The SAMI Galaxy Survey: a new method to estimate molecular gas surface densities from star formation rates

Stars form in cold molecular clouds. However, molecular gas is difficult to observe because the most abundant molecule (H₂) lacks a permanent dipole moment. Rotational transitions of CO are often used as a tracer of H₂, but CO is much less abundant and the conversion from CO intensity to H₂ mass is often highly uncertain. Here we present a new method for estimating the column density of cold molecular gas (Σ_gas) using optical spectroscopy. We utilize the spatially resolved Hα maps of flux and velocity dispersion from the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. We derive maps of Σ_gas by inverting the multi-freefall star formation relation, which connects the star formation rate surface density (Σ_SFR) with Σ_gas and the turbulent Mach number (M). Based on the measured range of Σ_SFR = 0.005-1.5 {M_{⊙} yr^{-1} kpc^{-2}} and M=18-130, we predict Σ_gas = 7-200 {M_{⊙} pc^{-2}} in the star-forming regions of our sample of 260 SAMI galaxies. These values are close to previously measured Σ_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 Σ_SFR, M and Σ_gas are enhanced by factors of 2.0, 1.6 and 1.3, respectively, compared to star-forming galaxies. We compare our predictions of Σ_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 Σ_gas, with an average deviation of 32 per cent from the actual Σ_gas.