Modelling the two point correlation function of galaxy clusters in the Sloan Digital Sky Survey

We study the clustering properties of the recently compiled SDSS cluster catalog using the two point correlation function in redshift space. We divide the total SDSS sample into two richness subsamples, roughly corresponding to Abell $R\ge 0$ and APM clusters, respectively. If the two point correlations are modeled as a power law, $\xi(r)=(r_{\circ}/r)^{\gamma}$, then the best-fitting parameters for the two subsamples are $r_{\circ}=20.7^{+4.0}_{-3.8} h^{-1}$ Mpc with $\gamma=1.6^{+0.4}_{-0.4}$ and $r_{\circ}=9.7^{+1.2}_{-1.2}$ with $\gamma=2.0^{+0.7}_{-0.5} h^{-1}$ Mpc, respectively. Our results are consistent with the dependence of cluster richness to the cluster correlation length. Finally, comparing the SDSS cluster correlation function with that predictions from three flat cosmological models ($\Omega_{\rm m}=0.3$) with dark energy (quintessence), we estimate the cluster redshift space distortion parameter $\beta \simeq \Omega_{\rm m}^{0.6}/b_{\circ}$ and the cluster bias at the present time. For the $\Lambda$CDM case we find $\beta=0.2^{+0.029}_{-0.016}$, which is in agreement with the results based on the large scale cluster motions.