SIMBAD references

We present a parametric strong-lensing analysis of three massive galaxy clusters for which Hubble Space Telescope imaging is available, as well as spectroscopy of multiply imaged systems and galaxy cluster members. Our aim is to probe the inner shape of dark matter haloes, in particular the existence of a core. We adopted the following working hypothesis: any group- or cluster-scale dark matter clump introduced in the modelling should be associated with a luminous counterpart. We also adopted some additional well-motivated priors in the analysis, even when this degraded the quality of the fit, quantified using the root mean square between the observed and model-generated images. In particular, in order to alleviate the degeneracy between the smooth underlying component and the galaxy-scale perturbers, we used the results from previous spectroscopic campaigns, which allowed us to fix the mass of the galaxy-scale component. In the unimodal galaxy cluster AS 1063, a core mass model is favoured over a non-core mass model, and this is also the case in the multimodal cluster MACS J0416. In the unimodal cluster MACS J1206, we fail to reproduce the strong-lensing constraints using a parametric approach within the adopted working hypothesis. We then successfully added a mild perturbation in the form of a superposition of B-spline potentials, which allowed us to obtain a decent fit (root mean square = 0.5''), and finally find that a core mass model is favoured. Overall, our analysis suggest evidence for core cluster-scale dark matter haloes in these three clusters. These findings may be useful for the interpretation within alternative dark matter scenario, such as self-interacting dark matter. We propose a working hypothesis for parametric strong-lensing modelling in which the quest for the best-fit model is balanced by the quest for presenting a physically motivated mass model, in particular by imposing priors.