Deciphering how stars form within turbulent, dense clouds of molecular gas has been a challenge. An innovative technique that uses a tree diagram provides insight into the process.
An understanding of how stars form has been hampered by the complexity of the clouds of cold molecular gas within which their formation occurs. To elucidate this process, the effects of gravity must be traced across a wide range of scales, particularly at the large distances over which it operates in these gas clouds. On page 63 of this issue, Goodman et al.1 show how a hierarchical tree diagram — a 'dendrogram' — can be used to disentangle the gravitational connections that tie the gas together on many different scales.
The movements of gas in molecular clouds are measured by spectral shifts. Depending on whether a parcel of gas is moving towards or away from the observer, the wavelength of the millimetre emission from a molecule such as carbon monoxide is shifted towards shorter ('blueshifted') or longer ('redshifted') wavelengths. By measuring these Doppler shifts at each point on the sky, one can determine the relative velocities of parcels of gas in the cloud along each line of sight. It turns out that the gas motions in such clouds are mainly highly supersonic. Indeed, computer simulations show2 that the network of dense filamentary structures seen in clouds is probably a direct consequence of such supersonic gas flows (Fig. 1).
As with many astronomical observations, however, we do not know the distance of any object (gas in this case) from Earth without using further painstaking methods. In observing molecular clouds, one is limited to measuring the two-dimensional position of the total gas emission on the sky. This measurement involves two coordinates that are akin to latitude and longitude on Earth's surface, as well as the relative velocity of gas at that position. Thus, a map of such a cloud is a sequence of position–position–velocity (p–p–v) measurements of the gas across the whole cloud. But without the ability to observe the full, three-dimensional gas cloud, how can its true structure be deduced, let alone the strength of the various forces that control where and when stars will form?
The approach usually taken to tackle this problem consists of segmenting the clumpy cloud into a collection of structures (clumps) using a computer program called CLUMPFIND. The end result is analogous to a topographical relief map of a mountain range. Such a map typically shows peaks that stand out from ridges or are isolated, and provide a series of contours that demarcate different elevations. If one now decided to break the range up into discrete 'mountains', one would identify the peaks and, using the various contour levels, try to decide whether smaller outcrops 'belonged' to a given mountain or were independent structures. In a p–p–v map of a molecular cloud, it is the contours and peaks of gas-column density — the sum of the emission from all gas parcels moving at a given velocity along a given line of sight — that play the role of topological relief in this mountain-range analogy.
The problem with this approach arises as soon as the results are used to try to provide insight into how stars form. For example, the column densities allow one to measure the masses of the clumps. One can then count the number of clumps with a given mass. The resulting distribution of clump masses is used to work out how star formation might occur3,4. With programs similar to CLUMPFIND, the data suggest that the clump-mass distribution closely resembles the distribution of star masses. A plausible but debated inference is that the origin of stellar masses may derive directly from the turbulent process that produced the clumps.
The fly in this ointment, however, as Goodman et al.1 show (see Fig. 1 of their Supplementary Information), is that if one adopts different threshold levels for contouring the maps, the column-density distribution changes. This is similar to the situation in a topographical relief map of a mountain range: the list of discrete mountains and their properties depends on the choice of threshold level picked to define mountains and smaller outcrops. This is unsettling — such an approach does not provide a completely objective way of measuring the actual distribution of column densities.
Enter the dendrogram technique advocated by the authors1. Rather than dividing the p–p–v data into a priori distinct structures in a subjective way, they use a method that is sensitive to the structures' intrinsic hierarchy (structure within structure). The data are broken up into 'leaves', 'branches' and 'trunks'. Leaves are identified as sufficiently strong maxima in the column-density maps, and connections between them are made by branches (their environs). The collection of physically related branches defines a trunk.
Every point on the dendrogram corresponds to a closed 'isosurface' on the map that encloses one or more column-density maxima (see Fig. 2 on page 64). The authors then show how physical properties can be ascribed to regions within these isosurfaces. A critical property is the 'virial' parameter — the ratio of the energy of the gas motions (which depends on the gas velocity in the region) to the gravitational energy (which depends on the mass and size of the region). If this ratio is sufficiently small, the gas in that region will be self-gravitating and prone to form stars. The dendrogram thus traces the relative strength of the gravitational force across the gas cloud.
Application of the dendrogram technique to observations of the gas cloud L1448, and to computer simulations in which only turbulence — and not self-gravity — is taken into account, shows inconsistencies. In contrast to the simulations, in which most of the gas is found to be self-gravitating on all spatial scales, the observations show that, although a large fraction of the gas is self-gravitating at large scales, at smaller scales that fraction is much lower.
Interestingly, strong local column-density maxima — which correspond to the dense gas 'cores' in which stars are observed to form — are sparser in Goodman and colleagues' dendrogram than those found with the CLUMPFIND algorithm, and turn out to be in larger regions of self-gravitating gas. And here we arrive at what may be the most tantalizing point of all. A debate that has enlivened star-formation theory for nearly a decade is how stars acquire their mass5. Do they accrete their gas from relatively isolated cores, or do they accrete material as they move about in a broader gravitational potential, gathering mass through competition with other dense regions in the same gravitationally bound region6 (the 'competitive accretion' picture)? Although neither hypothesis is amenable to definitive observational tests, the dendrogram method developed by Goodman et al. has the potential to answer this question and to identify the real conditions in which stars form.