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


The abundances of elements in stars are critical clues to stars’ origins. Observed star-to-star variations in logarithmic abundance within an open star cluster—a gravitationally bound ensemble of stars in the Galactic plane—are typically only about 0.01 to 0.05 over many elements1,2,3,4,5,6,7,8,9, which is noticeably smaller than the variation of about 0.06 to 0.3 seen in the interstellar medium from which the stars form10,11,12,13,14. It is unknown why star 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 simulations that trace the mixing of chemical elements as star-forming clouds assemble and collapse. We show that turbulent mixing during cloud assembly naturally produces a stellar abundance scatter at least five times smaller than that in the gas, which is sufficient to explain the observed chemical homogeneity of stars. Moreover, mixing occurs very early, so that regions with star formation efficiencies of about 10 per cent are nearly as well mixed as those with formation efficiencies of about 50 per cent. This implies that even regions that do not form bound clusters are likely to be well mixed, and improves the prospects of using ‘chemical tagging’ to reconstruct (via their unique chemical signatures, or tags) star clusters whose constituent stars have become unbound from one another and spread across the Galactic disk.

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Figure 1: Slices through simulation S at a variety of times, showing the total density and the densities of the passive scalar fields.
Figure 2: Distribution of gas in simulation S in density and mixing ratio at two different times.
Figure 3: Two measures of the stellar abundance scatter as a function of star formation efficiency in simulations S, L and C.


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This work was funded by NSF grants AST-0955300 and AST-1405962, NASA ATP grant NNX13AB84G, NASA TCAN grant NNX14AB52G, and NASA through Hubble Award number 13256 issued by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. The simulations reported in this research were carried out on the UCSC supercomputer Hyades, which is supported by the NSF (award number AST-1229745).

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Authors and Affiliations



Y.F. ran the simulations, produced all the figures, and wrote parts of the text. M.R.K. aided in the interpretation and wrote the other parts of the text.

Corresponding author

Correspondence to Mark R. Krumholz.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Variation in distance d between two stars in a test of how well our new particle-mesh gravity implementation can maintain the orbit of a binary.

a, Distance between two stars, d, minus initial distance, d0, in a test with d0 = 2Δx, where Δx is the cell size. The left-hand vertical axis shows the d − d0 normalized to d0, and the right-hand vertical axis shows it normalized to Δx. Perfect accuracy would be a flat line at d − d0 = 0. b, Same as a but for a test with d0 = 8Δx, so the two stars are initially separated by 8 cells.

Extended Data Figure 2 Comparison between the analytic solution for Bondi accretion and the numerical results produced by an ORION simulation.

a, Density normalized to density at infinity, ρ/ρ, versus radius normalized to the Bondi radius, r/rB. We show the analytic solution (black line), the result using ORION with its standard implementation of sink particle gravity (red squares), and the result using our newly implemented particle-mesh (PM) gravity method. The numerical results show averages over radial bins. To prevent the numerical results from lying completely on top of on another and from obscuring the line for the exact result, we show only every fourth radial bin, and the bins we show are offset between the two simulations. The dashed vertical line shows the accretion kernel radius of two cells. b, Same as a but now showing the infall velocity normalized to the sound speed, v/cs.

Extended Data Figure 3 Number of stars and star formation efficiency as a function of time.

a, Number of stars in simulations S, L, and C. b, Star formation efficiency ε versus time in the same simulations.

Extended Data Figure 4 Stellar abundance scatter S* versus gas abundance scatter Sg at the end of simulation S.

Extended Data Figure 5 Stellar abundance scatter S* as a function of gas abundance scatter Sg for runs S, S3, and S4, measured at the time when the star formation efficiency ε ≈ 0.06.

Extended Data Figure 6 Evolution of two measures of the abundance scatter versus star formation efficiency ε in runs S, S3, S4, and 512S1.

a, Evolution of Sslope, the factor by which the abundance scatter is reduced in the limit where the gas abundance scatter Sg is small. b, Evolution of Slimit, the maximum stellar abundance scatter in the limit of infinite gas abundance scatter.

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Feng, Y., Krumholz, M. Early turbulent mixing as the origin of chemical homogeneity in open star clusters. Nature 513, 523–525 (2014).

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