Interstellar turbulence. I. Retrieval of velocity field statistics

We demonstrate the capability of principal component analysis (PCA) as applied by Heyer & Schloerb to extract the statistics of turbulent interstellar velocity fields as measured by the energy spectrum, E(k) similar to k(-beta). Turbulent velocity and density fields with known statistics are generated from fractional Brownian motion simulations. These fields are translated to the observational domain, T (x, y, v), considering the excitation of molecular rotational energy levels and radiative transfer. Using PCA and the characterization of velocity and spatial scales from the eigenvectors and eigenimages, respectively, a relationship is identified that describes the magnitude of line profile differences, deltav, and the scale, L, over which these differences occur, deltav similar to L-alpha. From a series of models with varying values of beta, we find alpha = 0.33beta - 0.05 for 1 < beta < 3. This provides the basic calibration between the intrinsic velocity field statistics to observational measures and a diagnostic for turbulent flows in the interstellar medium. We also investigate the effects of noise, line opacity, and finite resolution on these results.