The use of positive matrix factorization in the analysis of molecular line spectra.

The authors present an analysis of ¹²CO spectra of the Thumbprint Nebula using a new method, positive matrix factorization (PMF). The complexity of the observed spectra and especially the non-Gaussian nature of the profiles make traditional analysis using fitted Gaussians impractical. Good results are obtained, however, with the use of PMF. PMF has already been applied to a large variety of problems and the authors present the first application of this method to the analysis of molecular emission line measurements. The method assumes the spectra to be the sum of a few basic components in velocity space and can determine the shapes as well as the intensities of the components. The only restriction is the positivity of both the basic profiles and their intensities. This prerequisite is sufficient to limit the range of possible solutions and to guarantee results that are easier to interpret than those determined by similar traditional methods, principal component analysis and factor analysis. PMF is also able to point out the existence of features that are contrary to the model assumptions, e.g. the existence of velocity gradients. In this article the authors explain the principles of PMF and illustrate its use with some simulated data before turning to the analysis of the ¹²CO spectra of the Thumbprint Nebula.