The halo mass function from the dark ages through the present day

We use an array of high-resolution N-body simulations to determine the mass function of dark matter haloes at redshifts 10-30. We develop a new method for compensating for the effects of finite simulation volume that allows us to find an approximation to the true ``global'' mass function. By simulating a wide range of volumes at different mass resolution, we calculate the abundance of haloes of mass 10^{5-12} Msun/h. The enables us to predict accurately the abundance of the haloes that host the sources that reionize the universe. In particular, we focus on the small mass haloes (>~10^{5.5-6} Msun/h) likely to harbour population III stars where gas cools by molecular hydrogen emission, early galaxies in which baryons cool by atomic hydrogen emission at virial temperature of ~10^4K (~10^{7.5-8} Msun/h), and massive galaxies that may be observable at redshift ~10. When we combine our data with simulations that include high mass halos at low redshift, we find that the best fit to the halo mass function depends not only on linear overdensity, as is commonly assumed in analytic models, but also upon the slope of the linear power spectrum at the scale of the halo mass. The Press-Schechter model gives a poor fit to the halo mass function at all epochs; the Sheth-Tormen model gives a better match to the simulations, but still underpredicts the abundance of rare objects at all times by up to 50%. Finally, we consider the consequences of the recently released WMAP 3-year cosmological parameters. These lead to much less structure at high redshift, reducing the number of z=10 ``mini-haloes'' by about one third and the number of z=30 galaxy hosts by nearly three orders of magnitude