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The extent to which turbulence mixes gas in the face of recurrent infusionsof fresh metals by supernovae (SN) could help provide important constraints onthe local star formation conditions. This includes predictions of themetallicity dispersion amongst metal poor stars, which suggests that theinterstellar medium was not very well mixed at these early times. The purposeof this {\it Letter} is to help isolate, via a series of numerical experiments,some of the key processes that regulate turbulent mixing of SN elements ingalactic disks. We study the gas interactions in small simulated patches of agalaxy disk with the goal of resolving the small-scale mixing effects of metalsat pc scales, which enables us to measure the turbulent diffusion coefficientin various galaxy environments. By investigating the statistics of variationsof $\alpha$ elements in these simulations, we are able to derive constraintsnot only on the allowed range of intrinsic yield variations in SN explosionsbut also on the star formation history of the Milky Way. We argue that theobserved dispersion of [Mg/Fe] in metal poor halo stars is compatible with thestar-forming conditions expected in dwarf satellites or in an early lowstar-forming Milky Way progenitor. In particular, metal variations in starsthat have not been phase-mixed can be used to infer the star-forming conditionsof disrupted dwarf satellites.

the astrophysical journal. letters

Supernova-driven turbulent metal mixing in high redshift galactic disks:  metallicity fluctuations in the interstellar medium and its imprints on metal  poor stars in the Milky Way