Application of principal component analysis to large-scale spectral line imaging studies of the interstellar medium

The multivariate statistical technique of principal component analysis (PCA) is described and demonstrated to be a valuable tool to consolidate the large amount of information obtained with spectroscopic imaging observations of the interstellar medium. Simple interstellar cloud models with varying degrees of complexity and Gaussian noise are constructed and analyzed to demonstrate the ability of PCA to statistically extract physical features and phenomena from the data and to gauge the effects of random noise upon the analysis. Principal components are calculated for high spatial dynamic range (CO)-C-12 and (CO)-C-13 data cubes of the Sh 155 (Cep OB3) cloud complex. These identify the three major emission components within the cloud and the spatial differences between (CO)-C-12 and (CO)-C-13 emissions. Higher order eigenimages identify small velocity fluctuations and therefore provide spatial information to the turbulent velocity held within the cloud. A size line width relationship delta upsilon similar to R(alpha) is derived from spatial and kinematic characterizations of the principal components of (CO)-C-12 emission from the Sh 155, Sh 235, Sh 140, and Gem OB1 cloud complexes. The power-law indices for these clouds range from 0.42 to 0.55 and are similar to those derived from an ensemble of clouds within the Galaxy found by Larson (1981) and Solomon et al. (1987). The size-line width relationship within a given cloud provides an important diagnostic to the variation of kinetic energy with size scale within turbulent flows of the interstellar medium.