We report results from numerical simulations of star formation in the early
universe that focus on the dynamical behavior of metal-free gas under different
initial and environmental conditions. In particular we investigate the role of
turbulence, which is thought to ubiquitously accompany the collapse of
high-redshift halos. We distinguish between two main cases: the birth of
Population III.1 stars - those which form in the pristine halos unaffected by
prior star formation - and the formation of Population III.2 stars - those
forming in halos where the gas is still metal free but has an increased
ionization fraction. This latter case can arise either from exposure to the
intense UV radiation of stellar sources in neighboring halos, or from the high
virial temperatures associated with the formation of massive halos, that is,
those with masses greater than 1e8 solar masses. We find that turbulent
primordial gas is highly susceptible to fragmentation in both cases, even for
turbulence in the subsonic regime, i.e. for rms velocity dispersions as low as
20 % of the sound speed. Contrary to our original expectations, fragmentation
is more vigorous and more widespread in pristine halos compared to pre-ionized
ones. We therefore predict Pop III.1 stars to be on average of somewhat lower
mass, and form in larger groups, than Pop III.2 stars. We find that fragment
masses cover over two orders of magnitude, indicating that the resulting
Population III initial mass function was significantly extended in mass as
well. This prompts the need for a large, high-resolution study of the formation
of dark matter minihalos that is capable of resolving the turbulent flows in
the gas at the moment when the baryons become self-gravitating. This would help
determine which, if any, of the initial conditions presented in our study are
realized in nature.Comment: Accepted for publication in Ap
