We analyse the spatial clustering properties of the RASS1 Bright Sample , an X-ray flux-limited catalogue of galaxy clusters selected from the southern part of the ROSAT All-Sky Survey .
The two-point correlation function \xi ( r ) of the whole sample is well fitted ( in an Einstein-de Sitter model ) by the power-law \xi = ( r / r _ { 0 } ) ^ { - \gamma } , with r _ { 0 } = 21.5 ^ { +3.4 } _ { -4.4 } h ^ { -1 } Mpc and \gamma = 2.11 ^ { +0.53 } _ { -0.56 } ( 95.4 per cent confidence level with one fitting parameter ) .
We use the RASS1 Bright Sample as a first application of a theoretical model which aims at predicting the clustering properties of X-ray clusters in flux-limited surveys for different cosmological scenarios .
The model uses the theoretical and empirical relations between mass , temperature and X-ray cluster luminosity , and fully accounts for the redshift evolution of the underlying dark matter clustering and cluster bias factor .
The comparison between observational results and theoretical predictions shows that the Einstein-de Sitter models display too low a correlation length , while models with a matter density parameter \Omega _ { 0 m } = 0.3 ( with or without a cosmological constant ) are successful in reproducing the observed clustering .
The dependence of the correlation length r _ { 0 } on the X-ray limiting flux and luminosity of the sample is generally consistent with the predictions of all our models .
Quantitative agreement is however only reached for \Omega _ { 0 m } = 0.3 models .
The model presented here can be reliably applied to future deeper X-ray cluster surveys : the study of their clustering properties will provide a useful complementary tool to the traditional cluster abundance analyses to constrain the cosmological parameters .