Virial Halo Mass Function in the Planck Cosmology

We study halo mass functions with high-resolution N-body simulations under a ΛCDM cosmology. Our simulations adopt the cosmological model that is consistent with recent measurements of the cosmic microwave backgrounds with the Planck satellite. We calibrate the halo mass functions for 10^8.5 ≲ M _vir/(h^-1 M_Θ) ≲ 10^{15.0-0.45 z} , where M_vir is the virial spherical-overdensity mass and redshift z ranges from 0 to 7. The halo mass function in our simulations can be fitted by a four-parameter model over a wide range of halo masses and redshifts, while we require some redshift evolution of the fitting parameters. Our new fitting formula of the mass function has a 5%-level precision, except for the highest masses at z ≤ 7. Our model predicts that the analytic prediction in Sheth & Tormen would overestimate the halo abundance at z = 6 with M_vir = 10^8.5-10 h^-1 M_Θ by 20%-30%. Our calibrated halo mass function provides a baseline model to constrain warm dark matter (WDM) by high-z galaxy number counts. We compare a cumulative luminosity function of galaxies at z = 6 with the total halo abundance based on our model and a recently proposed WDM correction. We find that WDM with its mass lighter than 2.71 keV is incompatible with the observed galaxy number density at a 2σ confidence level.