# Enhanced cluster lensing models with measured galaxy kinematics

## TL;DR

This paper improves galaxy cluster mass models by integrating stellar kinematics data with strong lensing, reducing uncertainties in sub-halo mass estimates and enabling better comparisons with cosmological simulations.

## Contribution

It introduces a method combining galaxy kinematics with lensing models to more accurately determine sub-halo properties in galaxy clusters.

## Key findings

- Kinematic data reduces degeneracy in sub-halo parameters.
- Consistent sub-halo scaling relations across clusters.
- Derived galaxy velocity dispersion functions match simulations.

## Abstract

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.