Euclid: Systematic uncertainties from the halo mass conversion on galaxy cluster number count data analyses

TL;DR

This paper investigates how different halo mass definitions and their conversions impact the accuracy of cosmological constraints from galaxy cluster counts, highlighting potential biases and proposing halo sparsity as a robust alternative.

Contribution

It demonstrates that using halo sparsity for mass conversion reduces systematic biases in cosmological parameter estimation from galaxy cluster data.

Findings

Standard mass conversion methods can cause biases over 2σ in parameter estimates.

Halo sparsity-based mass conversion results in biases smaller than statistical errors.

Systematic biases depend on the mass definition and assumed relations.

Abstract

The large catalogues of galaxy clusters expected from the Euclid survey will enable cosmological analyses of cluster number counts that require accurate cosmological model predictions. One possibility is to use parametric fits calibrated against $N$-body simulations, that capture the cosmological parameter dependence of the halo mass function. Several studies have shown that this can be obtained through a calibration against haloes with spherical masses defined at the virial overdensity. In contrast, if different mass definitions are used for the HMF and the scaling relation, a mapping between them is required. Here, we investigate the impact of such a mapping on the cosmological parameter constraints inferred from galaxy cluster number counts. Using synthetic data from $N$-body simulations, we show that the standard approach, which relies on assuming a concentration-mass relation, can introduce significant systematic bias. In particular, depending on the mass definition and the relation assumed, this can lead to biased constraints at more than 2$\sigma$ level. In contrast, we find that in all the cases we have considered, the mass conversion based on the halo sparsity statistics result in a systematic bias smaller than the statistical error.