Measuring Ω_m with the ROSAT Deep Cluster Survey

We analyze the ROSAT Deep Cluster Survey (RDCS) to derive cosmological constraints from the evolution of the cluster X-ray luminosity distribution. The sample contains 103 galaxy clusters out to z~=0.85 and flux limit F_lim=3×10^-14 ergs s^-1 cm^-2 (RDCS-3) in the [0.5-2.0] keV energy band, with a high-redshift extension containing four clusters at 0.90lim=1×10^-14 ergs s^-1 cm^-2 (RDCS-1). We assume cosmological models to be specified by the matter density parameter Ω_m, the rms fluctuation amplitude at the 8 h^-1 Mpc scale σ₈, and the shape parameter for the cold dark matter-like power spectrum Γ. Model predictions for the cluster mass function are converted into the X-ray luminosity function in two steps. First, we convert mass into intracluster gas temperature by assuming hydrostatic equilibrium. Then, temperature is converted into X-ray luminosity by using the most recent data on the L_X-T_X relation for nearby and distant clusters. These include the Chandra data for six distant clusters at 0.57m=0.35^+0.13_-0.10 and σ₈=0.66^+0.06_-0.05 for a spatially flat universe with a cosmological constant, with no significant constraint on Γ (errors correspond to 1 σ confidence levels for three fitting parameters). Even accounting for both theoretical and observational uncertainties in the mass-X-ray luminosity conversion, an Einstein-de Sitter model is always excluded at far more than the 3 σ level. We also show that the number of X-ray-bright clusters in RDCS-1 at z>0.9 is expected from the evolution inferred at z