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Strong gravitational lensing (SL) has emerged as a very accurate probe of themass distribution of cluster- and galaxy-scale dark matter (DM) haloes in theinner regions of galaxy clusters. The derived properties of DM haloes can becompared to the predictions of high-resolution cosmological simulations,providing us with a test of the Standard Cosmological Model. The usual choiceof simple power-law scaling relations to link the total mass of members withtheir luminosity is one of the possible inherent systematics within SL modelsof galaxy clusters, and thus on the derived cluster masses. Using newinformation on their structural parameters (from HST imaging) and kinematics(from MUSE data), we build the Fundamental Plane (FP) for the early-typegalaxies of the cluster Abell S1063. We take advantage of the calibrated FP todevelop an improved SL model of the total mass of the cluster core. The newmethod allows us to obtain more accurate and complex relations between theobservables describing cluster members, and to completely fix their mass fromtheir observed magnitudes and effective radii. Compared to the power-lawapproach, we find a different relation between the mass and the velocitydispersion of members, which shows a significant scatter. Thanks to a newestimate of the stellar mass of the cluster members from HST data, we measurethe cumulative projected mass profiles out to a radius of 350 kpc, for allbaryonic and DM components of the cluster. Finally, we compare the physicalproperties of the sub-haloes in our model and those predicted byhigh-resolution hydrodynamical simulations. We obtain compatible results interms of the stellar-over-total mass fraction of the members. On the otherhand, we confirm the recently reported discrepancy in terms of sub-halocompactness: at a fixed total mass value, simulated sub-haloes are less compactthan what our SL model predicts.

Improved strong lensing modelling of galaxy clusters using the  Fundamental Plane: detailed mapping of the baryonic and dark matter mass  distribution of Abell S1063