Table 8: The dust properties at selected water line frequencies for four typical models. The column density $N_{\rm {H_2}}$ required to produce $\tau =1$ for the dust at each frequency is given with the corresponding radii and temperatures.
Transition Frequency $\kappa_{\rm OH5}$ $N_{\rm {H_2}}$ r and T ( $\tau_{\rm dust}=1$ )

Model 1^c Model 2^d Model 3^e Model 4^f

GHz 10^-2 cm²g^-1a 10²³ cm^-2 AU K AU K AU K AU K

Ortho-H₂O transitions

1₁₀-1₀₁ 556 4.56 54.8 -^b - - - - - - -

2₁₂-1₀₁ 1669 32.7 7.6 45 97 62 73 9 188 - -

2₂₁-2₁₂ 1661 32.3 7.2 48 92 63 72 10 179 - -

3₁₂-3₀₃ 1097 17.3 14.5 - - 32 111 - - - -

3₁₂-2₁₂ 1153 18.5 13.5 15 240 34 107 - - - -

3₂₁-3₁₂ 1162 18.7 13.3 16 217 35 105 - - - -

Para-H₂O transitions

1₁₁-0₀₀ 1113 17.7 14.1 - - 33 109 - - - -

2₀₂-1₁₁ 987 14.4 17.3 - - 27 128 - - - -

2₁₁-2₀₂ 752 8.45 29.5 - - 16 213 - - - -

2₂₀-2₁₁ 1228 20.0 12.4 18 185 37 101 - - - -

3₃₁-4₀₄ 1893 40.9 6.1 64 78 74 65 12 154 - -

4₂₂-3₃₁ 916 12.2 20.4 - - 38 99 - - - -

4₂₂-4₁₃ 1207 19.6 12.7 17 193 23 144 - - - -

5₂₄-4₃₁ 970 13.9 17.9 - - 26 131 - - - -

^a Total gas and dust; ^b - indicates that the dust is optically thin throughout the entire envelope; ^c see text, $L=7~L_\odot$ , p=1.5, $n_0=5\times 10^6$ cm^-3; ^d see text, $L=7~L_\odot$ , p=2, $n_0=5\times 10^6$ cm^-3; ^e see text, $L=2~L_{\odot}$ , p=2, $n_0=4\times10^5$ cm^-3; ^f see text, $L=25~L_{\odot}$ , p=1.5, $n_0=1\times 10^6$ cm^-3.

**Table 8:** The dust properties at selected water line frequencies for four typical models. The column density $N_{\rm {H_2}}$ required to produce $\tau =1$ for the dust at each frequency is given with the corresponding radii and temperatures.
Transition	Frequency	$\kappa_{\rm OH5}$	$N_{\rm {H_2}}$	r and T ( $\tau_{\rm dust}=1$ )
				Model 1^c	Model 2^d	Model 3^e	Model 4^f
	GHz	10^-2 cm²g^-1a	10²³ cm^-2	AU	K	AU	K	AU	K	AU	K
Ortho-H₂O transitions
1₁₀-1₀₁	556	4.56	54.8	-^b	-	-	-	-	-	-	-
2₁₂-1₀₁	1669	32.7	7.6	45	97	62	73	9	188	-	-
2₂₁-2₁₂	1661	32.3	7.2	48	92	63	72	10	179	-	-
3₁₂-3₀₃	1097	17.3	14.5	-	-	32	111	-	-	-	-
3₁₂-2₁₂	1153	18.5	13.5	15	240	34	107	-	-	-	-
3₂₁-3₁₂	1162	18.7	13.3	16	217	35	105	-	-	-	-
Para-H₂O transitions
1₁₁-0₀₀	1113	17.7	14.1	-	-	33	109	-	-	-	-
2₀₂-1₁₁	987	14.4	17.3	-	-	27	128	-	-	-	-
2₁₁-2₀₂	752	8.45	29.5	-	-	16	213	-	-	-	-
2₂₀-2₁₁	1228	20.0	12.4	18	185	37	101	-	-	-	-
3₃₁-4₀₄	1893	40.9	6.1	64	78	74	65	12	154	-	-
4₂₂-3₃₁	916	12.2	20.4	-	-	38	99	-	-	-	-
4₂₂-4₁₃	1207	19.6	12.7	17	193	23	144	-	-	-	-
5₂₄-4₃₁	970	13.9	17.9	-	-	26	131	-	-	-	-

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