A new empirical method to estimate the molecular gas mass in galaxies

We find a tight correlation between the dust extinction, traced by the Balmer Decrement (BD$=$H$\alpha$/H$\beta$), the CO(1-0) line luminosity (L$_{CO}$) and total molecular gas mass (M$_{H2}$) in a sample of $222$ local star-forming galaxies drawn from the xCOLD GASS survey. As expected, the galaxy disk inclination affects the correlation by inducing a saturation of the Balmer decrement on highly inclined galaxies. Once this effect is taken into account, L$_{CO}$ and M$_{H2}$ can be expressed as a function of BD with a scatter of $\sim 0.3$ dex. We do not find any dependence on galaxy size, mass, morphology, star formation activity, and gas metallicity. The correlation disappears if the atomic gas phase is considered. This is likely due to the fact that the region traced by the BD, the stellar disk, is much smaller than the HI disk.