Aims. The lowest-mass galaxies, ultra-faint dwarf galaxies, promise unparalleled constraints on how feedback regulates galaxy formation, and on the small-scale matter power spectrum. Their inner dark-matter densities can also be used to constrain dark-matter models and to determine the most promising targets for potential signals from dark-matter annihilation or decay. However, these goals are limited by the current large uncertainties on the properties of the dark-matter haloes that these galaxies inhabit. In this paper, we present 201 new stellar line-of-sight velocities from the MUSE-Faint survey for the faint and ultra-faint dwarf galaxies Antlia B, Leo T, Hydra II, and Grus 1. Combining these with literature data, we obtain the tightest constraints to date on their dark-matter halo masses and inner dark-matter densities. Methods. We use the Jeans equations implemented in CJAM to model the density profiles and constrain the presence of dark-matter cores and solitons (a prediction of fuzzy dark-matter models). Further modelling is done with GravSphere to test the influence of the choice of modelling tool. We calculate masses, concentrations, and circular velocities from the profiles, include results for Eridanus 2 from our previous work, and compare these properties to theoretical scaling relations, deriving constraints on tidal stripping in the process.Results. We find that dark-matter cores as large as those of more massive dwarf galaxies are ruled out for our galaxies (core radius r c < 66-95 pc at the 68% confidence level). We constrain the soliton radii to r sol < 13-112 pc (68% confidence level). We find that the galaxies are consistent with not having been significantly tidally stripped within their half-light radii. The virial masses and concentrations are sensitive to the choice of dynamical modelling tool: GravSphere produces results consistent with M 200 ∼ 10 9 M , as expected from models in which ultra-faint dwarf galaxies are re-ionization fossils, while CJAM prefers haloes that are less massive.

We probed the dynamical mass profiles of ten galaxy clusters from the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS) using galaxy kinematics. We numerically solved the spherical Jeans equation and parameterize the dynamical mass profile and the galaxy velocity anisotropy profile using two general functions to ensure that our results are not biased toward any specific model. The mass-velocity anisotropy degeneracy is ameliorated by using two “virial shape parameters” that depend on the fourth moment of velocity distribution. The resulting velocity anisotropy estimates consistently show a nearly isotropic distribution in the inner regions, with an increasing radial anisotropy toward large radii. We compared our derived dynamical masses with those calculated from X-ray gas data assuming hydrostatic equilibrium, finding that massive and rich relaxed clusters generally present consistent mass measurements, while unrelaxed or low-richness clusters have systematically larger total masses than hydrostatic masses by, on average, 50%. This might help alleviate current tensions in the measurement of σ8, but it also leads to cluster baryon fractions below the cosmic value. Finally, our approach probes accelerations as low as 10−11 m s−2, comparable to the outskirts of individual late-type galaxies. We confirm that galaxy clusters deviate from the radial acceleration relation defined by galaxies.

We probe the outer dynamical mass profile of 16 galaxy clusters from the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS) using galaxy kinematics. Numerically solving the spherical Jeans equation, we parameterize the dynamical mass profile and the galaxy velocity anisotropy profile using two general functions to ensure that our results are not biased towards any specific model. The mass-velocity anisotropy degeneracy is broken by using two 'virial shape parameters' that depend on the fourth moment of velocity distribution. The resulting velocity anisotropy estimates consistently show a nearly isotropic distribution in the inner regions, with an increasing radial anisotropy towards large radii. We compare our derived dynamical masses with those calculated from X-ray gas data assuming hydrostatic equilibrium, finding that massive and rich relaxed clusters generally present consistent mass measurements, while unrelaxed or low-richness clusters have systematically larger total mass than hydrostatic mass by an average of 50%. This might help alleviate current tensions in the measurement of σ 8 , but it also leads to cluster baryon fractions below the cosmic value. Finally, our approach probes accelerations as low as 10 −11 m s −2 , comparable to the outskirts of individual late-type galaxies. We confirm that galaxy clusters deviate from the radial acceleration relation defined by galaxies.