Simulating the Universe with MICE: the abundance of massive clusters

We introduce a new set of large N-body runs, the Marenostrum Institut de Ciencies de l'Espai (MICE) simulations, that provide a unique combination of very large cosmological volumes with good mass resolution. They follow the gravitational evolution of similar to 8.5 billion particles (20483) in volumes covering up to similar to 15 Hubble volumes (i.e. 450 h-3 Gpc3), and sample over five decades in spatial resolution. Our main goal is to accurately model and calibrate basic cosmological probes that will be used by upcoming astronomical surveys of unprecedented volume. Here, we take advantage of the very large volumes of MICE to make a robust sampling of the high-mass tail of the halo mass function (MF). We discuss and avoid possible systematic effects in our study, and do a detailed analysis of different error estimators. We find that available fits to the local abundance of haloes match well the abundance estimated in the large volume of MICE up to M similar to 1014 h-1 M(circle dot), but significantly deviate for larger masses, underestimating the MF by 10 per cent (30 per cent) at M = 3.16 x 1014 h-1 M(circle dot) (1015 h-1 M(circle dot)). Similarly, the widely used Sheth & Tormen fit, if extrapolated to high redshift assuming universality, leads to an underestimation of the cluster abundance by 30, 20 and 15 per cent at z = 0, 0.5, 1 for fixed nu = delta(c)/Sigma approximate to 3 (corresponding to M similar to [7 - 2.5 - 0.8] x 1014 h-1 M(circle dot), respectively). We provide a recalibration of the MF over five orders of magnitude in mass [1010 < M/( h-1 M(circle dot)) < 1015], that accurately describes its redshift evolution up to z = 1. We explore the impact of this recalibration on the determination of the dark energy equation of state w, and conclude that using available fits that assume universal evolution for the cluster MF may systematically bias the estimate of w by as much as 50 per cent for medium-depth (z less than or similar to 1) surveys. The halo catalogues used in this analysis are publicly available at the MICE webpage, http://www.ice.cat/mice.