A new estimator of resolved molecular gas in nearby galaxies
  A relationship between dust-reprocessed light from recent star formation and
the amount of star-forming gas in a galaxy produces a correlation between WISE
12 $\mu$m emission and CO line emission. Here we explore this correlation on
kiloparsec scales with CO(1-0) maps from EDGE-CALIFA matched in resolution to
WISE 12 $\mu$m images. We find strong CO-12 $\mu$m correlations within each
galaxy and we show that the scatter in the global CO-12 $\mu$m correlation is
largely driven by differences from galaxy to galaxy. The correlation is
stronger than that between star formation rate and H$_2$ surface densities
($\Sigma(\mathrm{H_2})$). We explore multi-variable regression to predict
$\Sigma(\mathrm{H_2})$ in star-forming pixels using the WISE 12 $\mu$m data
combined with global and resolved galaxy properties, and provide the fit
parameters for the best estimators. We find that $\Sigma(\mathrm{H_2})$
estimators that include $\Sigma(\mathrm{12\>\mu m})$ are able to predict
$\Sigma(\mathrm{H_2})$ more accurately than estimators that include resolved
optical properties instead of $\Sigma(\mathrm{12\>\mu m})$. These results
suggest that 12 $\mu$m emission and H$_2$ as traced by CO emission are
physically connected at kiloparsec scales. This may be due to a connection
between polycyclic aromatic hydrocarbon (PAH) emission and the presence of
H$_2$. The best single-property estimator is $\log
\frac{\Sigma(\mathrm{H_2})}{\mathrm{M_\odot\>pc^{-2}}} = (0.48 \pm 0.01) +
(0.71 \pm 0.01)\log \frac{\Sigma(\mathrm{12\>\mu
m})}{\mathrm{L_\odot\>pc^{-2}}}$. This correlation can be used to efficiently
estimate $\Sigma(\mathrm{H_2})$ down to at least $1 \> M_\odot \>
\mathrm{pc^{-2}}$ in star-forming regions within nearby galaxies.
