Cosmological constraints from clustering properties of galaxy clusters

¹ Boaziçi 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. ([CITE]) 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 ΛCDM 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 ΛCDM model with . The values of the correlation length obtained, ( Mpc for ΛCDM), are larger than those found in the literature and comparable with the results found in Borgani et al. ([CITE]). 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 . The result shows an increase of r₀ with , and correlation lengths that are larger than in previous papers in literature (e.g. Moscardini et al. [CITE] (hereafter MMM); Suto et al. [CITE]). These differences are due essentially to the different , 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 , the contribution to density due to the cosmological constant, , the power-spectrum shape parameter Γ and normalization . If we fix Γ and , at the values suggested by different observational datasets, we obtain (for flat cosmological models with varying cosmological constant ) constraints on the matter density parameter: and at the 95.4 and 99.73 per cent levels, respectively, which is 20–30% larger than the values obtained MMM. Leaving Γ, and , free for the flat model, the constraints for Γ are , while for the open model . These values are smaller than those of MMM by about %. If we keep the values of fixed, we obtain the constraints in the plane. For the open model with the  region for Γ is 0.11–0.2 for it is 0.7 and 1.55. For the flat model with the region has and The values of  obtained are larger than those of MMM by . 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.