Stars form in cold molecular clouds. However, molecular gas is difficult to observe because the most abundant molecule (H_2_) lacks a permanent dipole moment. Rotational transitions of CO are often used as a tracer of H_2_, but CO is much less abundant and the conversion from CO intensity to H_2_ mass is often highly uncertain. Here we present a new method for estimating the column density of cold molecular gas ({Sigma}gas) using optical spectroscopy. We utilize the spatially resolved H{alpha} maps of flux and velocity dispersion from the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. We derive maps of {Sigma}gas by inverting the multi-freefall star formation relation, which connects the star formation rate surface density ({Sigma}SFR) with {Sigma}gas and the turbulent Mach number (M). Based on the measured range of {Sigma}SFR=0.005-1.5M_{sun}/yr/kpc^2^ and M=18-130, we predict {Sigma}_gas=7-200M_{sun}/pc^2^ in the star-forming regions of our sample of 260 SAMI galaxies. These values are close to previously measured {Sigma}_gas obtained directly with unresolved CO observations of similar galaxies at low redshift. We classify each galaxy in our sample as 'star-forming' (219) or 'composite/AGN/shock' (41), and find that in 'composite/AGN/shock' galaxies the average {Sigma}SFR, M and {Sigma}gas are enhanced by factors of 2.0, 1.6 and 1.3, respectively, compared to star-forming galaxies. We compare our predictions of {Sigma}gas with those obtained by inverting the Kennicutt-Schmidt relation and find that our new method is a factor of 2 more accurate in predicting {Sigma}gas, with an average deviation of 32 per cent from the actual {Sigma}gas.
Cone search capability for table J/MNRAS/468/3965/tablea1a (Spaxel-averaged physical parameters required to derive an estimate of the molecular gas surface density {Sigma}gas, star-forming classified galaxies)
Cone search capability for table J/MNRAS/468/3965/tablea1b (Spaxel-averaged physical parameters required to derive an estimate of the molecular gas surface density {Sigma}gas, composite/AGN/shock classified galaxies)
