Velocity Field Statistics in Star-Forming Regions. I. Centroid Velocity Observations

Abstract

The probability density functions (pdfs) of molecular line centroid velocity fluctuations and fluctuation differences at different spatial lags are estimated for several nearby molecular clouds with active internal star formation. The data consist of over 75,000 $^{13}$CO line profiles divided among twelve spatially and/or kinematically distinct regions. Although three regions (all in Mon R2) appear nearly Gaussian, the others show strong evidence for non-Gaussian, often nearly exponential, centroid velocity pdfs, possibly with power law contributions in the far tails. Evidence for nearly exponential centroid pdfs in the neutral HI component of the ISM is also presented, based on older optical and radio observations. These results are in contrast to pdfs found in isotropic incompressible turbulence experiments and simulations. Furthermore, no evidence is found for the scaling of difference pdf kurtosis with Reynolds number which is seen in incompressible turbulence, and the spatial distribution of high-amplitude velocity differences shows little indication of the filamentary appearance predicted by decay simulations dominated by vortical interactions. The variation with lag of the difference pdf moments is presented as a constraint on future simulations.