A Bayesian approach to strong lensing modelling of galaxy clusters

TLDR: In this article, a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence is described, using a publicly available Markov chain Monte-Carlo (MCMC) sampler, allowing us to avoid local minima in the likelihood functions.

Abstract: In this paper, we describe a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence We use a publicly available Markov chain Monte-Carlo (MCMC) sampler ('bayesys'), allowing us to avoid local minima in the likelihood functions To illustrate the power of the MCMC technique, we simulate three clusters of galaxies, each composed of a cluster-scale halo and a set of perturbing galaxy-scale subhalos We ray-trace three light beams through each model to produce a catalogue of multiple images, and then use the MCMC sampler to recover the model parameters in the three different lensing configurations We find that, for typical Hubble Space Telescope (HST)-quality imaging data, the total mass in the Einstein radius is recovered with ~1?5% error according to the considered lensing configuration However, we find that the mass of the galaxies is strongly degenerated with the cluster mass when no multiple images appear in the cluster centre The mass of the galaxies is generally recovered with a 20% error, largely due to the poorly constrained cut-off radius Finally, we describe how to rank models quantitatively using the Bayesian evidence We confirm the ability of strong lensing to constrain the mass profile in the central region of galaxy clusters in this way Ultimately, such a method applied to strong lensing clusters with a very large number of multiple images may provide unique geometrical constraints on cosmology The implementation of the MCMC sampler used in this paper has been done within the framework of the lenstool software package, which is publicly available