Counting of galaxy clusters with the S-Z effect of triaxial ellipsoidal model *

In the near future a large number of galaxy clusters will be observed in surveys based on the Sunyaev-Zel'dovich effect (SZE) . Both the spherical and ellipsoidal models of the dark matter of galaxy clusters are adopted to make theoretical predictions of the number of observable S-Z galaxy clusters, and to asses the effect of the cluster shape on the calculation. By means of the virial equilibrium condition the mass lower limit of the observable galaxy clusters is determined from given survey flux lower limit and the prediction of the number count of galaxy clusters is carried out by the mass function. The calculated results show that if the cosmological parameters are to be constrained by the S-Z surveys, then the uncertainty in the shape of the clusters should be taken into account.