The effect of non-radial motions on the CDM model predictions

In this paper we show how non-radial motions, originating from the tidal interaction of the irregular mass distribution within and around protoclusters, can solve some of the problems of the CDM model. Firstly the discrepancy between the CDM predicted two-points correlation function of clusters and the observed one. We compare the two-points correlation function, that we obtain taking account of non-radial motions, with that obtained by Sutherland & Efstathiou (1991) from the analysis of Geller & Hucra's (1988) deep redshift survey and with the data points for the APM clusters obtained by Efstathiou et al. (1992). Secondly the problem of the X-ray clusters abundance over-production predicted by the CDM model. In this case we compare the X-ray temperature distribution function, calculated using Press-Schechter theory and Evrard's (1990) prescriptions for the mass-temperature relation, taking also account of the non-radial motions, with Henry & Arnaud (1991) and Edge et al. (1990) X-ray temperature distributions for local clusters. We find that in both cases the model is in good agreement with experimental data. Finally we calculate the bias coefficient using a selection function that takes into account the effects of non-radial motions, and we show that the bias so obtained can account for a substantial part of the total bias required by observations on cluster scales.