Euclid preparation. Testing template-fitting models for the multipoles of the two-point clustering of galaxy clusters

Abstract

The Euclid satellite will deliver a catalogue of optically selected galaxy clusters spanning from around 2000 deg${}^2$ in Data Release (DR) 1 to around $14000$ deg${}^2$ in DR3. In this work, we assess the validity of cluster clustering (CC) models for template-fitting, which complements the full-shape methodology by providing cosmological information from the anisotropy of the redshift-space two-point correlation function (2PCF). Both methods will be used to analyse the cluster 2PCF multipoles with Euclid. We examined the multipoles of the two-point redshift-space clustering of galaxy clusters simulated with the semi-analytic PINOCCHIO code using third-order Lagrangian perturbation theory, assuming a Euclid DR1-like footprint of 500 deg${}^2$ in the northern hemisphere and 1400 deg${}^2$ in the southern hemisphere. We estimated the first three even multipoles of the 2PCF and associated covariance matrix from 1000 DR1-like synthetic catalogues. We studied the impact of modelling the relevant non-linearities, halo bias, and photometric redshift uncertainties on the 2PCF. We applied three clustering models to the mock catalogues at 0<z<2 and with a virial mass of $M_{\mathrm{vir}}>10^{14}{h}^{-1}{M}_{\odot }$ under realistic and optimistic photometric redshift uncertainty scenarios. We formulated a set of permissive and conservative criteria that ought to be fulfilled by the multipole cut-off scales and validated them against 100 mock catalogues via an inference of the growth rate multiplied by the matter power spectrum normalisation parameter, $f{\sigma }_8$. We tested the dispersion, Scoccimarro, and Taruya-Nishimichi-Saito models. We find that the dispersion model yields unbiased inferences on $f{\sigma }_8$ from CC down to 10 $h^{-1}$ Mpc in a DR1-like setting. All clustering models provide similar goodness-of-fit metrics in the presence of DR1-like cluster redshift uncertainties.

22 pages, 10 figures, accepted by A&A