ON THE DYNAMICS OF THE CORES OF GALAXY CLUSTERS

We have determined the radial velocity-dispersion profiles (VDPs) of 7 2 clusters, each with over 50 confirmed members. The velocity dispersi on sigma(v) in clusters is found to be a strong function of radius; th e largest gradients generally occur in the inner 0.5 h(-1) Mpc. In 27 clusters the VDP is significantly centrally peaked, while in 11 cases we find an 'inverted' profile, i.e. sigma(v) increases with distance f rom the centre in the inner 0.5 h(-1) Mpc. In four other clusters, who se VDPs were unclassifiable, we find hints of a central inversion of s igma(v). Several tests indicate that the observed fractions of peaked and inverted VDPs cannot be explained as the result of noise in the da ta alone. It is possible to reproduce most of the global features of t he VDPs with semi-analytical spherical models. The centrally peaked pr ofiles require density profiles with slopes as steep as-3.5 and core r adii as small as 0.03 h(-1) Mpc, whereas the inverted profiles require core radii larger than 0.2 h(-1) Mpc. The cluster mass profiles deriv ed from the data confirm this relation between profile shape and core radius. The most peaked VDPs are not associated with cooling flows, bu t they do show a significant correlation with the presence of a centra l giant galaxy. With these models we cannot explain the inverted profi les as the result of mass segregation alone, nor as the result of a va riation in the M/L-ratio or a cusp in the central density. The inverte d profiles seem to require unusually strong circularization of orbits (beta < -1.5), which is hard to reconcile with other calculations on t he dynamics of clusters. An alternative explanation is that inverted p rofiles result from anisotropic projection effects of structures in th e core. Because in 12 clusters the shape of the VDP is found to depend on the magnitude limit, we test all 53 clusters for which a sufficien t number of magnitudes are available for signs of luminosity segregati on (LS). In 12 clusters we find a signal of LS that is significant at the 99 per cent level, although the effect is generally limited to the five brightest galaxies. In 11 other clusters we find signs of an opp osite effect. There is hardly any correlation between signs of LS and other dynamically relevant properties. In all clusters (either with or without signs of LS) the velocity dispersions are in agreement with t he X-ray temperatures (i.e. beta = 1), for the entire galaxy populatio n as well as for the early-type galaxies or the galaxies with projecte d distances from the centre less than 0.5 h(-1) Mpc. The median relaxa tion time (orbital-decay time) for the inner 0.5 h(-1) Mpc, where the differences between the various VDPs are most prominent, is on average 0.45t(H), and ranges from 0.3t(H) for the peaked profiles to 0.6t(H) for the inverted VDPs. The region where the relaxation time is 0.2t(H) is within the errors equal to 0.27 h(-1) Mpc for all clusters, regard less of the type of VDP. Hence, the differences between the profiles a re unlikely to be due to large differences in the relaxation time.