  To constrain the properties of the first stars with the chemical abundance
patterns observed in metal-poor stars, one must identify any non-trivial
effects that the hydrodynamics of metal dispersal can imprint on the
abundances. We use realistic cosmological hydrodynamic simulations to quantify
the distribution of metals resulting from one Population III supernova and from
a small number of such supernovae exploding in close succession. Overall,
supernova ejecta are highly inhomogeneously dispersed throughout the
simulations. When the supernova bubbles collapse, quasi-virialized
metal-enriched clouds, fed by fallback from the bubbles and by streaming of
metal-free gas from the cosmic web, grow in the centers of the dark matter
halos. Partial turbulent homogenization on scales resolved in the simulation is
observed only in the densest clouds where the vortical time scales are short
enough to ensure true homogenization on subgrid scales. However, the abundances
in the clouds differ from the gross yields of the supernovae. Continuing the
simulations until the cloud have gone into gravitational collapse, we predict
that the abundances in second-generation stars will be deficient in the
innermost mass shells of the supernova (if only one has exploded) or in the
ejecta of the latest supernovae (when multiple have exploded). This indicates
that hydrodynamics gives rise to biases complicating the identification of
nucleosynthetic sources in the chemical abundance spaces of the surviving
stars.
