A Bayesian approach to gravitational lens model selection

Abstract

Strong gravitational lenses are unique cosmological probes. These produce multiple images of a single source. Whether a single galaxy, a group or a cluster, extracting cosmologically relevant information requires an accurate modeling of the lens mass distribution. A variety of models are available, nevertheless discrimination between them as primarily relied on the quality of fit without accounting for the size of the prior model parameter space. This is a problem of model selection that we address in the Bayesian statistics framework by evaluating Bayes' factors. Using simple test cases, we show that the assumption of more complicate lens models may not be justified given the level of accuracy of the available data. Images produced by strong gravitational lenses result of different light-paths. If the source behind the lens has a variable luminosity, this will manifest with a time delay between the images. This time delay t depends on the gravitational potential of the lens, and the underlying cosmological model. Therefore, we can derive constraints on cosmological parameters (in particular H0), provided a lens model is assumed. Hence, lens modeling as well as accurate measurements capable of discriminating between models are critical to the study of time delays. We aim to tackle this problem from the point of view of Bayesian model selection analysis (see e.g. [2]). A large number of lens models have been proposed in a vast literature. Given the fact that observables are limited to the position of the images, their time delay and flux ratio, we restrict our analysis to simple examples characterized by a few parameters. In particular we consider two models for lenses with two images, so called "double" lenses (for a review on lensing, see [1]). © Springer Science+Business Media New York 2013.