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Vol 457 | 1 January 2009 | doi:10.1038/nature07609 LETTERS A role for self-gravity at multiple length scales in the process of star formation Alyssa A. Goodman1,2, Erik W. Rosolowsky2,3, Michelle A. Borkin1{, Jonathan B. Foster2, Michael Halle1,4, Jens Kauffmann1,2 & Jaime E. Pineda2 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. Spectral-line mapping shows whole molecular clouds (typically tens to hundreds of parsecs across, and surrounded by atomic gas) to be marginally self-gravitating5. When attempts are made to further break down clouds into pieces using ‘segmentation’ routines, some self-gravitating structures are always found on whatever scale is sampled6,7. But no observational study to date has successfully used one spectral-line data cube to study how the role of self-gravity varies as a function of scale and conditions, within an individual region. Most past structure identification in molecular clouds has been explicitly non-hierarchical, which makes difficult the quantification of physical conditions on multiple scales using a single data set. Consider, for example, the often-used algorithm CLUMPFIND7. In three-dimensional (3D) spectral-line data cubes, CLUMPFIND operates as a watershed segmentation algorithm, identifying local maxima in the position–position–velocity (p–p–v) cube and assigning nearby emission to each local maximum. Figure 1 gives a two-dimensional (2D) view of L1448, our sample star-forming region, and Fig. 2 includes a CLUMPFIND decomposition of it based on 13CO observations. As with any algorithm that does not offer hierchically nested or overlapping features as an option, significant emission found between prominent clumps is typically either appended to the nearest clump or turned into a small, usually ‘pathological’, feature needed to encompass all the emission being modelled. When applied to molecular-line 10′ ≈ 0.75 pc Figure 1 | Near-infrared image of the L1448 star-forming region with contours of molecular emission overlaid. The channels of the colour image correspond to the near-infrared bands J (blue), H (green) and K (red), and the contours of integrated intensity are from 13CO(1–0) emission8. Integrated i