How baryons can significantly bias cluster count cosmology

We quantify two main pathways through which baryonic physics biases cluster count cosmology. We create mock cluster samples that reproduce the baryon content inferred from X-ray observations. We link clusters to their counterparts in a dark matter-only universe, whose abundances can be predicted robustly, by assuming the dark matter density profile is not significantly affected by baryons. We derive weak lensing halo masses and infer the best-fitting cosmological parameters $Ω_\mathrm{m}$, $S_8=σ_8(Ω_\mathrm{m}/0.3)^{0.2}$, and $w_0$ from the mock cluster sample. We find that because of the need to accommodate the change in the density profile due to the ejection of baryons, weak lensing mass calibrations are only unbiased if the concentration is left free when fitting the reduced shear with NFW profiles. However, even unbiased total mass estimates give rise to biased cosmological parameters if the measured mass functions are compared with predictions from dark matter-only simulations. This bias dominates for haloes with $m_\mathrm{500c} < 10^{14.5} \, h^{-1} \, \mathrm{M_\odot}$. For a stage IV-like cluster survey without mass estimation uncertainties, an area $\approx 15000 \, \mathrm{deg^2}$ and a constant mass cut of $m_\mathrm{200m,min} = 10^{14} \, h^{-1} \, \mathrm{M_\odot}$, the biases are $-11 \pm 1 \, \%$ in $Ω_\mathrm{m}$, $-3.29 \pm 0.04 \, \%$ in $S_8$, and $9 \pm 1.5 \, \%$ in $w_0$. The statistical significance of the baryonic bias depends on how accurately the actual uncertainty on individual cluster mass estimates is known. We suggest that rather than the total halo mass, the (re-scaled) dark matter mass inferred from the combination of weak lensing and observations of the hot gas, should be used for cluster count cosmology.

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