Spectral and photometric observations of nearby galaxies show a correlation between the strength of their mid-IR aromatic features, attributed to PAH molecules, and their metal abundance, leading to a deficiency of these features in low-metallicity galaxies. In this paper, we suggest that the observed correlation represents a trend of PAH abundance with galactic age, reflecting the delayed injection of carbon dust into the ISM by AGB stars in the final post-AGB phase of their evolution. AGB stars are the primary sources of PAHs and carbon dust in galaxies, and recycle their ejecta back to the interstellar medium only after a few hundred million years of evolution on the main sequence. In contrast, more massive stars that explode as Type II supernovae inject their metals and dust almost instantaneously after their formation. We first determined the PAH abundance in galaxies by constructing detailed models of UV-to-radio SED of galaxies that estimate the contribution of dust in PAH-free HII regions, and PAHs and dust from photodissociation regions, to the IR emission. All model components: the galaxies stellar content, properties of their HII regions, and their ionizing and non-ionizing radiation fields and dust abundances, are constrained by their observed multiwavelength spectrum. After determining the PAH and dust abundances in 35 nearby galaxies using our SED model, we use a chemical evolution model to show that the delayed injection of carbon dust by AGB stars provides a natural explanation to the dependence of the PAH content in galaxies with metallicity. We also show that larger dust particles giving rise to the far-IR emission follow a distinct evolutionary trend closely related to the injection of dust by massive stars into the ISM.
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