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We present the results of a set of simulations designed to quantify the selection function of the Bright SHARC survey for distant clusters. The statistical significance of the simulations relied on the creation of thousands of artificial clusters with redshifts and luminosities in the range 0.25<z<0.95 and 0.5<L_X<10x10^44 erg/s (0.5-2.0 keV). We created 1 standard and 19 varied distribution functions, each of which assumed a different set of cluster, cosmological and operational parameters. The parameters we varied included the values of Omega_0, Omega_Lambda, Beta, core radius and ellipticity. We also investigated how non-standard surface brightness profiles; cooling flows; and the ROSAT pointing target, influence the selection function in the Bright SHARC survey. For our standard set we adopted the parameters used during the derivation of the Bright SHARC Cluster X-ray Luminosity Function (CXLF), i.e. Omega_0=1, Omega_Lambda=0 and an isothermal Beta model with beta=0.67, r_c=250 kpc and e=0.15. We found that certain parameters have a dramatic effect on our ability to detect clusters, e.g. the presence of a NFW profile or a strong cooling flow profile, or the value of r_c and beta. Other parameters had very little effect, e.g. the type of ROSAT target and the cluster ellipticity. We show also that all the tested parameters have only a small influence on the computed luminosity of the clusters except the presence of a strong cooling flow. We conclude that the CXLF presented in Nichol et al. (1999) is robust (under the assumption of standard parameters), but stress the importance of cluster follow-up in order to better constrain the morphology of the distant clusters found in the Bright SHARC and other surveys.

We investigate in this paper the error on the cluster redshift estimate as a function of: (1) the number of galaxy structures along the line of sight; (2) the morphology of the clusters (regular/substructures); (3) the nature of the observed galaxies (cD/normal galaxies); (4) the number of observed galaxies; and (5) the distance of the clusters. We find that if we use cD galaxies we have errors of less than 2% (at the 1-$\sigma$ level) for the cluster distances except when the clusters are very complex. In those cases when we use five redshift measurements along the cluster lines of sight to compute the mean redshift, the mean redshift estimate error is less than 5% for the clusters closer than z=0.30. The same error of 5% for clusters in z=[0.30;0.60] requires about 12 redshifts measurements.