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.
The Figure shows the logarithmic difference between Sigma_gas(predicted) and Sigma_gas(measured) as a function of Sigma_SFR for various observational data sets (for details, see Fig. 8 in the paper). The grey data points show Sigma_gas(predicted) based on inverting the Kennicutt (1998) (K98) star formation relation, while the coloured data points show the prediction based on inverting the Salim et al. (2015) (SFK15) star formation relation, i.e., the new method to estimate Sigma_gas developed here. The horizontal line shows Sigma_gas(predicted) = Sigma_gas(measured), i.e., prefect prediction. The SAMI data point (filled blue circle) is an average over 56 of our SAMI Star-forming galaxies for which Herschel dust-to-gas estimates were available. We see that our new method based on SFK15 provides a significantly more accurate prediction of Sigma_gas than inverting the K98 relation, with an average deviation of 0.12 dex (32%) and 0.42 dex (160%) for SFK15 and K98, respectively.
We thank Mark Krumholz and the anonymous referee for their useful comments, which helped to improve this work. CF acknowledges funding provided by the Australian Research Council's (ARC) Discovery Projects (grants DP150104329 and DP170100603). DMS is supported by an Australian Government's New Colombo Plan scholarship. Support for AMM is provided by NASA through Hubble Fellowship grant #HST-HF2-51377 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. BAG gratefully acknowledges the support of the ARC as the recipient of a Future Fellowship (FT140101202). LJK gratefully acknowledges the support of an ARC Laureate Fellowship. SB acknowledges the funding support from the ARC through a Future Fellowship (FT140101166). SMC acknowledges the support of an ARC Future Fellowship (FT100100457). NS acknowledges support of a University of Sydney Postdoctoral Research Fellowship. The SAMI Galaxy Survey is based on observations made at the Anglo-Australian Telescope. The Sydney-AAO Multi-object Integral field spectrograph (SAMI) was developed jointly by the University of Sydney and the Australian Astronomical Observatory. The SAMI input catalogue is based on data taken from the Sloan Digital Sky Survey, the GAMA Survey and the VST ATLAS Survey. The SAMI Galaxy Survey is funded by the ARC Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020, and other participating institutions. The SAMI Galaxy Survey website is http://sami-survey.org.