The Aemulus Project II: Emulating the Halo Mass Function

Abstract: Existing models for the dependence of the halo mass function on cosmological parameters will become a limiting source of systematic uncertainty for cluster cosmology in the near future. We present a halo mass function emulator and demonstrate improved accuracy relative to state-of-the-art analytic models. In this work, mass is defined using an overdensity criteria of 200 relative to the mean background density. Our emulator is constructed from the AEMULUS simulations, a suite of 40 N-body simulations with snapshots from z=3 to z=0. These simulations cover the flat wCDM parameter space allowed by recent Cosmic Microwave Background, Baryon Acoustic Oscillation and Type Ia Supernovae results, varying the parameters w, Omega_m, Omega_b, sigma_8, N_{eff}, n_s, and H_0. We validate our emulator using five realizations of seven different cosmologies, for a total of 35 test simulations. These test simulations were not used in constructing the emulator, and were run with fully independent initial conditions. We use our test simulations to characterize the modeling uncertainty of the emulator, and introduce a novel way of marginalizing over the associated systematic uncertainty. We confirm non-universality in our halo mass function emulator as a function of both cosmological parameters and redshift. Our emulator achieves better than 1% precision over much of the relevant parameter space, and we demonstrate that the systematic uncertainty in our emulator will remain a negligible source of error for cluster abundance studies through at least the LSST Year 1 data set.