Quantitative diagnostic of the radiative pumping mechanism. (a) Plot of as a function of for the Galactic and extragalactic samples. The dashed line indicates . The lower insert shows these values in linear scale for Orion KL, with negative numbers of indicating emission in the 75 μm line. The upper insert shows vs. . Shading indicates the G₁, G₂, and G₃ groups defined according to the value of r (Sect. 3.3). (b) Same as (a), but zoomed-in on the extragalactic sources. Circles and triangles indicate ADGs and EDGs, respectively (Sect. 3.1). The green symbols show the same values, but for the 2₀₂ → 1₁₁ (emission) vs. the 2₂₀ ← 1₁₁ (absorption) in the two sources (Mrk 231 and Arp 220) in which the 101 μm line has been observed. The open circles show the position in this plane of the optically thin (τ₁₀₀ <  1, in gray) and optically thick (τ₁₀₀ >  1, in blue) model components used to fit the H₂O emission and absorption (Appendix B). The insert shows the 3₂₁ → 3₁₂-to-2₀₂ → 1₁₁ luminosity ratio vs. , and horizontal segments indicate the most likely ranges for the two sources that are undetected in H₂O 75 μm.