Euclid preparation

We present CosmoPostProcess , a simulation-based forward model algorithm calibrated to reproduce optical cluster observables in line with measurements taken with the Euclid space telescope. The main deliverable of CosmoPostProcess is a correction for stacked surface-density profiles, binned in terms of richness and redshift, that accounts for selection-related systematic effects. These corrections take into account the modification to the stacked weak lensing signal from richness-selected samples of clusters identified in the photometric Euclid survey compared with an unbiased reference sample. In this work, we focus on the Euclid richness definition currently foreseen for the cosmological analysis, which does not apply a colour selection. Euclid also provides an alternative richness estimate based on a red-sequence galaxy selection, which is not considered here. The algorithm processes N -body simulations by painting galaxies with a halo-occupation model and emulating the survey’s detection and richness-assignment algorithms. We implemented a novel algorithm to estimate the optical cluster centres from galaxy-projected densities and validated it against the official Euclid pipelines. The effect of baryonic physics on the halo density profiles is incorporated through a correction calibrated on hydrodynamical simulations, yielding total-matter profiles consistent with those measured in the reference hydrodynamical simulations. In validation against hydrodynamical simulations, the baryon-corrected excess surface density is in agreement to within 2% for cluster-centric radii, r ∈ [0.1, 5] h −1 Mpc. To assess the impact of the different contributions to the selection bias, we performed dedicated tests that included variations of both cosmological parameters and the parameters of the mass–richness relation. Across all these tests, the selection bias induced by projection alone follows a robust pattern: a large-scale structure that is physically correlated with the main halo and projected along the line of sight enhances the stacked surface density profile near the transition from one-halo to two-halo dominance, with a peak radius of about 1 h −1 Mpc and an amplitude of about 20–40%, with a dependence on richness and redshift. This behaviour is mild at low and intermediate redshifts ( z ≲ 0.7), where the impact remains at the level of a few per cent, but it becomes increasingly relevant at higher redshift ( z ≳ 0.7), with a more pronounced enhancement of the transition-scale peak. Finally, baryonic modifications remain sub-dominant outside the core, with an impact of about 2% beyond r ≳ 0.3 h −1 Mpc. As an outcome of this analysis, the CosmoPostProcess framework delivers radial profile corrections with associated uncertainties, combining the selection bias from projection effects with the impact of baryonic physics and miscentring. These corrections will be a key ingredient to ensure controlled systematics in the Euclid DR1 galaxy cluster cosmological analysis.

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