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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 nominal flux limit S=3.0 10^{-12}erg/s/cm2 for the ROSAT energy band (0.1-2.4)keV. Several tests are performed showing no significant incompletenesses of the REFLEX clusters with X-ray luminosities brighter than 10^{43}erg/s up to scales of about 800 Mpc/h. They also indicate that cosmic variance might be more important than previous studies suggest. We regard this as a warning not to draw general cosmological conclusions from cluster samples with a size smaller than REFLEX. Power spectra, P(k), of comoving cluster number densities are estimated for flux- and volume-limited subsamples. The most important result is the detection of a broad maximum within the comoving wavenumber range 0.022<k<0.030 h/Mpc. The data suggest an increase of the power spectral amplitude with X-ray luminosity. Compared to optically selected cluster samples the REFLEX P(k)is flatter for wavenumbers k<0.05 h/Mpc thus shifting the maximum of P(k) to larger scales. The smooth maximum is not consistent with the narrow peak detected at k=0.05 h/Mpc using the Abell/ACO richness $ge 0$ data. In the range 0.02<k<0.4 h/Mpc general agreement is found between the slope of the REFLEX P(k) and those obtained with optically selected galaxies. A semi-analytic description of the biased nonlinear power spectrum in redshift space gives the best agreement for low-density Cold Dark Matter models with or without a cosmological constant.
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 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 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