Principal component analysis and radiative transfer modelling of Spitzer Infrared Spectrograph spectra of ultraluminous infrared galaxies

The mid-infrared spectra of ultraluminous infrared galaxies (ULIRGs) contain a variety of spectral features that can be used as diagnostics to characterize the spectra. However, such diagnostics are biased by our prior prejudices on the origin of the features. Moreover, by using only part of the spectrum they do not utilize the full information content of the spectra. Blind statistical techniques such as principal component analysis (PCA) consider the whole spectrum, find correlated features and separate them out into distinct components. We further investigate the principal components (PCs) of ULIRGs derived in Wang et al. We quantitatively show that five PCs are optimal for describing the Infrared Spectrograph spectra. These five components (PC1-PC5) and the mean spectrum provide a template basis set that reproduces spectra of all z < 0.35 ULIRGs within the noise. For comparison, the spectra are also modelled with a combination of radiative transfer models of both starbursts and the dusty torus surrounding active galactic nuclei (AGN). The five PCs typically provide better fits than the models. We argue that the radiative transfer models require a colder dust component and have difficulty in modelling strong polycyclic aromatic hydrocarbon features. Aided by the models we also interpret the physical processes that the PCs represent. The third PC is shown to indicate the nature of the dominant power source, while PC1 is related to the inclination of the AGN torus. Finally, we use the five PCs to define a new classification scheme using 5D Gaussian mixture modelling and trained on widely used optical classifications. The five PCs, average spectra for the four classifications and the code to classify objects are made available at: http://www.phys.susx.ac.uk/pdh21/PCA/.