Expectations for Sz Cluster Counts: Mass Function versus X-ray Luminosity Function

We present a comparison of the SZ cluster counts predicted by the Press-Schechter (PS) mass function (MF) and the X-ray luminosity function (XLF) of clusters. The employment of the cluster XLF, together with the observationally determined X-ray luminosity(LX)-temperature(T ) relation, may allow us to estimate the SZ cluster counts in a more realistic manner, although such an empirical approach depends sensitively on our current knowledge of the dynamical properties of intracluster gas and its cosmic evolution. Using both the non-evolving and evolving XLFs of clusters suggested by X-ray observations, we calculate the expectations for SZ surveys of clusters with X-ray luminosity LX ≥ 3×10 44 erg s and LX ≥ 1× 10 43 erg s in the 0.5 2.0 band, respectively. The non-evolving XLF results in a significant excess of SZ cluster counts at high redshifts as compared with the evolving XLF, while a slightly steeper LX-T relation than the observed one is needed to reproduce the distributions of SZ clusters predicted by the standard PS formalism. It is pointed out that uncertainties in the cosmological application of future SZ cluster surveys via the standard PS formalism should be carefully studied. Subject headings: cosmology: theory — galaxies: clusters: general — X-rays: galaxies