### Baryon impact on the halo mass function: Fitting formulae and implications for cluster cosmology

(6 votes from 6 institutions)

We calibrate the halo mass function accounting for halo baryons and present fitting formulae for spherical overdensity masses $M_{500\textrm c}$, $M_{200\textrm c}$, and $M_{200\textrm m}$. We use the hydrodynamical Magneticum simulations, which are well suited because of their high resolution and large cosmological volumes of up to $\sim2$ Gpc$^3$. Baryonic effects globally decrease the masses of galaxy clusters, which, at given mass, results in a decrease of their number density. This effect vanishes at high redshift $z\sim2$ and for high masses $\gtrsim 5\times10^{14}M_\odot$. We perform cosmological analyses of three idealized approximations to the cluster surveys by the South Pole Telescope (SPT), Planck, and eROSITA. For the SPT-like and the Planck-like samples, we find that the impact of baryons on the cosmological results is negligible. In the eROSITA-like case, we find that neglecting the baryonic impact leads to an underestimate of $\Omega_\textrm m$ by about 0.01, which is comparable to the expected uncertainty from eROSITA. We compare our mass function fits with the literature. In particular, in the analysis of our Planck-like sample, results obtained using our mass function are shifted by $\Delta(\sigma_8)\simeq0.05$ with respect to results obtained using the Tinker et al. (2008) fit. This shift represents a large fraction of the observed difference between the latest results from Planck clusters and CMB anisotropies, and the tension is essentially removed. We discuss biases that can be introduced through inadequate mass function parametrizations that introduce false cosmological sensitivity. Additional work to calibrate the halo mass function is therefore crucial for progress in cluster cosmology.