The Lx-T, Lx-σ, and σ-T relations for groups and clusters of galaxies

While in the hierarchical model of structure formation, groups of galaxies are believed to be a scaled-down version of clusters of galaxies, a similarity break in the fundamental laws may occur on the group scale, reflecting a transition between galaxy-dominated and intracluster-medium-dominated properties. In this paper we present an extensive study of the relations between the X-ray luminosity(L-X), the temperature (T) of hot diffuse gas, and the velocity dispersion (sigma) of galaxies for groups and clusters of galaxies, based on the largest sample of 66 groups and 274 clusters drawn from the literature. Our best-fit L-X-T and L-X-sigma relations for groups are given by L-X proportional to T5.57+/-1.79 proportional to sigma(2.35+/-0.21), which deviates remarkably from those for clusters: L-X proportional to T2.79+/-0.08 proportional to sigma(5.30+/-0.21). The significance of these correlations has been justified by both the co-consistency test and the Kendall tau statistics. We have thus confirmed the existence of a similarity break in the L-X-T and L-X-sigma relations between groups and clusters as claimed in previous work, although the best-fit sigma-T relations remain roughly the same in the two systems: sigma proportional to T-0.64. Alternatively, the significant disagreement between the observationally fitted L-X-T and L-X-sigma relations for groups and those expected from a perfect hydrostatic equilibrium hypothesis indicates that the X-ray emission of individual galaxies and the nongravitational heating must play a potentially important role in the dynamical evolution of groups. Therefore, reasonable caution should be exercised in the cosmological applications of the dynamical properties of groups.