Non radial motions and the shapes and the abundance of clusters of galaxies

We study the effect of non-radial motions on the mass function, the velocit y dispersion function (hereafter VDF) and on the shape of clusters of galax ies using the model introduced in Del Popolo & Gambera (1998a,b, 1999). The mass function of clusters, obtained using the quoted model, is compared wi th the statistical data by Bahcall & Cen (1992, 1993) and Girardi et al. (1 998), while the VDF is compared with the Center for Astrophysics (hereafter CfA) data by Zabludoff et al. (1993) for local clusters and those of Matur e et al. (1996) and Fadda et al. (1996). In both cases the model prediction s are in good agreement with the observational data showing once more how n on-radial motions can reduce many of the discrepancies between Cold Dark Ma tter (hereafter CDM) model predictions and observational data. Finally we s tudy the effect of non-radial motions on the intrinsic shape of clusters of galaxies showing that non-radial motions produce clusters less elongated w ith respect to CDM model in agreement with de Theije et al. (1995, 1997) re sults.