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

We present [CII] observations of 20 strongly lensed dusty star forming galaxies at 2.1 < z < 5.7 using APEX and Herschel. The sources were selected on their 1.4 mm flux (S_1.4mm > 20 mJy) from the South Pole Telescope survey, with far-infrared (FIR) luminosities determined from extensive photometric data. The [CII] line is robustly detected in 17 sources, all but one being spectrally resolved. Eleven out of 20 sources observed in [CII] also have low-J CO detections from ATCA. A comparison with mid- and high-J CO lines from ALMA reveals consistent [CII] and CO velocity profiles, suggesting that there is little differential lensing between these species. The [CII], low-J CO and FIR data allow us to constrain the properties of the interstellar medium. We find [CII] 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 [CII] and CO emitting gas with a higher [CII] than CO excitation temperature, high CO optical depth tau_CO >> 1, and low to moderate [CII] optical depth tau_CII ~< 1. The geometric structure of photodissociation regions allows for such conditions.