We present an improved determination of the total mass distribution of three CLASH/Hubble Frontier Fields 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 _ { F 160 W } \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 .
Finally , we derive 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 .