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 (∑_gas) using optical spectroscopy. We utilize the spatially resolved Ha maps of flux and velocity dispersion from the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. We derive maps of ∑_gas by inverting the multi-freefall star formation relation, which connects the star formation rate surface density (∑_SFR) with ∑_gas and the turbulent Mach number (M). Based on the measured range of ∑_SFR = 0.005-1.5 M_⊙ yr^-1 kpc^-2 and M = 18-130, we predict 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 ∑_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 ∑_SFR, M and ∑_gas are enhanced by factors of 2.0, 1.6 and 1.3, respectively, compared to star-forming galaxies. We compare our predictions of ∑_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 ∑_gas, with an average deviation of 32 per cent from the actual ∑_gas.