The nature of the [C II] emission in dusty star-forming galaxies from the SPT survey

We present [C II] observations of 20 strongly lensed dusty star-forming galaxies at 2.1 < z < 5.7 using Atacama Pathfinder EXperiment and Herschel. The sources were selected on their 1.4 mm flux (S_{1.4 mm} > 20 mJy) from the South Pole Telescope (SPT) survey, with far-infrared (FIR) luminosities determined from extensive photometric data. The [C II] line is robustly detected in 17 sources, all but one being spectrally resolved. 11 out of 20 sources observed in [C II] also have low-J CO detections from Australia Telescope Compact Array. A comparison with mid- and high-J CO lines from Atacama Large Millimeter/submillimeter Array reveals consistent [C II] and CO velocity profiles, suggesting that there is little differential lensing between these species. The [C II], low-J CO and FIR data allow us to constrain the properties of the interstellar medium. We find [C II] to CO(1-0) luminosity ratios in the SPT sample of 5200 ± 1800, with significantly less scatter than in other samples. This line ratio can be best described by a medium of [C II] and CO emitting gas with a higher [C II] than CO excitation temperature, high CO optical depth τ_CO(1-0) ≫ 1, and low to moderate [C II] optical depth τ_{[C II]}≲ 1. The geometric structure of photodissociation regions allows for such conditions.