| Abstract
| - We present an improved determination of the total mass distribution of three massive clusters from the Cluster Lensing and Supernova Survey with Hubble and Hubble Frontier Fields, MACS J1206.2−0847 ( z = 0.44), MACS J0416.1−2403 ( z = 0.40), Abell S1063 ( z = 0.35). We specifically reconstructed 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 used integral-field spectroscopy in the cluster cores, from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, to measure the stellar velocity dispersion, σ, of 40−60 member galaxies per cluster, covering four to five magnitudes to mF160W ≃ 21.5. We verified the robustness and quantified the accuracy of the velocity dispersion measurements with extensive spectral simulations. With these data, we determined the normalization and slope of the galaxy L- σ Faber-Jackson relation in each cluster and used 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, σ0, and truncation radius, rcut, of sub-halos is strongly reduced, thus significantly alleviating possible systematics in the measurements of sub-halo masses. The three independent determinations of the σ0 − rcut scaling relation in each cluster are found to be fully consistent, enabling a statistical determination of sub-halo sizes as a function of σ0, or halo masses. Finally, we derived the galaxy central velocity dispersion functions of the three clusters projected within 16% of their virial radius, finding that they are well in agreement with each other. We argue that such a methodology, when applied to high-quality kinematics and strong lensing data, allows the sub-halo mass functions to be determined and compared with those obtained from cosmological simulations.
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