Constraining cosmological parameters with the clustering properties of galaxy clusters in optical and X-ray bands

Abstract

We use a theoretical model to predict the clustering properties of galaxy clusters. Our technique accounts for past light-cone effects on the observed clustering and follows the non-linear evolution in redshift of the underlying dark matter correlation function and cluster bias factor. A linear treatment of redshift-space distortions is also included. We perform a maximum-likelihood analysis by comparing the theoretical predictions to a set of observational data, in both the optical (two different subsamples of the APM catalogue and the EDCC catalogue) and X-ray band (RASS1 bright sample, BCS, XBACs, REFLEX). In the framework of cold dark matter models, we compute the constraints on cosmological parameters, such as the matter density Ω0m, the cosmological constant Ω0Λ, the power-spectrum shape parameter Γ and normalization σ8. Our results show that X-ray data are more powerful than optical ones, allowing smaller regions in the parameter space. If we fix Γ and σ8 to the values suggested by different observational data sets, we obtain strong constraints on the matter density parameter, Ω0m ≤ 0.5 and 0.2 ≤ Ω0m ≤ 0.35, for the optical and X-ray data, respectively. Allowing 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. Using the X-ray data only, we obtain Γ ∼ 0.1 and 0.4 ≲ σ8 ≲ 1-1 for the Einstein-de Sitter model, while 0.14 ≲ Γ ≲ 0.22 and 0.6 ≲ σ8 ≲ 1.3 for open and flat models with Ω0m = 0.3. Finally, we use our model to make predictions on the correlation length of galaxy clusters expected in future surveys. In particular, we show the results for an optical catalogue with characteristics similar to the EIS project and for a very deep X-ray catalogue with the characteristics of the XMW/LSS survey. We find that clusters at high redshifts are expected to have a larger correlation length than local ones.