X-ray temperature distribution function of clusters in presence of large non-radial motions

We consider the non-radial motions, originating in the outskirts of clusters of galaxies and we show how it may reduce the discrepancy between Cold Dark Matter (CDM) predicted X-ray temperature distribution function of clusters of galaxies and that really observed, so resolving the problem of the X-ray clusters abundance over-production predicted by the CDM model. We construct the X-ray temperature distribution function using Press-Schechter's (1974) theory and Evrard's (1990) prescriptions for the mass-temperature relation, taking also account of the non-radial motions originating from the gravitational interaction of the quadrupole moment of the protocluster. Then, we compare our X-ray temperature distribution function with the tidal field of the matter of the neighboring protostructures. We find that the model produces a reasonable cluster temperature distribution.