Evolution of the real-space correlation function from next generation cluster surveys

Recovering the real-space correlation function from photometric redshifts

¹ Université Côte d’Azur, OCA, CNRS, Lagrange, UMR 7293, CS 34229, 06304 Nice Cedex 4, France
e-mail: ssridhar@oca.eu
² INAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
³ Dipartimento di Fisica e Astronomia – Università di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴ INFN–Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy

Received: 22 July 2016
Accepted: 1 December 2016

Abstract

Context. The next generation of galaxy surveys will provide cluster catalogues probing an unprecedented range of scales, redshifts, and masses with large statistics. Their analysis should therefore enable us to probe the spatial distribution of clusters with high accuracy and derive tighter constraints on the cosmological parameters and the dark energy equation of state. However, for the majority of these surveys, redshifts of individual galaxies will be mostly estimated by multiband photometry which implies non-negligible errors in redshift resulting in potential difficulties in recovering the real-space clustering.

Aims. We investigate to which accuracy it is possible to recover the real-space two-point correlation function of galaxy clusters from cluster catalogues based on photometric redshifts, and test our ability to detect and measure the redshift and mass evolution of the correlation length r₀ and of the bias parameter b(M,z) as a function of the uncertainty on the cluster redshift estimate.

Methods. We calculate the correlation function for cluster sub-samples covering various mass and redshift bins selected from a 500 deg² light-cone limited to H < 24. In order to simulate the distribution of clusters in photometric redshift space, we assign to each cluster a redshift randomly extracted from a Gaussian distribution having a mean equal to the cluster cosmological redshift and a dispersion equal to σ_z. The dispersion is varied in the range ${\mathit{\sigma }}_{\mathrm{(}\mathit{z}\mathrm{=}\mathrm{0}\mathrm{)}}\mathrm{=}\frac{{\mathit{\sigma }}_{\mathit{z}}}{\mathrm{1}\mathrm{+}{\mathit{z}}_{\mathrm{c}}}\mathrm{=}\mathrm{0.005}\mathit{,}\mathrm{0.010}\mathit{,}\mathrm{0.030}$ and 0.050, in order to cover the typical values expected in forthcoming surveys. The correlation function in real-space is then computed through estimation and deprojection of w_p(r_p). Four mass ranges (from M_halo > 2 × 10¹³h^-1M_⊙ to M_halo > 2 × 10¹⁴h^-1M_⊙) and six redshift slices covering the redshift range [0, 2] are investigated, first using cosmological redshifts and then for the four photometric redshift configurations.

Results. From the analysis of the light-cone in cosmological redshifts we find a clear increase of the correlation amplitude as a function of redshift and mass. The evolution of the derived bias parameter b(M,z) is in fair agreement with theoretical expectations. We calculate the r₀−d relation up to our highest mass, highest redshift sample tested (z = 2,M_halo > 2 × 10¹⁴h^-1M_⊙). From our pilot sample limited to M_halo > 5 × 10¹³h^-1M_⊙(0.4 < z < 0.7), we find that the real-space correlation function can be recovered by deprojection of w_p(r_p) within an accuracy of 5% for σ_z = 0.001 × (1 + z_c) and within 10% for σ_z = 0.03 × (1 + z_c). For higher dispersions (besides σ_z > 0.05 × (1 + z_c)), the recovery becomes noisy and difficult. The evolution of the correlation in redshift and mass is clearly detected for all σ_z tested, but requires a large binning in redshift to be detected significantly between individual redshift slices when increasing σ_z. The best-fit parameters (r₀ and γ) as well as the bias obtained from the deprojection method for all σ_z are within the 1σ uncertainty of the z_c sample.