Mass distribution in nearby Abell clusters

We study the mass distribution in six nearby  ( z < 0.06)  relaxed Abell clusters of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of dark matter in galaxy clusters, we approximate their total density distribution by the Navarro, Frenk & White (NFW) formula characterized by virial mass and concentration. We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density. Using the velocity and position data for 120–420 galaxies per cluster we calculate, after removal of interlopers, the profiles of the lowest order even velocity moments, dispersion and kurtosis. We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations. Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration. The method is tested in detail on mock data extracted from the N -body simulations of dark matter haloes. We find that the best-fitting Galactic orbits are remarkably close to isotropic in most clusters. Using the fitted pairs of mass and concentration parameters for the six clusters, we conclude that the trend of decreasing concentration for higher masses found in the cosmological N -body simulations is consistent with the data. By scaling the individual cluster data by mass, we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample. The estimated concentration parameter then lies in the range  1.5 < c < 14  and the anisotropy parameter in the range  ?1.1 < β < 0.5  at the 95 per cent confidence level.