Enhanced cluster lensing models with measured galaxy kinematics

We present improved mass models of three CLASH/HFF massive clusters, MACS J1206.2-0847, MACS J0416.1-0403, Abell S1063. We reconstruct the subhalo mass component with robust stellar kinematics of cluster galaxies, coupled with precise strong lensing models from large samples of spectroscopically confirmed 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 $m_F160Wsimeq 21.5$. We test the accuracy of velocity dispersion measurements on mock spectra, thus quantifying the limiting signal-to-noise and minimum velocity ($sigma>80$ km/s) for the depth of the spectra presented here. With these data, we determine the normalization and slope of the Faber-Jackson relation in each cluster and use it a prior for the scaling relations of the sub-halo population in the lensing mass models. Compared to our previous lens models, the inclusion of stellar kinematics yields a similar precision in the predicted positions of the multiple images. However, the inherent degeneracy between the central effective velocity dispersion, $sigma_0$, and truncation radius, $r_cut$, of subhalos is strongly reduced, significantly alleviating systematics in the measurements of subhalo masses. The three independent determinations of the $sigma_0mbox-r_cut$ relation in each cluster are fully consistent, enabling a statistical determination of subhalo sizes at given $sigma_0$ or mass. Finally, we derive the galaxy central velocity dispersion functions of the three clusters projected within 16% of their virial radii, finding that they are well in agreement with each other. This methodology, when applied to high-quality kinematics and strong lensing data, allows the subhalo mass functions to be determined and compared with predictions from cosmological simulations.