Cosmological constraints from clustering properties of galaxy clusters

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 $\Omega_{{\rm m} }=0.3$. The values of the correlation length obtained, ($r_0\simeq 28.2 \pm 5.2~{h^{-1}}$ 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 $S_{{\rm lim}}$. 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. [CITE] (hereafter MMM); Suto et al. [CITE]). 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 Γ and normalization $\sigma_8$. If we fix Γ and $ \sigma_8$, at the values suggested by different observational datasets, we obtain (for flat cosmological models with varying cosmological constant $\Omega_{{\rm 0 \Lambda}} = 1 -\Omega_{{\rm 0m}}$ ) constraints on the matter density parameter: $0.25 \leq \Omega_{{\rm 0m} } \leq 0.45$ and $0.23 \leq \Omega_{{\rm 0m}} \leq 0.52$ at the 95.4 and 99.73 per cent levels, respectively, which is 20–30% larger than the values obtained MMM. Leaving Γ, and $\Omega_{{\rm m0}}$, free for the flat model, the constraints for Γ 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 $\Omega_{{\rm 0m}}=0.3$ the $2\sigma$ region for Γ is 0.11–0.2 for $\sigma_8$ it is 0.7 and 1.55. For the flat model with $\Omega_{{\rm 0m}}=0.3$ 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