A survey of the cold molecular gas in gravitationally lensed star-forming galaxies at z>2

Using the Australia Telescope Compact Array (ATCA), we conducted a survey of CO J=1-0 and J=2-1 line emission towards strongly lensed high-redshift dusty star forming galaxies (DSFGs) previously discovered with the South Pole Telescope (SPT). Our sample comprises 17 sources that had CO-based spectroscopic redshifts obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Atacama Pathfinder Experiment (APEX). We detect all sources with known redshifts in either CO J=1-0 or J=2-1. Twelve sources are detected in the 7-mm continuum. The derived CO luminosities imply gas masses in the range (0.5-11)x10^{10} M_sun and gas depletion timescales <200 Myr, using a CO to gas mass conversion factor alpha_CO=0.8 M_sun (K km/s pc^2)^{-1}. Combining the CO luminosities and dust masses, along with a fixed gas-to-dust ratio, we derive alpha_CO factors in the range 0.4-1.8, similar to what is found in other starbursting systems. We find small scatter in alpha_CO values within the sample, even though inherent variations in the spatial distribution of dust and gas in individual cases could bias the dust-based alpha_CO estimates. We find that lensing magnification factors based on the CO linewidth to luminosity relation (mu_CO) are highly unreliable, but particularly when mu<5. Finally, comparison of the gas and dynamical masses suggest that the average molecular gas fraction stays relatively constant at z=2-5 in the SPT DSFG sample.