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.
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