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.
Your institute does not have access to this article
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
De Silva, G. M., Freeman, K. C., Bland-Hawthorn, J., Asplund, M. & Bessell, M. S. Chemically tagging the HR 1614 moving group. Astron. J. 133, 694–704 (2007)
De Silva, G. M. et al. Chemical homogeneity in Collinder 261 and implications for chemical tagging. Astron. J. 133, 1161–1175 (2007)
Pancino, E., Carrera, R., Rossetti, E. & Gallart, C. Chemical abundance analysis of the open clusters Cr 110, NGC 2099 (M 37), NGC 2420, NGC 7789, and M 67 (NGC 2682). Astron. Astrophys. 511, A56 (2010)
Bubar, E. J. & King, J. R. Spectroscopic abundances and membership in the Wolf 630 moving group. Astron. J. 140, 293–318 (2010)
De Silva, G. M. et al. High-resolution elemental abundance analysis of the Hyades supercluster. Mon. Not. R. Astron. Soc. 415, 563–575 (2011)
Ting, Y.-S., De Silva, G. M., Freeman, K. C. & Parker, S. J. High-resolution elemental abundance analysis of the open cluster IC 4756. Mon. Not. R. Astron. Soc. 427, 882–892 (2012)
Reddy, A. B. S., Giridhar, S. & Lambert, D. L. Comprehensive abundance analysis of red giants in the open clusters NGC 752, 1817, 2360 and 2506. Mon. Not. R. Astron. Soc. 419, 1350–1361 (2012)
De Silva, G. M. et al. Search for associations containing young stars: chemical tagging IC 2391 and the Argus association. Mon. Not. R. Astron. Soc. 431, 1005–1018 (2013)
Reddy, A. B. S., Giridhar, S. & Lambert, D. L. Comprehensive abundance analysis of red giants in the open clusters NGC 2527, 2682, 2482, 2539, 2335, 2251 and 2266. Mon. Not. R. Astron. Soc. 431, 3338–3348 (2013)
Rosolowsky, E. & Simon, J. D. The M33 metallicity project: resolving the abundance gradient discrepancies in M33. Astrophys. J. 675, 1213–1222 (2008)
Sanders, N. E., Caldwell, N., McDowell, J. & Harding, P. The metallicity profile of M31 from spectroscopy of hundreds of H II regions and PNe. Astrophys. J. 758, 133 (2012)
Berg, D. A. et al. New radial abundance gradients for NGC 628 and NGC 2403. Astrophys. J. 775, 128 (2013)
Bresolin, F. The abundance scatter in M33 from H II regions: is there any evidence for azimuthal metallicity variations? Astrophys. J. 730, 129 (2011)
Li, Y., Bresolin, F. & Kennicutt, R. C., Jr Testing for azimuthal abundance gradients in M101. Astrophys. J. 766, 17 (2013)
Carroll-Nellenback, J., Frank, A. & Heitsch, F. The effects of inhomogeneities within colliding flows on the formation and evolution of molecular clouds. Astrophys. J. (submitted); preprint available at http://arXiv.org/abs/1304.1367 (2013)
Murray, S. D. & Lin, D. N. C. On the origin of metal homogeneities in globular clusters. Astrophys. J. 357, 105–112 (1990)
de Avillez, M. A. & Mac Low, M.-M. Mixing timescales in a supernova-driven interstellar medium. Astrophys. J. 581, 1047–1060 (2002)
Yang, C.-C. & Krumholz, M. Thermal-instability-driven turbulent mixing in galactic disks. I. Effective mixing of metals. Astrophys. J. 758, 48 (2012)
Truelove, J. K. et al. Self-gravitational hydrodynamics with three-dimensional adaptive mesh refinement: methodology and applications to molecular cloud collapse and fragmentation. Astrophys. J. 495, 821–852 (1998)
Klein, R. I. Star formation with 3-D adaptive mesh refinement: the collapse and fragmentation of molecular clouds. J. Comput. Appl. Math. 109, 123–152 (1999)
Krumholz, M. R., McKee, C. F. & Klein, R. I. Embedding Lagrangian sink particles in Eulerian grids. Astrophys. J. 611, 399–412 (2004)
Vázquez-Semadeni, E. et al. Molecular cloud evolution. II. From cloud formation to the early stages of star formation in decaying conditions. Astrophys. J. 657, 870–883 (2007)
Heitsch, F., Hartmann, L. W., Slyz, A. D., Devriendt, J. E. G. & Burkert, A. Cooling, gravity, and geometry: flow-driven massive core formation. Astrophys. J. 674, 316–328 (2008)
Tan, J. C., Krumholz, M. R. & McKee, C. F. Equilibrium star cluster formation. Astrophys. J. 641, L121–L124 (2006)
Krumholz, M. R. & Tan, J. C. Slow star formation in dense gas: evidence and implications. Astrophys. J. 654, 304–315 (2007)
Krumholz, M. R. The big problems in star formation: the star formation rate, stellar clustering, and the initial mass function. Phys. Rep. 539, 49–134 (2014)
Portegies Zwart, S. F. The lost siblings of the Sun. Astrophys. J. 696, L13–L16 (2009)
Bland-Hawthorn, J., Krumholz, M. R. & Freeman, K. The long-term evolution of the galactic disk traced by dissolving star clusters. Astrophys. J. 713, 166–179 (2010)
Mitschang, A. W., De Silva, G., Sharma, S. & Zucker, D. B. Quantifying chemical tagging: towards robust group finding in the Galaxy. Mon. Not. R. Astron. Soc. 428, 2321–2332 (2013)
Mitschang, A. W. et al. Quantitative chemical tagging, stellar ages and the chemo-dynamical evolution of the Galactic disc. Mon. Not. R. Astron. Soc. 438, 2753–2764 (2014)
Koyama, H. & Inutsuka, S.-i. An origin of supersonic motions in interstellar clouds. Astrophys. J. 564, L97–L100 (2002)
Hockney, R. W. & Eastwood, J. W. Computer Simulation using Particles (CRC Press, 1988)
Martel, H., Evans, N. J., II & Shapiro, P. R. Fragmentation and evolution of molecular clouds. I. Algorithm and first results. Astrophys. J. 163 (Suppl.). 122–144 (2006)
Freeman, K. & Bland-Hawthorn, J. The new galaxy: signatures of its formation. Annu. Rev. Astron. Astrophys. 40, 487–537 (2002)
Gilmore, G. et al. The Gaia-ESO Public Spectroscopic Survey. Messenger 147, 25–31 (2012)
Lada, C. J. & Lada, E. A. Embedded clusters in molecular clouds. Annu. Rev. Astron. Astrophys. 41, 57–115 (2003)
Bland-Hawthorn, J., Karlsson, T., Sharma, S., Krumholz, M. & Silk, J. The chemical signatures of the first star clusters in the Universe. Astrophys. J. 721, 582–596 (2010)
Bensby, T., Feltzing, S. & Oey, M. S. Exploring the Milky Way stellar disk. A detailed elemental abundance study of 714 F and G dwarf stars in the solar neighbourhood. Astron. Astrophys. 562, A71 (2014)
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).
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.
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.
About this article
Cite this article
Feng, Y., Krumholz, M. Early turbulent mixing as the origin of chemical homogeneity in open star clusters. Nature 513, 523–525 (2014). https://doi.org/10.1038/nature13662