Left panel: flux ratio between HCN(5-4) and [CI](1-0) as a function of the infrared luminosity. Our sources are represented by black filled squares and the average by a red star. The gray diamond represents the stacking of the cycle-0 SPT SMG spectra (Spilker et al. 2014). The blue filled circles are the local HCN(4-3) measurements of Zhang et al. (2014), where HCN(4-3) is converted into HCN(5-4) following the recipe described in Sect. 3.1, combined with the [CI](1-0) measurements of Rosenberg et al. (2015). Right panel: ratio between HCN(4-3) and ¹²CO(4-3) as a function of the infrared luminosity. As explained in Sect. 4.1, we used the HCN(5-4)/CO(5-4) or HCN(3-2)/CO(3-2) ratios, when the 4-3 transitions were not available. The purple cross is the measurement of Oteo et al. (2016) in SDP.9. The orange downwards triangles are two H-ATLAS sources provided in Yang’s Thesis (priv. comm.). The yellow triangle is the measurements of Danielson et al. (2011) in SMM J2135-0102.