M. Kerscher, J. Schmalzing, J. Retzlaff, S. Borgani, T. Buchert, S. Gottlöber, V. Müller, M. Plionis, H. Wagner
Monthly Notices of the Royal Astronomical Society, Volume 284, Issue 1, January 1997, Pages 73–84
Publication year: 1997


We determine the Minkowski functionals for a sample of Abell/ACO clusters, 401 with measured and 16 with estimated redshifts. The four Minkowski functionals (including the void probability function and the mean genus) deliver a global description of the spatial distribution of clusters on scales from 10 to 60 Mh−1 Mpc with a clear geometric interpretation. Comparisons with mock catalogues of N-body simulations using different variants of the CDM model demonstrate the discriminative power of the description. The standard CDM model and the model with a tilted perturbation spectrum cannot generate the Minkowski functionals of the cluster data, while a model with a cosmological constant and a model with breaking of the scale invariance of perturbations (BSI) yield compatible results.