2010MNRAS.408.2442W

We analyse kinematic data of 41 nearby (z < 0.1) relaxed galaxy clusters in terms of the projected phase-space density using a phenomenological, fully anisotropic model of the distribution function. We apply the Markov Chain Monte Carlo approach to place constraints on total mass distribution approximated by the universal Navarro, Frenk and White (NFW) profile and the profile of the anisotropy of galaxy orbits. We find the normalization of the mean mass-concentration relation is c = 6.9^+0.6_–0.7 at the virial mass M_v= 5x10¹⁴ M_☉. By comparison with the calibration from cosmological N-body simulations it is demonstrated that this result is fully consistent with σ₈ from 1-yr Wilkinson Microwave Anisotropy Probe (WMAP1) data release and agrees at ∼ 1σ level with that from WMAP5. Assuming a one-to-one correspondence between σ₈ and the normalization of the mass-concentration relation in the framework of the concordance model we estimate the normalization of the linear power spectrum to be σ₈= 0.91^+0.07_–0.08. Our constraints on the parameters of the mass profile are compared with estimates from X-ray observations and other methods based on galaxy kinematics. We also study correlations between the virial mass and different mass proxies including the velocity dispersion, the X-ray temperature and the X-ray luminosity. We demonstrate that the mass scaling relations with the velocity dispersion and the X-ray temperature are fully consistent with the predictions of the virial theorem.

We show that galaxy orbits are isotropic at the cluster centres (with the mean ratio of the radial-to-tangential velocity dispersions σ_r/σ_θ= 0.97±0.04) and radially anisotropic at the virial sphere (with the mean ratio σ_r/σ_θ= 1.75^+0.23_–0.19). Although the value of the central anisotropy appears to be universal, the anisotropy at the virial radius differs between clusters within the range 1 ≲ (σ_r_/σθ_) ≲ 2.

Utilizing the Bautz-Morgan morphological classification and information on the prominence of a cool core we select two subsamples of galaxy clusters corresponding to less and more advanced evolutionary states. It is demonstrated that less evolved clusters have shallower mass profiles and their galaxy orbits are more radially biased at the virial sphere. This property is consistent with the expected evolution of the mass profiles as well as with the observed orbital segregation of late- and early-type galaxies.