The effect of non-radial motions on the X-ray temperature distribution function and the two-point correlation function of clusters

We show how non-radial motions, originating in the outskirts of clusters of galaxies, may reduce the discrepancy between the Cold Dark Matter (CDM) predicted X-ray temperature distribution function of clusters of galaxies and the observed one and also the discrepancy between the CDM predicted two-point correlation function of clusters of galaxies and that observed. We compare Edge et al. (1990) and Henry & Arnaud (1991) data with the distribution function of X-ray temperature, calculated using Press- Schechter's (1974 - hereafter PS) theory and Evrard's (1990) prescriptions for the mass-temperature relation and taking account of the non-radial motions originating from the gravitational interaction of the quadrupole moment of the protocluster with the tidal field of the matter of the neighboring protostructures. We find that the model produces a reasonable clusters temperature distribution. We compare the two-point cluster correlation function which takes account of the non-radial motions both with that obtained by Sutherland & Efstathiou (1991), from the analysis of Huchra's et al. (1990) deep redshift survey, and with the data points for the Automatic Plate Measuring (APM) clusters, computed by Efstathiou et al. (1992a), showing that non-radial motions reduce the discrepancy between the theoretical and the obsservational correlation function.