I describe the multivariate technique of Principal Component Analysis and its application to spectroscopic imaging data of the molecular interstellar medium. The technique identifies differences in line profiles with respect to the noise level at various scales. It is assumed that such differences arise from fluctuations within turbulent flows. From the resultant eigenvectors and eigenimages, a size line width relationship, (δv ∼ τα), can be constructed which describes the relationship between the magnitude of velocity fluctuations and the angular scale over which these occur for a given region. From a sample of selected molecular regions in the outer Galaxy, I find the power law exponent varies from 0.4 to 0.7. Thus, the turbulent flows within molecular regions of the Galaxy do not follow the Kolmogorov-Obukhov relation for incompressible turbulence. Implications of these results are discussed with respect to the injection and dissipation of kinetic energy in molecular regions.

Introduction

In the early, pioneering days of millimeter wave astronomy, the presence of turbulent flows within molecular regions of the Galaxy was inferred from the supersonic line widths of CO spectra. Since that time, telescope and detector technology has advanced such that one can now routinely construct detailed images of molecular emission from which the properties of interstellar turbulence can, in principle, be derived. In practice, statistical descriptions of the observations are required to fully exploit the available information.