EDP Sciences
Free Access
Volume 398, Number 3, February II 2003
Page(s) 867 - 877
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361:20021715
Published online 28 January 2003

A&A 398, 867-877 (2003)
DOI: 10.1051/0004-6361:20021715

The REFLEX galaxy cluster survey

VII. $\Omega\mathsf{_{m}}$ and $\sigma_8$ from cluster abundance and large-scale clustering
P. Schuecker1, H. Böhringer1, C. A. Collins2 and L. Guzzo3

1  Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße 1, 85740 Garching, Germany
2  Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf, Birkenhead CH41 1LD, UK
3  INAF-Osservatorio di Brera, via Bianchi, 22055 Merate (LC), Italy

(Received 14 August 2002 / Accepted 14 November 2002 )

For the first time the large-scale clustering and the mean abundance of galaxy clusters are analysed simultaneously to get precise constraints on the normalized cosmic matter density $\Omega_{\rm m}$ and the linear theory RMS fluctuations in mass $\sigma_8$. A self-consistent likelihood analysis is described which combines, in a natural and optimal manner, a battery of sensitive cosmological tests where observational data are represented by the (Karhunen-Loéve) eigenvectors of the sample correlation matrix. This method breaks the degeneracy between $\Omega_{\rm m}$ and $\sigma_8$. The cosmological tests are performed with the ROSAT ESO Flux-Limited X-ray (REFLEX) cluster sample. The computations assume cosmologically flat geometries and a non-evolving cluster population mainly over the redshift range 0<z<0.3. The REFLEX sample gives the cosmological constraints and their $1\sigma$ random errors of $\Omega_{\rm m}\,=\,0.341\,^{+0.031}_{-0.029}$ and $\sigma_8\,=\,0.711\,^{+0.039}_{-0.031}$. Possible systematic errors are evaluated by estimating the effects of uncertainties in the value of the Hubble constant, the baryon density, the spectral slope of the initial scalar fluctuations, the mass/X-ray luminosity relation and its intrinsic scatter, the biasing scheme, and the cluster mass density profile. All these contributions sum up to total systematic errors of $\sigma_{\Omega_{\rm m}}=^{+0.087}_{-0.071}$ and $\sigma_{\sigma_8}=^{+0.120}_{-0.162}$.

Key words: cosmology: cosmological parameters -- X-rays: galaxies: clusters

Offprint request: P. Schuecker, peters@mpe.mpg.de

© ESO 2003

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