2015ApJ...811..124S

We present spatially resolved imaging obtained with the Australia Telescope Compact Array (ATCA) of three CO lines in two high-redshift gravitationally lensed dusty star-forming galaxies, discovered by the South Pole Telescope. Strong lensing allows us to probe the structure and dynamics of the molecular gas in these two objects, at z = 2.78 and z = 5.66, with effective source-plane resolution of less than 1 kpc. We model the lensed emission from multiple CO transitions and the dust continuum in a consistent manner, finding that the cold molecular gas as traced by low-J CO always has a larger half-light radius than the 870 µm dust continuum emission. This size difference leads to up to 50% differences in the magnification factor for the cold gas compared to dust. In the z = 2.78 galaxy, these CO observations confirm that the background source is undergoing a major merger, while the velocity field of the other source is more complex. We use the ATCA CO observations and comparable resolution Atacama Large Millimeter/submillimeter Array dust continuum imaging of the same objects to constrain the CO-H₂ conversion factor with three different procedures, finding good agreement between the methods and values consistent with those found for rapidly star-forming systems. We discuss these galaxies in the context of the star formation–gas mass surface density relation, noting that the change in emitting area with observed CO transition must be accounted for when comparing high-redshift galaxies to their lower redshift counterparts.