Improved strong lensing modelling of galaxy clusters using the
  Fundamental Plane: Detailed mapping of the baryonic and dark matter mass
  distribution of Abell S1063
  From Hubble Frontier Fields photometry, and data from the Multi Unit
Spectroscopic Explorer on the Very Large Telescope, we build the Fundamental
Plane (FP) relation for the early-type galaxies of the cluster Abell S1063. We
use this relation to develop an improved strong lensing model of the total mass
distribution of the cluster, determining the velocity dispersions of all 222
cluster members included in the model from their measured structural
parameters. Fixing the hot gas component from X-ray data, the mass density
distributions of the diffuse dark matter haloes are optimised by comparing the
observed and model-predicted positions of 55 multiple images of 20 background
sources, distributed over the redshift range $0.73-6.11$. We determine the
uncertainties on the model parameters with Monte Carlo Markov chains. Compared
to previous works, our model allows for the inclusion of a scatter on the
relation between the total mass and the velocity dispersion of cluster members,
which also shows a shallower slope. We notice a lower statistical uncertainty
on the value of some parameters, such as the core radius, of the diffuse mass
component of the cluster. Thanks to a new estimate of the stellar mass of all
members, we measure the cumulative projected mass profiles out to a radius of
350 kpc, for all baryonic and dark matter components of the cluster. At the
outermost radius, we find a baryon fraction of $0.147 \pm 0.002$. We compare
the sub-haloes as described by our model with recent hydrodynamical
cosmological simulations. We find good agreement in terms of the stellar over
total mass fraction. On the other hand, we report some discrepancies in terms
of the maximum circular velocity, which is an indication of their compactness,
and the sub-halo mass function in the central cluster regions.
