Density and velocity fluctuations on virtually all scales observed with modern telescopes show that molecular clouds (MCs) are turbulent. The forcing and structural characteristics of this turbulence are, however, still poorly understood. To shed light on this subject, we study two limiting cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing and compressive (curl-free) forcing, and compare our results to observations. We solve the equations of hydrodynamics on grids with up to 10243 cells for purely solenoidal and purely compressive forcing. Eleven lower-resolution models with different forcing mixtures are also analysed. Using Fourier spectra and Delta-variance, we find velocity dispersion-size relations consistent with observations and independent numerical simulations, irrespective of the type of forcing. However, compressive forcing yields stronger compression at the same RMS Mach number than solenoidal forcing, resulting in a three times larger standard deviation of volumetric and column density probability distributions (PDFs). We compare our results to different characterisations of several observed regions, and find evidence of different forcing functions. Column density PDFs in the Perseus MC suggest the presence of a mainly compressive forcing agent within a shell, driven by a massive star. Although the PDFs are close to log-normal, they have non-Gaussian skewness and kurtosis caused by intermittency. Centroid velocity increments measured in the Polaris Flare on intermediate scales agree with solenoidal forcing on that scale. However, Delta-variance analysis of the column density in the Polaris Flare suggests that turbulence is driven on large scales, with a significant compressive component on the forcing scale. This indicates that, although likely driven with mostly compressive modes on large scales, turbulence can behave like solenoidal turbulence on smaller scales. Principal component analysis of G216-2.5 and most of the Rosette MC agree with solenoidal forcing, but the interior of an ionised shell within the Rosette MC displays clear signatures of compressive forcing. The strong dependence of the density PDF on the type of forcing must be taken into account in any theory using the PDF to predict properties of star formation. We supply a quantitative description of this dependence. We find that different observed regions show evidence of different mixtures of compressive and solenoidal forcing, with more compressive forcing occurring primarily in swept-up shells. Finally, we emphasise the role of the sonic scale for protostellar core formation, because core formation close to the sonic scale would naturally explain the observed subsonic velocity dispersions of protostellar cores.
The following movie shows that ompressive forcing (right-hand panel) produces significantly stronger density fluctuations than solenoidal forcing (left-hand panel) for the same Mach number of the turbulence.
[ Sol_vs_Comp_coldens_FederrathEtAl2010.mp4, 3.7MB high-res mp4 ]
This movie shows the projected vorticity:
[ Sol_vs_Comp_vort_FederrathEtAl2010.mp4, 6.9MB high-res mp4 ]
This movie shows the projected divergence of the velocity field:
[ Sol_vs_Comp_divv_FederrathEtAl2010.mp4, 17MB high-res mp4 ]
This movie shows slices through the gas density and Mach number:
[ Sol_vs_Comp_slices_FederrathEtAl2010.mp4, 12MB high-res mp4 ]
A number of synthetic observations and data products including column density maps and position-position-velocity (PPV) cubes are available for direct download from the STARFORMAT webpage.
We thank Robi Banerjee, Paul Clark, Simon Glover, Alyssa Goodman, Patrick Hennebelle, Alexei Kritsuk, Alex Lazarian, Daniel Price, Stefan Schmeja, and Nicola Schneider for interesting discussions and valuable comments on the present work. We thank the referee, Chris Brunt for suggesting a parameter study with different forcing ratios zeta, and for clarifying the effects of projection-smoothing and intensity-weighting in observations of centroid velocity maps. The Delta-variance tool used in this study was provided by Volker Ossenkopf and parallelised by Philipp Grothaus. We are grateful to Alyssa Goodman, Jaime Pineda, and Nicola Schneider for sending us their Perseus MC, and Cygnus X raw data. C.F. acknowledges financial support by the International Max Planck Research School for Astronomy and Cosmic Physics (IMPRS-A) and the Heidelberg Graduate School of Fundamental Physics (HGSFP). The HGSFP is funded by the Excellence Initiative of the German Research Foundation DFG GSC 129/1. This work was partly finished while C.F. was visiting the American Museum of Natural History as a Kade fellow. R.S.K. and C.F. acknowledge financial support from the German Bundesministerium für Bildung und Forschung via the ASTRONET project STAR FORMAT (grant 05A09VHA). R.S.K. furthermore acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG) under grants No. KL 1358/1, KL 1358/4, KL 1359/5, KL 1359/10, and KL 1359/11. R.S.K. thanks for subsidies from a Frontier grant of Heidelberg University sponsored by the German Excellence Initiative and for support from the Landesstiftung Baden-Württemberg via their program International Collaboration II (grant P-LS- SPII/18 ). M.-M.M.L. acknowledges partial support for his work from NASA Origins of Solar Systems grant NNX07AI74G. The simulations used computational resources from the HLRBII project grant h0972 at Leibniz Rechenzentrum Garching. The software used in this work was in part developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago.