  Emission from polycyclic aromatic hydrocarbons (PAHs) is a promising tool for
estimating star formation rate (SFR) in galaxies, but the origin of its sources
of excitation, which include not only young but possibly also old stars,
remains uncertain. We analyze Spitzer mid-infrared mapping-mode spectroscopic
observations of the nuclear and extra-nuclear regions of 33 nearby galaxies to
study the contribution of evolved stars to PAH emission. In combination with
photometric measurements derived from ultraviolet, H{\alpha}, and infrared
images, the spatially resolved spectral decomposition enables us to
characterize the PAH emission, SFR, and stellar mass of the sample galaxies on
sub-kpc scales. We demonstrate that the traditional empirical correlation
between PAH luminosity and SFR has a secondary dependence on specific SFR, or,
equivalently, stellar mass. Ultraviolet-faint regions with lower specific SFRs
and hence greater fraction of evolved stars emit stronger PAH emission at fixed
SFR than ultraviolet-bright regions. We reformulate the PAH-based SFR estimator
by explicitly introducing stellar mass as a second parameter to account for the
contribution of evolved stars to PAH excitation. The influence of evolved stars
can explain the sub-linear correlation between PAH emission and SFR, and it can
partly account for the PAH deficit in dwarf galaxies and low-metallicity
environments.
