The ROSAT-ESO flux-limited X-ray (REFLEX) galaxy cluster survey -: III.: The power spectrum

We present a measure of the power spectrum on scales from 15 to 800 h(-1) Mpe 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(-1) cm(-2) 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(-1) up to scales of about 600 h(-1) Mpc. 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 less than or equal to k less than or equal to 0.030 h Mpc(-1). 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 less than or equal to 0.05 h Mpc(-1) 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(-1) using the Abell/ACO richness greater than or equal to0 data. In the range 0.02 less than or equal to k less than or equal to 0.4 h Mpc(-1) general agreement is found between the slope of the REFLEX P(k) and those obtained with optically selected galaxies. X 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.