Singular value decomposition: A tool to separate elementary contributions in ISOCAM spectral maps

Singular value decomposition (SVD) is applied to a mid-infrared ISOCAM spectral map of NGC 7023. As a first result, this decomposition provides a mathematical analysis of the map in terms of a linear combination of elementary spectra. After further processing, it is shown that the spectrum observed on each pixel can be described as the physical superposition of four components. Three of them can be attributed to the intrinsic spectra of polycyclic aromatic hydrocarbons (PAH), very small grains and larger dust grains respectively. The fourth component is a differential spectrum that could trace the ionisation state of PAHs.