Phase-space shapes of clusters and rich groups of galaxies

Context. Clusters and groups of galaxies are highly aspherical, with shapes approximated by nearly prolate ellipsoids of revolution. An equally fundamental property is the shape of these objects in velocity space which is the anisotropy of the global velocity dispersion tensor. Although many studies address the problem of the shape in position space, there has been no attempt to measure shapes in velocity space. Aims. Here we make use of kinematical data comprising similar to 600 nearby clusters and rich groups of galaxies from the Sloan Digital Sky Survey to place constraints on the phase-space shapes of these objects, i.e. their shapes in both position and velocity space. Methods. We show that the line of sight velocity dispersion normalised by a mass-dependent velocity scale correlates with the apparent elongation, with circular (elongated) clusters exhibiting an excessive (decremental) normalised velocity dispersion. This correlation holds for dynamically young or old clusters and, therefore, it originates from projecting their intrinsic phase-space shapes rather than from dynamical evolution. It signifies that clusters are preferentially prolate not only in position space, but also in velocity space. This property allows us to break the degeneracy between oblate and prolate models and thus to deproject the apparent elongations and the line of sight velocity dispersions obtaining constraints on the axial ratios of the ellipsoids approximating cluster shapes in 3D position or velocity space. Results. The distribution of the axial ratios in position space is found to be well approximated by a Gaussian with a mean, mu = 0.66 +/- 0.01, and a dispersion, sigma = 0.07 +/- 0.008. The velocity ellipsoids representing the shapes in velocity space are more spherical, with a mean axial ratio of 0.78 +/- 0.03. Conclusions. The mean axial ratio of the velocity ellipsoids points to a highly anisotropic velocity distribution and, therefore, to a strong dependance of the observed velocity dispersions on the angle between the line of sight and the semi-principle axes of the clusters. This finding has important implications for mass measurements based on the line of sight velocity dispersion profiles in individual clusters. For typical axial ratios of the velocity ellipsoids in the analysed cluster sample, systematic errors on the mass estimates inferred from the line of sight velocity dispersions become comparable to statistical uncertainties for galaxy clusters with as few as 40 spectroscopic redshifts.