We present a detailed mass reconstruction and a novel study on the substructure properties in the core of the Cluster Lensing And Supernova survey with Hubble (CLASH) and Frontier Fields galaxy cluster MACS J0416.1−2403. We show and employ our extensive spectroscopic data set taken with the VIsible Multi-Object Spectrograph (VIMOS) instrument as part of our CLASH-VLT program, to confirm spectroscopically 10 strong lensing systems and to select a sample of 175 plausible cluster members to a limiting stellar mass of log(M * /M ⊙ ) ≃ 8.6. We reproduce the measured positions of a set of 30 multiple images with a remarkable median offset of only 0.3 ′′ by means of a comprehensive strong lensing model comprised of 2 cluster dark-matter halos, represented by cored elliptical pseudoisothermal mass distributions, and the cluster member components, parametrized with dual pseudoisothermal total mass profiles. The latter have total mass-to-light ratios increasing with the galaxy HST /WFC3 near-IR (F160W) luminosities. The measurement of the total enclosed mass within the Einstein radius is accurate to ∼ 5%, including the systematic uncertainties estimated from six distinct mass models. We emphasize that the use of multiple-image systems with spectroscopic redshifts and knowledge of cluster membership based on extensive spectroscopic information is key to constructing robust high-resolution mass maps. We also produce magnification maps over the central area that is covered with HST observations. We investigate the galaxy contribution, both in terms of total and stellar mass, to the total mass budget of the cluster. When compared with the outcomes of cosmological N -body simulations, our results point to a lack of massive subhalos in the inner regions of simulated clusters with total masses similar to that of MACS J0416.1−2403. Our findings of the location and shape of the cluster dark-matter halo density profiles and on the cluster substructures provide intriguing tests of the assumed collisionless, cold nature of dark matter and of the role played by baryons in the process of structure formation.

Aims. We constrain the mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z = 0.44 CLASH cluster MACS J1206.2-0847, using the projected phase-space distribution of cluster galaxies in combination with gravitational lensing. Methods. We use an unprecedented data-set of 600 redshifts for cluster members, obtained as part of a VLT/VIMOS large program, to constrain the cluster mass profile over the radial range ∼0-5 Mpc (0-2.5 virial radii) using the MAMPOSSt and Caustic methods. We then add external constraints from our previous gravitational lensing analysis. We invert the Jeans equation to obtain the velocity-anisotropy profiles of cluster members. With the mass-density and velocity-anisotropy profiles we then obtain the first determination of a cluster pseudo-phase-space density profile. Results. The kinematics and lensing determinations of the cluster mass profile are in excellent agreement. This is very well fitted by a NFW model with mass M 200 = (1.4 ± 0.2) × 10 15 M and concentration c 200 = 6 ± 1, only slightly higher than theoretical expectations. Other mass profile models also provide acceptable fits to our data, of (slightly) lower (Burkert, Hernquist, and Softened Isothermal Sphere) or comparable (Einasto) quality than NFW. The velocity anisotropy profiles of the passive and star-forming cluster members are similar, close to isotropic near the center and increasingly radial outside. Passive cluster members follow extremely well the theoretical expectations for the pseudo-phase-space density profile and the relation between the slope of the mass-density profile and the velocity anisotropy. Star-forming cluster members show marginal deviations from theoretical expectations. Conclusions. This is the most accurate determination of a cluster mass profile out to a radius of 5 Mpc, and the only determination of the velocityanisotropy and pseudo-phase-space density profiles of both passive and star-forming galaxies for an individual cluster. These profiles provide constraints on the dynamical history of the cluster and its galaxies. Prospects for extending this analysis to a larger cluster sample are discussed.

We carried out a detailed strong lensing analysis of a sub-sample of eight galaxy clusters of the Cluster Lensing And Supernova survey with Hubble (CLASH) in the redshift range of z cluster = [0.23 − 0.59] using extensive spectroscopic information, primarily from the Multi Unit Spectroscopic Explorer (MUSE) archival data and complemented with CLASH-VLT redshift measurements. The observed positions of the multiple images of strongly lensed background sources were used to constrain parametric models describing the cluster total mass distributions. Different models were tested in each cluster depending on the complexity of its mass distribution and on the number of detected multiple images. Four clusters show more than five spectroscopically confirmed multiple image families. In this sample, we did not make use of families that are only photometrically identified in order to reduce model degeneracies between the values of the total mass of a cluster source redshifts, in addition to systematics due to the potential misidentifications of multiple images. For the remaining four clusters, we used additional families without any spectroscopic confirmation to increase the number of strong lensing constraints up to the number of free parameters in our parametric models. We present spectroscopic confirmation of 27 multiply lensed sources, with no previous spectroscopic measurements, spanning over the redshift range of z src = [0.7 − 6.1]. Moreover, we confirm an average of 48 galaxy members in the core of each cluster thanks to the high efficiency and large field of view of MUSE. We used this information to derive precise strong lensing models, projected total mass distributions, and magnification maps. We show that, despite having different properties (i.e. number of mass components, total mass, redshift, etc), the projected total mass and mass density profiles of all clusters have very similar shapes when rescaled by independent measurements of M 200c and R 200c . Specifically, we measured the mean value of the projected total mass of our cluster sample within 10 (20)% of R 200c to be 0.13 (0.32) of M 200c , with a remarkably small scatter of 5 (6)%. Furthermore, the large number of high-z sources and the precise magnification maps derived in this work for four clusters add up to the sample of high-quality gravitational telescopes to be used to study the faint and distant Universe.