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Abstract. The so-called "strong" Polycyclic Aromatic Hydrocarbons (PAHs) hypothesis postulates that isolated PAHs, which are thought to be the carriers of the Unidentified Infrared Bands, ought to be also responsible for a large number of Diffuse Interstellar Bands (DIBs). In this framework, the spectral profile of such DIBs should be due to unresolved rotational structure of vibronic absorption bands, the rotation of the molecule being by and large governed by the interaction with the interstellar radiation field. In this paper we quantitatively test the above hypothesis against the observational constraint of DIBs profile invariance, by using Monte-Carlo methods to model the photophysics of a prototypical interstellar PAH, namely the ovalene cation (C 32 H + 14 ). Our results show that the predicted rotational band profiles are remarkably insensitive to both the ambient conditions and the assumed values of some poorly known parameters. The present model therefore offers a quantitative link between any given PAH and the observed DIB profiles, providing a valuable tool for molecular identification.

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