Constraints on the fluctuation amplitude and density parameter from X-ray cluster number counts

We derive constraints on the fluctuation amplitude σ8 and the cosmological density parameter Ω0 in cold dark matter (CDM) universes from the observed logN -logS relation of X-ray clusters. The 95 percent confidence limits on σ8 in the CDM models with n = 1 and h = 0.7 are expressed as (0.52± 0.02)Ω −0.35−0.90Ω0+0.76Ω20 0 (Ω0 < 0.75; λ0 = 1 − Ω0) and (0.52 ± 0.02)Ω −0.29−0.91Ω0+0.73Ω20 0 (Ω0 < 0.65; λ0 = 0), where n is the primordial spectral index, and h and λ0 are the dimensionless Hubble and cosmological constants. These limits are consistent with, but much stronger than, those from the X-ray temperature functions due to better statistical significance of the observed logN -logS . In the case of n = 1 and h = 0.7, we find that the CDM models with (Ω0, λ0, σ8) = (0.3, 0.7, 1) and (0.45, 0, 0.8) simultaneously account for the cluster logN -logS , X-ray temperature functions, and the COBE 4yr data. We also discuss several uncertainties which may change the limits on Ω0 and σ8 from the logN -logS relation. Subject headings: cosmology: theory – dark matter – galaxies: clusters: general – X-rays: galaxies submitted to The Astrophysical Journal (Letters)