Halo mass function: baryon impact, fitting formulae, and implications for cluster cosmology

We use a set of hydrodynamical and dark matter-only (DMonly) simulations to calibrate the halo mass function (HMF). We explore the impact of baryons, propose an improved parametrization for spherical overdensity masses, and identify differences between our DMonly HMF and previously published HMFs. We use the Magneticum simulations, which are well suited because of their accurate treatment of baryons, high resolution, and large cosmological volumes of up to (3818 Mpc)(3). Baryonic effects globally decrease the masses of galaxy clusters, which, at a given mass, results in a decrease of their number density. This effect vanishes at high redshift z similar to 2 and for high masses M-200m greater than or similar to 10(14)M(circle dot). We perform cosmological analyses of three idealized approximations to the cluster surveys by the South Pole Telescope (SPT), Planck, and eROSITA. We pursue two main questions. (1) What is the impact of baryons? - for the SPT-like and the Planck-like samples, the impact of baryons on cosmological results is negligible. In the eROSITA-like case, however, neglecting the baryonic impact leads to an underestimate of Omega(m) by about 0.01, which is comparable to the expected uncertainty from eROSITA. (2) How does our DMonly HMF compare with previous work? - for the Planck-like sample, results obtained using our DMonly HMF are shifted by Delta(sigma(8)) similar or equal to (sigma(8)(Omega(m)/0.27)(0.3)) similar or equal to 0.02 with respect to results obtained using the Tinker et al. fit. This suggests that using our HMF would shift results from Planck clusters towards better agreement with cosmic-microwave-background anisotropy measurements. Finally, we discuss biases that can be introduced through inadequate HMF parametrizations that introduce false cosmological sensitivity.