Statistical analysis of the galaxy cluster distribution from next generation cluster surveys

I aim to study to which accuracy it is actually possible to recover the real-space to-point correlation function from cluster catalogues based on photometric redshifts. I make use of cluster sub-samples selected from a light-cone simulated catalogue. Photometric redshifts are assigned to each cluster by randomly extracting from a Gaussian distribution having a dispersion varied in the range σ (z=0) = 0.005 a 0.050. The correlation function in real-space is computed through deprojection method. Four mass ranges and six redshifts slices covering the redshift range 0<z<2 are investigated, using cosmological redshifts (Zc) and then using photometric redshifts. A clear increase of the correlation amplitude with redshift and mass is found. The evolution of the bias parameter b(M,z) is in fair agreement with the theoretical expectations. The existence of the r0-d relation up to the highest mass, highest redshift sample is tested and is confirmed. It is found that the real-space correlation function can be recovered within and accuracy of 10% for σ (z=0) = 0.030. The best-fit parameters as well as the bias for all σz, are within the 1σ uncertainty of the Zc sample. (author)