Capturing halos at high redshifts

We study the evolution of the mass function of dark matter halos in the concordance Lambda CDM model at high redshift. We employ overlapping (multiple realization) numerical simulations to cover a wide range of halo masses, 10(7)-10(15) h(-1) M-circle dot, with redshift coverage beginning at z = 20. The Press-Schechter mass function is significantly discrepant from the simulation results at high redshifts. Of the more recently proposed mass functions, our results are in best agreement with those of Warren and coworkers. The statistics of the simulations-along with good control over systematics-allow for fits accurate to the level of 20% at all redshifts. We provide a concise discussion of various issues in defining and computing the halo mass function and how these are addressed in our simulations.