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 galaxyscale 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 HST-quality imaging data, the total mass in the Einstein radius is recovered with ∼ 1% to 5% error according to the considered lensing configuration. However, we find that the mass of the galaxies is strongly degenerate 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, due largely 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. ‡ PACS numbers: 90 98.62.Sb 07.05.Kf 98.65.Cw 95.35.+d ‡

While clusters of galaxies are considered one of the most important cosmological probes, the standard spherical modelling of the dark matter and the intracluster medium is only a rough approximation. Indeed, it is well established both theoretically and observationally that galaxy clusters are much better approximated as triaxial ob-

We present a strong-lensing analysis of MACSJ0717.5+3745 (hereafter MACS J0717), based on the full depth of the Hubble Frontier Field (HFF) observations, which brings the number of multiply imaged systems to 61, ten of which have been spectroscopically confirmed. The total number of images comprised in these systems rises to 165, compared to 48 images in 16 systems before the HFF observations. Our analysis uses a parametric mass reconstruction technique, as implemented in the L software, and the subset of the 132 most secure multiple images to constrain a mass distribution composed of four large-scale mass components (spatially aligned with the four main light concentrations) and a multitude of galaxy-scale perturbers. We find a superposition of cored isothermal mass components to provide a good fit to the observational constraints, resulting in a very shallow mass distribution for the smooth (large-scale) component. Given the implications of such a flat mass profile, we investigate whether a model composed of "peaky" non-cored mass components can also reproduce the observational constraints. We find that such a non-cored mass model reproduces the observational constraints equally well, in the sense that both models give comparable total rms. Although the total (smooth dark matter component plus galaxy-scale perturbers) mass distributions of both models are consistent, as are the integrated two-dimensional mass profiles, we find that the smooth and the galaxy-scale components are very different. We conclude that, even in the HFF era, the generic degeneracy between smooth and galaxy-scale components is not broken, in particular in such a complex galaxy cluster. Consequently, insights into the mass distribution of MACS J0717 remain limited, emphasizing the need for additional probes beyond strong lensing. Our findings also have implications for estimates of the lensing magnification. We show that the amplification difference between the two models is larger than the error associated with either model, and that this additional systematic uncertainty is approximately the difference in magnification obtained by the different groups of modelers using pre-HFF data. This uncertainty decreases the area of the image plane where we can reliably study the high-redshift Universe by 50 to 70%.

The existence of strong lensing systems with Einstein radii covering the full mass spectrum, from ∼ 1 − 2 (produced by galaxy scale dark matter haloes) to > 10 (produced by galaxy cluster scale haloes) have long been predicted. Many lenses with Einstein radii around 1 − 2 and above 10 have been reported but very few in between. In this article, we present a sample of 13 strong lensing systems with Einstein radii in the range 3 − 8 (or image separations in the range 6 − 16 ), i.e. systems produced by galaxy group scale dark matter haloes. This group sample spans a redshift range from 0.3 to 0.8. This opens a new window of exploration in the mass spectrum, around 10 13 -10 14 M , a crucial range for understanding the transition between galaxies and galaxy clusters, and a range that have not been extensively probed with lensing techniques. These systems constitute a subsample of the Strong Lensing Legacy Survey (SL2S), which aims to discover strong lensing systems in the Canada France Hawaii Telescope Legacy Survey (CFHTLS). The sample is based on a search over 100 square degrees, implying a number density of ∼ 0.13 groups per square degree. Our analysis is based on multi-colour CFHTLS images complemented with Hubble Space Telescope imaging and ground based spectroscopy. Large scale properties are derived from both the light distribution of elliptical galaxies group members and weak lensing of the faint background galaxy population. On small scales, the strong lensing analysis yields Einstein radii between 2.5 and 8 . On larger scales, strong lens centres coincide with peaks of light distribution, suggesting that light traces mass. Most of the luminosity maps have complicated shapes, implying that these intermediate mass structures may be dynamically young. A weak lensing signal is detected for 6 groups and upper limits are provided for 6 others. Fitting the reduced shear with a Singular Isothermal Sphere, we find σ SIS ∼ 500 km s −1 with large error bars and an upper limit of ∼ 900 km s −1 for the whole sample (except for the highest redshift structure whose velocity dispersion is consistent with that of a galaxy cluster). The mass-to-light ratio for the sample is found to be M/L i ∼ 250 (solar units, corrected for evolution), with an upper limit of 500. This compares with mass-to-light ratios of small groups (with σ SIS ∼ 300 km s −1 ) and galaxy clusters (with σ SIS > 1 000 km s −1 ), thus bridging the gap between these mass scales. The group sample released in this paper will be complemented with other observations, providing a unique sample to study this important intermediate mass range in further detail.