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A new X-ray selected and X-ray flux-limited galaxy cluster sample is presented. Based on the ROSAT All-Sky Survey the 63 brightest clusters with galactic latitude |bII| >= 20 deg and flux fx (0. 1-2. 4 keV) >= 2 * 10^-11 ergs/s/cm² have been compiled. Gravitational masses have been determined utilizing intracluster gas density profiles, derived mainly from ROSAT PSPC pointed observations, and gas temperatures, as published mainly from ASCA observations, assuming hydrostatic equilibrium. This sample and an extended sample of 106 galaxy clusters is used to establish the X-ray luminosity--gravitational mass relation. From the complete sample the galaxy cluster mass function is determined and used to constrain the mean cosmic matter density and the amplitude of mass fluctuations. Comparison to Press--Schechter type model mass functions in the framework of Cold Dark Matter cosmological models and a Harrison--Zeldovich initial density fluctuation spectrum yields the constraints OmegaM = 0. 12^+0. 06-₀. ₀₄ and sigma8 = 0. 96^+0. 15-₀. ₁₂ (90% c. l. ). Various possible systematic uncertainties are quantified. Adding all identified systematic uncertainties to the statistical uncertainty in a worst case fashion results in an upper limit OmegaM < 0. 31. For comparison to previous results a relation sigma8 = 0. 43 OmegaM^-0. 38 is derived. The mass function is integrated to show that the contribution of mass bound within virialized cluster regions to the total matter density is small, i. e. , OmegaCluster = 0. 012^+0. 003-₀. ₀₀₄ for cluster masses larger than 6. 4^+0. 7-₀. ₆ * 10^13 h₅₀^-1 Msun.
Reiprich et al. (Sun,) studied this question.
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