Early turbulent mixing as the origin of chemical homogeneity in open star clusters

The abundances of elements in stars are a critical clue to their origins. Observed star-to-star variations in logarithmic abundance within an open cluster are typically only $\sim 0.01-0.05$ over many elements, significantly smaller than the variation of $\sim 0.06-0.3$ seen in the interstellar medium from which the stars form. It is unknown why clusters are so homogenous, and whether homogeneity should also prevail in regions of lower star formation efficiency that do not produce bound clusters. Here we report adaptive mesh simulations using passively-advected scalars in order to trace the mixing of chemical elements as star-forming clouds form and collapse. We show that turbulent mixing during cloud assembly naturally produces a stellar abundance scatter at least ~5 times smaller than that in the gas, sufficient to fully explain the observed chemical homogeneity of stars. Moreover, mixing occurs very early, so that regions with efficiencies $\varepsilon \sim 10\%$ are nearly as well-mixed as those with $\varepsilon\sim 50\%$. This implies that even regions that do not form bound clusters are likely to be well-mixed, and enhances the prospects for using chemical tagging to reconstruct dissolved star clusters via their unique chemical signatures.