Intrinsic, observed, and retrieved properties of interstellar turbulence

We generate synthetic observations of three-dimensional, self-gravitating MHD simulations of the interstellar medium ( ISM) to evaluate the ability of principal component analysis (PCA) to measure the scale dependence of turbulent velocity fluctuations in molecular clouds. Scaling exponents, alpha, observationally obtained from the coupled characteristic scales for line pro. le variability in velocity, deltav, and in space, L, where deltav proportional to L-alpha, are compared with the intrinsic scaling exponents of the MHD velocity fields. We determine the approximate structure function order at which PCA operates in order to then verify a previously established calibration of the PCA method. We also analyze the statistical properties of projected velocity line centroid fields, including effects of intermittent velocity fluctuations, density inhomogeneity, and opacity, and examine the relationship of the projected two-dimensional statistics to the intrinsic three-dimensional statistics. Using PCA, we infer steep three-dimensional energy spectra in the molecular ISM, generally steeper than can be accounted for by Kolmogorov turbulence or possibly even shock-dominated turbulence.