Testing the "strong" PAHs hypothesis. II. A quantitative link between DIBs and far-IR emission features

In Paper I we proved the profile invariance of the first permitted electronic transition of the typical Polycyclic Aromatic Hydrocarbon cation C32H14+ as a first necessary check for the ``strong'' PAHs hypothesis. In this paper we derive a quantitative relation between the intensities of the former band, which ought to be observable in absorption in the visible range, and those of the far-IR bands, which are predicted by the PAH model to be simultaneously present in emission. Contrary to the mid-IR bands, collectively known as ``Unidentified Infrared Bands'' (UIBs), which do not discriminate specific molecules, the far IR, skeletal bands can be expected to be a fingerprint of each single species. This fact provides a number of independent constraints which must be simultaneously fulfilled for a successful PAH identification. Our approach thus offers a powerful criterion for the identification of specific PAHs, both in the presently available ISO data and in those of the forthcoming SIRTF and Herschel missions. As an interesting by-product, we quantitatively evaluate the impact of isotopic substitutions (13C->12C and D -> H) on the resulting infrared emission bands.