The potential link between neutral and/or ionized polycyclic aromatic hydrocarbons (PAHs) and the diffuse interstellar band (DIB) carriers is examined. Based on the study of the general physical and chemical properties of PAHs, an assessment is made of their possible contribution to the DIB carriers. It is found that, under the conditions reigning in the diffuse interstellar medium, PAHs can be present in the form of neutral molecules as well as positive and/or negative ions. The charge distribution of small PAHs is dominated, however, by two charge states at one time with compact PAHs present only in the neutral and cationic forms. Each PAH has a distinct spectral signature depending on its charge state. Moreover, the spectra of ionized PAHs are always clearly dominated by a single band in the DIB spectral range. In the case of compact PAH ions, the strongest absorption band is of type A (i.e., the band is broad, falls in the high-energy range of the spectrum, and possesses a large oscillator strength), and seems to correlate with strong and broad DIBs. For noncompact PAH ions, the strongest absorption band is of type I (i.e., the band is narrow, falls in the low-energy range of the spectrum, and possesses a small oscillator strength), and seems to correlate with weak and narrow DIBs. Potential molecular size and structure constraints for interstellar PAHs are derived by comparing known DIB characteristics to the spectroscopic properties of PAHs. It is found that (i) only neutral PAHs larger than about 30 carbon atoms could, if present, contribute to the DIBs. (ii) For compact PAHs, only ions with less than about 250 carbon atoms could, if present, contribute to the DIBs. (iii) The observed distribution of the DIBs between strong/moderate and broad bands on the one hand and weak and narow bands on the other can easily be interpreted in the context of the PAH proposal by a distribution of compact and noncompact PAH ions, respectively. A plausible correlation between PAH charge states and DIB "families" is thus provided by the PAH-DIB proposal. Following this proposal, DIB families would reflect conditions within a cloud which locally determine the relative importance of cations, anions, and neutral species, rather than tracers of a specific species. Observational predictions are given to establish the viability of the PAH hypothesis. It is concluded that small PAH ions are very promising candidates as DIB carriers provided their population is dominated by a finite number (100-200) of species. A key test for the PAH proposal, consisting of laboratory and astronomical investigations in the ultraviolet range, is called for.
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