Cosmological Implications of Number Counts of Clusters of Galaxies: log N–log S in X-Ray and Submm Bands

Abstract

We have computed the number counts of clusters of galaxies, the log N–log S relations, in X-ray and submm bands based on the Press-Schechter theory. We paid particular attention to a set of theoretical models which well reproduce the ROSAT soft X-ray log N–log S, and explored possibilities to further constrain the models from future observations in hard X-ray and submm bands. The former is closely related to the ASCA, AXAF, and Astro-E missions, while the latter to the PLANCK and LMSA projects. We have shown that one can break the degeneracy in an acceptable parameter region on the Ω0–σ8 plane by combining the X-ray and submm number counts. Models which reproduce the ROSAT 0.5–2 keV band log N–log S will have N(> S) ∼ (150–300)(S/10−12 erg cm−2 s−1)−1.3 str−1 at S ≳ 10−12 erg cm−2 s−1 in the 2–10 keV band, and N(> Sv) ∼ (102–104)(Sv/100 mJy)−1.5 str−1 at Sv ≳ 100 mJy in the submm (0.85 mm) band. The amplitude of log N–log S is very sensitive to the model parameters in the submm band. We also computed the redshift evolution of the cluster number counts and compared it with that of the X-ray brightest Abell-type clusters. The results, although still preliminary, point to low density (Ω0 ∼ 0.3) universes. The contribution of clusters to the X-ray and submm background radiations is shown to be insignificant in any model compatible with the ROSAT log N–log S relation.