Impact of the Relative Motion between the Dark Matter and Baryons on the
  First Stars
  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 halos 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 minihalos 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% of the star formation (averaged on
a 3 Mpc scale) is confined to 35% of the volume at z=20 (and just 18% at z=40).
In addition, we estimate the redshift of the first star to be z ~ 65, which
includes a delay of Dz ~ 5 due to the relative velocity.
