Modeled H₂O line ratios in C_outer as a function of dust temperature. Triangles, squares, pentagons, and circles show results for H₂O columns per unit τ₅₀ of 8 × 10¹⁷, 4 × 10¹⁷, 2 × 10¹⁷, and 1 × 10¹⁷, respectively. In all models τ₁₀₀ = 1. Dashed lines indicate the observed ratios and the dotted lines are their 1σ uncertainties. The contribution from C_core is not included in this figure, but it is expected to slightly raise the 2₁₁ → 2₀₂/ 2₀₂ → 1₁₁ and 4₂₂ → 4₁₃/ 2₀₂ → 1₁₁ ratios. The overall best fit, including the core contribution, is shown in Fig. 4