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A role for self-gravity at multiple length scales in the process of star formation


Self-gravity plays a decisive role in the final stages of star formation, where dense cores (size 0.1 parsecs) inside molecular clouds collapse to form star-plus-disk systems1. But self-gravity’s role at earlier times (and on larger length scales, such as 1 parsec) is unclear; some molecular cloud simulations that do not include self-gravity suggest that ‘turbulent fragmentation’ alone is sufficient to create a mass distribution of dense cores that resembles, and sets, the stellar initial mass function2. Here we report a ‘dendrogram’ (hierarchical tree-diagram) analysis that reveals that self-gravity plays a significant role over the full range of possible scales traced by 13CO observations in the L1448 molecular cloud, but not everywhere in the observed region. In particular, more than 90 per cent of the compact ‘pre-stellar cores’ traced by peaks of dust emission3 are projected on the sky within one of the dendrogram’s self-gravitating ‘leaves’. As these peaks mark the locations of already-forming stars, or of those probably about to form, a self-gravitating cocoon seems a critical condition for their existence. Turbulent fragmentation simulations without self-gravity—even of unmagnetized isothermal material—can yield mass and velocity power spectra very similar to what is observed in clouds like L1448. But a dendrogram of such a simulation4 shows that nearly all the gas in it (much more than in the observations) appears to be self-gravitating. A potentially significant role for gravity in ‘non-self-gravitating’ simulations suggests inconsistency in simulation assumptions and output, and that it is necessary to include self-gravity in any realistic simulation of the star-formation process on subparsec scales.

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Figure 1: Near-infrared image of the L1448 star-forming region with contours of molecular emission overlaid.
Figure 2: Comparison of the ‘dendrogram’ and ‘CLUMPFIND’ feature-identification algorithms as applied to 13 CO emission from the L1448 region of Perseus.
Figure 3: Schematic illustration of the dendrogram process.
Figure 4: The fraction of self-gravitating emission as a function of scale in L1448 and a comparable simulation.

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We thank A. Munshi for putting us in touch with M. Thomas and colleagues at Right Hemisphere, whose software and assistance enabled the interactive PDF in this paper; P. Padoan for providing the simulated data cube; R. Shetty for comments on the paper; F. Shu for suggesting we extend our analysis to measure boundedness of ppv ‘bound’ objects in ppp space using simulations; and S. Hyman, Provost of Harvard University, for supporting the start-up of the Initiative in Innovative Computing at Harvard, which substantially enabled the creation of this work. 3D Slicer is developed by the National Alliance for Medical Image Computing and funded by the National Institutes of Health grant U54-EB005149. The COMPLETE group is supported in part by the National Science Foundation. E.W.R. is supported by the NSF AST-0502605.

Author Contributions The dendrogram algorithm and software was created by E.W.R. The interactive figures were assembled by M.A.B., J.K. and M.H. using software from Right Hemisphere and Adobe. J.K. and M.H. worked to allow 3D Slicer to plot the surfaces relevant to the dendrograms shown in the 3D figures. J.B.F. produced Fig. 1, and J.E.P. carried out the ‘CLUMPFINDing’ analysis shown in Fig. 2 and Supplementary Fig. 1. A.A.G. wrote most of the text, and all authors contributed their thoughts to the discussions and analysis that led to this work.

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Correspondence to Alyssa A. Goodman.

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The 3D Slicer software used to create the surface renderings is available at

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Goodman, A., Rosolowsky, E., Borkin, M. et al. A role for self-gravity at multiple length scales in the process of star formation. Nature 457, 63–66 (2009).

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