NEW INSIGHTS ON THE INNER MASS DISTRIBUTION OF MASSIVE GALAXY CLUSTERS FROM A COMBINATION OF STRONG LENSING AND GALAXY KINEMATICS

Galaxy clusters are important astrophysical laboratories to study the nature of Dark Matter (DM), whose physical properties are still unknown. In particular, a detailed investigation of the mass distribution of cluster halos, by dissecting the DM and baryonic components, can provide stringent tests of the Cold Dark Matter paradigm of structure formation. Over the last decade, strong gravitational lensing has become one of the most powerful techniques to study the total mass distribution in the Universe, particularly on galaxy and cluster scale. In recent years, dedicated large imaging surveys with HST and ground-based spectroscopic campaigns on sizeable samples of massive galaxy clusters have ushered a new generation of high-precision strong lensing models, via the identification of a large number of multiple images and cluster members. In this thesis, we extend beyond the state of the art these new cluster lens models, including the stellar kinematics of a significant fraction of cluster galaxies measured with the integral field spectrograph MUSE on the VLT. This study focuses on three massive clusters MACS~J1206.2$-$0847, MACS~J0416.1$-$2403, and Abell S1063 at $zsim 0.4$ with HST imaging and VLT spectroscopy data of unprecedented quality. Specifically, we measured the stellar velocity dispersion, $sigma$, of 40-60 member galaxies per cluster with MUSE, covering 4-5 magnitudes down to $mF160W simeq 21.5$. The robustness and accuracy of the velocity dispersion measurements were tested with extensive spectral simulations. We determined the normalization and slope of the galaxy Faber-Jackson relation in each cluster, and include this prior information in the cluster lens models. We find that using this novel technique, the inherent degeneracy between different mass components and possible systematics on model parameters are strongly reduced and the mass density profiles of the cluster galaxies are now robustly constrained. Once re-normalized to the same absolute luminosity, our kinematic lens models predict consistent masses and sizes of sub-halos as a function of galaxy velocity dispersions. Moreover, extending previous findings, we derive consistent sub-halo mass velocity dispersion functions for the three clusters. By comparing the observed sub-halo mass distribution from our cluster lens models with the predictions of high-resolution N-body and hydrodynamical cosmological simulations, we find a lack of compact sub-structures in the corresponding inner regions of simulated clusters, whereas the sub-halo mass functions are found in good agreement. We still do not understand whether the origin of these differences has to be ascribed to numerical or resolution effects in the simulations, or to some physical aspect missing in the Cold Dark Matter framework. An additional method to investigate the mass distribution of cluster galaxies is to exploit galaxy scale strong lensing systems (GSSLS), in which a single cluster galaxy produces highly magnified multiple images on kpc scale around lens galaxies. We show how strong lensing modeling of GSSLS in the cluster field, in combination with spatially resolved stellar kinematics of the lens galaxies, can further constrain the structure and sizes of cluster sub-halos. Finally, in an effort to include in our lens models the measured cluster member stellar velocity dispersions and the observed scatter of the Faber-Jackson relation, we develop and made public a python module that expands the capabilities of common lens modeling tools. The methodology of high-precision lens modeling developed in this thesis will find important applications in the near future when large numbers of cosmic lenses will be discovered with large-area surveys. In particular, by exploiting lensing clusters as powerful cosmic telescopes to investigate galaxies in the early Universe and in cosmographic applications with gravitational time delay techniques.