Simulations of Early Baryonic Structure Formation with Stream Velocity: I. Halo Abundance

It has been recently shown that the relative velocity between the dark matter and the baryons (vbc) at the time of recombination can affect the structure formation in the early universe (Tseliakhovich & Hirata 2010). We statistically quantify this effect using large cosmological simulations. We use three different high resolution sets of simulations (with separate transfer functions for baryons and dark matter) that vary in box size, particle number, and the value of the relative velocity between dark matter and baryons. We show that the total number density of halos is suppressed by ~ 20% at z = 25 for vbc = 1{\sigma}(vbc), where {\sigma}(vbc) is the variance of the relative velocity, while for vbc = 3.4{\sigma}(vbc) the relative suppression at the same redshift reaches 50%, remaining at or above the 30% level all the way to z = 11. We also find high abundance of "empty halos", i.e., halos that have gas fraction below half of the cosmic mean baryonic fraction fb. Specifically we find that for vbc = 1{\sigma}(vbc) all halos below 10^5M\odot are empty at z \geq 19. The high abundance of empty halos results in significant delay in the formation of gas rich mini-halos and the first galaxies.