Mass and light in galaxy clusters: The case of Abell 370

In the cold dark matter (CDM) paradigm, an association between the hypothetic dark matter (DM) and its stellar counterpart is expected. However, parametric strong-lensing studies of galaxy clusters often display misleading features: DM components on the group or cluster scale without any stellar counterpart, offsets between the two components that are larger than what might be allowed by CDM or self-interacting DM models, or significant unexplained external shear components. This is the case in the galaxy cluster Abell 370, whose mass distribution has been the subject of several studies that were motivated by a wealth of data. The cluster was described parametrically with strong-lensing techniques by a model with four dark matter clumps and galaxy-scale perturbers, and with a significant external shear component, whose physical origin remains a challenge. The dark matter distribution features a mass clump without a stellar counterpart and a significant offset between one of the dark matter clumps and its associated stellar counterpart. This paper is based on BUFFALO data, and we begin by revisiting this mass model. Sampling this complex parameter space with Markov chain Monte Carlo (MCMC) techniques, we find a solution that does not require any external shear and provides a slightly better root mean square (RMS) than previous models (0.7 '' compared to 0.9 ''). Investigating this new solution further, in particular, by varying the parameters that lead the MCMC sampler, we present a class of models that can accurately reproduce the strong-lensing data, but whose parameters for the dark matter component are poorly constrained. This limits any insights into its properties. We then developed a model in which each large-scale dark matter component must be associated with a stellar counterpart. This model with three dark matter clumps cannot reproduce the observational constraints with an RMS smaller than 2.3 '', and the parameters describing this dark matter component remain poorly constrained. Examining the total projected mass maps, we find a good agreement between the total mass and the stellar distribution, which are both bimodal to first order. We interpret the misleading features of the mass model with four dark matter clumps and the failure of the mass model with three dark matter clumps as being symptomatic of the lacking realism of a parametric description of the dark matter distribution in such a complex merging cluster. We encourage caution and attention on the outputs of parametric strong-lensing modelling. We briefly discuss the implications of our results for using Abell 370 as a gravitational telescope. With the class of models that reproduce the strong- lensing data, we computed the magnifications for background Ly alpha emitters, and we present the critical curves obtained for the redshift of the Dragon arc, whose recent observations with the James Webb Space Telescope prompted interest. Finally, in light of our results, we discuss the strategy of choosing merging (multi-modal) clusters as gravitational telescopes compared to simple (unimodal) clusters.