Clusters of galaxies compared withN-body simulations: Masses and mass segregation

With three virially stableN-body simulations of Wielen, we show that use of the expression for the total mass derived from averaged quantities (velocity dispersion and mean harmonic radius) yields an overestimate of the mass by as much as a factor of 2–3, and use of the heaviest mass sample gives an underestimate by a factor of 2–3. The estimate of the mass using mass weighted quantities (i.e., derived from the customary definition of kinetic and potential energies) yields a better value irrespective of mass sample as applied to late time intervals of the models (three two-body relaxation times). The uncertainty is at most 50%. This suggests that it is better to employ the mass weighted expression for the mass when determining cluster masses. The virial ratio, which is a ratio of the mass weighted/averaged expression for the potential energy, is found to vary between 1 and 2. We conclude that ratios for observed clusters 4–10 cannot be explained even by the imprecision of the expression for the mass using averaged quantities, and certainly implies the presence of unseen matter. Total masses via customary application of the virial theorem are calculated for 39 clusters, and total masses for 12 clusters are calculated by a variant of the usual application. The distribution of cluster masses is also presented and briefly discussed. Mass segregation in Wielen's models is studied in terms of the binding energy per unit mass of the heavy sample compared with the light sample. The general absence of mass segregation in relaxed clusters and the large virial discrepancies are attributed to a population of many low-mass objects that may constitute the bulk mass of clusters of galaxies.