Phase-space shapes of clusters and rich groups of galaxies

Abstract

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. Here we make use of kinematical data comprising around 600 nearby clusters and rich groups of galaxies from the SDSS to place constraints on the phase-space shapes of these objects, i.e. their shapes in both position and velocity space. 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. The distribution of the axial ratios in position space is found to be well approximated by a Gaussian with a mean 0.66+/-0.01 and a dispersion 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. 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.