CLASH-VLT: A highly precise strong lensing model of the galaxy cluster RXC J2248.7 - 4431 (Abell S1063) and prospects for cosmography

Aims. We perform a comprehensive study of the total mass distribution of the galaxy cluster RXC J2248.7-4431 (z = 0.348) with a set of high-precision strong lensing models, which take advantage of extensive spectroscopic information on many multiply lensed systems. In the effort to understand and quantify inherent systematics in parametric strong lensing modelling, we explore a collection of 22 models in which we use different samples of multiple image families, different parametrizations of the mass distribution and cosmological parameters. Methods. As input information for the strong lensing models, we use the Cluster Lensing And Supernova survey with Hubble (CLASH) imaging data and spectroscopic follow-up observations, with the VIsible Multi-Object Spectrograph (VIMOS) and Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT), to identify and characterize bona fide multiple image families and measure their redshifts down to mF814W ? 26. A total of 16 background sources, over the redshift range 1.0-6.1, are multiply lensed into 47 images, 24 of which are spectroscopically confirmed and belong to ten individual sources. These also include a multiply lensed Lyman-α blob at z = 3.118. The cluster total mass distribution and underlying cosmology in the models are optimized by matching the observed positions of the multiple images on the lens plane. Bayesian Markov chain Monte Carlo techniques are used to quantify errors and covariances of the best-fit parameters. Results. We show that with a careful selection of a large sample of spectroscopically confirmed multiple images, the best-fit model can reproduce their observed positions with a rms scatter of 0.? 30.? 3 in a fixed flat ΛCDM cosmology, whereas the lack of spectroscopic information or the use of inaccurate photometric redshifts can lead to biases in the values of the model parameters. We find that the best-fit parametrization for the cluster total mass distribution is composed of an elliptical pseudo-isothermal mass distribution with a significant core for the overall cluster halo and truncated pseudo-isothermal mass profiles for the cluster galaxies. We show that by adding bona fide photometric-selected multiple images to the sample of spectroscopic families, one can slightly improve constraints on the model parameters. In particular, we find that the degeneracy between the lens total mass distribution and the underlying geometry of the Universe, which is probed via angular diameter distance ratios between the lens and sources and the observer and sources, can be partially removed. Allowing cosmological parameters to vary together with the cluster parameters, we find (at 68% confidence level) Ωm = 0.25+ 0.13-0.16 and w = -1.07+ 0.16-0.42 for a flat ΛCDM model, and Ωm = 0.31+ 0.12-0.13 and ΩΛ = 0.38+ 0.38-0.27 for a Universe with w = -1 and free curvature. Finally, using toy models mimicking the overall configuration of multiple images and cluster total mass distribution, we estimate the impact of the line-of-sight mass structure on the positional rms to be 0.? 3 ± 00.? 3 ± 0.? 1. We argue that the apparent sensitivity of our lensing model to cosmography is due to the combination of the regular potential shape of RXC J2248, a large number of bona fide multiple images out to z = 6.1, and a relatively modest presence of intervening large-scale structure, as revealed by our spectroscopic survey.