Cosmological constraints from clustering properties of galaxy clusters

Free access article

Issue		A&A Volume 432, Number 3, March IV 2005


Page(s)		771 - 781
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:20041535

A&A 432, 771-781 (2005)
DOI: 10.1051/0004-6361:20041535

Cosmological constraints from clustering properties of galaxy clusters

A. Del Popolo^{1, 2}, N. Ercan¹ and I. S. Yesilyurt¹

¹ Bo $\breve{\rm g}$ aziçi University, Physics Department, 80815 Bebek, Istanbul, Turkey
e-mail: antonino.delpopolo@boun.edu.tr
² Dipartimento di Matematica, Università Statale di Bergamo, via dei Caniana, 2, 24127, Bergamo, Italy

(Received 25 June 2004 / Accepted 19 October 2004)

Abstract
In this paper, we discuss improvements of the Suto et al. (2000) model, in the light of recent theoretical developments (new theoretical mass functions, a more accurate mass-temperature relation and an improved bias model) to predict the clustering properties of galaxy clusters and to obtain constraints on cosmological parameters. We re-derive the two-point correlation function of clusters of galaxies for OCDM and $\Lambda$ CDM cosmological models, and we compare these results with the observed spatial correlation function for clusters in RASS1 (ROSAT All-Sky Survey 1), and in XBACs (X-RAY Brighest Abell-Type) samples. The comparison shows that the best agreement is obtained for the $\Lambda$ CDM model with $\Omega_{{\rm m} }=0.3$ . The values of the correlation length obtained, ( $r_0\simeq 28.2 \pm 5.2~{h^{-1}}$ Mpc for $\Lambda$ CDM), are larger than those found in the literature and comparable with the results found in Borgani et al. (1999). In order to study the possible dependence of the clustering properties of the X-ray clusters on the observational characteristics defining the survey, we calculated the values of the correlation length r₀ in the catalogues where we vary the limiting X-ray flux $S_{{\rm lim}}$ . The result shows an increase of r₀ with $L_{{\rm lim}}$ , and correlation lengths that are larger than in previous papers in literature (e.g. Moscardini et al. 2001 (hereafter MMM); Suto et al. 2000). These differences are due essentially to the different M-T, mass function and bias model used in this paper. Then, we perform a maximum-likelihood analysis by comparing the theoretical predictions to a set of observational data in the X-ray band (RASS1 Bright Sample, BCS (Rosat Brightest Cluster Sample), XBACs, REFLEX (ROSAT-ESO Flux Limited X-Ray Sample)), similarly to MMM. In the framework of cold dark matter models, we compute the constraints on cosmological parameters, such as the matter density $\Omega_{{\rm m}}$ , the contribution to density due to the cosmological constant, $\Omega_{\Lambda}$ , the power-spectrum shape parameter $\Gamma$ and normalization $\sigma_8$ . If we fix $\Gamma$ and $\sigma_8$ , at the values suggested by different observational datasets, we obtain (for flat cosmological models with varying cosmological constant $\Omega_{{\rm0 \Lambda}} = 1 -\Omega_{{\rm0m}}$ ) constraints on the matter density parameter: $0.25 \leq \Omega_{{\rm0m} } \leq 0.45$ and $0.23 \leq \Omega_{{\rm0m}} \leq 0.52$ at the 95.4 and 99.73 per cent levels, respectively, which is 20-30% larger than the values obtained MMM. Leaving $\Gamma$ , and $\Omega_{{\rm m0}}$ , free for the flat model, the constraints for $\Gamma$ are $0.1 \leq \Gamma \leq 0.14$ , while for the open model $0.09 \leq \Gamma \leq 0.13$ . These values are smaller than those of MMM by about 20-30%. If we keep the values of $\Omega_{\Lambda}$ fixed, we obtain the constraints in the $\Gamma-\sigma_8$ plane. For the open model with $\Omega_{{\rm0m}}=0.3$ the $2\sigma$ region for $\Gamma$ is 0.11-0.2 for $\sigma_8$ it is 0.7 and 1.55. For the flat model with $\Omega_{{\rm0m}}=0.3$ the $2\sigma$ region has $0.13 \leq\Gamma \leq 0.2$ and $0.8 \leq \sigma_8 \leq 1.6$ The values of $\sigma_8$ obtained are larger than those of MMM by $\simeq$ $20 \%$ . If we allow the shape parameter to vary, we find that the clustering properties of clusters are almost independent of the matter density parameter and of the presence of a cosmological constant, while they appear to be strongly dependent on the shape parameter.

Key words: cosmology: large-scale structure of Universe

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