Clustering of CODEX clusters

Aims. We analyze the autocorrelation function of a large contiguous sample of galaxy clusters, the Constrain Dark Energy with X-ray (CODEX) sample, in which we take particular care of cluster definition. These clusters were X-ray selected using the RASS survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the SDSS. We develop methods for precisely accounting for the sample selection effects on the clustering and demonstrate their robustness using numerical simulations. Methods. Using the clean CODEX sample, which was obtained by applying a redshift-dependent richness selection, we computed the two-point autocorrelation function of galaxy clusters in the $0.1<z<0.3$ and $0.3<z<0.5$ redshift bins. We compared the bias in the measured correlation function with values obtained in numerical simulations using a similar cluster mass range. Results. By fitting a power law, we measured a correlation length $r_0=18.7 pm 1.1$ and slope $gamma=1.98 pm 0.14$ for the correlation function in the full redshift range. By fixing the other cosmological parameters to their WMAP9 values, we reproduced the observed shape of the correlation function under the following cosmological conditions: $Omega_{m_0}=0.22^{+0.04}_{-0.03}$ and $S_8=sigma_8 (Omega_{m_0} /0.3)^{0.5}=0.85^{+0.10}_{-0.08}$ with estimated additional systematic errors of $sigma_{Omega_{m_0}} = 0.02$ and $sigma_{S_8} = 0.20$. We illustrate the complementarity of clustering constraints by combining them with CODEX cosmological constraints based on the X-ray luminosity function, deriving $Omega_{m_0} = 0.25 pm 0.01$ and $sigma_8 = 0.81^{+0.01}_{-0.02}$ with an estimated additional systematic error of $sigma_{Omega_{m_0}} = 0.07$ and $sigma_{sigma_8} = 0.04$. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.