Mass, velocity anisotropy, and pseudo phase-space density profiles of Abell 2142

Aim: We aim to compute the mass and velocity anisotropy profiles of Abell 2142 and, from there, the pseudo phase--space density profile $Q(r)$ and the density slope - velocity anisotropy $\beta - \gamma$ relation, and then to compare them with theoretical expectations. Methods: The mass profiles were obtained by using three techniques based on member galaxy kinematics, namely the caustic method, the method of Dispersion - Kurtosis, and MAMPOSSt. Through the inversion of the Jeans equation, it was possible to compute the velocity anisotropy profiles. Results: The mass profiles, as well as the virial values of mass and radius, computed with the different techniques agree with one another and with the estimates coming from X-ray and weak lensing studies. A concordance mass profile is obtained by averaging the lensing, X-ray, and kinematics determinations. The cluster mass profile is well fitted by an NFW profile with $c=4.0 \pm 0.5$. The population of red and blue galaxies appear to have a different velocity anisotropy configuration, since red galaxies are almost isotropic, while blue galaxies are radially anisotropic, with a weak dependence on radius. The $Q(r)$ profile for the red galaxy population agrees with the theoretical results found in cosmological simulations, suggesting that any bias, relative to the dark matter particles, in velocity dispersion of the red component is independent of radius. The $\beta - \gamma$ relation for red galaxies matches the theoretical relation only in the inner region. The deviations might be due to the use of galaxies as tracers of the gravitational potential, unlike the non--collisional tracer used in the theoretical relation.Comment: 14 pages, 14 figures. Consolidated version including the Corrigendum published on A&

The relation between velocity dispersion and mass in simulated clusters of galaxies: dependence on the tracer and the baryonic physics

[Abridged] We present an analysis of the relation between the masses of cluster- and group-sized halos, extracted from $\Lambda$CDM cosmological N-body and hydrodynamic simulations, and their velocity dispersions, at different redshifts from $z=2$ to $z=0$. The main aim of this analysis is to understand how the implementation of baryonic physics in simulations affects such relation, i.e. to what extent the use of the velocity dispersion as a proxy for cluster mass determination is hampered by the imperfect knowledge of the baryonic physics. In our analysis we use several sets of simulations with different physics implemented. Velocity dispersions are determined using three different tracers, DM particles, subhalos, and galaxies. We confirm that DM particles trace a relation that is fully consistent with the theoretical expectations based on the virial theorem and with previous results presented in the literature. On the other hand, subhalos and galaxies trace steeper relations, and with larger values of the normalization. Such relations imply that galaxies and subhalos have a $\sim10$ per cent velocity bias relative to the DM particles, which can be either positive or negative, depending on halo mass, redshift and physics implemented in the simulation. We explain these differences as due to dynamical processes, namely dynamical friction and tidal disruption, acting on substructures and galaxies, but not on DM particles. These processes appear to be more or less effective, depending on the halo masses and the importance of baryon cooling, and may create a non-trivial dependence of the velocity bias and the \soneD--\Mtwo relation on the tracer, the halo mass and its redshift. These results are relevant in view of the application of velocity dispersion as a proxy for cluster masses in ongoing and future large redshift surveys.Comment: 13 pages, 16 figures. Minor modifications to match the version in press on MNRA