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 800h 1 Mpc 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 : 01 0 12 erg s 1 cm 2 for the ROSAT energy band (0:1 2:4) keV. Several tests are performed showing no signicant incompletenesses of the REFLEX clusters with X-ray luminosities brighter than 10 43 erg s 1 up to scales of about 800h 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 wavenum- ber range 0:022 k 0:030h 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 0:05h Mpc 1 thus shifting the maximum of P (k) to larger scales. The smooth maximum is not consis- tent with the narrow peak detected at k =0 :05h Mpc 1 using the Abell/ACO richness0 data. In the range 0:02 k 0:4h Mpc 1 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.