Possibility of using 3.3$\mu$m PAH luminosity as a molecular gas mass estimator

We present CO(1-0) observations of 50 star-forming galaxies at 0.01<z<0.35, for which 3.3$\,\mu$m PAH emission flux or its upper limit is available. A scaling relation between 3.3$\,\mu$m PAH luminosity and CO(1-0) luminosity is established covering ~2 orders of magnitude in total IR luminosity and CO luminosity, with a scatter of ~0.23 dex: $\mathrm{log}\,L_\mathrm{3.3}/\mathrm{L}_\odot=(1.00\pm0.07)\times\mathrm{log}\,L_\mathrm{CO(1-0)}^\prime/(\mathrm{K\,km\,s^{-1}\,pc^2})+(-1.10\pm0.70)$. The slope is near unity, allowing the use of a single value of $\langle\mathrm{log}\,(L_\mathrm{3.3}/L_\mathrm{CO(1-0)}^\prime)\rangle=-1.09\pm0.36~[\mathrm{L}_\odot/(\mathrm{K\,km\,s^{-1}\,pc^2})]$ in the conversion between 3.3$\,\mu$m PAH and CO luminosities. The variation in the $L_\mathrm{3.3}/L_\mathrm{CO}^\prime$ ratio is not dependent on the galaxy properties, including total IR luminosity, stellar mass, and SFR excess. The total gas mass, estimated using dust-to-gas ratio and dust mass, is correlated with 3.3$\,\mu$m PAH luminosity, in line with the prescription using $\alpha_\mathrm{CO}=0.8-4.5$ covering both normal star-forming galaxies and starburst galaxies. AGN-dominated galaxies tend to have a lower $L_\mathrm{3.3}/L_\mathrm{CO}^\prime$ than non-AGN galaxies, which needs to be investigated further with an increased sample size. The established $L_\mathrm{3.3}$-$L_\mathrm{CO}^\prime$ correlation is expected to be applicable to wide-field near-infrared spectrophotometric surveys that allow the detection of 3.3$\,\mu$m emission from numerous low-redshift galaxies.