Enhanced cluster lensing models with measured galaxy kinematics
  We present an improved determination of the total mass distribution of three
CLASH/HFF massive clusters, MACS J1206.2-0847 (z=0.44), MACS J0416.1-2403
(z=0.40), Abell S1063 (z=0.35). We specifically reconstruct the sub-halo mass
component with robust stellar kinematics information of cluster galaxies, in
combination with precise strong lensing models based on large samples of
spectroscopically identified multiple images. We use VLT/MUSE integral-field
spectroscopy in the cluster cores to measure the stellar velocity dispersion,
$\sigma$, of 40-60 member galaxies per cluster, covering 4-5 magnitudes to
$m_{F160W}\simeq 21.5$. We verify the robustness and quantify the accuracy of
the velocity dispersion measurements with extensive spectral simulations. With
these data, we determine the normalization and slope of the galaxy
$L\mbox{-}\sigma$ Faber-Jackson relation in each cluster and use these
parameters as a prior for the scaling relations of the sub-halo population in
the mass distribution modeling. When compared to our previous lens models, the
inclusion of member galaxies' kinematics provides a similar precision in
reproducing the positions of the multiple images. However, the inherent
degeneracy between the central effective velocity dispersion, $\sigma_0$, and
truncation radius, $r_{cut}$, of sub-halos is strongly reduced, thus
significantly alleviating possible systematics in the measurements of sub-halo
masses. The three independent determinations of the $\sigma_0\mbox{-}r_{cut}$
scaling relation in each cluster are found to be fully consistent, enabling a
statistical determination of sub-halo sizes as a function of $\sigma_0$, or
halo masses. We derive galaxy central velocity dispersion functions of the
three clusters and found them in agreement with each other. Sub-halo mass
functions determined with this method can be compared with those obtained from
cosmological simulations.
