Impact of the relative motion between the dark matter and baryons on the first stars: Semi-analytical modelling

Recently the initial supersonic relative velocity between the dark matter and baryons was shown to have an important effect on galaxy formation at high redshift. We study the impact of this relative motion on the distribution of the star-forming haloes and on the formation redshift of the very first star. We include a new aspect of the relative velocity effect found in recent simulations by fitting their results to obtain the spatially varying minimum halo mass needed for molecular cooling. Thus, the relative velocities have three separate effects: suppression of the halo abundance, suppression of the gas content within each halo and boosting of the minimum cooling mass. We show that the two suppressions (of gas content and of halo abundance) are the primary effects on the small minihaloes that cannot form stars, while the cooling mass boost combines with the abundance suppression to produce order unity fluctuations in stellar density. We quantify the large-scale inhomogeneity of galaxies, finding that 68 percent of the star formation (averaged on a 3Mpc scale) is confined to 35 percent of the volume at z= 20 (and just 18 percent at z= 40). In addition, we estimate the first observable star to be formed at redshift z= 65 (t∼ 33Myr) which includes a delay of Δz∼ 5 (Δt∼ 3.6Myr) due to the relative velocity.