Flux ratio between the 13CO and 12CO as a function of the infrared luminosity. The same transition of both lines is used to compute these ratios. Our sources are represented by black filled squares and their average properties by a red star. The two serendipitous detections obtained during the first redshift-search campaign in SPT0529-54 and SPT0532-50 (Weiß et al. 2013) are shown using orange pentagons. The gray diamond shows the average ratio measured by Spilker et al. (2014) using a stacking of the full redshift-search SPT sample. The local sample from Costagliola et al. (2011) is plotted with a blue filled circle. The yellow triangle and the green cross are the high-z measurements of Danielson et al. (2013) in SMM J2135-0102 and Henkel et al. (2010) in the Cloverleaf quasar.
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