The halo mass function through the cosmic ages

In this paper, we investigate how the dark matter halo mass function evolves with redshift, based on a suite of very large (with N-p = 3072(3)-6000(3) particles) cosmological N-body simulations. Our halo catalogue data span a redshift range of z = 0-30, allowing us to probe the mass function from the Dark Ages to the present. We utilize both the friends-of-friends (FOF) and spherical overdensity (SO) halo-finding methods to directly compare the mass function derived using these commonly used halo definitions. The mass function from SO haloes exhibits a clear evolution with redshift, especially during the recent era of dark energy dominance (z < 1). We provide a redshift-parametrized fit for the SO mass function valid for the entire redshift range to within similar to 20 per cent as well as a scheme to calculate the mass function for haloes with arbitrary overdensities. The FOF mass function displays a weaker evolution with redshift. We provide a 'universal' fit for the FOF mass function, fitted to data across the entire redshift range simultaneously, and observe redshift evolution in our data versus this fit. The relative evolution of the mass functions derived via the two methods is compared. For an SO halo defined via an overdensity of 178 versus the background matter density and an FOF halo defined via a linking length of 0.2 times the mean interparticle separation we find that the mass functions most closely match at z = 0. The disparity at z = 0 between the FOF and SO mass functions resides in their high-mass tails where the collapsed fraction of mass in SO haloes is similar to 80 per cent of that in FOF haloes. This difference grows with redshift so that, by z > 20, the SO algorithm finds a similar to 50-80 per cent lower collapsed fraction in high-mass haloes than the FOF algorithm.