Toward a halo mass function for precision cosmology: the limits of universality

TL;DR

This paper measures the dark matter halo mass function in cosmological simulations, finds it cannot be universally described across redshifts and mass definitions, and provides improved fitting functions for precision cosmology.

Contribution

It introduces new calibration and fitting functions for the halo mass function that account for its non-universality across redshifts and overdensity definitions.

Findings

Mass function calibrated to 5% accuracy at z=0 for a wide mass range.

Universal fitting functions are insufficient; the amplitude decreases with redshift.

Evidence of redshift evolution in the shape of the halo mass function.

Abstract

We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat LCDM cosmology and investigate its evolution at z<~2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at z=0 for virial masses in the range 10^{11} Msol/h < M < 10^{15} Msol/h, to <~ 5%. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at z=0 and earlier epochs. In addition to these formulae, which improve on previous approximations by 10-20%, our main finding is that the mass function cannot be represented by a universal fitting function at this level of accuracy. The amplitude of the "universal" function decreases monotonically by ~20-50%, depending on the mass definition, from z=0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.