  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.
