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.