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 (median Pearson $r = 0.85$) 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 over the same set of pixels (median $r=0.71$). We explore multi-variable regression to predict $\Sigma(\mathrm{H_2})$ surface density 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 $\Sigma(\mathrm{H_2})$ with $>10$% better accuracy than estimators that include resolved optical properties ($\Sigma(\mathrm{SFR}),\Sigma(\mathrm{M_*}),A_V$ and $12+\log\mathrm{O/H}$) instead of $\Sigma(\mathrm{12\mu m})$. The best single-property estimator is $\log \frac{\Sigma(\mathrm{H_2})}{\mathrm{M_\odot\>pc^{-2}}} = (0.49 \pm 0.01) + (0.71 \pm 0.01)\log \frac{\Sigma(\mathrm{12\mu m})}{\mathrm{L_\odot\>pc^{-2}}}$, with an average predictive accuracy of 0.19 dex per pixel, and intrinsic scatter of 0.17 dex. This correlation can be used to efficiently estimate H$_2$ surface densities down to at least $1 \> M_\odot \> \mathrm{pc^{-2}}$ on small spatial scales within nearby galaxies. This correlation may prove useful to probe even lower gas densities with the better mid-infrared sensitivities expected from the James Webb Space Telescope.