  It has recently been demonstrated that coherent relative streaming velocities
of order 30 km / s between dark matter and gas permeated the universe on scales
below a few Mpc directly after recombination. We here use a series of
high-resolution moving-mesh calculations to show that these supersonic motions
significantly influence the virialization of the gas in minihalos, and delay
the formation of the first stars. As the gas streams into minihalos with bulk
velocities around 1 km / s at z ~ 20, the additional momentum and energy input
reduces the gas fractions and central densities of the halos, increasing the
typical virial mass required for efficient cooling by a factor of three, and
delaying Population III star formation by dz ~ 4. Since the distribution of the
magnitude of the streaming velocities is narrowly peaked around a
non-negligible value, this effect is important in most regions of the universe.
As a consequence, the increased minimum halo mass implies a reduction of the
absolute number of minihalos that can be expected to cool and form Population
III stars by up to an order of magnitude. We further find that the streaming
velocities increase the turbulent velocity dispersion of the minihalo gas,
which could affect its ability to fragment and hence alter the mass function of
the first stars.
