Clustering of CODEX clusters

Context. The clustering of galaxy clusters links the spatial nonuniformity of dark matter halos to the growth of the primordial spectrum of perturbations. The amplitude of the clustering signal is widely used to estimate the halo mass of astrophysical objects. The advent of cluster mass calibrations enables using clustering in cosmological studies.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 ROentgen SATellite All-Sky Survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the Sloan Digital Sky Survey. 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<0.3 and 0.3<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 +/- 1.1 and slope gamma =1.98 +/- 0.14 for the correlation function in the full redshift range. By fixing the other cosmological parameters to their nine-year Wilkinson Microwave Anisotropy Probe values, we reproduced the observed shape of the correlation function under the following cosmological conditions: Omega m0 = 0.22-0.03+0.04 Omega m 0 = 0 . 22 - 0.03 + 0.04 and S8 = sigma 8(Omega m0/0.3)0.5 = 0.85-0.08+0.10 S 8 = sigma 8 ( Omega m 0 / 0.3 ) 0.5 = 0 . 85 - 0.08 + 0.10 with estimated additional systematic errors of sigma Omega m0=0.02 and sigma S8=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 m0=0.25 +/- 0.01 and sigma (8) = 0.81(-0.02)(+0.01) sigma 8 = 0 . 81 - 0.02 + 0.01 with an estimated additional systematic error of sigma Omega m0=0.07 and sigma sigma 8=0.04. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.

Automated summary

The study analyzed the autocorrelation function of a large sample of galaxy clusters, CAREX, and paid particular attention to cluster definition. Methods were developed to account precisely for sample selection effects on clustering, which were demonstrated to be robust using numerical simulations. The fitting of a power law resulted in measurements of correlation length and slope, providing valuable cosmological constraints.