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The mass function of galaxy clusters is a sensitive tracer of the gravitational evolution of the cosmic large-scale structure and serves as an important census of the fraction of matter bound in large structures. We obtain the mass function by fitting the observed cluster X-ray luminosity distribution from the REFLEX galaxy cluster survey to models of cosmological structure formation. We marginalise over uncertainties in the cosmological parameters as well as those of the relevant galaxy cluster scaling relations. The mass function is determined with an uncertainty less than 10% in the mass range 3 x 10^12 to 5 x 10^14 M$_odot$. For the cumulative mass function we find a slope at the low mass end consistent with a value of -1, while the mass rich end cut-off is milder than a Schechter function with an exponential term exp($- M^delta$) with $delta$ smaller than 1. Changing the Hubble parameter in the range $H_0 = 67 - 73 km s^-1 Mpc^{-1}$ or allowing the total neutrino mass to have a value between 0 - 0.4 eV causes variations less than the uncertainties. We estimate the fraction of mass locked up in galaxy clusters: about 4.4% of the matter in the Universe is bound in clusters (inside $r_200$) with a mass larger than 10^14 M$_odot$ and 14% to clusters and groups with a mass larger than 10^13 M$_odot$ at the present Universe. We also discuss the evolution of the galaxy cluster population with redshift. Our results imply that there is hardly any clusters with a mass > 10^15 M$_odot$ above a redshift of z = 1.
We present the catalogue of the REFLEX Cluster Survey providing information on the X-ray properties, redshifts, and some identification details of the clusters in the REFLEX sample. The catalogue describes a statistically complete X-ray flux-limited
We present a measure of the power spectrum on scales from 15 to 800 Mpc/h using the ROSAT-ESO Flux-Limited X-Ray(REFLEX) galaxy cluster catalogue. The REFLEX survey provides a sample of the 452 X-ray brightest southern clusters of galaxies with the n
The ROSAT-ESO Flux Limited X-ray (REFLEX) galaxy cluster survey and the 2dF Galaxy Redshift Survey (2dFGRS) respectively comprise the largest, homogeneous X-ray selected cluster catalogue and completed galaxy redshift survey. In this work we combine
The Karhunen-Lo{e}ve (KL) eigenvectors and eigenvalues of the sample correlation matrix are used to analyse the spatial fluctuations of the REFLEX clusters of galaxies. The method avoids the disturbing effects of correlated power spectral densities w
The X-ray galaxy cluster sample from the REFLEX Cluster Survey, which covers the X-ray brightest galaxy clusters detected in the ROSAT All-Sky Survey in the southern sky, is used to construct the X-ray luminosity function of clusters in the local Uni