Antonaldo Diaferio

Galaxy clusters are among the most powerful laboratories to probe fundamental physics, from the formation of cosmic structures to the nature of dark matter, dark energy, and gravity. Realizing their full potential requires accurate and unbiased determinations of their mass profiles, a longstanding challenge in cluster cosmology. In this context, the kinematics of member galaxies in clusters has become a key tool to reconstruct the mass distribution and investigate the dynamical properties of clusters. The advent of large spectroscopic datasets has enabled the application of increasingly sophisticated models and robust techniques, which make kinematic analyses competitive with other probes of cluster dynamics. In this review, we provide a comprehensive overview of cluster kinematics, covering the main methods to infer dynamical masses and mass profiles, their physical assumptions, and the impact of systematics, such as deviation from dynamical equilibrium, triaxiality, and substructures. We discuss the complementarity with other techniques to investigate the structure of clusters and highlight recent applications to tests cosmological models. We focus in particular on the role of kinematical studies in constraining the dark sector (dark matter and dark energy) and in providing novel insights into the behavior of gravity at Mpc scales. Finally, we outline current limitations and future prospects, emphasizing that the combination of improved modeling and forthcoming spectroscopic surveys will establish cluster kinematics as a fundamental probe in the era of precision cosmology.

We investigate the formation of the large-scale cosmic structure in a scalar-tensor theory of gravity belonging to the class of the Brans-Dicke theories. The universe contains baryonic matter alone and neither dark matter nor dark energy. The two arbitrary functions of the scalar field characterizing the kinetic term and the self-interaction potential are set to W ( φ ) = -1 and V ( φ ) = -Ξ φ , respectively, with Ξ a positive constant. In the weak-field limit, the theory reduces to Refracted Gravity, a non-relativistic theory whose modified Poisson equation contains the scalar field φ that provides the gravitational boost required to describe the dynamics of galaxies and galaxy clusters without dark matter. In a flat, matter-dominated, homogeneous and isotropic universe the same scalar field φ drives the accelerated expansion of the universe and describes the observed redshift evolution of the Hubble-Lemaître parameter H ( z ). However, in the equation of the growth factor of the linear perturbation theory, the form of V ( φ ) makes the coefficient of the source of the gravitational field proportional to H ^-1 ( z ); therefore the gravitational field is strongly suppressed at early times and structure formation is delayed to redshift z< 1, in disagreement with the observation of formed galaxies at much larger redshifts. In addition, the form of W ( φ ) and a linear V ( φ ) imply that φ generates twice the gravitational boost on massive particles than on photons, with possible observable consequences on the gravitational lensing phenomenon. It remains to be investigated whether different choices of W ( φ ) and V ( φ ), that can still make the theory reduce to Refracted Gravity in the weak-field limit, might alleviate these problems.

We measure galaxy stellar mass functions (SMFs) for nine of the most massive galaxy clusters in the local Universe (0.07 < z < 0.11) using deep and complete spectroscopy from the MAssive Cluster Survey with Hectospec (MACH). We construct the cluster SMFs down to log ( M * / M ⊙ ) ≳ 8.5 . For comparison, we measure the SMF for field galaxies, complete to log ( M * / M ⊙ ) ≳ 10.5 , based on Sloan Digital Sky Survey spectroscopy over the same redshift range. The mean MACH SMF shows a shape similar to that of the field SMF but with a significantly higher amplitude at log ( M * / M ⊙ ) < 11.4 . At log ( M * / M ⊙ ) > 11.4 , the MACH SMF shows a clear excess, indicating the contribution of massive galaxies, including brightest cluster galaxies (BCGs). Based on homogeneous MACH spectroscopy, we compare SMF shapes for quiescent and star-forming members as a function of the cluster-centric distance. The quiescent SMFs display a curved shape with a peak at log ( M * / M ⊙ ) ≈ 10.5 ; the star-forming SMFs decline monotonically with increasing stellar mass. We further compare the mean MACH SMF with SMFs derived from similarly massive clusters in the IllustrisTNG-300 simulations. The shape of the observed and simulated SMFs agrees well overall. However, the MACH clusters contain roughly a factor of 2 more galaxies at 9.0 < log ( M * / M ⊙ ) < 10.5 . These results demonstrate that constructing cluster SMFs from complete spectroscopic samples can test simulations and provide powerful constraints on galaxy formation and evolution in dense environments.

The Blooming Tree (BT) algorithm, based on the hierarchical clustering method, is designed to identify clusters, groups, and substructures from galaxy redshift surveys. We apply the BT algorithm to a wide-field (10 × 10 deg²) spectroscopic data set centered on the galaxy cluster A2029. The BT algorithm effectively identifies all the X-ray luminous clusters and most of the optical clusters known in the literature, numerous groups, and the filaments surrounding the clusters, associating a list of galaxy members to each structure. By lowering the detection threshold, the BT algorithm also identifies the three superclusters in the field. The BT algorithm arranges the clusters and groups that make up the superclusters in a hierarchical tree according to their pairwise binding energy: the algorithm thus unveils the possible accretion history of each supercluster and their future evolution. These results show how the BT algorithm can represent a crucial tool to investigate the formation and evolution of cosmic structures on nonlinear and mildly nonlinear scales.

We present clumi+, a self-consistent, multiprobe methodology for reconstructing the mass distribution in and around galaxy clusters by combining gravitational lensing and dynamical observations. Building on the joint likelihood framework of K. Umetsu, clumi+ integrates weak-lensing shear and magnification data with projected escape velocity measurements in the cluster infall region, yielding tighter constraints on the gravitational potential without relying on equilibrium assumptions. The mass distribution is modeled using a flexible, piecewise-defined convergence profile that characterizes the azimuthally averaged surface mass density within the lensing field, transitioning to a projected power-law form at larger radii where phase-space constraints complement lensing. Additional strong-lensing constraints are incorporated via central aperture-mass measurements, enabling full-scale mass reconstruction from the cluster core to the outskirts. We validate clumi+ using synthetic weak-lensing and phase-space data for a massive cluster from the IllustrisTNG simulations, demonstrating unbiased recovery of projected and three-dimensional mass profiles and achieving 10%–30% improvement in precision at large radii. As a case study, we apply clumi+ to A2261, combining Subaru and Hubble Space Telescope weak+strong-lensing data with spectroscopic measurements from the Hectospec Cluster Survey. This analysis demonstrates the power of multiprobe, equilibrium-free modeling for robust cluster mass reconstruction.

Refracted gravity (RG) is a classical theory of gravity where a gravitational permittivity, ϵ(ρ), namely, a monotonically increasing function of the local density, ρ, is introduced in the Poisson equation to mimic the effect of dark matter at astrophysical scales. We used high-precision spectroscopic data of two massive galaxy clusters, MACS J1206.2-0847 at a redshift of z = 0.44 and Abell S1063 (RXC J2248.7-4431) at z = 0.35, to determine the total gravitational potential in the context of RG. We also sought to constrain the three (supposedly universal) free parameters of this model. Using an upgraded version of the MG-MAMPOSST algorithm, we performed a kinematic analysis that combines the velocity distribution of the cluster galaxies and the velocity dispersion profile of the stars within the brightest cluster galaxy (BCG). This unprecedented dataset used was obtained from an extensive spectroscopic campaign carried out with the VIMOS and MUSE spectrographs at the ESO VLT. We found that RG describes the kinematics of these two clusters as well as Newtonian gravity, although the latter is slightly preferred. However, (i) each cluster requires a different set of the three free RG parameters and (ii) the two sets are inconsistent with other results in the literature at different scales. We discuss the limitation of the method used to constrain the RG parameters, as well as possible systematic effects, which can give rise to the observed tension; notably, these are deviations from the spherical symmetry and from the dynamical equilibrium of the clusters.

We show how the star formation activity of galaxies is progressively inhibited from the outer region to the center of the massive cluster A2142. From an extended spectroscopic redshift survey of 2239 galaxies covering a circular area of radius ∼11 Mpc from the cluster center, we extract a sample of 333 galaxies with known stellar mass, star formation rate, and spectral index D _n 4000. We use the Blooming Tree algorithm to identify the substructures of the cluster and separate the galaxy sample into substructure galaxies, halo galaxies, and outskirt galaxies. The substructure and halo galaxies are cluster members, whereas the outskirt galaxies are only weakly gravitationally bound to the cluster. For the cluster members, the star formation rate per stellar mass decreases with decreasing distance R from the cluster center. Similarly, the spectral index D _n 4000 increases with R, indicating an increasing average age of the stellar population in galaxies closer to the cluster center. In addition, star formation in substructure galaxies is generally more active than in halo galaxies and less active than in outskirt galaxies, proving that substructures tend to slow down the transition between field galaxies and cluster galaxies. We finally show that most actively star-forming galaxies are within the cluster infall region, whereas most galaxies in the central region are quiescent.