Apparent H₂O luminosity versus apparent infrared luminosity of high-redshift sources, for H₂O Line 1 (2₁₁ − 2₀₂, 752.03 GHz) with the Arp 220 H₂O line ratio (see text), compared to local ULIRGs (μL_IR < 4 × 10¹²  L_⊙, Yang et al., in prep.). The dashed diagonal lines have constant L_H2O/L_IR ratios 6.8 × 10^-6 and 2.6 × 10^-6, equal to those of Arp 220 and Mrk 231. Because of their peculiarities, values for SDP.81 and G12.v2.30 (underestimated by factors possibly up to ~1.5−2 because they are very extended, see text), and those of APM 08279+5255 and Mrk 231 (type 1 and type 2 QSOs, respectively) are printed in blue.