Towards a more holistic description of galaxy clusters

Strong gravitational lensing allows to map the total (dark matter and baryonic) density within galaxy clusters; while X-ray and SZ effect observations unveil the Intra-Cluster Medium (ICM) baryonic physics. After presenting both methods, I will display the analytical relationship between both the DM and ICM fluids, under reasonable hypotheses (hydrostatic equilibrium, self-similar ICM temperature profile). I will then review the joint X-lensing analysis of cluster Abell S1063, and the new avenues it opens to study the physics of galaxy clusters, and in particular of dark matter.