Model results showing the luminosity of the H₂O line 6 (3₂₁−3₁₂) as a function of the product of the monochromatic luminosities at 75 and 179 μm. Luminosities are calculated for a source with R_eff = 100 pc, N_H2O/ΔV = 10¹⁵cm^-2/(km s^-1), and ΔV = 100 kms^-1. Blue squares indicate models with τ₁₀₀ = 0.1, resulting in optically thin or moderately thick H₂O emission, without collisional excitation. Magenta squares show results for the same models but with collisional excitation included with T_gas = 150 K and n_H2 = 3 × 10⁵ cm^-3. Green symbols indicate models with τ₁₀₀ = 1.0, resulting in optically thick H₂O emission. For optically thin H₂O emission and without collisional excitation, the models indicate a linear correlation between L_H2O and L₇₅ × L₁₇₉ (red line).