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

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$σ$ 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.

Figures (12)

• Figure 1: Left panel: halo mass function from the Uchuu halo catalogues with virial masses at $z=0.0$ (purple dotted line), $0.5$ (green dotted line), $1.0$ (dark-turquoise dotted line) and $1.5$ (light-blue dotted line) against the re-calibrated Euclid-HMF (solid lines), the Euclid-HMF predictions (short-dashed lines), the HMF parametrisation from Tinker_2008 (dash-dotted lines) and 2016MNRAS.456.2486D (short-dash-dotted lines). The different colours correspond to the various redshift snapshots. Right panels: relative difference with respect to the Uchuu HMF from $z=0$ (top) to $1.5$ (bottom). The shaded area corresponds to the Poisson errors.
• Figure 2: Number counts for haloes with virial masses $M_{\rm vir}\ge 3\times 10^{13}\,{\rm M}_{\odot}\,h^{-1}$ ( left panel) and $M_{\rm vir}\ge 10^{14}\,{\rm M}_{\odot}\,h^{-1}$ ( right panel) as function of redshift from the Uchuu data (light-blue solid line) against the predictions obtained assuming Euclid/Uchuu-HMF (dark-blue solid line with tri marker), Euclid-HMF (red solid line with star marker), 2016MNRAS.456.2486D (goldenrod solid line with cross marker) and Tinker_2008 (pink solid line with triangle marker). The bottom panels show the relative differences with respect to the Uchuu data. The shaded area corresponds to the Poisson errors.
• Figure 3: Top panels: number counts as function of redshift obtained from the Uchuu-HMF at $M_{200}$ (light-blue solid line) for haloes with masses $M_{200}\geq 3\times 10^{13}\,{\rm M}_{\odot}\,h^{-1}$ ( left panel) and $M_{200}\geq 1\times 10^{14}\,{\rm M}_{\odot}\,h^{-1}$ ( right panel) in redshift bins of size $\Delta{z}=0.1$ in the case a survey with sky coverage of $15\,000$ deg$^2$. The other curves correspond to the number counts obtained assuming the Euclid/Uchuu-HMF for the different mass conversion models: non-parametric stochastic (goldenrod solid line with star marker), parametric deterministic (pink solid line with circle marker), parametric stochastic (brown solid line with square marker) and second, the predictions obtained assuming 2016MNRAS.456.2486D (dark-blue solid line with triangle marker) and Tinker_2008 (red solid line triangle-left marker). The lower plots in each panel show the relative difference with respect to the Uchuu data, where the shaded area corresponds to the Poisson errors. Bottom panels: as in the top panels for haloes with masses $M_{500}$ in the case of the low-mass cut sample with $M_{500}\geq 3\times 10^{13}\,{\rm M}_{\odot}\,h^{-1}$ (left panel) and high-mass cut with $M_{500}\geq 10^{14}\,{\rm M}_{\odot}\,h^{-1}$ (right).
• Figure 4: Mean and standard deviation of the marginalised constraints on $\Omega_{\rm m}$ ( top panels) and $\sigma_8$ ( bottom panels) inferred from the analysis of Uchuu data at $M_{200}$ ( left panels) and $M_{500}$ ( right panels). In each panel the left-hand (right-hand) side corresponds to the low (high) mass cuts. These have been obtained by applying the mass conversion to the Euclid/Uchuu-HMF calibrated at $M_{\rm vir}$ using the NPS (magenta star points) the PD (filled circles) and PS (filled squares) mass conversion approaches. In the PD and PS cases we have assumed concentration-mass relation from the Uchuu dataset Ishiyama_2021 (olive green) and the relations from 2014MNRAS.441.3359D (cyan), 2013ApJ...766...32B (dark blue), 2011ApJ...740..102K (violet) and 2008MNRAS.390L..64D (dark green). The vertical lines shows the fiducial values of $\Omega_{\rm m}$ and $\sigma_8$ respectively.
• Figure 5: Top panel: number counts of haloes detected at $M_{\rm vir}$ from the Flagship light-cone catalogue (green solid line) with $M_{\rm vir}\ge 10^{14}\,{\rm M}_{\odot}h^{-1}$ over a sky area of ${\pi}/{2}$ sr in bins of size $\Delta{z}=0.1$ against the predictions from the Euclid/Uchuu-HMF (orange solid line) and the Euclid-HMF (brown solid line). Bottom panel: relative difference with respect to the Flagship number counts. The shaded area correspond to the Poisson noise.