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 (Sigma_gas) using optical spectroscopy. We utilise 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 (Mach). Based on the measured range of Sigma_SFR = 0.005-1.5 M_sol/yr/kpc^2 and Mach = 18-130, we predict Sigma_gas = 7-200 M_sol/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, Mach, 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 two more accurate in predicting Sigma_gas, with an average deviation of 32% from the actual Sigma_gas.