Simulations of Early Baryonic Structure Formation with Stream Velocity: II. The Gas Fraction

Understanding the gas content of high redshift halos is crucial for studying the formation of the first generation of galaxies and reionization. Recently, Tseliakhovich & Hirata showed that the relative "stream" velocity between the dark matter and baryons at the time of recombination - formally a second order effect, but an unusually large one - can influence the later structure formation history of the Universe. We quantify the effect of the stream velocity on the so-called "characteristic mass" - the minimum mass of a dark matter halo capable of retaining most of its baryons throughout its formation epoch - using three different high-resolution sets of cosmological 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 the dark matter and baryons. In order to understand this effect theoretically, we generalize the linear theory filtering mass to properly account for the difference between the dark matter and baryonic density fluctuation evolution induced by the stream velocity. We show that the new filtering mass provides an accurate estimate for the characteristic mass, while other theoretical ansatzes for the characteristic mass are substantially less precise.