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 consolid ate the large amount of information obtained with spectroscopic imagin g observations of the interstellar medium. Simple interstellar cloud m odels with varying degrees of complexity and Gaussian noise are constr ucted 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 c alculated 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 i dentify small velocity fluctuations and therefore provide spatial info rmation to the turbulent velocity held within the cloud. A size line w idth relationship delta upsilon similar to R(alpha) is derived from sp atial and kinematic characterizations of the principal components of ( CO)-C-12 emission from the Sh 155, Sh 235, Sh 140, and Gem OB1 cloud c omplexes. 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 dia gnostic to the variation of kinetic energy with size scale within turb ulent flows of the interstellar medium.