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 study the characteristics of the galaxy cluster samples expected from the European Space Agency's Euclid satellite and forecast constraints on parameters describing a variety of cosmological models. The method used in this paper, based on the Fisher Matrix approach, is the same one used to provide the constraints presented in the Euclid Red Book (Laureijs et al. 2011). We describe the analytical approach to compute the selection function of the photometric and spectroscopic cluster surveys. Based on the photometric selection function, we forecast the constraints on a number of cosmological parameter sets corresponding to different extensions of the standard ΛCDM model, including a redshift-dependent Equation of State for Dark Energy, primordial non-Gaussianity, modified gravity and non-vanishing neutrino masses. Our results show that Euclid clusters will be extremely powerful in constraining the amplitude of the matter power spectrum σ 8 and the mass density parameter Ω m . The dynamical evolution of dark energy will be constrained to ∆w 0 = 0.03 and ∆w a = 0.2 with free curvature Ω k , resulting in a (w 0 , w a ) Figure of Merit (FoM) of 291. Including the Planck CMB covariance matrix, thereby information on the geometry of the universe, improves the constraints to ∆w 0 = 0.02, ∆w a = 0.07 and a FoM= 802. The amplitude of primordial nonGaussianity, parametrised by f NL , will be constrained to ∆ f NL ≃ 6.6 for the local shape scenario, from Euclid clusters alone. Using only Euclid clusters, the growth factor parameter γ, which signals deviations from General Relativity, will be constrained to ∆γ = 0.02, and the neutrino density parameter to ∆Ω ν = 0.0013 (or ∆ m ν = 0.01). We emphasise that knowledge of the observable-mass scaling relation will be crucial to constrain cosmological parameters from a cluster catalogue. The Euclid mission will have a clear advantage in this respect, thanks to its imaging and spectroscopic capabilities that will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies. This information will be further complemented by wide-area multi-wavelength external cluster surveys that will already be available when Euclid flies. c 0000 RAS 2 B. Sartoris et al.

We report the spectroscopic confirmation of 22 new multiply lensed sources behind the Hubble Frontier Field (HFF) galaxy cluster MACS J0416.1−2403 (MACS 0416), using archival data from the Multi Unit Spectroscopic Explorer (MUSE) on the VLT. Combining with previous spectroscopic measurements of 15 other multiply imaged sources, we have obtained a sample of 102 secure multiple images with measured redshifts, the largest to date in a single strong lensing system. The newly confirmed sources are largely lowluminosity Lyman-α emitters with redshift in the range [3.08−6.15]. With such a large number of secure constraints, and a significantly improved sample of galaxy members in the cluster core, we have improved our previous strong lensing model and obtained a robust determination of the projected total mass distribution of MACS 0416. We find evidence of three cored dark-matter halos, adding to the known complexity of this merging system. The total mass density profile, as well as the sub-halo population, are found to be in good agreement with previous works. We update and make public the redshift catalog of MACS 0416 from our previous spectroscopic campaign with the new MUSE redshifts. We also release lensing maps (convergence, shear, magnification) in the standard HFF format.

We present VIMOS-VLT spectroscopy of the Frontier Fields cluster MACS J0416. 1-2403 (z=0.397). Taken as part of the CLASH-VLT survey, the large spectroscopic campaign provided more than 4000 reliable redshifts over ∼ 600 arcmin 2 , including ∼ 800 cluster member galaxies. The unprecedented sample of cluster members at this redshift allows us to perform a highly detailed dynamical and structural analysis of the cluster out to ∼ 2.2 r 200 (∼ 4 Mpc). Our analysis of substructures reveals a complex system composed of a main massive cluster (M 200 ∼ 0.9 × 10 15 M ⊙ and σ V,r200 ∼ 1000 km s −1 ) presenting two major features: i) a bimodal velocity distribution, showing two central peaks separated by ∆V rf ∼ 1100 km s −1 with comparable galaxy content and velocity dispersion, ii) a projected elongation of the main substructures along the NE-SW direction, with a prominent subclump ∼ 600 kpc SW of the center and an isolated BCG approximately halfway between the center and the SW clump. We also detect a low mass structure at z ∼ 0.390, ∼ 10 ′ south of the cluster center, projected at ∼ 3 Mpc, with a relative line-of-sight velocity of ∆V rf ∼-1700 km s −1 . The cluster mass profile that we obtain through our dynamical analysis deviates significantly from the "universal" NFW, being best fit by a Softened Isothermal Sphere model instead. The mass profile measured from the galaxy dynamics is found to be in relatively good agreement with those obtained from strong and weak lensing, as well as with that from the X-rays, despite the clearly unrelaxed nature of the cluster. Our results reveal overall a complex dynamical state of this massive cluster and support the hypothesis that the two main subclusters are being observed in a pre-collisional phase, in line with recent findings from radio and deep X-ray data. With this article we also release the entire redshift catalog of 4386 sources in the field of this cluster, which includes 60 identified Chandra X-ray sources and 105 JVLA radio sources.