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 where we use different samples of multiple image families , different parametrizations of the mass distribution , as well as cosmological parameters .
As input information for the strong lensing models , we use the CLASH HST imaging data and spectroscopic follow-up observations , carried out with the VIMOS and MUSE spectrographs on the VLT , to identify and characterize bona-fide multiple image families , and measure their redshifts down to m _ { F 814 W } \simeq 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 10 individual sources .
These also include a multiply lensed Lyman- \alpha 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 .
MCMC techniques are used to quantify errors and covariances of the best-fit parameters .
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 \arcsec . 3 in a fixed flat \Lambda CDM 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 parametrisation 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 further , although 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 , probed via angular diameter distance ratios between the lens and the sources and the observer and the sources , can be partially removed .
Allowing cosmological parameters to vary together with the cluster parameters , we find ( at 68 \% confidence level ) \Omega _ { m } = 0.25 ^ { +0.13 } _ { -0.16 } and w = -1.07 ^ { +0.16 } _ { -0.42 } for a flat \Lambda CDM model , and \Omega _ { m } = 0.31 ^ { +0.12 } _ { -0.13 } and \Omega _ { \Lambda } = 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 \arcsec . 3 \pm 0 \arcsec . 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 .