  We present optical and mid-infrared photometry of a statistically complete
sample of 29 very faint dwarf galaxies (M_r > -15 mag) selected from the SDSS
spectroscopic sample and observed in the mid-infrared with Spitzer IRAC. This
sample contains nearby (redshift z<0.005) galaxies three magnitudes fainter
than previously studied samples. We compare our sample with other star-forming
galaxies that have been observed with both IRAC and SDSS. We examine the
relationship of the infrared color, sensitive to PAH abundance, with
star-formation rates, gas-phase metallicities and radiation hardness, all
estimated from optical emission lines. Consistent with studies of more luminous
dwarfs, we find that the very faint dwarf galaxies show much weaker PAH
emission than more luminous galaxies with similar specific star-formation
rates. Unlike more luminous galaxies, we find that the very faint dwarf
galaxies show no significant dependence at all of PAH emission on
star-formation rate, metallicity, or radiation hardness, despite the fact that
the sample spans a significant range in all of these quantities. When the very
faint dwarfs in our sample are compared with more luminous (M_r ~ -18 mag)
dwarfs, we find that PAH emission depends on metallicity and radiation
hardness. These two parameters are correlated; we look at the PAH-metallicity
relation at fixed radiation hardness and the PAH-hardness relation at fixed
metallicity. This test shows that the PAH emission in dwarf galaxies depends
most directly on metallicity.
