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

Abstract

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, i.e., how similar in chemical abundance do we expect a pair of stars to be as a function of the distance between their formation sites. 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 $\approx 10^{-3}$ 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 initial spatial structure of the metals at the onset of collapse, the final stellar abundances are highly correlated on distances below a few pc, and nearly uncorrelated on larger distances. Consequently, the star formation process defines a natural size scale of $\sim 1$ pc for chemically-homogenous star clusters, suggesting that any clusters identified as homogenous in chemical space must have formed within $\sim 1$ pc of one another. However, in order to distinguish different star clusters in chemical space, observations across multiple elements will be 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 ISM is of order tens of pc, comparable to the sizes of individual molecular clouds.