Turbulent velocity structure in molecular clouds

We compare velocity structure observed in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to the velocity structure of a suite of simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We examine different methods of characterising the structure, including a scanning-beam method that provides an objective measurement of Larson's size-linewidth relation, structure functions, velocity and velocity difference probability distribution functions (PDFs), and the Δ-variance wavelet transform, and use them to compare models and observations. The Δ-variance is most sensitive to characteristic scales and scaling laws, but is limited in its application by a lack of intensity weighting so that its results are easily dominated by observational noise in maps with large empty areas. The scanning-beam size-linewidth relation is more robust with respect to noisy data. Obtaining the global velocity scaling behaviour requires that large-scale trends in the maps not be removed but treated as part of the turbulent cascade. We compare the true velocity PDF in our models to simulated observations of velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better unless the map size is comparable to the total line-of-sight thickness of the cloud. Comparison of line profiles to velocity centroid PDFs can thus be used to measure the line-of-sight depth of a cloud. The observed density and velocity structure is consistent with supersonic turbulence with a driving scale at or above the size of the molecular cloud and dissipative processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. Over most of the observed range of scales the velocity structure is that of a shock-dominated medium driven from large scale. The velocity PDFs exclude small-scale driving such as that from stellar outflows as a dominant process in the observed region. In the models, large-scale driving is the only process that produces deviations from a Gaussian PDF shape consistent with observations, almost independent of the strength of driving or magnetic field. Strong magnetic fields impose a clear anisotropy on the velocity field, reducing the velocity variance in directions perpendicular to the field.