Mixing of metals during star cluster formation: statistics and implications for chemical tagging

Ongoing surveys are in the process of measuring the chemical abundances in large numbers of stars, with the ultimate goal of reconstructing the formation history of the Milky Way using abundances as tracers. However, interpretation of these data requires that we understand the relationship between stellar distributions in chemical and physical space. We investigate this question by simulating the gravitational collapse of a turbulent molecular cloud extracted from a galaxy-scale simulation, seeded with chemical inhomogeneities with different initial spatial scales. We follow the collapse from galactic scales down to resolutions scales of approximate to 10(-3) pc, and find that, during this process, turbulence mixes the metal patterns, reducing the abundance scatter initially present in the gas by an amount that depends on the initial scale of inhomogeneity of each metal field. However, we find that regardless of the spatial structure of the metals at the onset of collapse, the final stellar abundances are highly correlated only on distances below a few pc. Consequently, the star formation process defines a natural size scale of similar to 1 pc for chemically homogeneous star clusters, suggesting that any clusters identified as homogeneous in chemical space must have formed within similar to 1 pc of one another. However, in order to distinguish different star clusters in chemical space, observations across multiple elements are required, and the elements that are likely to be most efficient at separating distinct clusters in chemical space are those whose correlation length in the interstellar medium is of the order of tens of pc, comparable to the sizes of individual molecular clouds.