Open AccessCosmological constraints from the clustering properties of the X‐ray Brightest Abell‐type Cluster sample
Author(s) -
Borgani S.,
Plionis M.,
Kolokotronis V.
Publication year - 1999
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1999.02468.x
Subject(s) - physics , astrophysics , amplitude , cluster (spacecraft) , spectral density , luminosity , correlation function (quantum field theory) , limit (mathematics) , parameter space , flux (metallurgy) , radius , statistics , quantum mechanics , mathematical analysis , galaxy , computer science , programming language , materials science , mathematics , computer security , dielectric , metallurgy
We present an analysis of the two‐point correlation function, ξ (r), of the X‐ray Brightest Abell‐type Cluster sample (XBACs) of Ebeling et al. and of the cosmological constraints that it provides. If ξ (r) is modelled as a power‐law, ξ (r)=(r 0/r ) γ , we find r 0≃ 26.0 ± 4.5 h ‐1 Mpc and γ≃ 2.0 ± 0.4, with errors corresponding to 2 σ uncertainties for one significant fitting parameter. As a general feature, ξ (r) is found to remain positive up to r ≃ 50–55 h ‐1 Mpc, after which it declines and crosses zero. Only a marginal increase of the correlation amplitude is found as the flux limit is increased from 5 × 10 ‐12 to 12 × 10 ‐12 erg s ‐1 cm ‐2 , thus indicating a weak dependence of the correlation amplitude on the cluster X‐ray luminosity. Furthermore, we present a method to predict correlation functions for flux‐limited X‐ray cluster samples from cosmological models. The method is based on the analytical recipe by Mo & White and on an empirical approach to convert cluster fluxes into masses. We use a maximum likelihood method to place constraints on the model parameter space from the XBACs ξ (r). For scale‐free primordial spectra, we find that the shape parameter of the power spectrum is determined to lie in the 2 σ range 0.05 ≤Γλ 0.20. As for the amplitude of the power spectrum, we find σ 8 ≃ 0.4–0.8 for Ο 0=1 and σ 8 ≃ 0.8–2.0 for Ο 0=0.3 . The latter result is in complete agreement with, although less constraining than, results based on the local cluster abundance.