses, complete above an observational cut. Mandatory. The method allows to recover the distribution in Einstein radius and mass density slope of the galaxy population in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available. Conclusions. Complete samples of lenses are a powerful asset to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population.