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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 which affects all previous cluster measurements on Gpc scales. Comprehensive tests use a large set of independent REFLEX-like mock cluster samples extracted from the Hubble Volume Simulation. It is found that unbiased measurements on Gpc scales are possible with the REFLEX data. The distribution of the KL eigenvalues are consistent with a Gaussian random field on the 93.4% confidence level. Assuming spatially flat cold dark matter models, the marginalization of the likelihood contours over different sample volumes, fiducial cosmologies, mass/X-ray luminosity relations and baryon densities, yields the 95.4% confidence interval for the matter density of $0.03<Omega_mh^2<0.19$. The N-body simulations show that cosmic variance, although difficult to estimate, is expected to increase the confidence intervals by about 50%.
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
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
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 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 fittin
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